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Vertical Wind Tunnel for Prediction of Rocket Flight Dynamics

Vertical Wind Tunnel for Prediction of Rocket Flight Dynamics aerospace Article Vertical Wind Tunnel for Prediction of Rocket Flight Dynamics 1 1 1 1 , Hoani Bryson , Hans Philipp Sültrop , George Buchanan , Christopher Hann *, 2 2 1 1 1 Malcolm Snowdon , Avinash Rao , Adam Slee , Kieran Fanning , David Wright , 3 1 4 5 Jason McVicar , Brett Clark , Graeme Harris and Xiao Qi Chen Department of Electrical and Computer Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand; hoani.bryson@gmail.com (H.B.); philipp.sueltrop@pg.canterbury.ac.nz (H.P.S.); georgebuchanannz@gmail.com (G.B.); a.slee@rocketlab.co.nz (A.S.); kieranfanning@hotmail.co.nz (K.F.); djwnz@hotmail.com (D.W.); clarkbab@gmail.com (B.C.) Rocket Lab Ltd., 3A Airpark Drive, Auckland 2022, New Zealand; malcolm.snowdon@gmail.com (M.S.); avinash.rao43@gmail.com (A.R.) School of Engineering and Information and Communication Technology (ICT), University of Tasmania, Private Bag 65, Hobart 7001, Australia; jason.j.mcvicar@gmail.com Engineering and Architecture Department, Christchurch Polytechnic Institute of Technology (CPIT), P.O. Box 540, Christchurch Mail Centre, Christchurch 8140, New Zealand; Graeme.Harris@cpit.ac.nz Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand; xiaoqi.chen@canterbury.ac.nz * Correspondence: chris.hann@canterbury.ac.nz; Tel.: +64-3-364-2987 (ext. 7242); Fax: +64-3-364-2264 Academic Editor: Raffaello Mariani Received: 1 February 2016; Accepted: 22 March 2016; Published: 29 March 2016 Abstract: A customized vertical wind tunnel has been built by the University of Canterbury Rocketry group (UC Rocketry). This wind tunnel has been critical for the success of UC Rocketry as it allows the optimization of avionics and control systems before flight. This paper outlines the construction of the wind tunnel and includes an analysis of flow quality including swirl. A minimal modelling methodology for roll dynamics is developed that can extrapolate wind tunnel behavior at low wind speeds to much higher velocities encountered during flight. The models were shown to capture the roll flight dynamics in two rocket launches with mean roll angle errors varying from 0.26 to 1.5 across the flight data. The identified model parameters showed consistent and predictable variations over both wind tunnel tests and flight, including canard–fin interaction behavior. These results demonstrate that the vertical wind tunnel is an important tool for the modelling and control of sounding rockets. Keywords: rocketry; canard actuation; vertical wind tunnel; flow quality; minimal modelling; roll dynamics; PD control; minimal modelling 1. Introduction A customized vertical wind tunnel has been built by the University of Canterbury (UC) Rocketry Research group [1] to test advanced control systems for application on small sounding rockets at subsonic and supersonic speeds. The common approach to designing and analyzing supersonic rockets is to quantitatively identify aerodynamics in a supersonic wind tunnel. However, these types of wind tunnels have large power requirements and are thus very costly, and usually have much shorter run times around 0.1–0.2 s [2]. Another approach to subsonic and supersonic flow analysis is Computational Fluid Dynamics (CFD). For example, canard–fin interactions have been well studied and modelled with CFD using Aerospace 2016, 3, 10; doi:10.3390/aerospace3020010 www.mdpi.com/journal/aerospace Aerospace 2016, 3, 10 2 of 27 wind tunnel data with relatively good predictions for the smaller angle of attacks [3,4]. However, the available comparisons in the literature are usually for static movements of the canards, so it is not clear how well the CFD models predict transient response in flight. Only very limited comparisons between flight and wind tunnel data have been published and are typically old NASA technical notes (e.g., [5–7]). The results of [6] show a reasonable prediction of pitch flight dynamics in terms of the frequency and phase responses of the pitching velocity per unit canard-fin-deflection frequency, however no roll comparisons are given and CFD analysis is not performed. Hence, although CFD analysis is commonly used for predicting rocket response in a wind tunnel, it has not been fully validated in flight. For the case of hypersonic flow, no vehicle has been flown long enough to obtain the data needed to improve the model accuracy and hypersonic wind tunnels only provide very short durations. Thus, in general, although CFD are useful for gaining trends on the expected flight response, they are not sufficiently accurate to design robust control systems and hence, extensive flight testing is usually required. In addition to CFD, there are a number of empirical approaches to modelling subsonic and supersonic rocket steady state aerodynamics. These methods are primarily based on NASA wind tunnel data and have been developed into engineering-level and intermediate-level aerodynamic prediction codes [7–9]. The models have also been extended to include canard interaction [10,11] but the experimental work is restricted to wind tunnels, so only considers steady state responses to fixed canard angles. Therefore, these methods are primarily for designing responsive canards in missiles and have not been used to understand actual rocket flight, where there are very fast movements and transient effects that often behave very differently to steady state response in a wind tunnel. This paper develops models of rocket roll dynamics that are first identified in the wind tunnel at low speeds and then validated on actual rocket launches at much higher speeds. This type of validation is unique in the literature as most other approaches do not go any further than wind tunnel evaluation [10,11]. The UC rocketry modelling and control methodology is to use a combination of dynamic subsonic wind tunnel testing and sounding rocket launches, to test qualitatively methodologies that have the ability to account for new dynamics in real-time. In other words, the approach is to model the rocket response in the wind tunnel during a control actuation that will be implemented in a flight. In addition, the damping or lift coefficients are not needed to be precisely known before launch, as any uncertainty from the wind tunnel tests, can be accounted for “on-the-fly” during the rocket flight. This UC rocketry control methodology has been successfully validated on several subsonic launches including an unstable rocket. For more details and results see [1]. The vertical wind tunnel has been a critical component to the success of UC Rocketry. In particular, it is important for obtaining quantitative information on the first few seconds of flight and can be used to estimate a full subsonic flight response using minimal modelling and parameter identification [12]. In addition, the vertical test section allows a much simpler and more accurate way of testing roll dynamics since the rocket can be suspended from a string. In a standard horizontal wind tunnel there is extra friction since an additional moving surface, like a bearing is required, so roll response is less realistic. For pitch and yaw dynamics, a gimbal frame [13] is used to allow three of freedom control. This gimbal frame set up is important for debugging the avionics control hardware and software before flight. To test the stability of a fully fueled rocket, two sets of strings are horizontally attached from one edge of the wind tunnel to the center of mass of the rocket, which allows movement in one axis. Hence this vertical wind tunnel has a number of unique features tailored for rocket flight analysis. A typical closed-circuit subsonic horizontal wind tunnel has a motor powered fan which blows air around a looping tube [14]. The settling chamber usually contains a honeycomb flow straightener followed by several wire mesh screens to reduce turbulence [15]. Following the settling chamber, and just prior to the test section, is a contraction in the tube, which increases air speed. The test section is where the test article is placed and data is collected. A diffuser, which is a gradually diverging section of tube, is placed after the test section to decrease the velocity and thus decrease power requirements. Aerospace 2016, 3, 10 3 of 27 Curved vanes guide air around corners [16]. The disadvantage of using a closed-circuit is that more space and materials are required to construct the back loop of the circuit. The curved vanes are complex features and an additional expense in the construction. Heat exchangers are often needed to keep the Aerospace 2016, 3, 10 3 of 27 tunnel at the desired temperature, since the same air is being re-circulated through the circuit many times and may deviate significantly from the ambient air temperature [16]. exchangers are often needed to keep the tunnel at the desired temperature, since the same air is being re-circulated through the circuit many times and may deviate significantly from the ambient A key part of the UC Rocketry wind tunnel design is the use of bendy plywood [17] due to its air temperature [16]. low cost, light weight and ease of constructing a circular cross section. Another advantage is that with A key part of the UC Rocketry wind tunnel design is the use of bendy plywood [17] due to its a circular shape less material can be used to give the same cross-sectional area. That is, if the shape low cost, light weight and ease of constructing a circular cross section. Another advantage is that was changed to a square with side length equal to the circle’s diameter, the volume of space would be with a circular shape less material can be used to give the same cross-sectional area. That is, if the greater and manufacturing simpler, but the maximum displacement of the rocket that can be achieved shape was changed to a square with side length equal to the circle’s diameter, the volume of space in any direction, would still be the same as for the circle. Thus the extra power required in the fan to would be greater and manufacturing simpler, but the maximum displacement of the rocket that can maintain a given flow velocity in the square configuration is effectively wasted. The vertical orientation be achieved in any direction, would still be the same as for the circle. Thus the extra power required in the fan to maintain a given flow velocity in the square configuration is effectively wasted. The also avoids the large floor and building space requirements needed for horizontal wind tunnels, and vertical orientation also avoids the large floor and building space requirements needed for was assembled outdoors in a fenced enclosure further simplifying space allocation. A 15 kW fan was horizontal wind tunnels, and was assembled outdoors in a fenced enclosure further simplifying already in existence in the Department of Electrical and Computer Engineering at UC, so the wind space allocation. A 15 kW fan was already in existence in the Department of Electrical and Computer tunnel was essentially built around this fan which was at the base and sitting on the ground. Engineering at UC, so the wind tunnel was essentially built around this fan which was at the base This paper details some of the design and construction of the wind tunnel, methods for and sitting on the ground. overcoming swirl induced from the fan, and presents a number of wind tunnel and flight results. This paper details some of the design and construction of the wind tunnel, methods for A key finding is that the vertical wind tunnel can provide realistic roll predictions of rocket flights well overcoming swirl induced from the fan, and presents a number of wind tunnel and flight results. beyond A key the find wind ing is t speeds hat tthat he vert can icabe l wind generated tunnel can p by the rovide re current alist fan, ic rol and l predi it c pr tions of ro ovides an cket excellent flights test well beyond the wind speeds that can be generated by the current fan, and it provides an excellent platform for modelling rocket behavior and validating parameter identification methods prior to flight. test platform for modelling rocket behavior and validating parameter identification methods prior to For example, similar canard–fin interaction roll dynamics observed and identified in the wind tunnel flight. For example, similar canard–fin interaction roll dynamics observed and identified in the wind were also seen in the subsequent rocket flight. The results show that it is possible to create a low-cost tunnel were also seen in the subsequent rocket flight. The results show that it is possible to create a wind tunnel with excellent flow characteristics, and thus provides a very valuable research tool for low-cost wind tunnel with excellent flow characteristics, and thus provides a very valuable research modelling and control of sounding rockets. tool for modelling and control of sounding rockets. 2. Methodology—Wind Tunnel 2. Methodology—Wind Tunnel This section outlines the design and manufacture processes of the customized vertical wind tunnel This section outlines the design and manufacture processes of the customized vertical wind tunnel used by UC Rocketry as shown in Figure 1. used by UC Rocketry as shown in Figure 1. Figure 1. Customized vertical wind tunnel for Sounding Rockets. Figure 1. Customized vertical wind tunnel for Sounding Rockets. Aerospace 2016, 3, 10 4 of 27 2.1. Concept and Design To simplify the mounting of the rocket and to provide realistic roll response testing, the key design specification was to allow the mounting of the rocket vertically by suspending from the nose cone. Therefore a vertical suck-down wind tunnel was designed. Due to the significant vertical height requirement, the structure was stored outside in a caged enclosure adjacent to the High Voltage Lab, which meant that it needed to be weather resistant. The wind tunnel was designed in individual sections with bolted joints between each section. This approach simplifies fabrication and assembly as the components could be added to or taken from the wind tunnel as required. To create a sufficient quality of flow in the wind tunnel, aluminium honeycomb was used as a flow conditioner. This flow straightener was critical, particularly since winds affect the flow. Another important part of the design was utilizing an existing 1 m diameter, 15 kW fan and speed controller. Thus, the wind tunnel structure was effectively built around the fan. Since the test section was chosen to have a diameter of 0.6 m, wide angle diffusers were necessary to reduce the height of the wind tunnel. Bendy plywood was chosen for the structure as it was easy to form into the required shapes and significantly reduces manufacturing complexity and time, as compared to sheet-metal or fiberglass. The overall rocket wind tunnel design consisted of five main components: the flow conditioner, reducer, test section, diffuser and fan. These components are summarized as follows: The flow conditioner was a cylindrical section at the inlet of the tunnel with an internal diameter of 1.4 m and a 9 mm wall thickness. The flow conditioner holds the honeycomb and a mesh screen. The reducer took the flow from the 1.4 m internal diameter flow conditioner to the 0.6 m internal diameter test section. This contraction before the test section can also reduce velocity fluctuations and form a more uniform flow. The reducer walls were fabricated from 6 mm bendy ply so that it would fit into the smaller internal diameter of the test section. The test section was 2 m long, had an internal diameter of 0.6 m and was formed with 6 mm bendy ply. Due to the length and thin walls of the test section a 77  38 mm length of pine was run down each side. The door for the test section was then framed using 75  38 mm pine and 17 mm plywood. The frame was then removed and the door cut from the test section. At the bottom of the test section, a metal grille recessed into a plywood ring was placed to protect the fan. The diffuser transitioned the flow from the 0.6 m internal diameter test section to the 1 m internal diameter fan housing. The diffuser was also made from 6 mm bendy ply. The fan was 1 m diameter and had up to 15 kW available in power. The blade angle was at 23 so was left unchanged. The fan was on wheels, and could be adjusted to meet flush with the diffuser. In addition, the wind tunnel was secured to the wall of the High Voltage (HV) lab by a permanent scaffold and a winch was used to open a lid on the wind tunnel during operation and closed after testing to ensure no rain came into the wind tunnel and fan. 2.2. Construction 2.2.1. General Methods Bendy ply was used for the outer skin of the wind tunnel. Bendy ply is plywood with the two outer lamination grains aligned, and forming most of the thickness of the sheet. A thin central lamination bonded the two outer laminations together with the grain running perpendicular to the outer laminations. This property allows the plywood to be bent down to tight radii without the need for steam/heat, see Figure 2. Aerospace 2016, 3, 10 5 of 27 Aerospace 2016, 3, 10 5 of 27 Aerospace 2016, 3, 10 5 of 27 Aerospace 2016, 3, 10 5 of 27 Figure 2. A sheet of 6 mm bendy ply. Figure 2. A sheet of 6 mm bendy ply. Figure 2. A sheet of 6 mm bendy ply. The rest of the tunnel structure was constructed from standard 17 mm plywood and 75 × 38 mm Figure 2. A sheet of 6 mm bendy ply. The rest of the tunnel structure was constructed from standard 17 mm plywood and 75 × 38 mm pine. The 17 mm plywood was used to form the flanges on the ends of each section. To reduce the The rest of the tunnel structure was constructed from standard 17 mm plywood and 75  38 mm pine. The 17 mm plywood was used to form the flanges on the ends of each section. To reduce the amount of material wastage, each flange was made up from four quarter flanges. The parts were cut pine. The 17 mm plywood was used to form the flanges on the ends of each section. To reduce the The rest of the tunnel structure was constructed from standard 17 mm plywood and 75 × 38 mm amount of material wastage, each flange was made up from four quarter flanges. The parts were cut using a jigsaw. The sections of the wind tunnel were fabricated by forming individual outer skin pine. The 17 mm plywood was used to form the flanges on the ends of each section. To reduce the amount of material wastage, each flange was made up from four quarter flanges. The parts were cut using a jigsaw. The sections of the wind tunnel were fabricated by forming individual outer skin amount of material wastage, each flange was made up from four quarter flanges. The parts were cut pieces to the flanges, and securing with wood screws, as shown in Figure 3a. Once a complete using a jigsaw. The sections of the wind tunnel were fabricated by forming individual outer skin pieces pieces to the flanges, and securing with wood screws, as shown in Figure 3a. Once a complete using a jigsaw. The sections of the wind tunnel were fabricated by forming individual outer skin section had been secured, the screws were backed off, epoxy resin with West Systems 403 modifier to the flanges, and securing with wood screws, as shown in Figure 3a. Once a complete section had section had been secured, the screws were backed off, epoxy resin with West Systems 403 modifier pieces to the flanges, and securing with wood screws, as shown in Figure 3a. Once a complete was worked into the gap, and the screws were again tightened. The flange joints were then been secured, the screws were backed off, epoxy resin with West Systems 403 modifier was worked was worked into the gap, and the screws were again tightened. The flange joints were then section had been secured, the screws were backed off, epoxy resin with West Systems 403 modifier reinforced with 200 g woven fiberglass cloth, see Figure 3b. The 75 × 38 mm pine was used to add into the gap, and the screws were again tightened. The flange joints were then reinforced with 200 g reinfo was worked into rced with 200 g the wov gap, en fiberg and the lass screws were cloth, see Figure 3 again ti b. The ghtened. The 75 × 38 mm p flange joi ine wa nts were then s used to add strength to the openings in the tunnel and provide mounting points for fixtures, see Figure 4. woven fiberglass cloth, see Figure 3b. The 75  38 mm pine was used to add strength to the openings strength to the openings in the tunnel and provide mounting points for fixtures, see Figure 4. reinforced with 200 g woven fiberglass cloth, see Figure 3b. The 75 × 38 mm pine was used to add in the tunnel and provide mounting points for fixtures, see Figure 4. strength to the openings in the tunnel and provide mounting points for fixtures, see Figure 4. (a) (b) (a) (b) (a) (b) Figure 3. (a) A sheet of 6 mm bendy ply; (b) Flange joint with 200 g woven cloth reinforcement. Figure 3. (a) A sheet of 6 mm bendy ply; (b) Flange joint with 200 g woven cloth reinforcement. Figure 3. (a) A sheet of 6 mm bendy ply; (b) Flange joint with 200 g woven cloth reinforcement. Figure 3. (a) A sheet of 6 mm bendy ply; (b) Flange joint with 200 g woven cloth reinforcement. Figure 4. 75 × 38 mm pine lengths used for reinforcement and framing. Figure 4. 75 × 38 mm pine lengths used for reinforcement and framing. Figure 4. 75  38 mm pine lengths used for reinforcement and framing. Figure 4. 75 × 38 mm pine lengths used for reinforcement and framing. Aerospace 2016, 3, 10 6 of 27 Aerospace 2016, 3, 10 6 of 27 Aerospace 2016, 3, 10 6 of 27 Aerospace 2016, 3, 10 6 of 27 The internal surface of the tunnel was not perfectly smooth due to the outer skin joints, The internal surface of the tunnel was not perfectly smooth due to the outer skin joints, The internal surface of the tunnel was not perfectly smooth due to the outer skin joints, The internal surface of the tunnel was not perfectly smooth due to the outer skin joints, screw-heads, excess glue and manufacturing imperfections on the inner plywood face. Therefore, all screw-heads, excess glue and manufacturing imperfections on the inner plywood face. Therefore, all screw-heads, excess glue and manufacturing imperfections on the inner plywood face. Therefore, all screw-heads, excess glue and manufacturing imperfections on the inner plywood face. Therefore, all internal surfaces and flange faces were sanded smooth. It was also necessary to fill voids on the internal surfaces and flange faces were sanded smooth. It was also necessary to fill voids on the internal surfaces and flange faces were sanded smooth. It was also necessary to fill voids on the inner internal surfaces and flange faces were sanded smooth. It was also necessary to fill voids on the inner side of the skin; both along the seams and behind the screw heads. Poly-filler was applied to inner side of the skin; both along the seams and behind the screw heads. Poly-filler was applied to side of the skin; both along the seams and behind the screw heads. Poly-filler was applied to these inner side of the skin; both along the seams and behind the screw heads. Poly-filler was applied to these areas and sanded back, so that the flow in the tunnel would not be disrupted, as shown in these areas and sanded back, so that the flow in the tunnel would not be disrupted, as shown in areas and sanded back, so that the flow in the tunnel would not be disrupted, as shown in Figure 5. these areas and sanded back, so that the flow in the tunnel would not be disrupted, as shown in Figure 5. Figure 5. Figure 5. (a) (b) (a) (b) (a) (b) Figure 5. Poly filler (a) before sanding; (b) after sanding. Figure Figure 5. 5. Poly Poly f filler iller ((a a)) before before sanding; ( sanding; ( b b ) aft ) after er sanding. sanding. Figure 5. Poly filler (a) before sanding; (b) after sanding. 2.2.2. Flow Conditioner and Fan Grille 2.2.2. Flow Conditioner and Fan Grille 2.2.2. Flow Conditioner and Fan Grille 2.2.2. Flow Conditioner and Fan Grille The flow conditioner was constructed similarly to the rest of the tunnel but required some The flow conditioner was constructed similarly to the rest of the tunnel but required some The flow conditioner was constructed similarly to the rest of the tunnel but required some The flow conditioner was constructed similarly to the rest of the tunnel but required some additional features. To support the honey comb, a 9 mm ledge was built for it to rest upon. In additional features. To support the honey comb, a 9 mm ledge was built for it to rest upon. In additional features. To support the honey comb, a 9 mm ledge was built for it to rest upon. In addition, additional features. To support the honey comb, a 9 mm ledge was built for it to rest upon. In addition, a galvanized wire mesh was put across the flow conditioner. The square sheet of addition, a galvanized wire mesh was put across the flow conditioner. The square sheet of a galvanized wire mesh was put across the flow conditioner. The square sheet of honeycomb was cut addition, a galvanized wire mesh was put across the flow conditioner. The square sheet of honeycomb was cut to fit the circular flow conditioner, see Figure 6. honeycomb was cut to fit the circular flow conditioner, see Figure 6. to fit the circular flow conditioner, see Figure 6. honeycomb was cut to fit the circular flow conditioner, see Figure 6. Figure 6. Honeycomb edge cut to match internal diameter of flow conditioner. Figure 6. Honeycomb edge cut to match internal diameter of flow conditioner. Figure 6. Honeycomb edge cut to match internal diameter of flow conditioner. Figure 6. Honeycomb edge cut to match internal diameter of flow conditioner. To prevent damage to the fan due to falling objects, a simple grille was fabricated. A plywood To prevent damage to the fan due to falling objects, a simple grille was fabricated. A plywood To prevent damage to the fan due to falling objects, a simple grille was fabricated. A plywood To prevent damage to the fan due to falling objects, a simple grille was fabricated. A plywood ring was cut with an internal diameter matching the internal diameter of the test section, and outside ring was cut with an internal diameter matching the internal diameter of the test section, and outside ring was cut with an internal diameter matching the internal diameter of the test section, and outside ring was cut with an internal diameter matching the internal diameter of the test section, and outside diameter matching the outer diameter of the flanges. A recess was cut along the inside edge of the diameter matching the outer diameter of the flanges. A recess was cut along the inside edge of the diameter matching the outer diameter of the flanges. A recess was cut along the inside edge of the diameter matching the outer diameter of the flanges. A recess was cut along the inside edge of the flange using a router to form a ledge for the grille to rest on, as shown in Figure 7. flange using a router to form a ledge for the grille to rest on, as shown in Figure 7. flange using a router to form a ledge for the grille to rest on, as shown in Figure 7. flange using a router to form a ledge for the grille to rest on, as shown in Figure 7. Figure 7. Wind tunnel grille to protect fan. Figure 7. Wind tunnel grille to protect fan. Figure 7. Wind tunnel grille to protect fan. Figure 7. Wind tunnel grille to protect fan. Aerospace 2016, 3, 10 7 of 27 Aerospace 2016, 3, 10 7 of 27 3. Methodology—Rocket Systems and Modelling 3. Methodology—Rocket Systems and Modelling 3.1. Improvements to Airframe and Avionics Stack 3.1. Improvements to Airframe and Avionics Stack Since the launch of Smokey at the end of 2014 [12], there have been a number of improvements Since the launch of Smokey at the end of 2014 [12], there have been a number of improvements implemented to the rocket systems. These improvements can be seen in Figure 8, which shows the implemented to the rocket systems. These improvements can be seen in Figure 8, which shows three launch configurations of the Smokey and Tasha III airframes. The Smokey and Tasha III the three launch configurations of the Smokey and Tasha III airframes. The Smokey and Tasha III airframe designs are aerodynamically equivalent. Both designs have identical canard, fin, tube airframe designs are aerodynamically equivalent. Both designs have identical canard, fin, tube length, length, tube diameter and nose cone geometry. The main difference between the two airframes was tube diameter and nose cone geometry. The main difference between the two airframes was the the manufacturing process for attaching the back fins. manufacturing process for attaching the back fins. Figure 8. Improvements to airframe and avionics stack. (a) Smokey; (b) Tasha III, launch 1; (c) Tasha III, Figure 8. Improvements to airframe and avionics stack. (a) Smokey; (b) Tasha III, launch 1; (c) Tasha launch 2. III, launch 2. Smokey used Acrylonitrile butadiene styrene (ABS) 3D printed fins and canards. The strength Smokey used Acrylonitrile butadiene styrene (ABS) 3D printed fins and canards. The strength of of these parts were appropriate for subsonic flight; however, they can be damaged on landing these parts were appropriate for subsonic flight; however, they can be damaged on landing resulting resulting in more time spent repairing the airframe. To overcome this problem, Tasha III also used in more time spent repairing the airframe. To overcome this problem, Tasha III also used 3D printed 3D printed fins, but they were laminated to the airframe with fiberglass. Two of the Tasha III’s 3D fins, but they were laminated to the airframe with fiberglass. Two of the Tasha III’s 3D printed canards printed canards were damaged after its first flight, so on its second flight we used our supersonic were damaged after its first flight, so on its second flight we used our supersonic capable stack, which capable stack, which has fiberglass canards. has fiberglass canards. Cameras were placed in Tasha III allowing the recording of flights to provide an insight on how Cameras were placed in Tasha III allowing the recording of flights to provide an insight on how the on-board avionics were performing. Some holes were cut in the airframe, with one of the the on-board avionics were performing. Some holes were cut in the airframe, with one of the cameras cameras placed out one side of the airframe by 10 mm. Smokey did not use an on-board camera, so it placed out one side of the airframe by 10 mm. Smokey did not use an on-board camera, so it had no had no camera holes. camera holes. UC Rocketry’s supersonic launches require a device to report where the rocket lands. Both UC Rocketry’s supersonic launches require a device to report where the rocket lands. Both Tasha Tasha III flights included the Spot Tracker to test its capability to report landing locations. The Spot III flights included the Spot Tracker to test its capability to report landing locations. The Spot Tracker Tracker and cameras are the main reason the Tasha III vehicle was heavier than Smokey. The second and cameras are the main reason the Tasha III vehicle was heavier than Smokey. The second Tasha III Tasha III launch was heavier than the first Tasha III launch, because the avionics were exchanged to launch was heavier than the first Tasha III launch, because the avionics were exchanged to the more the more robust supersonic capable avionics. robust supersonic capable avionics. Each launch of the Smokey and Tasha III airframes had different properties. Between each Each launch of the Smokey and Tasha III airframes had different properties. Between each launch, launch, changes were made to the internal avionics which affects the mass of the vehicle. Changes in changes were made to the internal avionics which affects the mass of the vehicle. Changes in mass mass affect the torques and airspeeds experienced during flight. Table 1 summarizes the key affect the torques and airspeeds experienced during flight. Table 1 summarizes the key differences differences between the vehicles for each launch. between the vehicles for each launch. Aerospace 2016, 3, 10 8 of 27 Table 1. Vehicle comparisons between Smokey and Tasha III. Property Smokey Tasha III Launch 1 Tasha III Launch 2 Aerospace 2016, 3, 10 8 of 27 Mass 3.0 kg 3.47 kg 3.99 kg Length 1.52 m 1.51 m 1.51 m Table 1. Vehicle comparisons between Smokey and Tasha III. Z-axis 2 2 2 0.00311 kg·m 0.00361 kg·m 0.00393 kg·m Property Inertia Smokey Tasha III Launch 1 Tasha III Launch 2 Mass 3.0 kg 3.47 kg 3.99 kg 3D printed PLA with 3D printed PLA with Length Fin material 1.52 3D p m rinted ABS 1.51 m 1.51 m 2 fibreglass lami 2 nation fibre glass lamination 2 Z-axis Inertia 0.00311 kg m 0.00361 kg m 0.00393 kg m Fin material 3D printed ABS 3D printed PLA with fibreglass lamination 3D printed PLA with fibre glass lamination Canards 3D printed ABS 3D printed ABS Fibre glass moulded Canards 3D printed ABS 3D printed ABS Fibre glass moulded Subsonic capable with Supersonic capable with Avionics Subsonic capable Subsonic capable with spot tracker Supersonic capable with spot tracker Avionics Subsonic capable spot tracker spot tracker 3.2. Testing Rocket Stability 3.2. Testing Rocket Stability A major advantage of the vertical wind tunnel is that it is a straightforward way to test rocket A major advantage of the vertical wind tunnel is that it is a straightforward way to test rocket stability before flight. UC Rocketry has developed the following procedure for testing stability: stability before flight. UC Rocketry has developed the following procedure for testing stability: Assemble the rocket with a dummy mass motor. • Assemble the rocket with a dummy mass motor. Measure the center of mass by balancing the rocket on a beam less than 20 mm wide. Mark the • Measure the center of mass by balancing the rocket on a beam less than 20 mm wide. Mark the center of mass. center of mass. Fix a pipe clamp, with string tied securely to both ends of the pipe clamp to the rocket, at the • Fix a pipe clamp, with string tied securely to both ends of the pipe clamp to the rocket, at the measured center of mass. measured center of mass. Feed the string from both sides of the clamp through the two 4 mm holes on the sides of the wind • Feed the string from both sides of the clamp through the two 4 mm holes on the sides of the tunnel. Tie the string around the back of the wind tunnel, and tension the ropes to lift the center wind tunnel. Tie the string around the back of the wind tunnel, and tension the ropes to lift the of mass of the rocket as close as possible to the holes in the side of the wind tunnel. center of mass of the rocket as close as possible to the holes in the side of the wind tunnel. Attach the nose tip of the rocket to the vertical string. The purpose of this string is to prevent • Attach the nose tip of the rocket to the vertical string. The purpose of this string is to prevent an an unstable rocket from damaging the walls, or prevent the rocket from falling should the clamps unstable rocket from damaging the walls, or prevent the rocket from falling should the clamps slip. The vertical string should be taut only when the nose of the rocket is close to the wind slip. The vertical string should be taut only when the nose of the rocket is close to the wind tunnel walls. tunnel walls. Start the wind tunnel, and check the rocket straightens at 15, 20 and 30 m/s. • Start the wind tunnel, and check the rocket straightens at 15, 20 and 30 m/s. Figure 9 gives a picture of a stability test set up. Figure 9 gives a picture of a stability test set up. (a) (b) Figure 9. Stability set up (a) connection to string; (b) connection to center of mass of rocket. Figure 9. Stability set up (a) connection to string; (b) connection to center of mass of rocket. Since these tests were for roll control only, the exact margin of stability in terms of the number Since these tests were for roll control only, the exact margin of stability in terms of the number of of calibres, was not determined. The main aim of the test in Figure 9, was to prove general stability calibres, was not determined. The main aim of the test in Figure 9, was to prove general stability so so that it would be safe to launch. An experimental determination of the center of pressure using this that it would be safe to launch. An experimental determination of the center of pressure using this method will be investigated in future work for pitch and yaw modelling. method will be investigated in future work for pitch and yaw modelling. Aerospace 2016, 3, 10 9 of 27 3.3. Rocket Roll Dynamics Modelling In both launches and all wind tunnel tests in this paper, only roll dynamics were investigated. This section outlines the modelling and parameter identification techniques used to understand and predict the rocket roll dynamics during flight. 3.3.1. Minimal Model The roll model is extended from a previously used model [12] which includes the effect of velocity on the damping and normal forces in the roll axis. Ignoring the yaw term in Equation (6) of [13] and lumping the parameter d into the coefficients of the roll fin angle and damping yields: . 1 a I p  r v A bu ptq p (1) f in 2 v where the definition of the parameters is given in the Notation. Expanding out Equation (1), and including the effects of disturbance and defining the roll angle gives the differential equation model: . 1 1 I p   r v A a p r v A bpu ptq u ptqq (2) p f in dist 2 2 f  p (3) where u ptq u ptq lumps the effects of fin canard interaction, thrust offsets that may impart a roll dist dist and atmospheric effects into a single time-varying parameter. It is shown in the results section that when there are sudden fin movements, it’s critical to allow fast changes in the disturbance at these points to provide a good match to the data. To model these effects, the disturbance is written in the form: u ptq  Y F (4) dist k k k1 pu  u q d,k d,k1 Y  u pt  T q (5) k d,k1 k1 pT  T q k k1 F  Hpt  T q Hpt  T q (6) k k1 k where Hptq  heaviside function, T , . . . , T  user defined time points (7) 0 N u , . . . , u  unknown constants identified from data (8) d,0 d,N 3.3.2. Parameter Identification To ensure the optimum possible model is obtained with good numerical parameter identifiability, a grid search is applied to the main parameters excluding the disturbance, which is identified using non-linear regression. This method was applied for both an open-loop model, where u ptq is f in measured directly by encoders on the rocket and a closed-loop model where u ptq is defined from f in a standard proportional derivative controller plus the addition of a pre-defined input. Mathematically these models are defined: Open-loop : u ptq  u ptq  fin movement measured from encoder (9) f in f in, OL Closed-loop : u ptq  u ptq  k pRptq fptqq k pR ptq pptqq u ptq (10) f in f in, C L d in put where k  proportional gain, k  derivative gain (11) p d Rptq  pR  R qHpsinp2p f tqq R (12) 0 1 0 1 Aerospace 2016, 3, 10 10 of 27 The reference function Rptq in Equation (12) is an alternating square wave of frequency f (Hz) between the values of R and R . This function allows multiple step responses to be analyzed from 0 1 wind tunnel tests and rocket flights. The function u ptq is set to 0 for the wind tunnel tests and the in put first flight, but is defined as a chirp function with varying amplitudes for the second flight to increase flight dynamics for a rigorous test of the model. The optimization is set up by first fixing the damping a and torque constant b. Two objective functions are defined: OL F pU q  rf pt q f pt q , . . . , f pt q f pt qs (13) d data 0 OL 0 data end OL end a,b C L F pU q  rf pt q f pt q , . . . , f pt q f pt qs (14) d data 0 C L 0 data end C L end a,b U  u , . . . , u (15) d d, 0 d, N where f ptq  measured roll angle, t , . . . , t  data time points (16) data end f ptq  roll angle solution to Equationsp2q –p9q for given a, b and U (17) OL d f ptq  roll angle solution to Equationsp2q –p8q ,p10q –p12q , for given a, b and U (18) C L d A range of values of a and b are then selected: <  ta kDa, k  0, . . . , N u ,<  b kDb, k  0, . . . , N (19) a min a b min b For each a and b from the ranges in Equation (19), the open-loop and closed-loop identified disturbance values are defined: OL U  non-linear least squares solution to Equation p13q (20) C L U  non-linear least squares solution to Equation p14q (21) The final model parameters that best fit the data are then defined: OL OL OL OL OL OL OL OL ˆ ˆ ˆ X  a , b , U : F pU q  min mean F pU q (22) OL OL d d a,b d a , b taP< , bP< u C L C L C L C L C L C L C L C L ˆ ˆ ˆ X  a , b , U : F pU q  min mean F pU q (23) C L C L d d a,b d a , b taP< , bP< u Equations (22) and (23) represent a grid search over all the values in Equation (19), where for each pair of a and b a non-linear regression is performed to determine the corresponding disturbance values. This non-linear regression uses the command “lsqnonlin” in Matlab. 4. Results and Discussion 4.1. Wind Tunnel Flow Quality Measurements from a hot wire anemometer placed at various positions from the boundary showed that there are negligible boundary effects greater than 200 mm from the wall, with less than 5% reduction in wind speed at 100 mm from the wall. Since the diameter of the sounding rockets in this research are 80 mm with a 60 mm canard and fin radial distance, the outermost point of the rocket is 160 mm from the wall. Hence, the volume of the test section used in this research, has close to uniform flow. Most importantly, the results from the prediction of rocket flight roll response from wind tunnel derived parameters presented in the sections below, demonstrate that the test section has adequate flow quality for this research. Aerospace 2016, 3, 10 11 of 27 this research are 80 mm with a 60 mm canard and fin radial distance, the outermost point of the rocket is 160 mm from the wall. Hence, the volume of the test section used in this research, has close to uniform flow. Most importantly, the results from the prediction of rocket flight roll response from wind tunnel derived parameters presented in the sections below, demonstrate that the test section has adequate flow quality for this research. Aerospace 2016, 3, 10 11 of 27 4.1.1. Turbulence Intensity 4.1.1. Turbulence Intensity To demonstrate the quality of the flow over time, in the wind tunnel, a Kestrel 4500 wind sensor [18] w To demonstrate as placed the 200quality mm from the edge a of the flow over t the bottom of time, in the the d wind oor itunnel, n Figure a1.Kestr This posi el 4500 tion was wind sensor [18] was placed 200 mm from the edge at the bottom of the door in Figure 1. This position fixed throughout the experiment. This sensor measures every 2 s and outputs a wind speed measurement was fixed thr rounded to the neare oughout the experiment. st 0.1 m/s. A fine This sensor r resolution win measures every d sensor w 2 s and outputs ith a higher frequency a wind speed measurement rounded to the nearest 0.1 m/s. A finer resolution wind sensor with a higher frequency was not required for this analysis, since wind speeds less than 0.1 m/s have a negligible effect on rocket dyn was not requir amics. In ed for ad thi dition, turbulen s analysis, since ce properties wind speeds are less independent of than 0.1 m/s the ti havem ae sca negligible le so this test i effect on s rocket dynamics. In addition, turbulence properties are independent of the time scale so this test adequate to characterize the turbulence intensity in the wind tunnel. The revolutions per minute (R is PM) adequate refereto nce on t characterize he fan was the set turbulence to a sequ intensity ence of va inlu the es defi wind ned tunnel. by: The revolutions per minute (RPM) reference on the fan was set to a sequence of values defined by: RPM = 570, 870,1100,1400,1650,1700 [ ] (24) ref RP M  r570, 870, 1100, 1400, 1650, 1700s (24) re f Taking into account the controller time constant, the times when the fan reaches steady state are: Taking into account the controller time constant, the times when the fan reaches steady state are: T = 100, 230, 390, 550, 718, 858 (s) [ ] (25) RPM T  r100, 230, 390, 550, 718, 858s psq (25) RP M The measured wind speed is shown in Figure 10. At each steady state there are only very small The measured wind speed is shown in Figure 10. At each steady state there are only very small oscillations, showing that the flow is close to laminar. Figure 11a shows a plot of the RPM versus oscillations, showing that the flow is close to laminar. Figure 11a shows a plot of the RPM versus wind wind speed and Figure 11b plots the turbulence intensity Γ versus wind speed which is defined: speed and Figure 11b plots the turbulence intensity G versus wind speed which is defined: σ () v Γ= () v , σ≡ standard deviation, v ≡ wind speed (26) s pvq Gpvq  , s  standard deviation, v  wind speed (26) mean(v) meanpvq There is a correlation of R = 0.9999 for RPM versus wind speed, thus the fan controller is There is a correlation of R = 0.9999 for RPM versus wind speed, thus the fan controller is creating creating a very linear response. The turbulence intensity is very low and less than 0.04% over all a very linear response. The turbulence intensity is very low and less than 0.04% over all wind wind speeds tested. speeds tested. Figure 10. Measured wind speed (from Kestrel) versus time for different revolutions per minute (RPM) Figure 10. Measured wind speed (from Kestrel) versus time for different revolutions per minute values in the fan. (RPM) values in the fan. wind speed (m/s) -1 wind speed (m s ) Aerospace 2016, 3, 10 12 of 27 Aerospace 2016, 3, 10 12 of 27 Aerospace 2016, 3, 10 12 of 27 wind speed (m/s) wind speed (m/s) (a) (b) (a) (b) Figure 11. (a) RPM versus wind speed; (b) Turbulence intensity versus wind speed. Figure 11. (a) RPM versus wind speed; (b) Turbulence intensity versus wind speed. Figure 11. (a) RPM versus wind speed; (b) Turbulence intensity versus wind speed. 4.1.2. Swirl 4.1.2. Swirl 4.1.2. Swirl It was noticed that in every airframe tested in the wind tunnel, there was a roll rate with the It was noticed that in every airframe tested in the wind tunnel, there was a roll rate with the canards set to 0. However, it was not initially known what percentage was of this roll rate, caused by It was noticed that in every airframe tested in the wind tunnel, there was a roll rate with the canards set to 0. However, it was not initially known what percentage was of this roll rate, caused by fin offsets in the airframe or swirl in the wind tunnel. To characterize the swirl, several sets of canards set to 0. However, it was not initially known what percentage was of this roll rate, caused fin offsets in the airframe or swirl in the wind tunnel. To characterize the swirl, several sets of aluminium fins were machined to provide a baseline where there was no fin offset. The fins were by fin offsets in the airframe or swirl in the wind tunnel. To characterize the swirl, several sets of aluminium fins were machined to provide a baseline where there was no fin offset. The fins were made from two thin sheets of aluminium formed in a cross. These fins were attached to a steel pipe aluminium fins were machined to provide a baseline where there was no fin offset. The fins were made made from two thin sheets of aluminium formed in a cross. These fins were attached to a steel pipe and suspended by string in the wind tunnel as shown in Figure 12. Tests showed that the roll rate from two thin sheets of aluminium formed in a cross. These fins were attached to a steel pipe and and suspended by string in the wind tunnel as shown in Figure 12. Tests showed that the roll rate observed was highly dependent on the total diameter of the fins. For a diameter less than 100 mm, suspended observed was hi by string ghly dependent on the tota in the wind tunnel as shown l diam in eter Figur of t eh12 e fin . Tests s. For a d showed iamthat eter les thesr t oll han rate 100 m observed m, there was no roll rate and greater than 300 mm the roll rate was very low. This result suggests that was there was no highly dependent roll rate a on nd the grea total ter tha diameter n 300 mm of the the fins. roll rat For e wa a diameter s very low. Th less than is resu 100 lt smm, ugges ther ts th eat was the swirl is mainly isolated to a concentric ring between 100 and 300 mm from the centre of the wind the swirl is mainly isolated to a concentric ring between 100 and 300 mm from the centre of the wind no roll rate and greater than 300 mm the roll rate was very low. This result suggests that the swirl is tutnnel. unnel. The The fifi n set n set t t hh at at wa wa ss chosen chosen for for de detta aile iled d ana ana ly ly ss is is h h aa d d a a di di am am ete er of ter of 202 00 m 0 m m which m m which m axia m xiized mized mainly isolated to a concentric ring between 100 and 300 mm from the centre of the wind tunnel. The the roll rate the roll rate . . fin set that was chosen for detailed analysis had a diameter of 200 mm which maximized the roll rate. Figure 12. Aluminium fin set up. Figure 12. Aluminium fin set up. Figure 12. Aluminium fin set up. The first test was to take a video of the 200 mm aluminium fin rocket for 5 min at the maximum The first test was to take a video of the 200 mm aluminium fin rocket for 5 min at the maximum wind speed of 30 m/s and visually count the number of revolutions to work out the average roll rate. The first test was to take a video of the 200 mm aluminium fin rocket for 5 min at the maximum wind speed of 30 m/s and visually count the number of revolutions to work out the average roll rate. The result was 87.0 deg/s which demonstrates there was certainly a relatively significant swirl in the wind speed of 30 m/s and visually count the number of revolutions to work out the average roll rate. The res wind t uu ltnne wal.s 8 To overcome 7.0 deg/s which demon this swirl, an stegg cr rates tat here e w a was c s plac eed rtaiup t nly o a re a h le aight tively of s 2 ignif 0 cm icin ant a hex swia rl in gon t he The result was 87.0 deg/s which demonstrates there was certainly a relatively significant swirl in the wind t shape on the unnel. To overcome grill at the bottom of this swirl the wi , an egg cr nd tunnel ate w , just a as plac bove the fa ed up ton, a h ase shown ight of i2 n0 Figure 13 cm in a hex . Thi asgon wind tunnel. To overcome this swirl, an egg crate was placed up to a height of 20 cm in a hexagon egg crate effectively provided an additional flow straightener reducing the swirl as it was near the shape on the grill at the bottom of the wind tunnel, just above the fan, as shown in Figure 13. This shape on the grill at the bottom of the wind tunnel, just above the fan, as shown in Figure 13. This egg fan which caused the swirl. Another video was then taken of the aluminium fin rocket and the egg crate effectively provided an additional flow straightener reducing the swirl as it was near the crate effectively provided an additional flow straightener reducing the swirl as it was near the fan average roll rate observed was 25.7 deg/s which is a 340% reduction in the swirl. There were also fan which caused the swirl. Another video was then taken of the aluminium fin rocket and the which caused the swirl. Another video was then taken of the aluminium fin rocket and the average roll several periods where there was no roll rate. average roll rate observed was 25.7 deg/s which is a 340% reduction in the swirl. There were also rate observed was 25.7 deg/s which is a 340% reduction in the swirl. There were also several periods several periods where there was no roll rate. where there was no roll rate. mean wind speed (m/s) mean wind speed (m/s) turbulence intensity (m/s) turbulence intensity (m/s) Aerospace 2016, 3, 10 13 of 27 Aerospace 2016, 3, 10 13 of 27 Aerospace 2016, 3, 10 13 of 27 Aerospace 2016, 3, 10 13 of 27 Figure 13. Egg crate used as a flow straightener to reduce swirl. Figure 13. Egg crate used as a flow straightener to reduce swirl. Figure 13. Egg crate used as a flow straightener to reduce swirl. Figure 13. Egg crate used as a flow straightener to reduce swirl. To fully characterize the impact of the flow straightener with various wind speeds on the Tasha To fully characterize the impact of the flow straightener with various wind speeds on the Tasha To fully characterize the impact of the flow straightener with various wind speeds on the Tasha III To fully characterize the impact of the flow straightener with various wind speeds on the Tasha III rocket, an uncontrolled airframe with the same dimensions as Figure 8b was placed in the wind III rocket, an uncontrolled airframe with the same dimensions as Figure 8b was placed in the wind rocket, an uncontrolled airframe with the same dimensions as Figure 8b was placed in the wind tunnel. III rocket, an uncontrolled airframe with the same dimensions as Figure 8b was placed in the wind tunnel. This airframe was primarily used to test the parachute before implementing the controlled tunnel. This airframe was primarily used to test the parachute before implementing the controlled This airframe was primarily used to test the parachute before implementing the controlled launch, so tunnel. This airframe was primarily used to test the parachute before implementing the controlled launch, so had slightly different back fins as a result of natural manufacturing variations, launch, so had slightly different back fins as a result of natural manufacturing variations, had launch, so h slightly difa fer d s entligback htly fins different as a bac result k fin of natural s as a manufacturing result of natura variations, l manufactbut uring v wasaessentially riations, but was essentially the same rocket. The specific rocket in Figure 8b was not available for this test as but was essentially the same rocket. The specific rocket in Figure 8b was not available for this test as the but was e same rocket. ssentially The the specific same rocket. rocket in The Figur specific e 8b rocke was not t in available Figure 8b wa fors not this av test aias labthe le for back thisfins test a wer s e the back fins were damaged on landing due to swinging into rocky ground with a large gust of the back fins were damaged on landing due to swinging into rocky ground with a large gust of the back fins were damaged on landing due to swinging into rocky ground with a large gust of damaged on landing due to swinging into rocky ground with a large gust of wind, just as it landed. wind, just as it landed. wind, j wind, j ust ust asas it i land t land ed. ed. The canards were set to 0 and roll rate data logging was enabled. Figure 14a plots the roll rate The canards were set to 0 and roll rate data logging was enabled. Figure 14a plots the roll rate The can The can ards ards were set to were set to 0 0 and ro and roll rate ll rate data data log logg ging ing was en was en abled. abled. Fig Fig uu re re 14a p 14a p lots the roll r lots the roll r atea te response for two experiments with and without the flow straightener. The RPM inputs used in each response for two experiments with and without the flow straightener. The RPM inputs used in each response for two experiments with and without the flow straightener. The RPM inputs used in each response for two experiments with and without the flow straightener. The RPM inputs used in each experiment are plotted in Figure 14b. Figure 14a shows that the flow straightener has significantly experiment are plotted in Figure 14b. Figure 14a shows that the flow straightener has significantly experiment are plotted in Figure 14b. Figure 14a shows that the flow straightener has significantly experiment are plotted in Figure 14b. Figure 14a shows that the flow straightener has significantly reduced reduced the the roll roll r rate ate of the of the r rocket. The ocket. The mean mean ab absolute solute stea steady dy sta state te rol roll l ra rate te fofor r the two experiments the two experiments reduced the roll rate of the rocket. The mean absolute steady state roll rate for the two experiments reduced the roll rate of the rocket. The mean absolute steady state roll rate for the two experiments wer were plotted e plotted against againsthe t the co corr rrespondin esponding g mean mean ste steady ady state veloc state velocity ity in F in Figur igure e 15. 15. were plotted against the corresponding mean steady state velocity in Figure 15. were plotted against the corresponding mean steady state velocity in Figure 15. (a) (b) (a) (b) Figure 14. Tasha III results with and without flow straightener (a) RPM inputs; (b) roll rate response. (a) (b) Figure 14. Tasha III results with and without flow straightener (a) RPM inputs; (b) roll rate response. Figure 14. Tasha III results with and without flow straightener (a) RPM inputs; (b) roll rate response. Figure 14. Tasha III results with and without flow straightener (a) RPM inputs; (b) roll rate response. mean wind speed (m/s) mean wind speed (m/s) Figure 15. Mean steady state roll rate with and without flow straightener. mean wind speed (m/s) Figure 15. Mean steady state roll rate with and without flow straightener. Figure 15. Mean steady state roll rate with and without flow straightener. Figure 15. Mean steady state roll rate with and without flow straightener. mean |p | (deg/s) ss -1 mean |p | (deg/s) mean p ss(deg/s -1 ) mean|p | (deg s | ss | ) -1 ss mean|p | (deg s ) mean|p | (deg s ) ss ss Aerospace 2016, 3, 10 14 of 27 As a final analysis of these experiments, the effective steady state fin offset is computed using Aerospace 2016, 3, 10 14 of 27 known values of the damping α and torque constant β of the airframe as discussed in the next & u = 0 section. Specifically, at steady state, the roll rate p , so assuming that , the disturbance in fin,ss As a final analysis of these experiments, the effective steady state fin offset is computed using Equation (2) can be solved to yield: known values of the damping and torque constant of the airframe as discussed in the next section. Specifically, at steady state, the roll rate p, so assuming that u  0, the disturbance in Equation (2) αp f in,ss ss u = (27) fin offset can be solved to yield: βv a pss ss u  (27) f in o f f set bv ss where “ss” refers to the steady state value for each steady state wind speed v which is computed ss where “ss” refers to the steady state value for each steady state wind speed v which is computed ss from the average of the velocity during the steady state period of interest. This analysis allows a from the average of the velocity during the steady state period of interest. This analysis allows characterization of the swirl in terms of the effective canard angle. Note that the canards and extra a characterization of the swirl in terms of the effective canard angle. Note that the canards and extra fin area in Tasha III, as well as a larger diameter airframe would cause significantly more damping in fin area in Tasha III, as well as a larger diameter airframe would cause significantly more damping Tasha III than in the aluminium fin rocket of Figure 12. Therefore, it’s reasonable to assume that the in Tasha III than in the aluminium fin rocket of Figure 12. Therefore, it’s reasonable to assume that very small amount of swirl remaining after the addition of the flow straightener would have a the very small amount of swirl remaining after the addition of the flow straightener would have negligible effect on the Tasha III rocket. The aluminium fin rocket also has a very low moment of a negligible effect on the Tasha III rocket. The aluminium fin rocket also has a very low moment of inertia, so the threshold of torque required to overcome the damping in the fins, would be much inertia, so the threshold of torque required to overcome the damping in the fins, would be much lower lower in this rocket and thus much more sensitive to swirl than Tasha III. in this rocket and thus much more sensitive to swirl than Tasha III. A plot of u versus v for both experiments, is given in Figure 16. This figure shows that fin offset ss A plot of u versus v or both experiments, is given in Figure 16. This figure shows that in ss f in o f f set in the case of no flow straightener, the swirl has a greater effect at the lower velocities. This result the case of no flow straightener, the swirl has a greater effect at the lower velocities. This result was was expected since the vertical component in the wind tunnel would not be sufficiently high to expected since the vertical component in the wind tunnel would not be sufficiently high to overcome overcome the horizontal component induced from the swirl. However, with the flow straightener the horizontal component induced from the swirl. However, with the flow straightener there was there was very little difference in the fin offset over all velocities, which provides further evidence very little difference in the fin offset over all velocities, which provides further evidence that there is that there is negligible swirl in this case. Subtracting the two curves in Figure 16 provides a measure negligible swirl in this case. Subtracting the two curves in Figure 16 provides a measure of the swirl in 1 −1 of the swirl in terms of the effective canard offset. After 20 m·s , there is an average of about 2° of terms of the effective canard offset. After 20 m s , there is an average of about 2 of swirl in the wind swirl in the wind tunnel. This value will need to be subtracted from future tests to get a better tunnel. This value will need to be subtracted from future tests to get a better estimate of the true fin estimate of the true fin offset for flight prediction. offset for flight prediction. wind speed (m/s) Figure 16. The equivalent fin offset versus velocity representing swirl in the wind tunnel. Figure 16. The equivalent fin offset versus velocity representing swirl in the wind tunnel. 4.2. Tasha III—Launch 1 4.2. Tasha III—Launch 1 T Tash ashaa III III fro from m Figure Figure 88b b was was launched launched fr from K om Kaitor aitorete Sp ete Spitit on on 22 22 July July 201 2015. 5. The ai The aim m of t of this his launch was primarily to test the new avionics stack and fibreglass rear fins. In the previous flight launch was primarily to test the new avionics stack and fibreglass rear fins. In the previous flight of of Smokey Smokey [12], the fins we [12], the fins wer re 3D pr e 3D printed. inted. The re The raso eason n for the fibreglass was for the fibreglass was to provide further to provide further strengthening suitable for supersonic flights in future research. In addition, to gain some useful data strengthening suitable for supersonic flights in future research. In addition, to gain some useful data fr from the laun om the launch, ch, a PD cont a PD contr rolle oller r was was implemented implemented d during uring fl flight ight in both the thrust a in both the thrust and nd coa coast st peri periods. ods. Since the vehicle was finished only days before the launch, there was not sufficient time to do a full Since the vehicle was finished only days before the launch, there was not sufficient time to do a full Aerospace 2016, 3, 10 15 of 27 Aerospace 2016, 3, 10 15 of 27 wind tunnel test, analysis of data and rigorous testing of gains. The only wind tunnel test performed was the stability test of Section 3.2. wind tunnel test, analysis of data and rigorous testing of gains. The only wind tunnel test performed For the flight, the gains chosen were k == 1, k 0.1, which were known to give a reasonable pd was the stability test of Section 3.2. response from previous wind tunnel testing of Smokey with the gimbal frame [12]. The reference For the flight, the gains chosen were k  1, k  0.1, which were known to give a reasonable was chosen to be a series of responses starting at 0° for a pre-determined amount after clearing the response from previous wind tunnel testing of Smokey with the gimbal frame [12]. The reference was launch guide, followed by an alternation between −15° and 15° every second. As a precaution, since chosen to be a series of responses starting at 0 for a pre-determined amount after clearing the launch this was the first flight with the avionics, a maximum limit of 6° was enforced in each canard. guide, followed by an alternation between 15 and 15 every second. As a precaution, since this was Unfortunately, there was a significant fin offset in the airframe which was greater than the the first flight with the avionics, a maximum limit of 6 was enforced in each canard. Unfortunately, canards could compensate for with this maximum limit, so only about 1 s of oscillatory data was there was a significant fin offset in the airframe which was greater than the canards could compensate obtained. However, this data set was sufficient to identify parameters and thus analyse the rocket for with this maximum limit, so only about 1 s of oscillatory data was obtained. However, this data set roll response. was sufficient to identify parameters and thus analyse the rocket roll response. The apogee for this flight was 522 m, the time to apogee was 10.2 s and the maximum velocity The apogee for this flight was 522 m, the time to apogee was 10.2 s and the maximum velocity was −1 −1 1 1 was 97 m·s . The wind speed was very low on the day, varying between 1 and 2 m·s on the ground. 97 m s . The wind speed was very low on the day, varying between 1 and 2 m s on the ground. The flight was successful and the rocket safely recovered apart from a couple of broken canards that The flight was successful and the rocket safely recovered apart from a couple of broken canards that were easily replaced. Figure 17 shows video stills from the ignition, take-off, onboard footage and were easily replaced. Figure 17 shows video stills from the ignition, take-off, onboard footage and parachute recovery. parachute recovery. Figure 17. Figure 17. Tash Tasha a II III I lau launch nch 1 1 st stills ills ( (a a) i ) ignition; gnition; ( (b b) take-off; ) take-off; ( (c c) ) onboard v onboard video; ideo; ( (d d)) recovery. recovery. Since there was only one step response from 0° to −15°, the control reference is modeled by a Since there was only one step response from 0 to 15 , the control reference is modeled by single Heaviside function and the proportional derivative (PD) control command is defined: a single Heaviside function and the proportional derivative (PD) control command is defined: uu=− max{min{uu ˆ , }, }H (tT ) (28) cmd cmd max min PD u  maxtmintu , u u , u u Hpt  T q (28) max PD cmd cmd min ˆ ′ uk=− (R(t) φ(t))+− k (R (t) p(t)) (29) cmd p d 1 u ˆ  k pRptq fptqq k pR ptq pptqq (29) cmd p d Rt () = R −−() RR H(t−T −1) (30) Rptq  R00 pR  R1qHpt  T PD 1q (30) 0 0 1 PD 6 p 6 p 15p 66 ππ−−15π u  , u  , R  0, R  , k  1, k  0.1, T  0.42 (31) max min 0 1 p PD uR ==,,uk =0,R= , =1,k d=0.1,T=0.42 (31) max min 01 p d PD 180 180 180 180 180 180 The Heaviside function in Equation (28) provides a delay of T after the launch detect to ensure PD The Heaviside function in Equation (28) provides a delay of T after the launch detect to the rocket is well clear of the launch guide before starting control. For launch PD detection to occur, the on ensure the rocket is well clear of the launch guide before starting control. For launch detection to board accelerometer on the rocket’s vertical axis needs to detect a consistent 2 g or higher acceleration over occur, the on 0.2 s. This board requir accele ement rometer on t prevents sensor he rocket’s v errors oremotor rtical amisfir xis needs to dete es from triggering ct a consistent 2 g or launch control. higher acceleration over 0.2 s. This requirement prevents sensor errors or motor misfires from Once the launch is detected, the rocket’s vertical axis acceleration is transformed to the earth reference frame triggerand ing then launch cont double integrated rol. Once t to he la determine unch is the det rocket’s ected, the rocket’s vertical axis acce height above the launch guide.ler Usi ation is ng the transformed to the earth reference frame and then double integrated to determine the rocket’s height two conditions of launch detection and launch guide clearance enables safe conditions for actuating the above t rocket’s he la canar unch guid ds. e. Using the two conditions of launch detection and launch guide clearance enables safe conditions for actuating the rocket’s canards. The roll rate data including all the key points of the launch are given in Figure 18, where t  0 corresponds The roll to rat 1.5 e dat s befor a incl eudin launch. g all t The he k contr ey point ol was s of t started he launch whenare thegiv rocket en in F height igure was 18, wher 2 m above e t =the 0 4 m launch guide. However, due to the specified 0.2 s delay in the launch detect, the actual altitude corresponds to 1.5 s before launch. The control was started when the rocket height was 2 m above when control started was 7 m which was 0.63 s after lift-off. Aerospace 2016, 3, 10 16 of 27 Aerospace 2016, 3, 10 16 of 27 the 4 m launch guide. However, due to the specified 0.2 s delay in the launch detect, the actual the 4 m launch guide. However, due to the specified 0.2 s delay in the launch detect, the actual altitude when control started was 7 m which was 0.63 s after lift-off. Aerospace 2016, 3, 10 16 of 27 altitude when control started was 7 m which was 0.63 s after lift-off. control end of true starts thrust 100 launch control end of true parachute time starts thrust 100 launch deployment parachute time deployment -100 -100 launch detect -200 launch detect -200 -300 02 46 8 10 12 -300 time (s) 02 46 8 10 12 time (s) Figure 18. Roll rate response for Tasha III launch 1 including key points in the launch. Figure 18. Roll rate response for Tasha III launch 1 including key points in the launch. Figure 18. Roll rate response for Tasha III launch 1 including key points in the launch. The commanded and encoder measured canard roll angle are defined as the average of all The commanded and encoder measured canard roll angle are defined as the average of all canard inputs which is standard in the literature [19]: The commanded and encoder measured canard roll angle are defined as the average of all canard canard inputs which is standard in the literature [19]: inputs which is standard in the literature [19]: cmd++ cmd cmd+ cmd 12 3 4 u = (32) cmd cmd++ cmd cmd+ cmd 12 3 4 u = (32) cmd cmd cmd cmd cmd 1 2 3 4 u  4 (32) cmd enc++ enc enc+ enc 12 3 4 u = (33) enc enc++ enc enc+ enc 12 3 4 enc enc 4 enc enc 1 2 3 4 u = (33) enc u  (33) enc The data is analyzed from just before control starts up to a couple of seconds before the The data is analyzed from just before control starts up to a couple of seconds before the parachute The data is analyzed from just before control starts up to a couple of seconds before the parachute deployment. The roll rate and fin angle u which is computed from Equation (33) enc deployment. The roll rate and fin angle u which is computed from Equation (33) using the encoder enc parachute deployment. The roll rate and fin angle u which is computed from Equation (33) enc using the encoder outputs enc,, … enc for each canard, are plotted in Figure 19, where the time is outputs enc , . . . , enc for each canar14 d, are plotted in Figure 19, where the time is reset to 0. Note that 1 4 using the encoder outputs enc,, … enc for each canard, are plotted in Figure 19, where the time is reset to 0. Note tha for some of the thrust t foperiod r some of andthe thrust peri all of the coast od period and a all ll of the coa the canards st peri are set od a atll the theirca maximum nards are set a values t reset to 0. Note that for some of the thrust period and all of the coast period all the canards are set at thei of 6r m , yet axithe mur m val oll rate ues of stays 6°, yet the rol negative. The l rarte eason stays ne is ther gat eive. is a The fin re offset ason which is there is i lar s a ger finthan offset the wh 6 ich that is their maximum values of 6°, yet the roll rate stays negative. The reason is there is a fin offset which is lthe arger tha canards n the 6° tha can compensate t the can for ar.ds can compensate for. larger than the 6° that the canards can compensate for. -2 -2 -4 -4 -6 -6 0 246 8 time (s) 0 246 8 (a) (time b) (s) (a) (b) Figure 19. Data for analysis (a) Roll rate response; (b) Measured canard angle from encoders. Figure 19. Data for analysis (a) Roll rate response; (b) Measured canard angle from encoders. Figure 19. Data for analysis (a) Roll rate response; (b) Measured canard angle from encoders. To identify the torque constant β, damping α and disturbance ut () from the roll model of dist To identify the torque constant , damping and disturbance u ptq from the roll model of dist To identify the torque constant β, damping α and disturbance ut () from the roll model of dist Equations (2)–(8), the first step is to specify the range in the β and α values as given in Equation (19). Equations (2)–(8), the first step is to specify the range in the and values as given in Equation (19). Equations (2)–(8), the first step is to specify the range in the β and α values as given in Equation (19). These ranges are defined: These ranges are defined: These ranges are defined: <  t1, 2, . . . , 60u , <  t5, 5.5, 6.5, 7, . . . , 15u (34) roll rate (deg/s) roll rate (deg/s) measured canard angle (deg) measured canard angle (deg) Aerospace 2016, 3, 10 17 of 27 ℜ= {1, 2,…, 60} , ℜ= {5, 5.5, 6.5, 7,…,15} (34) α β The next step is to define the time values for the disturbance changes in Equation (7). These Aerospace 2016, 3, 10 17 of 27 values are equally spaced in both the thrust period and the coast period of the data which are denoted in Figure 19a. Let N be the number of time points in the thrust period and N the thrust coast The next step is to define the time values for the disturbance changes in Equation (7). These values number of time points in coast period. The values in Equation (7) are defined: are equally spaced in both the thrust period and the coast period of the data which are denoted in Figure 19a. Let N be the number of time points in the thrust period and N the number of time thrust coast thrust T =ii,1 =…, ,N (35) i thrust points in coast period. The values in Equation (7) are defined: thrust thrust (TT − ) T  i end , i th1, rust . . . , N (35) i thrust Tj = T+=,1j ,…,N (36) N + j thrust N coast thrust thrust coast pT  T q end thrust T  T j , j  1, . . . , N (36) N j thrust coast Since there are no dynamics in the canards during coast, N is set to the minimum possible thrust coast coast value which obtains a reasonable match in the coast period. It was found empirically that higher Since there are no dynamics in the canards during coast, N is set to the minimum possible coast values than 2 do not help identifiability due to the lack of dynamics during this period, and a value value which obtains a reasonable match in the coast period. It was found empirically that higher of 1 gave a consistently large error. Therefore is set to 2 for all the analysis on this launch. The values than 2 do not help identifiability due to the coalack st of dynamics during this period, and a value of 1 value o gave a f consistently was laralso ge err min or.iTher mizeefor d and it was foun e N is set to 2d for that all the analysis was also on this launch. a good The choice. value N N = 2 coast thrust thrust of N was also minimized and it was found that N = 2 was also a good choice. Higher values Higher val thrust ues gave a progressively better match to the da thrust ta in the thrust period as would be gave a progressively better match to the data in the thrust period as would be expected, but were expected, but were much slower computationally. Specifically, the values from gave N =… 2, , 6 thrust much slower computationally. Specifically, the values from N = 2, ,6 gave virtually identical thrust virtually identical results with an improvement in the match to the roll angle by less than 0.1°. More results with an improvement in the match to the roll angle by less than 0.1 . More importantly, the importantly, the identified damping remained unchanged and the torque constant only varied by a identified damping remained unchanged and the torque constant only varied by a maximum of 0.05. maximum of 0.05. The results for N = 2 and are defined: N = 2 thrust coast The results for N = 2 and N = 2 are defined: thrust coast α= 8.5, β = 10.0 (37) best,, OL best OL a  8.5, b  10.0 (37) best,OL best,OL μ ≡ mean absolute error in roll rate = 9.82 deg/s (38) ||pO , L m  mean absolute error in roll rate  9.82 deg{s (38) | p|,OL μ ≡ mean absolute error in roll rate = 1.51 deg/s m  mean absolute error in roll angle  1.51 deg{s (39) (39) || φ|f,OL|,OL The model response is plotted against the measured values for both the roll rate and roll angle The model response is plotted against the measured values for both the roll rate and roll angle in Figure 20. A zoomed in plot of Figure 20a is given in Figure 21a and the identified time-varying in Figure 20. A zoomed in plot of Figure 20a is given in Figure 21a and the identified time-varying disturbance is plotted in Figure 21b. disturbance is plotted in Figure 21b. model -200 data -400 -600 -800 -1000 -1200 -1400 0 246 8 time (s) (a) (b) Figure 20. Model response versus data (a) Roll angle response; (b) Roll rate response. Figure 20. Model response versus data (a) Roll angle response; (b) Roll rate response. roll rate (deg/s) Aerospace 2016, 3, 10 18 of 27 Aerospace 2016, 3, 10 18 of 27 model canard-fin interaction data dominates response -2 Second PD controlled fin offset First PD -10 response dominates controlled -4 (reference -15 deg) response response -20 (reference 0 deg) -6 -30 -8 -40 00.5 11.5 02468 time (s) time (s) (a) (b) Figure 21. (a) Zoomed in roll angle response versus data; (b) Identified disturbance. Figure 21. (a) Zoomed in roll angle response versus data; (b) Identified disturbance. Figure 21a shows that although there is some error in the first controlled response, the overall Figure 21a shows that although there is some error in the first controlled response, the overall trends are captured accurately. For example the data drops 27.2° from the local maximum at t = 0.49 s trends are captured accurately. For example the data drops 27.2 from the local maximum at t = 0.49 s to the local minimum at t = 1.02 s where the model predicts a drop of 26.15° which corresponds to to the local minimum at t = 1.02 s where the model predicts a drop of 26.15 which corresponds to less than 4% error. The model also captures all the coast period, in both the roll angle and roll rate, as less than 4% error. The model also captures all the coast period, in both the roll angle and roll rate, as shown in Figure 20. The disturbance is quite low initially in the first 0.5 s of the data. This behavior is shown in Figure 20. The disturbance is quite low initially in the first 0.5 s of the data. This behavior is caused due to low velocity and therefore the canard–fin disturbance dominates the dynamics, as the caused due to low velocity and therefore the canard–fin disturbance dominates the dynamics, as the fin offset takes some time to take effect. After about 1 s the disturbance rapidly converges to a near fin offset takes some time to take effect. After about 1 s the disturbance rapidly converges to a near constant value around −7° which remains for the rest of the flight with only a minor increase at the constant value around 7 which remains for the rest of the flight with only a minor increase at the end. The results of Figures 20 and 21 and Equations (38) and (39) show that quite a simple model end. The results of Figures 20 and 21 and Equations (38) and (39) show that quite a simple model with with a relatively smooth disturbance function, is very effective in capturing the rocket roll response. a relatively smooth disturbance function, is very effective in capturing the rocket roll response. Note that the second PD controlled roll response in Figure 21a has a very large steady state Note that the second PD controlled roll response in Figure 21a has a very large steady state error, error, since the reference was −15°. The reason for this error is that the fin offset is having a major since the reference was 15 . The reason for this error is that the fin offset is having a major effect due effect due to the increased velocity and the maximum and minimum canard constraints do not to the increased velocity and the maximum and minimum canard constraints do not provide enough provide enough actuation to overcome this fin offset. However, the goal of this launch was not actuation to overcome this fin offset. However, the goal of this launch was not control, but to test the control, but to test the logistics of the new launch vehicle and avionics and provide an initial logistics of the new launch vehicle and avionics and provide an initial proof-of-concept of the model proof-of-concept of the model and methods. and methods. The final validation of the model and methods for this launch is to match the closed-loop model The final validation of the model and methods for this launch is to match the closed-loop model of Equations (28)–(31) to the data. The results are: of Equations (28)–(31) to the data. The results are: α= 7.5, β = 10.0 (40) best,, CL best CL a  7.5, b  10.0 (40) best,C L best,C L μ ≡ mean absolute error in roll rate = 9.76 deg/s (41) ||pO , L m  mean absolute error in roll rate  9.76 deg{s (41) | p|,C L μ ≡ mean absolute error in roll rate = 1.50 deg (42) || φ ,OL m  mean absolute error in roll angle  1.50deg (42) |f|,C L These results are very close to the open-loop response with a mean error difference of 0.06 deg/s These results are very close to the open-loop response with a mean error difference of 0.06 deg/s in the roll rate and 0.01° in the roll angle. However, there are some small differences in the thrust in the roll rate and 0.01 in the roll angle. However, there are some small differences in the thrust period in the roll angle as shown in Figure 22a, but the overall behavior of the two responses are period in the roll angle as shown in Figure 22a, but the overall behavior of the two responses are very similar. In addition, apart from a small period in the thrust, the identified closed and open-loop very similar. In addition, apart from a small period in the thrust, the identified closed and open-loop disturbances are virtually identical as shown in Figure 22b. disturbances are virtually identical as shown in Figure 22b. Hence, in summary, there is no noticeable change in the output responses and identified parameters when using the closed-loop model over of the open-loop model, although the closed-loop model typically takes about 50% longer to simulate. The advantage of the open-loop model computationally is that the roll rate is decoupled from the roll angle which is simpler to handle numerically. Aerospace 2016, 3, 10 19 of 27 Aerospace 2016, 3, 10 19 of 27 closed-loop model measured -10 -20 Aerospace 2016, 3, 10 19 of 27 -30 -40 0 0.5 1 1.5 closed-loop model measured 0 time (s) (a) (b) -10 Figure 22. (a) Roll angle closed loop response versus data; (b) Identified disturbance comparison. Figure 22. (a) Roll angle closed loop response versus data; (b) Identified disturbance comparison. -20 4.3. Tasha III—Launch 2 Hence, in summary, there is no noticeable change in the output responses and identified A new vehicle was manufactured for the second launch including fibreglassing the rear fins and -30 parameters when using the closed-loop model over of the open-loop model, although the closed-loop 3D printing two new canards to replace the ones that were broken during the Tasha III launch 1, see model typically takes about 50% longer to simulate. The advantage of the open-loop model Figure 8c. For this vehicle, a number of controlled step responses were performed in the wind tunnel -40 0 0.5 1 1.5 computationally is that the roll rate is decoupled from the roll angle which is simpler to shortly before the launch. Hence, there is a good amount of data to identify torque, damping and time (s) handle numerically. disturbances and to analyze the capability of the wind tunnel tests to predict flight response. (a) (b) Figure 22. (a) Roll angle closed loop response versus data; (b) Identified disturbance comparison. 4.3. T 4. asha 3.1. Wind III—Launch Tunnel St 2 ep Responses The rocket was suspended from a string, and 8 step responses were performed with a A new vehicle was manufactured for the second launch including fibreglassing the rear fins and 4.3. Tasha III—Launch 2 −1 −1 magnitude of 45°, at a wind speed of 22 m·s . The highest wind speed of 30 m·s was not used in 3D printing two new canards to replace the ones that were broken during the Tasha III launch 1, see A new vehicle was manufactured for the second launch including fibreglassing the rear fins and this case, as it was found that this airframe also had a fin offset, so it was spinning rapidly and Figure 8c. For this vehicle, a number of controlled step responses were performed in the wind tunnel 3D printing two new canards to replace the ones that were broken during the Tasha III launch 1, see starting to swing backwards and forwards, risking damaging the canards. The gains and frequency shortly before the launch. Hence, there is a good amount of data to identify torque, damping and Figure 8c. For this vehicle, a number of controlled step responses were performed in the wind tunnel were reduced and the parameters in Equations (11) and (12) are defined: disturbances and to analyze the capability of the wind tunnel tests to predict flight response. shortly before the launch. Hence, there is a good amount of data to identify torque, damping and 45π disturbances and to analyze the capability of the wind tunnel tests to predict flight response. kf == 0.5, k 0.05, = 0.1,R= ,R= 0 (43) pd 00 1 4.3.1. Wind Tunnel Step Responses 4.3.1. Wind Tunnel Step Responses The rocket was suspended from a string, and 8 step responses were performed with a magnitude The roll angle and roll rate responses are plotted in Figure 23. 1 1 The rocket was suspended from a string, and 8 step responses were performed with a of 45 , at a wind speed of 22 m s . The highest wind speed of 30 m s was not used in this case, as −1 −1 magnitude of 45°, at a wind speed of 22 m·s . The highest wind speed of 30 m·s was not used in it was found that this airframe also had a fin offset, so it was spinning rapidly and starting to swing this ca40 se, as it was found that this airframe also had a fin offset, so it was spinning rapidly and backwards and forwards, risking damaging the canards. The gains and frequency were reduced and starting to swing backwards and forwards, risking damaging the canards. The gains and frequency the parameters in Equations (11) and (12) are defined: were reduced and the parameters in Equations (11) and (12) are defined: 45p 10 45π k  0.5, k  0.05, f  0.1, R  , R  0 (43) p 0 0 d 1 kf == 0.5, k 0.05, = 0.1,R= ,R= 0 (43) pd 00 1 -50 -10 The roll angle and roll rate responses are plotted in Figure 23. The roll angle and roll rate responses are plotted in Figure 23. -20 -30 -100 0 2040 6080 0 20406080 time (s) time (s) (a) (b) Figure 23. Wind tunnel 45 degree step responses (a) Roll angle; (b) Roll rate. Figure 23 shows there are significantly different overshoots and rise times for each step -50 response as well as a major difference in dynamics depending on the direction of rotation, which is -10 likely caused by the fin offset in the airframe. To account for these variations, the model of Equations -20 (2)–(12) is identified for each individual step response. Since the oscillations reduce quite quickly -30 -100 0 2040 6080 0 20406080 time (s) time (s) (a) (b) Figure 23. Wind tunnel 45 degree step responses (a) Roll angle; (b) Roll rate. Figure 23. Wind tunnel 45 degree step responses (a) Roll angle; (b) Roll rate. Figure 23 shows there are significantly different overshoots and rise times for each step response as well as a major difference in dynamics depending on the direction of rotation, which is likely caused by the fin offset in the airframe. To account for these variations, the model of Equations (2)–(12) is identified for each individual step response. Since the oscillations reduce quite quickly u (deg) u (deg) dist dist Aerospace 2016, 3, 10 20 of 27 Figure 23 shows there are significantly different overshoots and rise times for each step response as well as a major difference in dynamics depending on the direction of rotation, which is likely caused Aerospace 2016, 3, 10 20 of 27 by the fin offset in the airframe. To account for these variations, the model of Equations (2)–(12) is identified for each individual step response. Since the oscillations reduce quite quickly after the first after the first peak, only the first half of the data in each step response is used for the parameter peak, only the first half of the data in each step response is used for the parameter identification. The identification. The remaining half is essentially disturbances in the wind tunnel, and there are very remaining half is essentially disturbances in the wind tunnel, and there are very few canard dynamics few canard dynamics so it does not contribute to identifiability. The time points in the disturbance so it does not contribute to identifiability. The time points in the disturbance model of Equations (4)–(8) model of Equations (4)–(8) were chosen to be simply the beginning and end points with N = 1 were chosen to be simply the beginning and end points with N = 1 in Equation (4). Since 5 s is analyzed in Equation (4). Since 5 s is analyzed in each data set, and time is reset to 0 each time, the time points in each data set, and time is reset to 0 each time, the time points are defined: are defined: TT== 0, 5 T  0, T  5 (4(44) 4) 001 1 For the grid search and non-linear regression algorithm, the ranges of the parameters are taken For the grid search and non-linear regression algorithm, the ranges of the parameters are taken from Equation (34). The results identified parameters and mean model response errors for the from Equation (34). The results identified parameters and mean model response errors for the open-loop model of Equation (9) are given in Table 2. An example set of model responses is plotted open-loop model of Equation (9) are given in Table 2. An example set of model responses is plotted in in Figure 24, which is the sixth step response in Figure 23. Both the roll angle and roll rate match Figure 24, which is the sixth step response in Figure 23. Both the roll angle and roll rate match very very closely to the measured data, even with a very simple linear model, for disturbance across the closely to the measured data, even with a very simple linear model, for disturbance across the whole whole data set considered. data set considered. model 40 measured -10 -20 time(s) (a) (b) Figure 24. Open-loop model response versus measured data (a) Roll angle; (b) Roll rate. Figure 24. Open-loop model response versus measured data (a) Roll angle; (b) Roll rate. Table 2. Summary of the identified model parameters for each of the 8 wind tunnel step responses. Table 2. Summary of the identified model parameters for each of the 8 wind tunnel step responses. β [,uu ] [μμ  ,] Step Response α dd 01 ||pO , L |φ|,OL Step Response ru , u s m , m d 0 d 1 |p|,OL |f|,OL 1 13 10.5 [−5.59,−7.71] [1.64,6.23] 1 13 10.5 [5.59,7.71] [1.64,6.23] 2 15 6.5 [−5.82,−6.10] [0.70,2.38] 2 15 6.5 [5.82,6.10] [0.70,2.38] 3 22 10.5 [−6.04,−6.35] [1.13,4.40] 3 22 10.5 [6.04,6.35] [1.13,4.40] 4 15 6.0 [−4.18,−7.16] [0.42,2.08] 4 15 6.0 [4.18,7.16] [0.42,2.08] 5 25 12.5 [−5.90,−6.51] [0.82,2.92] 5 25 12.5 [5.90,6.51] [0.82,2.92] 6 23 10.5 [5.12,6.25] [0.26,1.66] 6 23 10.5 [−5.12,−6.25] [0.26,1.66] 7 15 10.5 [6.11,7.41] [1.43,5.84] 7 15 10.5 [−6.11,7.41] [1.43,5.84] 8 27 10.0 [5.47,5.44] [0.60,2.66] 8 27 10.0 [−5.47,−5.44] [0.60,2.66] Mean 19.4 9.6 [5.47,6.62] [0.88,3.52] Mean 19.4 9.6 [−5.47,6.62] [0.88,3.52] Table Table 2 sho 2 shows ws there there is is a significant a significant v variation ariation of parameters of parameters acrossac the ross the step responses. step respons The average es. The average model error over all tests was 0.88° and 3.52 deg/s for the roll angle and roll rate model error over all tests was 0.88 and 3.52 deg/s for the roll angle and roll rate respectively. The size respectively. of the step r esponse The size of th was e step r 45 , soethe spon average se was 45° model , so the erraverage ors in T able model e 2 vary rrors frin T om a0.6% ble 2 var to 3.6% y from of 0.6% to 3.6% of the change in roll angle. Hence, the model and methods are very effective at the change in roll angle. Hence, the model and methods are very effective at capturing rocket roll capturing rocket roll response in the vertical wind tunnel. The disturbances in column 4 of Table 2 show a trend for a lower disturbance in the first period, which was similar to the flight in Figure 22b, showing that the canard-fin interaction effects can minimize the effect of fin offset in the airframe. The average fin offset across all tests was −6.1°, so taking into account the swirl this value corresponds to −4.1°. The wide range of values of the damping, torque constant and fin offsets in Aerospace 2016, 3, 10 21 of 27 response in the vertical wind tunnel. The disturbances in column 4 of Table 2 show a trend for a lower disturbance in the first period, which was similar to the flight in Figure 22b, showing that the canard-fin interaction effects can minimize the effect of fin offset in the airframe. The average fin offset across all Aerospace 2016, 3, 10 21 of 27 tests was 6.1 , so taking into account the swirl this value corresponds to 4.1 . The wide range of values of the damping, torque constant and fin offsets in Table 2 give the range of uncertainty in the Table 2 give the range of uncertainty in the launch, and will be compared with the flight data in the launch, and will be compared with the flight data in the next section. next section. 4.3.2. Flight Data 4.3.2. Flight Data Tasha III from Figure 8c was launched from Kaitorete Spit on 4 December 2015. The aims of this Tasha III from Figure 8c was launched from Kaitorete Spit on 4 December 2015. The aims of this launch included testing the rocket under a greater amount of actuations and to overcome the fin offset launch included testing the rocket under a greater amount of actuations and to overcome the fin problem that occurred in the July launch as detailed in Section 4.2. Importantly, the launch provided offset problem that occurred in the July launch as detailed in Section 4.2. Importantly, the launch a characterization of the ability of the wind tunnel to predict flight dynamics far outside the wind provided a characterization of the ability of the wind tunnel to predict flight dynamics far outside speeds that can be generated by the fan. Since the wind speed for the wind tunnel data was only the wind speeds that can be generated by the fan. Since the wind speed for the wind tunnel data was 22 m s , this launch provided a rigorous test of how well the model could be extrapolated to higher −1 only 22 m·s , this launch provided a rigorous test of how well the model could be extrapolated to wind speeds. The apogee for this flight was 422 m, and the maximum velocity was 81 m s which −1 higher wind speeds. The apogee for this flight was 422 m, and the maximum velocity was 81 m·s were much lower than the July launch, due to the increased weight from the more robust, supersonic which were much lower than the July launch, due to the increased weight from the more robust, capable avionics stack. The wind speed was reasonably low on the day with an average ground speed supersonic capable avionics stack. The wind speed was reasonably low on the day with an average −1 of 3 m s . Figure 25 shows several stills of the rocket moving up and leaving the launch guide. ground speed of 3 m·s . Figure 25 shows several stills of the rocket moving up and leaving the The launch guide. The over overall launch was aall launch success although was a success the back altho fins ugh the b were damaged ack fins wer on landing, e damaged due on landing, to a sudden gust due to of wind a sudd that en gu pushed st of wi the nd that rocketpushe onto d stony the rocket o ground. nto stony ground. Figure 25. Sequence of stills showing Tasha III rocket moving up and leaving launch guide. Figure 25. Sequence of stills showing Tasha III rocket moving up and leaving launch guide. The controller for this launch was a single step response from 0° to −20°, which occurred 2 s The controller for this launch was a single step response from 0 to 20 , which occurred 2 s after after the controller was switched on. The canard limits were increased to ±9° in this launch to the controller was switched on. The canard limits were increased to 9 in this launch to overcome overcome the fin offset from the first launch. In addition, some open-loop oscillatory inputs were the fin offset from the first launch. In addition, some open-loop oscillatory inputs were included in the included in the PD control signal of Equation (10). This input signal was implemented 0.4 s after the PD control signal of Equation (10). This input signal was implemented 0.4 s after the control started control started and was stopped 5 s after the −20° step response. The input was a modified chirp and was stopped 5 s after the 20 step response. The input was a modified chirp signal defined: signal defined: ut ()tA=+ ( ΔA(t))sin(( ω ( )+Δωt))t u ptq  p A D Aptqqsin() ppw ptq Dwptqqtq (45)(45) 0 0 ininput put 00 4π t 4p t At =ω , ()tA = 2π(2− ),Δ ( ),Δω(t )≡ random variation on signal (46) A  , w ptq  2pp2  q, D Aptq, Dwptq  random variation on signal (46) 0 0 180 10 180 10 A plot of the applied input signal is given in Figure 26. A plot of the applied input signal is given in Figure 26. The roll rate data including all the key points of the launch are given in Figure 27, where t = 0 The roll rate data including all the key points of the launch are given in Figure 27, where t = 0 corresponds to 1.5 s before take-off. For this launch, two accelerometers were used to improve corresponds to 1.5 s before take-off. For this launch, two accelerometers were used to improve the the robustness in the launch detect and the delay threshold was reduced to 0.1 s. In addition, the robustness in the launch detect and the delay threshold was reduced to 0.1 s. In addition, the accelerometer threshold increased to 2.5 g. Similarly to the Tasha III launch 1, the control was started accelerometer threshold increased to 2.5 g. Similarly to the Tasha III launch 1, the control was started when the rocket height was 2 m above the 4 m launch guide. when the rocket height was 2 m above the 4 m launch guide. Aerospace 2016, 3, 10 22 of 27 Aerospace 2016, 3, 10 22 of 27 Aerospace 2016, 3, 10 22 of 27 -2 -2 -4 -4 -6 -6 -8 0246 8 -8 0246 time (s) 8 time (s) Figure 26. Input signal applied to PD Controller (t = 0 corresponds to start of controller). Figure 26. Input signal applied to PD Controller (t = 0 corresponds to start of controller). Figure 26. Input signal applied to PD Controller (t = 0 corresponds to start of controller). Figure 27. Roll rate response for Tasha III launch 2 including key points in the launch. Figure 27. Roll rate response for Tasha III launch 2 including key points in the launch. Figure 27. Roll rate response for Tasha III launch 2 including key points in the launch. For this launch, the data is split into the two PD controlled responses with the set point of 0° followed by −20° which was 2 s later. A sharp change in roll rate can be seen for this second set point For this launch, the data is split into the two PD controlled responses with the set point of 0° For this launch, the data is split into the two PD controlled responses with the set point of 0 at about 4 s in Figure 27. The first period of analysis is started at 2.4 s in Figure 27 which is 0.4 s after followed by −20° which was 2 s later. A sharp change in roll rate can be seen for this second set point followed by 20 which was 2 s later. A sharp change in roll rate can be seen for this second set the control st at about 4 s inarts and Figure 27 corr . Th esponds to t e first period h e imp of analemen lysis ita s st tion arteof d at the i 2.4 s nput si in Fig gna urel from 27 which Figure 26 is 0.4 s aft . Thi es r point at about 4 s in Figure 27. The first period of analysis is started at 2.4 s in Figure 27 which is st the control st arting pointarts and was chosen corrsesponds to t ince there arhee imp signif lemen icant o tasti cil on latof ory dyn the ina put si mics gna in tlh from e canaFi rds which gure 26. will This 0.4 s after the control starts and corresponds to the implementation of the input signal from Figure 26. ensure good identifiability of the model parameters. The second period of analysis starts at 4 s in starting point was chosen since there are significant oscillatory dynamics in the canards which will This starting point was chosen since there are significant oscillatory dynamics in the canards which Figure 27, which is when the set point changes from 0° to −20°. ensure good identifiability of the model parameters. The second period of analysis starts at 4 s in will ensure good identifiability of the model parameters. The second period of analysis starts at 4 s in Figure 27, which is when the set point changes from 0° to −20°. For the first period, a similar approach to the Tasha III launch 1 model is applied, where N Figure 27, which is when the set point changes from 0 to 20 . For the first period, a similar approach to the Tasha III launch 1 model is applied, where N equally spaced points are chosen, and is increased until there is no significantly further For the first period, a similar approach to the 1 Tasha III launch 1 model is applied, where N equally equally spaced points are chosen, and N is increased until there is no significantly further spaced points are chosen, and N is increased until there is no significantly further improvement in the improvement in the fit to the data. Th 1 e values of N investigated were from 1 to 6 points. For fit to the data. The values of N investigated were from 1 to 6 points. For N = 1, ,4, the best model 1 N 1 improvement in the fit to the data. The values of investigated were from 1 to 6 points. For N =… 1, , 4 , the best model fits had average roll angle errors of 2.36, 2.15, 0.57 and 0.26° fits had average roll angle errors of 2.36, 2.15, 0.57 and 0.26 respectively. There was no significant N =… 1, , 4 , the best model fits had average roll angle errors of 2.36, 2.15, 0.57 and 0.26° respectively. There was no significant improvement for N = 5 and 6 and the parameters remained improvement for N = 5 and 6 and the parameters remained virtually identical for N = 3, ,6. Hence 1 1 respectively. There was no significant improvement for N = 5 and 6 and the parameters remained a value of N = 4 is chosen for the final model. The results ar 1 e defined: roll ra rolte ( l radeg/ te (deg/ s) s) Aerospace 2016, 3, 10 23 of 27 Aerospace 2016, 3, 10 23 of 27 virtually identical for N =… 3, , 6 . Hence a value of N = 4 is chosen for the final model. The virtually identical for N =… 3, , 6 . Hence a value of N = 4 is chosen for the final model. The Aerospace 2016, 3, 10 1 1 23 of 27 1 1 results are de results are defined fined: : α= 23.0,β = 9.0 α= 23.0,β = 9.0 (4 (47) 7) bbeest st,, ,, O OLL be best st O OLL a  23.0, b  9.0 (47) best,OL best,OL μ ≡ mean absolute error in roll rate = 4.10 deg/s μ ≡ mean absolute error in roll rate = 4.10 deg/s (48) (48) ||pO , L ||pO , L m  mean absolute error in roll rate  4.10 deg{s (48) | p|,OL μ ≡ mean absolute error in roll angle = 0.26 deg/s μ ≡ mean absolute error in roll angle = 0.26 deg/s (49) m  mean absolute error in roll angle  0.26 deg{s (4 (49) 9) || φ ,OL || φ ,OL |f|,OL The The model re model response sponse fo forr the roll an the roll angle gle and and roll rate roll rate ar are e shown in shown in Figur Figure e 28 28 an and d the offset an the offset angle gle is is The model response for the roll angle and roll rate are shown in Figure 28 and the offset angle is plotted in Figure 29. plotted in Figure 29. plotted in Figure 29. model model 4 measured measured 2 2 0 0 -2 -2 -4 -4 -6 -6 -8 -8 00.5 11.5 00.5 11.5 time (s) time (s) (a) (b) (a) (b) Figure 28. Figure 28. Mod Mode elled lled roll roll angle angle ( (a a) and roll rate ) and roll rate ( (b b) ) versus versus the measured data the measured data for for first first analysis perio analysis period d. . Figure 28. Modelled roll angle (a) and roll rate (b) versus the measured data for first analysis period. -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 -6 -6 -7 -7 -8 -8 0 0.5 1 1.5 0 0.5 1 1.5 time (s) time (s) Figure 29. Identified time-varying offset angle u for first analysis period. offset Figure 29. Identified time-varying offset angle uu for first analysis period. Figure 29. Identified time-varying offset angle for first analysis period. offset offset The results of Equation (47) are close to the average wind tunnel predicted values of 19.4 and 9.6 The The r re esu sulltts of Eq s of Equa uati tion (4 on (47) 7) a ar re c e cllos ose to e to the the a av ver erage age wind wind ttu unnel predicted nnel predicted values values of 19.4 and of 19.4 and in Table 2, with errors of 15.7% and 4.4%, respectively. The offset angles in Figure 29 are all within the 9.6 in Table 2, with errors of 15.7% and 4.4%, respectively. The offset angles in Figure 29 are all 9.6 in Table 2, with errors of 15.7% and 4.4%, respectively. The offset angles in Figure 29 are all range of values of the wind tunnel tests as well. There is also a similar trend of lower offset angles for wi withi thin n the range of the range of v va alues of the wi lues of the wind nd tunnel tunnel test tests s as we as well. Ther ll. There e is is also also a sim a simiilar lar trend o trend off lower lower the smaller fin movements as was the case in the wind tunnel. The mean offset angle of Figure 29 was offset angles for the smaller fin movements as was the case in the wind tunnel. The mean offset angle offset angles for the smaller fin movements as was the case in the wind tunnel. The mean offset angle 4.9 which is 0.8 greater than the average of 4.1 predicted in the wind tunnel. This value corresponds of Figure 29 was 4.9° which is 0.8° greater than the average of 4.1° predicted in the wind tunnel. This of Figure 29 was 4.9° which is 0.8° greater than the average of 4.1° predicted in the wind tunnel. This to an error of 16.3% but well within the expected variation of Table 2. value corresponds to an error of 16.3% but well within the expected variation of Table 2. value corresponds to an error of 16.3% but well within the expected variation of Table 2. A similar procedure was applied to the second period of data corresponding to a reference angle of 20 . In this case, a value of N = 2 was sufficient for the modelling and the identified parameters are defined: a  23.0, b  9.0 (50) best,OL best,OL Aerospace 2016, 3, 10 24 of 27 Aerospace 2016, 3, 10 24 of 27 A similar procedure was applied to the second period of data corresponding to a reference A similar procedure was applied to the second period of data corresponding to a reference angle of −20°. In this case, a value of was sufficient for the modelling and the identified N = 2 angle of −20°. In this case, a value of was sufficient for the modelling and the identified N = 2 parameters are defined: parameters are defined: Aerospace 2016, 3, 10 24 of 27 α= 48.0,β = 8.0 (50) best,, OL best OL α= 48.0,β = 8.0 (50) best,, OL best OL μ ≡ mean absolute error in roll rate = 8.32 deg/s (51) ||pO , L m  mean absolute error in roll rate  8.32 deg{s (51) μ | p|,OL≡ mean absolute error in roll rate = 8.32 deg/s (51) ||pO , L μ ≡ mean absolute error in roll angle = 0.99 deg/s m  mean absolute error in roll angle  0.99 deg{s (5 (52) 2) || φ|f,OL |,OL μ ≡ mean absolute error in roll angle = 0.99 deg/s (52) || φ ,OL The model responses for the roll angle and roll rate are shown in Figure 30 and the offset angle is The model responses for the roll angle and roll rate are shown in Figure 30 and the offset angle The model responses for the roll angle and roll rate are shown in Figure 30 and the offset angle plotted in Figure 31. is plotted in Figure 31. is plotted in Figure 31. model 0 m mode easur l ed measured -5 -5 -10 -10 -15 -15 -20 -20 -25 -25 -30 012 345 -30 012 345 time (s) time (s) (a) (b) (a) (b) Figure 30. Modelled roll angle (a) and roll rate (b) versus the measured data for second analysis period. Figure 30. Modelled roll angle (a) and roll rate (b) versus the measured data for second analysis period. Figure 30. Modelled roll angle (a) and roll rate (b) versus the measured data for second analysis period. -8.5 -8.5 -9 -9 -9.5 -9.5 -10 -10 012 34 5 012 34 5 time (s) time (s) Figure 31. Identified time-varying offset angle u for second analysis period. offset Figure 31. Figure 31. Iddentified entified time-var time-varying ying offset angle offset angle uu for for secon secondd analysis analysis peri period. od. offset offset The modeled torque constant in Equation (50) is reasonably close to the wind tunnel predicted The modeled torque constant in Equation (50) is reasonably close to the wind tunnel predicted The modeled torque constant in Equation (50) is reasonably close to the wind tunnel predicted value of 9.6 with an error of 16.7%, however the damping is significantly larger than all the damping value of 9.6 with an error of 16.7%, however the damping is significantly larger than all the damping value of 9.6 with an error of 16.7%, however the damping is significantly larger than all the damping values of Table 2. This extra damping is likely due to the rocket pitching over with an increasing values of Table 2. This extra damping is likely due to the rocket pitching over with an increasing angle values of Table 2. This extra damping is likely due to the rocket pitching over with an increasing angle of attack as well as the higher velocity. On the other hand, the average identified offset of of attack as well as the higher velocity. On the other hand, the average identified offset of Figure 31 angle of attack as well as the higher velocity. On the other hand, the average identified offset of Figure 31 is −4.7°, which is even closer to the wind tunnel average of 4.1°. Hence, although the is 4.7 , which is even closer to the wind tunnel average of 4.1 . Hence, although the damping is Figure 31 is −4.7°, which is even closer to the wind tunnel average of 4.1°. Hence, although the damping is less accurate in the post-thrust period, the torque constant and the offset angles are both less accurate in the post-thrust period, the torque constant and the offset angles are both accurately damping is less accurate in the post-thrust period, the torque constant and the offset angles are both accurately predicted for all stages of the flight, which are more important for control design. A predicted for all stages of the flight, which are more important for control design. A similar analysis has accurately predicted for all stages of the flight, which are more important for control design. A been performed for the closed-loop responses, but since the results were very similar to the open-loop analysis above, these results are not shown. Note that the torque constant values of = 8 and = 9 in this second Tasha III launch are reasonably close to value of = 10 identified in the first Tasha III launch. However, both of the values of damping in the second launch are considerably larger than the damping from the first launch. Aerospace 2016, 3, 10 25 of 27 This result is probably because there were a lot less dynamics in the first launch so the damping was less identifiable. 5. Conclusions A vertical wind tunnel has been designed and built at the University of Canterbury. This wind tunnel has been specifically customized for sounding rocket research and has a unique feature of allowing the rocket to be suspended by string for accurate prediction of roll dynamics. It is also very useful for testing stability before flight. The flow of the wind tunnel was analyzed in detail and turbulence intensity was estimated to be less than 0.04%. However, there was a reasonable amount of swirl equivalent to 2 of canard fin. This swirl was dramatically reduced to a negligible amount by using an egg crate at the bottom of the wind tunnel near the fan to straighten the flow. Two new airframes were developed in this research with a supersonic capable avionics stack in the second vehicle. Both rockets had reinforced fiberglass to give strength to the fins, but it was found that they had significant fin offset, with post-thrust average values of about 7 for the first vehicle and 5 for the second. Wind tunnel tests on the second vehicle revealed a high roll rate, which suggested a combination of swirl and fin offset. After the second flight, tests with and without the flow straightener using a similar airframe, showed that swirl could be modeled by the equivalent canard offset. This value was then used to compare the wind tunnel tests of the second vehicle to the flight data. A minimal modelling approach for roll dynamics was developed using a velocity dependent model and a piecewise-linear time-varying canard offset function. Open and closed loop models were considered with PD control, with encoders used to measure the canard movements. A combination of a grid search and non-linear regression provided a rigorous way of identifying the parameters. The models identified gave an excellent match to the flight data in both launches, with quite a smooth varying canard offset profile. It was found that with high dynamic movement in the canards the identified fin offset was lower, showing that canard–fin interaction dominates during these periods. This phenomenon occurred in both the wind tunnel tests and flight. A significant outcome of this paper was proving that wind tunnel tests give accurate predictions of the torque constant and fin offset and importantly, the resulting minimal roll models predict flight behavior closely. The damping is typically underestimated in the wind tunnel so a greater uncertainty should be included in this parameter for future control design. In summary, the vertical wind tunnel at the University of Canterbury is a unique facility and a key part of the success of UC Rocketry. A combination of wind tunnel tests and rocket launches have allowed a thorough understanding of rocket flight and control. Acknowledgments: Funded by the Rutherford Discovery Fellowship, Royal Society New Zealand; Callaghan Innovation PhD Fellowships; and Rocket Lab Ltd. Author Contributions: Hoani Bryson, Hans Philipp Sültrop, George Buchanan, Christopher Hann, Malcolm Snowdon, Avinash Rao, Adam Slee, Kieran Fanning, David Wright: developed the hardware, did the experiments, analyzed the data, developed models and wrote the paper. Jason McVicar, Brett Clark, Graeme Harris and Xiao Qi Chen: helped to construct the wind tunnel including setting up the fan and controller, provided expertise and advice on the flow quality and instrumentation and sensors for the wind tunnel tests, and contributed to writing the paper. Conflicts of Interest: The authors declare no conflict of interest. Notation I Inertia in roll axis (kg/m ) r Air density (kg/m ) a Damping constant (m ) b Torque constant (m) u Roll fin angle (rad) f in Aerospace 2016, 3, 10 26 of 27 A Cross sectional area (m ) p Roll rate (rad/s) v velocity (m/s) k , k Proportional and derivative gains Rptq Reference angle (rad) u , . . . , u Time-varying disturbance offset angle parameters (rad) d,0 d,N f Measured roll angle (rad) data f , f Open and closed loop numerical solutions to roll equations (rad) OL C L < ,< Ranges for , in the grid search for parameter identification a b G Turbulence intensity (m/s) s Standard deviation of wind speed (m/s) u Commanded canard angle (rad) cmd u Measured canard angle by encoder (rad) enc cmd , . . . , cmd Individual canard commands (rad) 1 2 enc , . . . , enc Individually measured encoders (rad) 1 2 u , u Minimum and maximum canard limits for actuation (rad) min max m , m Mean absolute roll rate for open loop and closed loop controllers | p|,OL | p|,C L m , m Mean absolute roll angle for open loop and closed loop controllers |f|,OL |f|,C L u Open loop input signal into PD controller in put Abbreviations PD Proportional-derivative NASA The National Aeronautics and Space Administration UC University of Canterbury CFD Computational Fluid Dynamics RPM Revolutions per minute OL Open loop CL Closed loop References 1. UC Rocketry Project. Available online: http://ucrocketry.org/ (accessed on 1 March 2016). 2. Schrijer, F.; Bannink, W. Description and Flow Assessment of the Delft Hypersonic Ludwieg Tube. J. Spacecr. Rocket. 2010, 47, 125–133. [CrossRef] 3. Spirito, J.D.; Vaughn, M.E., Jr.; Washington, W.D. Numerical Investigation of Canard-Controlled Missile with Planar and Grid fins. J. Spacecr. Rocket. 2003, 40, 363–370. [CrossRef] 4. Silton, S.I.; Fresconi, F. Effect of Canard Interactions on Aerodynamic Performance of a Fin-Stabilized Projectile. J. Spacecr. Rocket. 2015, 52, 1430–1442. [CrossRef] 5. Curfman, H.J.; Grisby, C.E. Longitudinal Stability and Control Characteristics of a Canard Missile Configuration for Mach Numbers from 1.1 to 1.93 as Determined from Free-Flight and Wind-Tunnel Investigations; Technical Report for NASA Langley Aeronautical Laboratory: Hampton, VA, USA, 1952. Available online: http://ntrs.nasa.gov/ archive/nasa/casi.ntrs.nasa.gov/19930087105.pdf (accessed on 1 March 2016). 6. Dollyhigh, S.M. Subsonic and Supersonic Longitudinal Stability and Control Characteristics of an Aft-Tail Fighter Configuration with Cambered and Uncambered Wings and Cambered Fuselage; Technical Report for NASA Langley Research Center: Hampton, VA, USA, 1977. Available online: http://ntrs.nasa.gov/archive/nasa/ casi.ntrs.nasa.gov/19770024149.pdf (accessed on 1 March 2016). Aerospace 2016, 3, 10 27 of 27 7. Blair, A.B., Jr.; Hernandez, G. Effect of Tail-Fin Span on Stability and Control Characteristics of a Canard-Controlled Missile at Supersonic Mach Numbers; Technical Report for NASA Langley Research Center: Hampton, VA, USA, 1983. Available online: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19830019688.pdf (accessed on 1 March 2016). 8. Dillenius, M.F.E.; Lesieutre, D.J.; Hegedus, M.C.; Perkins, S.C., Jr.; Love, J.F.; Lesieutre, T.O. Engineering- Intermediate- and High-Level Aerodynamic Prediction Methods and Applications. J. Spacecr. Rocket. 1999, 36, 609–620. [CrossRef] 9. Lesieutre, D.J.; Love, J.F.; Dillenius, M.F.E. Prediction of the Nonlinear Aerodynamic Characteristics of Tandem-Control and Rolling-Tail Missiles. In Proceedings of the AIAA Atmospheric Flight Mechanics Conference and Exhibit, AIAA 2002-4511, Monterey, CA, USA, 6 August 2002. 10. Beresh, S.J.; Smith, J.A.; Henfling, J.F.; Grasser, T.W.; Spillers, R.W. Interaction of a Fin Trailing Vortex with a Downstream Control Surface. J. Spacecr. Rocket. 2009, 46, 318–328. [CrossRef] 11. Lesieutre, D.J.; Quijano, O. Studies of Vortex Interference Associated with Missile Configurations. In Proceedings of the 52nd Aerospace Sciences Meeting, AIAA SciTech (AIAA 2014-0213), National Harbor, MD, USA, 13–17 January 2014. 12. Buchanan, G.; Wright, D.; Hann, C.E.; Bryson, H.; Snowdon, M.; Rao, A.; Slee, A.; Sültrop, H.P.; Jochle-Rings, B.; Barker, Z.; et al. The Development of Rocketry Capability in New Zealand—World Record Rocket and First of its Kind Rocketry Course. Aerospace 2015, 2, 91–117. [CrossRef] 13. Hann, C.E.; Snowdon, M.; Rao, A.; Winn, O.; Wongvanich, N.; Chen, X.Q. Minimal Modelling Approach to Describe Turbulent Rocket Roll Dynamics in a Vertical Wind Tunnel. Proc. Inst. Mech. Eng. G J. Aerosp. Eng. 2012, 226, 1042–1060. [CrossRef] 14. Assato, M.; Moraes, L.F.; Chisaki, M. Investigation of a Boundary-Layer Control System by Air Blowing in a Closed-Circuit Subsonic Wind Tunnel. In Proceedings of the 45th AIAA Aerospace Sciences Meeting and Exhibit, Aerospace Sciences Meetings, Reno, NV, USA, 8–11 January 2007. 15. Seo, Y. Effect of hydraulic diameter of flow straighteners on turbulence intensity in square wind tunnel. HVAC R Res. 2013, 19, 141–147. 16. Wind Tunnel Design. Available online: http://www-htgl.stanford.edu/bradshaw/tunnel/index.html (accessed on 1 March 2016). 17. BBS Timbers Ltd. Available online: http://bbstimbers.co.nz/flexible-plywood-bendy-plywood/ (accessed on 1 March 2016). 18. Kestrel AU Pocket Weather Instruments. Available online: http://kestrelmeters.com.au/ (accessed on 1 March 2016). 19. Sioruis, G.M. Missile Guidance and Control Systems; Springer-Verlag Inc.: New York, NY, USA, 2004. © 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Aerospace Multidisciplinary Digital Publishing Institute

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aerospace Article Vertical Wind Tunnel for Prediction of Rocket Flight Dynamics 1 1 1 1 , Hoani Bryson , Hans Philipp Sültrop , George Buchanan , Christopher Hann *, 2 2 1 1 1 Malcolm Snowdon , Avinash Rao , Adam Slee , Kieran Fanning , David Wright , 3 1 4 5 Jason McVicar , Brett Clark , Graeme Harris and Xiao Qi Chen Department of Electrical and Computer Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand; hoani.bryson@gmail.com (H.B.); philipp.sueltrop@pg.canterbury.ac.nz (H.P.S.); georgebuchanannz@gmail.com (G.B.); a.slee@rocketlab.co.nz (A.S.); kieranfanning@hotmail.co.nz (K.F.); djwnz@hotmail.com (D.W.); clarkbab@gmail.com (B.C.) Rocket Lab Ltd., 3A Airpark Drive, Auckland 2022, New Zealand; malcolm.snowdon@gmail.com (M.S.); avinash.rao43@gmail.com (A.R.) School of Engineering and Information and Communication Technology (ICT), University of Tasmania, Private Bag 65, Hobart 7001, Australia; jason.j.mcvicar@gmail.com Engineering and Architecture Department, Christchurch Polytechnic Institute of Technology (CPIT), P.O. Box 540, Christchurch Mail Centre, Christchurch 8140, New Zealand; Graeme.Harris@cpit.ac.nz Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand; xiaoqi.chen@canterbury.ac.nz * Correspondence: chris.hann@canterbury.ac.nz; Tel.: +64-3-364-2987 (ext. 7242); Fax: +64-3-364-2264 Academic Editor: Raffaello Mariani Received: 1 February 2016; Accepted: 22 March 2016; Published: 29 March 2016 Abstract: A customized vertical wind tunnel has been built by the University of Canterbury Rocketry group (UC Rocketry). This wind tunnel has been critical for the success of UC Rocketry as it allows the optimization of avionics and control systems before flight. This paper outlines the construction of the wind tunnel and includes an analysis of flow quality including swirl. A minimal modelling methodology for roll dynamics is developed that can extrapolate wind tunnel behavior at low wind speeds to much higher velocities encountered during flight. The models were shown to capture the roll flight dynamics in two rocket launches with mean roll angle errors varying from 0.26 to 1.5 across the flight data. The identified model parameters showed consistent and predictable variations over both wind tunnel tests and flight, including canard–fin interaction behavior. These results demonstrate that the vertical wind tunnel is an important tool for the modelling and control of sounding rockets. Keywords: rocketry; canard actuation; vertical wind tunnel; flow quality; minimal modelling; roll dynamics; PD control; minimal modelling 1. Introduction A customized vertical wind tunnel has been built by the University of Canterbury (UC) Rocketry Research group [1] to test advanced control systems for application on small sounding rockets at subsonic and supersonic speeds. The common approach to designing and analyzing supersonic rockets is to quantitatively identify aerodynamics in a supersonic wind tunnel. However, these types of wind tunnels have large power requirements and are thus very costly, and usually have much shorter run times around 0.1–0.2 s [2]. Another approach to subsonic and supersonic flow analysis is Computational Fluid Dynamics (CFD). For example, canard–fin interactions have been well studied and modelled with CFD using Aerospace 2016, 3, 10; doi:10.3390/aerospace3020010 www.mdpi.com/journal/aerospace Aerospace 2016, 3, 10 2 of 27 wind tunnel data with relatively good predictions for the smaller angle of attacks [3,4]. However, the available comparisons in the literature are usually for static movements of the canards, so it is not clear how well the CFD models predict transient response in flight. Only very limited comparisons between flight and wind tunnel data have been published and are typically old NASA technical notes (e.g., [5–7]). The results of [6] show a reasonable prediction of pitch flight dynamics in terms of the frequency and phase responses of the pitching velocity per unit canard-fin-deflection frequency, however no roll comparisons are given and CFD analysis is not performed. Hence, although CFD analysis is commonly used for predicting rocket response in a wind tunnel, it has not been fully validated in flight. For the case of hypersonic flow, no vehicle has been flown long enough to obtain the data needed to improve the model accuracy and hypersonic wind tunnels only provide very short durations. Thus, in general, although CFD are useful for gaining trends on the expected flight response, they are not sufficiently accurate to design robust control systems and hence, extensive flight testing is usually required. In addition to CFD, there are a number of empirical approaches to modelling subsonic and supersonic rocket steady state aerodynamics. These methods are primarily based on NASA wind tunnel data and have been developed into engineering-level and intermediate-level aerodynamic prediction codes [7–9]. The models have also been extended to include canard interaction [10,11] but the experimental work is restricted to wind tunnels, so only considers steady state responses to fixed canard angles. Therefore, these methods are primarily for designing responsive canards in missiles and have not been used to understand actual rocket flight, where there are very fast movements and transient effects that often behave very differently to steady state response in a wind tunnel. This paper develops models of rocket roll dynamics that are first identified in the wind tunnel at low speeds and then validated on actual rocket launches at much higher speeds. This type of validation is unique in the literature as most other approaches do not go any further than wind tunnel evaluation [10,11]. The UC rocketry modelling and control methodology is to use a combination of dynamic subsonic wind tunnel testing and sounding rocket launches, to test qualitatively methodologies that have the ability to account for new dynamics in real-time. In other words, the approach is to model the rocket response in the wind tunnel during a control actuation that will be implemented in a flight. In addition, the damping or lift coefficients are not needed to be precisely known before launch, as any uncertainty from the wind tunnel tests, can be accounted for “on-the-fly” during the rocket flight. This UC rocketry control methodology has been successfully validated on several subsonic launches including an unstable rocket. For more details and results see [1]. The vertical wind tunnel has been a critical component to the success of UC Rocketry. In particular, it is important for obtaining quantitative information on the first few seconds of flight and can be used to estimate a full subsonic flight response using minimal modelling and parameter identification [12]. In addition, the vertical test section allows a much simpler and more accurate way of testing roll dynamics since the rocket can be suspended from a string. In a standard horizontal wind tunnel there is extra friction since an additional moving surface, like a bearing is required, so roll response is less realistic. For pitch and yaw dynamics, a gimbal frame [13] is used to allow three of freedom control. This gimbal frame set up is important for debugging the avionics control hardware and software before flight. To test the stability of a fully fueled rocket, two sets of strings are horizontally attached from one edge of the wind tunnel to the center of mass of the rocket, which allows movement in one axis. Hence this vertical wind tunnel has a number of unique features tailored for rocket flight analysis. A typical closed-circuit subsonic horizontal wind tunnel has a motor powered fan which blows air around a looping tube [14]. The settling chamber usually contains a honeycomb flow straightener followed by several wire mesh screens to reduce turbulence [15]. Following the settling chamber, and just prior to the test section, is a contraction in the tube, which increases air speed. The test section is where the test article is placed and data is collected. A diffuser, which is a gradually diverging section of tube, is placed after the test section to decrease the velocity and thus decrease power requirements. Aerospace 2016, 3, 10 3 of 27 Curved vanes guide air around corners [16]. The disadvantage of using a closed-circuit is that more space and materials are required to construct the back loop of the circuit. The curved vanes are complex features and an additional expense in the construction. Heat exchangers are often needed to keep the Aerospace 2016, 3, 10 3 of 27 tunnel at the desired temperature, since the same air is being re-circulated through the circuit many times and may deviate significantly from the ambient air temperature [16]. exchangers are often needed to keep the tunnel at the desired temperature, since the same air is being re-circulated through the circuit many times and may deviate significantly from the ambient A key part of the UC Rocketry wind tunnel design is the use of bendy plywood [17] due to its air temperature [16]. low cost, light weight and ease of constructing a circular cross section. Another advantage is that with A key part of the UC Rocketry wind tunnel design is the use of bendy plywood [17] due to its a circular shape less material can be used to give the same cross-sectional area. That is, if the shape low cost, light weight and ease of constructing a circular cross section. Another advantage is that was changed to a square with side length equal to the circle’s diameter, the volume of space would be with a circular shape less material can be used to give the same cross-sectional area. That is, if the greater and manufacturing simpler, but the maximum displacement of the rocket that can be achieved shape was changed to a square with side length equal to the circle’s diameter, the volume of space in any direction, would still be the same as for the circle. Thus the extra power required in the fan to would be greater and manufacturing simpler, but the maximum displacement of the rocket that can maintain a given flow velocity in the square configuration is effectively wasted. The vertical orientation be achieved in any direction, would still be the same as for the circle. Thus the extra power required in the fan to maintain a given flow velocity in the square configuration is effectively wasted. The also avoids the large floor and building space requirements needed for horizontal wind tunnels, and vertical orientation also avoids the large floor and building space requirements needed for was assembled outdoors in a fenced enclosure further simplifying space allocation. A 15 kW fan was horizontal wind tunnels, and was assembled outdoors in a fenced enclosure further simplifying already in existence in the Department of Electrical and Computer Engineering at UC, so the wind space allocation. A 15 kW fan was already in existence in the Department of Electrical and Computer tunnel was essentially built around this fan which was at the base and sitting on the ground. Engineering at UC, so the wind tunnel was essentially built around this fan which was at the base This paper details some of the design and construction of the wind tunnel, methods for and sitting on the ground. overcoming swirl induced from the fan, and presents a number of wind tunnel and flight results. This paper details some of the design and construction of the wind tunnel, methods for A key finding is that the vertical wind tunnel can provide realistic roll predictions of rocket flights well overcoming swirl induced from the fan, and presents a number of wind tunnel and flight results. beyond A key the find wind ing is t speeds hat tthat he vert can icabe l wind generated tunnel can p by the rovide re current alist fan, ic rol and l predi it c pr tions of ro ovides an cket excellent flights test well beyond the wind speeds that can be generated by the current fan, and it provides an excellent platform for modelling rocket behavior and validating parameter identification methods prior to flight. test platform for modelling rocket behavior and validating parameter identification methods prior to For example, similar canard–fin interaction roll dynamics observed and identified in the wind tunnel flight. For example, similar canard–fin interaction roll dynamics observed and identified in the wind were also seen in the subsequent rocket flight. The results show that it is possible to create a low-cost tunnel were also seen in the subsequent rocket flight. The results show that it is possible to create a wind tunnel with excellent flow characteristics, and thus provides a very valuable research tool for low-cost wind tunnel with excellent flow characteristics, and thus provides a very valuable research modelling and control of sounding rockets. tool for modelling and control of sounding rockets. 2. Methodology—Wind Tunnel 2. Methodology—Wind Tunnel This section outlines the design and manufacture processes of the customized vertical wind tunnel This section outlines the design and manufacture processes of the customized vertical wind tunnel used by UC Rocketry as shown in Figure 1. used by UC Rocketry as shown in Figure 1. Figure 1. Customized vertical wind tunnel for Sounding Rockets. Figure 1. Customized vertical wind tunnel for Sounding Rockets. Aerospace 2016, 3, 10 4 of 27 2.1. Concept and Design To simplify the mounting of the rocket and to provide realistic roll response testing, the key design specification was to allow the mounting of the rocket vertically by suspending from the nose cone. Therefore a vertical suck-down wind tunnel was designed. Due to the significant vertical height requirement, the structure was stored outside in a caged enclosure adjacent to the High Voltage Lab, which meant that it needed to be weather resistant. The wind tunnel was designed in individual sections with bolted joints between each section. This approach simplifies fabrication and assembly as the components could be added to or taken from the wind tunnel as required. To create a sufficient quality of flow in the wind tunnel, aluminium honeycomb was used as a flow conditioner. This flow straightener was critical, particularly since winds affect the flow. Another important part of the design was utilizing an existing 1 m diameter, 15 kW fan and speed controller. Thus, the wind tunnel structure was effectively built around the fan. Since the test section was chosen to have a diameter of 0.6 m, wide angle diffusers were necessary to reduce the height of the wind tunnel. Bendy plywood was chosen for the structure as it was easy to form into the required shapes and significantly reduces manufacturing complexity and time, as compared to sheet-metal or fiberglass. The overall rocket wind tunnel design consisted of five main components: the flow conditioner, reducer, test section, diffuser and fan. These components are summarized as follows: The flow conditioner was a cylindrical section at the inlet of the tunnel with an internal diameter of 1.4 m and a 9 mm wall thickness. The flow conditioner holds the honeycomb and a mesh screen. The reducer took the flow from the 1.4 m internal diameter flow conditioner to the 0.6 m internal diameter test section. This contraction before the test section can also reduce velocity fluctuations and form a more uniform flow. The reducer walls were fabricated from 6 mm bendy ply so that it would fit into the smaller internal diameter of the test section. The test section was 2 m long, had an internal diameter of 0.6 m and was formed with 6 mm bendy ply. Due to the length and thin walls of the test section a 77  38 mm length of pine was run down each side. The door for the test section was then framed using 75  38 mm pine and 17 mm plywood. The frame was then removed and the door cut from the test section. At the bottom of the test section, a metal grille recessed into a plywood ring was placed to protect the fan. The diffuser transitioned the flow from the 0.6 m internal diameter test section to the 1 m internal diameter fan housing. The diffuser was also made from 6 mm bendy ply. The fan was 1 m diameter and had up to 15 kW available in power. The blade angle was at 23 so was left unchanged. The fan was on wheels, and could be adjusted to meet flush with the diffuser. In addition, the wind tunnel was secured to the wall of the High Voltage (HV) lab by a permanent scaffold and a winch was used to open a lid on the wind tunnel during operation and closed after testing to ensure no rain came into the wind tunnel and fan. 2.2. Construction 2.2.1. General Methods Bendy ply was used for the outer skin of the wind tunnel. Bendy ply is plywood with the two outer lamination grains aligned, and forming most of the thickness of the sheet. A thin central lamination bonded the two outer laminations together with the grain running perpendicular to the outer laminations. This property allows the plywood to be bent down to tight radii without the need for steam/heat, see Figure 2. Aerospace 2016, 3, 10 5 of 27 Aerospace 2016, 3, 10 5 of 27 Aerospace 2016, 3, 10 5 of 27 Aerospace 2016, 3, 10 5 of 27 Figure 2. A sheet of 6 mm bendy ply. Figure 2. A sheet of 6 mm bendy ply. Figure 2. A sheet of 6 mm bendy ply. The rest of the tunnel structure was constructed from standard 17 mm plywood and 75 × 38 mm Figure 2. A sheet of 6 mm bendy ply. The rest of the tunnel structure was constructed from standard 17 mm plywood and 75 × 38 mm pine. The 17 mm plywood was used to form the flanges on the ends of each section. To reduce the The rest of the tunnel structure was constructed from standard 17 mm plywood and 75  38 mm pine. The 17 mm plywood was used to form the flanges on the ends of each section. To reduce the amount of material wastage, each flange was made up from four quarter flanges. The parts were cut pine. The 17 mm plywood was used to form the flanges on the ends of each section. To reduce the The rest of the tunnel structure was constructed from standard 17 mm plywood and 75 × 38 mm amount of material wastage, each flange was made up from four quarter flanges. The parts were cut using a jigsaw. The sections of the wind tunnel were fabricated by forming individual outer skin pine. The 17 mm plywood was used to form the flanges on the ends of each section. To reduce the amount of material wastage, each flange was made up from four quarter flanges. The parts were cut using a jigsaw. The sections of the wind tunnel were fabricated by forming individual outer skin amount of material wastage, each flange was made up from four quarter flanges. The parts were cut pieces to the flanges, and securing with wood screws, as shown in Figure 3a. Once a complete using a jigsaw. The sections of the wind tunnel were fabricated by forming individual outer skin pieces pieces to the flanges, and securing with wood screws, as shown in Figure 3a. Once a complete using a jigsaw. The sections of the wind tunnel were fabricated by forming individual outer skin section had been secured, the screws were backed off, epoxy resin with West Systems 403 modifier to the flanges, and securing with wood screws, as shown in Figure 3a. Once a complete section had section had been secured, the screws were backed off, epoxy resin with West Systems 403 modifier pieces to the flanges, and securing with wood screws, as shown in Figure 3a. Once a complete was worked into the gap, and the screws were again tightened. The flange joints were then been secured, the screws were backed off, epoxy resin with West Systems 403 modifier was worked was worked into the gap, and the screws were again tightened. The flange joints were then section had been secured, the screws were backed off, epoxy resin with West Systems 403 modifier reinforced with 200 g woven fiberglass cloth, see Figure 3b. The 75 × 38 mm pine was used to add into the gap, and the screws were again tightened. The flange joints were then reinforced with 200 g reinfo was worked into rced with 200 g the wov gap, en fiberg and the lass screws were cloth, see Figure 3 again ti b. The ghtened. The 75 × 38 mm p flange joi ine wa nts were then s used to add strength to the openings in the tunnel and provide mounting points for fixtures, see Figure 4. woven fiberglass cloth, see Figure 3b. The 75  38 mm pine was used to add strength to the openings strength to the openings in the tunnel and provide mounting points for fixtures, see Figure 4. reinforced with 200 g woven fiberglass cloth, see Figure 3b. The 75 × 38 mm pine was used to add in the tunnel and provide mounting points for fixtures, see Figure 4. strength to the openings in the tunnel and provide mounting points for fixtures, see Figure 4. (a) (b) (a) (b) (a) (b) Figure 3. (a) A sheet of 6 mm bendy ply; (b) Flange joint with 200 g woven cloth reinforcement. Figure 3. (a) A sheet of 6 mm bendy ply; (b) Flange joint with 200 g woven cloth reinforcement. Figure 3. (a) A sheet of 6 mm bendy ply; (b) Flange joint with 200 g woven cloth reinforcement. Figure 3. (a) A sheet of 6 mm bendy ply; (b) Flange joint with 200 g woven cloth reinforcement. Figure 4. 75 × 38 mm pine lengths used for reinforcement and framing. Figure 4. 75 × 38 mm pine lengths used for reinforcement and framing. Figure 4. 75  38 mm pine lengths used for reinforcement and framing. Figure 4. 75 × 38 mm pine lengths used for reinforcement and framing. Aerospace 2016, 3, 10 6 of 27 Aerospace 2016, 3, 10 6 of 27 Aerospace 2016, 3, 10 6 of 27 Aerospace 2016, 3, 10 6 of 27 The internal surface of the tunnel was not perfectly smooth due to the outer skin joints, The internal surface of the tunnel was not perfectly smooth due to the outer skin joints, The internal surface of the tunnel was not perfectly smooth due to the outer skin joints, The internal surface of the tunnel was not perfectly smooth due to the outer skin joints, screw-heads, excess glue and manufacturing imperfections on the inner plywood face. Therefore, all screw-heads, excess glue and manufacturing imperfections on the inner plywood face. Therefore, all screw-heads, excess glue and manufacturing imperfections on the inner plywood face. Therefore, all screw-heads, excess glue and manufacturing imperfections on the inner plywood face. Therefore, all internal surfaces and flange faces were sanded smooth. It was also necessary to fill voids on the internal surfaces and flange faces were sanded smooth. It was also necessary to fill voids on the internal surfaces and flange faces were sanded smooth. It was also necessary to fill voids on the inner internal surfaces and flange faces were sanded smooth. It was also necessary to fill voids on the inner side of the skin; both along the seams and behind the screw heads. Poly-filler was applied to inner side of the skin; both along the seams and behind the screw heads. Poly-filler was applied to side of the skin; both along the seams and behind the screw heads. Poly-filler was applied to these inner side of the skin; both along the seams and behind the screw heads. Poly-filler was applied to these areas and sanded back, so that the flow in the tunnel would not be disrupted, as shown in these areas and sanded back, so that the flow in the tunnel would not be disrupted, as shown in areas and sanded back, so that the flow in the tunnel would not be disrupted, as shown in Figure 5. these areas and sanded back, so that the flow in the tunnel would not be disrupted, as shown in Figure 5. Figure 5. Figure 5. (a) (b) (a) (b) (a) (b) Figure 5. Poly filler (a) before sanding; (b) after sanding. Figure Figure 5. 5. Poly Poly f filler iller ((a a)) before before sanding; ( sanding; ( b b ) aft ) after er sanding. sanding. Figure 5. Poly filler (a) before sanding; (b) after sanding. 2.2.2. Flow Conditioner and Fan Grille 2.2.2. Flow Conditioner and Fan Grille 2.2.2. Flow Conditioner and Fan Grille 2.2.2. Flow Conditioner and Fan Grille The flow conditioner was constructed similarly to the rest of the tunnel but required some The flow conditioner was constructed similarly to the rest of the tunnel but required some The flow conditioner was constructed similarly to the rest of the tunnel but required some The flow conditioner was constructed similarly to the rest of the tunnel but required some additional features. To support the honey comb, a 9 mm ledge was built for it to rest upon. In additional features. To support the honey comb, a 9 mm ledge was built for it to rest upon. In additional features. To support the honey comb, a 9 mm ledge was built for it to rest upon. In addition, additional features. To support the honey comb, a 9 mm ledge was built for it to rest upon. In addition, a galvanized wire mesh was put across the flow conditioner. The square sheet of addition, a galvanized wire mesh was put across the flow conditioner. The square sheet of a galvanized wire mesh was put across the flow conditioner. The square sheet of honeycomb was cut addition, a galvanized wire mesh was put across the flow conditioner. The square sheet of honeycomb was cut to fit the circular flow conditioner, see Figure 6. honeycomb was cut to fit the circular flow conditioner, see Figure 6. to fit the circular flow conditioner, see Figure 6. honeycomb was cut to fit the circular flow conditioner, see Figure 6. Figure 6. Honeycomb edge cut to match internal diameter of flow conditioner. Figure 6. Honeycomb edge cut to match internal diameter of flow conditioner. Figure 6. Honeycomb edge cut to match internal diameter of flow conditioner. Figure 6. Honeycomb edge cut to match internal diameter of flow conditioner. To prevent damage to the fan due to falling objects, a simple grille was fabricated. A plywood To prevent damage to the fan due to falling objects, a simple grille was fabricated. A plywood To prevent damage to the fan due to falling objects, a simple grille was fabricated. A plywood To prevent damage to the fan due to falling objects, a simple grille was fabricated. A plywood ring was cut with an internal diameter matching the internal diameter of the test section, and outside ring was cut with an internal diameter matching the internal diameter of the test section, and outside ring was cut with an internal diameter matching the internal diameter of the test section, and outside ring was cut with an internal diameter matching the internal diameter of the test section, and outside diameter matching the outer diameter of the flanges. A recess was cut along the inside edge of the diameter matching the outer diameter of the flanges. A recess was cut along the inside edge of the diameter matching the outer diameter of the flanges. A recess was cut along the inside edge of the diameter matching the outer diameter of the flanges. A recess was cut along the inside edge of the flange using a router to form a ledge for the grille to rest on, as shown in Figure 7. flange using a router to form a ledge for the grille to rest on, as shown in Figure 7. flange using a router to form a ledge for the grille to rest on, as shown in Figure 7. flange using a router to form a ledge for the grille to rest on, as shown in Figure 7. Figure 7. Wind tunnel grille to protect fan. Figure 7. Wind tunnel grille to protect fan. Figure 7. Wind tunnel grille to protect fan. Figure 7. Wind tunnel grille to protect fan. Aerospace 2016, 3, 10 7 of 27 Aerospace 2016, 3, 10 7 of 27 3. Methodology—Rocket Systems and Modelling 3. Methodology—Rocket Systems and Modelling 3.1. Improvements to Airframe and Avionics Stack 3.1. Improvements to Airframe and Avionics Stack Since the launch of Smokey at the end of 2014 [12], there have been a number of improvements Since the launch of Smokey at the end of 2014 [12], there have been a number of improvements implemented to the rocket systems. These improvements can be seen in Figure 8, which shows the implemented to the rocket systems. These improvements can be seen in Figure 8, which shows three launch configurations of the Smokey and Tasha III airframes. The Smokey and Tasha III the three launch configurations of the Smokey and Tasha III airframes. The Smokey and Tasha III airframe designs are aerodynamically equivalent. Both designs have identical canard, fin, tube airframe designs are aerodynamically equivalent. Both designs have identical canard, fin, tube length, length, tube diameter and nose cone geometry. The main difference between the two airframes was tube diameter and nose cone geometry. The main difference between the two airframes was the the manufacturing process for attaching the back fins. manufacturing process for attaching the back fins. Figure 8. Improvements to airframe and avionics stack. (a) Smokey; (b) Tasha III, launch 1; (c) Tasha III, Figure 8. Improvements to airframe and avionics stack. (a) Smokey; (b) Tasha III, launch 1; (c) Tasha launch 2. III, launch 2. Smokey used Acrylonitrile butadiene styrene (ABS) 3D printed fins and canards. The strength Smokey used Acrylonitrile butadiene styrene (ABS) 3D printed fins and canards. The strength of of these parts were appropriate for subsonic flight; however, they can be damaged on landing these parts were appropriate for subsonic flight; however, they can be damaged on landing resulting resulting in more time spent repairing the airframe. To overcome this problem, Tasha III also used in more time spent repairing the airframe. To overcome this problem, Tasha III also used 3D printed 3D printed fins, but they were laminated to the airframe with fiberglass. Two of the Tasha III’s 3D fins, but they were laminated to the airframe with fiberglass. Two of the Tasha III’s 3D printed canards printed canards were damaged after its first flight, so on its second flight we used our supersonic were damaged after its first flight, so on its second flight we used our supersonic capable stack, which capable stack, which has fiberglass canards. has fiberglass canards. Cameras were placed in Tasha III allowing the recording of flights to provide an insight on how Cameras were placed in Tasha III allowing the recording of flights to provide an insight on how the on-board avionics were performing. Some holes were cut in the airframe, with one of the the on-board avionics were performing. Some holes were cut in the airframe, with one of the cameras cameras placed out one side of the airframe by 10 mm. Smokey did not use an on-board camera, so it placed out one side of the airframe by 10 mm. Smokey did not use an on-board camera, so it had no had no camera holes. camera holes. UC Rocketry’s supersonic launches require a device to report where the rocket lands. Both UC Rocketry’s supersonic launches require a device to report where the rocket lands. Both Tasha Tasha III flights included the Spot Tracker to test its capability to report landing locations. The Spot III flights included the Spot Tracker to test its capability to report landing locations. The Spot Tracker Tracker and cameras are the main reason the Tasha III vehicle was heavier than Smokey. The second and cameras are the main reason the Tasha III vehicle was heavier than Smokey. The second Tasha III Tasha III launch was heavier than the first Tasha III launch, because the avionics were exchanged to launch was heavier than the first Tasha III launch, because the avionics were exchanged to the more the more robust supersonic capable avionics. robust supersonic capable avionics. Each launch of the Smokey and Tasha III airframes had different properties. Between each Each launch of the Smokey and Tasha III airframes had different properties. Between each launch, launch, changes were made to the internal avionics which affects the mass of the vehicle. Changes in changes were made to the internal avionics which affects the mass of the vehicle. Changes in mass mass affect the torques and airspeeds experienced during flight. Table 1 summarizes the key affect the torques and airspeeds experienced during flight. Table 1 summarizes the key differences differences between the vehicles for each launch. between the vehicles for each launch. Aerospace 2016, 3, 10 8 of 27 Table 1. Vehicle comparisons between Smokey and Tasha III. Property Smokey Tasha III Launch 1 Tasha III Launch 2 Aerospace 2016, 3, 10 8 of 27 Mass 3.0 kg 3.47 kg 3.99 kg Length 1.52 m 1.51 m 1.51 m Table 1. Vehicle comparisons between Smokey and Tasha III. Z-axis 2 2 2 0.00311 kg·m 0.00361 kg·m 0.00393 kg·m Property Inertia Smokey Tasha III Launch 1 Tasha III Launch 2 Mass 3.0 kg 3.47 kg 3.99 kg 3D printed PLA with 3D printed PLA with Length Fin material 1.52 3D p m rinted ABS 1.51 m 1.51 m 2 fibreglass lami 2 nation fibre glass lamination 2 Z-axis Inertia 0.00311 kg m 0.00361 kg m 0.00393 kg m Fin material 3D printed ABS 3D printed PLA with fibreglass lamination 3D printed PLA with fibre glass lamination Canards 3D printed ABS 3D printed ABS Fibre glass moulded Canards 3D printed ABS 3D printed ABS Fibre glass moulded Subsonic capable with Supersonic capable with Avionics Subsonic capable Subsonic capable with spot tracker Supersonic capable with spot tracker Avionics Subsonic capable spot tracker spot tracker 3.2. Testing Rocket Stability 3.2. Testing Rocket Stability A major advantage of the vertical wind tunnel is that it is a straightforward way to test rocket A major advantage of the vertical wind tunnel is that it is a straightforward way to test rocket stability before flight. UC Rocketry has developed the following procedure for testing stability: stability before flight. UC Rocketry has developed the following procedure for testing stability: Assemble the rocket with a dummy mass motor. • Assemble the rocket with a dummy mass motor. Measure the center of mass by balancing the rocket on a beam less than 20 mm wide. Mark the • Measure the center of mass by balancing the rocket on a beam less than 20 mm wide. Mark the center of mass. center of mass. Fix a pipe clamp, with string tied securely to both ends of the pipe clamp to the rocket, at the • Fix a pipe clamp, with string tied securely to both ends of the pipe clamp to the rocket, at the measured center of mass. measured center of mass. Feed the string from both sides of the clamp through the two 4 mm holes on the sides of the wind • Feed the string from both sides of the clamp through the two 4 mm holes on the sides of the tunnel. Tie the string around the back of the wind tunnel, and tension the ropes to lift the center wind tunnel. Tie the string around the back of the wind tunnel, and tension the ropes to lift the of mass of the rocket as close as possible to the holes in the side of the wind tunnel. center of mass of the rocket as close as possible to the holes in the side of the wind tunnel. Attach the nose tip of the rocket to the vertical string. The purpose of this string is to prevent • Attach the nose tip of the rocket to the vertical string. The purpose of this string is to prevent an an unstable rocket from damaging the walls, or prevent the rocket from falling should the clamps unstable rocket from damaging the walls, or prevent the rocket from falling should the clamps slip. The vertical string should be taut only when the nose of the rocket is close to the wind slip. The vertical string should be taut only when the nose of the rocket is close to the wind tunnel walls. tunnel walls. Start the wind tunnel, and check the rocket straightens at 15, 20 and 30 m/s. • Start the wind tunnel, and check the rocket straightens at 15, 20 and 30 m/s. Figure 9 gives a picture of a stability test set up. Figure 9 gives a picture of a stability test set up. (a) (b) Figure 9. Stability set up (a) connection to string; (b) connection to center of mass of rocket. Figure 9. Stability set up (a) connection to string; (b) connection to center of mass of rocket. Since these tests were for roll control only, the exact margin of stability in terms of the number Since these tests were for roll control only, the exact margin of stability in terms of the number of of calibres, was not determined. The main aim of the test in Figure 9, was to prove general stability calibres, was not determined. The main aim of the test in Figure 9, was to prove general stability so so that it would be safe to launch. An experimental determination of the center of pressure using this that it would be safe to launch. An experimental determination of the center of pressure using this method will be investigated in future work for pitch and yaw modelling. method will be investigated in future work for pitch and yaw modelling. Aerospace 2016, 3, 10 9 of 27 3.3. Rocket Roll Dynamics Modelling In both launches and all wind tunnel tests in this paper, only roll dynamics were investigated. This section outlines the modelling and parameter identification techniques used to understand and predict the rocket roll dynamics during flight. 3.3.1. Minimal Model The roll model is extended from a previously used model [12] which includes the effect of velocity on the damping and normal forces in the roll axis. Ignoring the yaw term in Equation (6) of [13] and lumping the parameter d into the coefficients of the roll fin angle and damping yields: . 1 a I p  r v A bu ptq p (1) f in 2 v where the definition of the parameters is given in the Notation. Expanding out Equation (1), and including the effects of disturbance and defining the roll angle gives the differential equation model: . 1 1 I p   r v A a p r v A bpu ptq u ptqq (2) p f in dist 2 2 f  p (3) where u ptq u ptq lumps the effects of fin canard interaction, thrust offsets that may impart a roll dist dist and atmospheric effects into a single time-varying parameter. It is shown in the results section that when there are sudden fin movements, it’s critical to allow fast changes in the disturbance at these points to provide a good match to the data. To model these effects, the disturbance is written in the form: u ptq  Y F (4) dist k k k1 pu  u q d,k d,k1 Y  u pt  T q (5) k d,k1 k1 pT  T q k k1 F  Hpt  T q Hpt  T q (6) k k1 k where Hptq  heaviside function, T , . . . , T  user defined time points (7) 0 N u , . . . , u  unknown constants identified from data (8) d,0 d,N 3.3.2. Parameter Identification To ensure the optimum possible model is obtained with good numerical parameter identifiability, a grid search is applied to the main parameters excluding the disturbance, which is identified using non-linear regression. This method was applied for both an open-loop model, where u ptq is f in measured directly by encoders on the rocket and a closed-loop model where u ptq is defined from f in a standard proportional derivative controller plus the addition of a pre-defined input. Mathematically these models are defined: Open-loop : u ptq  u ptq  fin movement measured from encoder (9) f in f in, OL Closed-loop : u ptq  u ptq  k pRptq fptqq k pR ptq pptqq u ptq (10) f in f in, C L d in put where k  proportional gain, k  derivative gain (11) p d Rptq  pR  R qHpsinp2p f tqq R (12) 0 1 0 1 Aerospace 2016, 3, 10 10 of 27 The reference function Rptq in Equation (12) is an alternating square wave of frequency f (Hz) between the values of R and R . This function allows multiple step responses to be analyzed from 0 1 wind tunnel tests and rocket flights. The function u ptq is set to 0 for the wind tunnel tests and the in put first flight, but is defined as a chirp function with varying amplitudes for the second flight to increase flight dynamics for a rigorous test of the model. The optimization is set up by first fixing the damping a and torque constant b. Two objective functions are defined: OL F pU q  rf pt q f pt q , . . . , f pt q f pt qs (13) d data 0 OL 0 data end OL end a,b C L F pU q  rf pt q f pt q , . . . , f pt q f pt qs (14) d data 0 C L 0 data end C L end a,b U  u , . . . , u (15) d d, 0 d, N where f ptq  measured roll angle, t , . . . , t  data time points (16) data end f ptq  roll angle solution to Equationsp2q –p9q for given a, b and U (17) OL d f ptq  roll angle solution to Equationsp2q –p8q ,p10q –p12q , for given a, b and U (18) C L d A range of values of a and b are then selected: <  ta kDa, k  0, . . . , N u ,<  b kDb, k  0, . . . , N (19) a min a b min b For each a and b from the ranges in Equation (19), the open-loop and closed-loop identified disturbance values are defined: OL U  non-linear least squares solution to Equation p13q (20) C L U  non-linear least squares solution to Equation p14q (21) The final model parameters that best fit the data are then defined: OL OL OL OL OL OL OL OL ˆ ˆ ˆ X  a , b , U : F pU q  min mean F pU q (22) OL OL d d a,b d a , b taP< , bP< u C L C L C L C L C L C L C L C L ˆ ˆ ˆ X  a , b , U : F pU q  min mean F pU q (23) C L C L d d a,b d a , b taP< , bP< u Equations (22) and (23) represent a grid search over all the values in Equation (19), where for each pair of a and b a non-linear regression is performed to determine the corresponding disturbance values. This non-linear regression uses the command “lsqnonlin” in Matlab. 4. Results and Discussion 4.1. Wind Tunnel Flow Quality Measurements from a hot wire anemometer placed at various positions from the boundary showed that there are negligible boundary effects greater than 200 mm from the wall, with less than 5% reduction in wind speed at 100 mm from the wall. Since the diameter of the sounding rockets in this research are 80 mm with a 60 mm canard and fin radial distance, the outermost point of the rocket is 160 mm from the wall. Hence, the volume of the test section used in this research, has close to uniform flow. Most importantly, the results from the prediction of rocket flight roll response from wind tunnel derived parameters presented in the sections below, demonstrate that the test section has adequate flow quality for this research. Aerospace 2016, 3, 10 11 of 27 this research are 80 mm with a 60 mm canard and fin radial distance, the outermost point of the rocket is 160 mm from the wall. Hence, the volume of the test section used in this research, has close to uniform flow. Most importantly, the results from the prediction of rocket flight roll response from wind tunnel derived parameters presented in the sections below, demonstrate that the test section has adequate flow quality for this research. Aerospace 2016, 3, 10 11 of 27 4.1.1. Turbulence Intensity 4.1.1. Turbulence Intensity To demonstrate the quality of the flow over time, in the wind tunnel, a Kestrel 4500 wind sensor [18] w To demonstrate as placed the 200quality mm from the edge a of the flow over t the bottom of time, in the the d wind oor itunnel, n Figure a1.Kestr This posi el 4500 tion was wind sensor [18] was placed 200 mm from the edge at the bottom of the door in Figure 1. This position fixed throughout the experiment. This sensor measures every 2 s and outputs a wind speed measurement was fixed thr rounded to the neare oughout the experiment. st 0.1 m/s. A fine This sensor r resolution win measures every d sensor w 2 s and outputs ith a higher frequency a wind speed measurement rounded to the nearest 0.1 m/s. A finer resolution wind sensor with a higher frequency was not required for this analysis, since wind speeds less than 0.1 m/s have a negligible effect on rocket dyn was not requir amics. In ed for ad thi dition, turbulen s analysis, since ce properties wind speeds are less independent of than 0.1 m/s the ti havem ae sca negligible le so this test i effect on s rocket dynamics. In addition, turbulence properties are independent of the time scale so this test adequate to characterize the turbulence intensity in the wind tunnel. The revolutions per minute (R is PM) adequate refereto nce on t characterize he fan was the set turbulence to a sequ intensity ence of va inlu the es defi wind ned tunnel. by: The revolutions per minute (RPM) reference on the fan was set to a sequence of values defined by: RPM = 570, 870,1100,1400,1650,1700 [ ] (24) ref RP M  r570, 870, 1100, 1400, 1650, 1700s (24) re f Taking into account the controller time constant, the times when the fan reaches steady state are: Taking into account the controller time constant, the times when the fan reaches steady state are: T = 100, 230, 390, 550, 718, 858 (s) [ ] (25) RPM T  r100, 230, 390, 550, 718, 858s psq (25) RP M The measured wind speed is shown in Figure 10. At each steady state there are only very small The measured wind speed is shown in Figure 10. At each steady state there are only very small oscillations, showing that the flow is close to laminar. Figure 11a shows a plot of the RPM versus oscillations, showing that the flow is close to laminar. Figure 11a shows a plot of the RPM versus wind wind speed and Figure 11b plots the turbulence intensity Γ versus wind speed which is defined: speed and Figure 11b plots the turbulence intensity G versus wind speed which is defined: σ () v Γ= () v , σ≡ standard deviation, v ≡ wind speed (26) s pvq Gpvq  , s  standard deviation, v  wind speed (26) mean(v) meanpvq There is a correlation of R = 0.9999 for RPM versus wind speed, thus the fan controller is There is a correlation of R = 0.9999 for RPM versus wind speed, thus the fan controller is creating creating a very linear response. The turbulence intensity is very low and less than 0.04% over all a very linear response. The turbulence intensity is very low and less than 0.04% over all wind wind speeds tested. speeds tested. Figure 10. Measured wind speed (from Kestrel) versus time for different revolutions per minute (RPM) Figure 10. Measured wind speed (from Kestrel) versus time for different revolutions per minute values in the fan. (RPM) values in the fan. wind speed (m/s) -1 wind speed (m s ) Aerospace 2016, 3, 10 12 of 27 Aerospace 2016, 3, 10 12 of 27 Aerospace 2016, 3, 10 12 of 27 wind speed (m/s) wind speed (m/s) (a) (b) (a) (b) Figure 11. (a) RPM versus wind speed; (b) Turbulence intensity versus wind speed. Figure 11. (a) RPM versus wind speed; (b) Turbulence intensity versus wind speed. Figure 11. (a) RPM versus wind speed; (b) Turbulence intensity versus wind speed. 4.1.2. Swirl 4.1.2. Swirl 4.1.2. Swirl It was noticed that in every airframe tested in the wind tunnel, there was a roll rate with the It was noticed that in every airframe tested in the wind tunnel, there was a roll rate with the canards set to 0. However, it was not initially known what percentage was of this roll rate, caused by It was noticed that in every airframe tested in the wind tunnel, there was a roll rate with the canards set to 0. However, it was not initially known what percentage was of this roll rate, caused by fin offsets in the airframe or swirl in the wind tunnel. To characterize the swirl, several sets of canards set to 0. However, it was not initially known what percentage was of this roll rate, caused fin offsets in the airframe or swirl in the wind tunnel. To characterize the swirl, several sets of aluminium fins were machined to provide a baseline where there was no fin offset. The fins were by fin offsets in the airframe or swirl in the wind tunnel. To characterize the swirl, several sets of aluminium fins were machined to provide a baseline where there was no fin offset. The fins were made from two thin sheets of aluminium formed in a cross. These fins were attached to a steel pipe aluminium fins were machined to provide a baseline where there was no fin offset. The fins were made made from two thin sheets of aluminium formed in a cross. These fins were attached to a steel pipe and suspended by string in the wind tunnel as shown in Figure 12. Tests showed that the roll rate from two thin sheets of aluminium formed in a cross. These fins were attached to a steel pipe and and suspended by string in the wind tunnel as shown in Figure 12. Tests showed that the roll rate observed was highly dependent on the total diameter of the fins. For a diameter less than 100 mm, suspended observed was hi by string ghly dependent on the tota in the wind tunnel as shown l diam in eter Figur of t eh12 e fin . Tests s. For a d showed iamthat eter les thesr t oll han rate 100 m observed m, there was no roll rate and greater than 300 mm the roll rate was very low. This result suggests that was there was no highly dependent roll rate a on nd the grea total ter tha diameter n 300 mm of the the fins. roll rat For e wa a diameter s very low. Th less than is resu 100 lt smm, ugges ther ts th eat was the swirl is mainly isolated to a concentric ring between 100 and 300 mm from the centre of the wind the swirl is mainly isolated to a concentric ring between 100 and 300 mm from the centre of the wind no roll rate and greater than 300 mm the roll rate was very low. This result suggests that the swirl is tutnnel. unnel. The The fifi n set n set t t hh at at wa wa ss chosen chosen for for de detta aile iled d ana ana ly ly ss is is h h aa d d a a di di am am ete er of ter of 202 00 m 0 m m which m m which m axia m xiized mized mainly isolated to a concentric ring between 100 and 300 mm from the centre of the wind tunnel. The the roll rate the roll rate . . fin set that was chosen for detailed analysis had a diameter of 200 mm which maximized the roll rate. Figure 12. Aluminium fin set up. Figure 12. Aluminium fin set up. Figure 12. Aluminium fin set up. The first test was to take a video of the 200 mm aluminium fin rocket for 5 min at the maximum The first test was to take a video of the 200 mm aluminium fin rocket for 5 min at the maximum wind speed of 30 m/s and visually count the number of revolutions to work out the average roll rate. The first test was to take a video of the 200 mm aluminium fin rocket for 5 min at the maximum wind speed of 30 m/s and visually count the number of revolutions to work out the average roll rate. The result was 87.0 deg/s which demonstrates there was certainly a relatively significant swirl in the wind speed of 30 m/s and visually count the number of revolutions to work out the average roll rate. The res wind t uu ltnne wal.s 8 To overcome 7.0 deg/s which demon this swirl, an stegg cr rates tat here e w a was c s plac eed rtaiup t nly o a re a h le aight tively of s 2 ignif 0 cm icin ant a hex swia rl in gon t he The result was 87.0 deg/s which demonstrates there was certainly a relatively significant swirl in the wind t shape on the unnel. To overcome grill at the bottom of this swirl the wi , an egg cr nd tunnel ate w , just a as plac bove the fa ed up ton, a h ase shown ight of i2 n0 Figure 13 cm in a hex . Thi asgon wind tunnel. To overcome this swirl, an egg crate was placed up to a height of 20 cm in a hexagon egg crate effectively provided an additional flow straightener reducing the swirl as it was near the shape on the grill at the bottom of the wind tunnel, just above the fan, as shown in Figure 13. This shape on the grill at the bottom of the wind tunnel, just above the fan, as shown in Figure 13. This egg fan which caused the swirl. Another video was then taken of the aluminium fin rocket and the egg crate effectively provided an additional flow straightener reducing the swirl as it was near the crate effectively provided an additional flow straightener reducing the swirl as it was near the fan average roll rate observed was 25.7 deg/s which is a 340% reduction in the swirl. There were also fan which caused the swirl. Another video was then taken of the aluminium fin rocket and the which caused the swirl. Another video was then taken of the aluminium fin rocket and the average roll several periods where there was no roll rate. average roll rate observed was 25.7 deg/s which is a 340% reduction in the swirl. There were also rate observed was 25.7 deg/s which is a 340% reduction in the swirl. There were also several periods several periods where there was no roll rate. where there was no roll rate. mean wind speed (m/s) mean wind speed (m/s) turbulence intensity (m/s) turbulence intensity (m/s) Aerospace 2016, 3, 10 13 of 27 Aerospace 2016, 3, 10 13 of 27 Aerospace 2016, 3, 10 13 of 27 Aerospace 2016, 3, 10 13 of 27 Figure 13. Egg crate used as a flow straightener to reduce swirl. Figure 13. Egg crate used as a flow straightener to reduce swirl. Figure 13. Egg crate used as a flow straightener to reduce swirl. Figure 13. Egg crate used as a flow straightener to reduce swirl. To fully characterize the impact of the flow straightener with various wind speeds on the Tasha To fully characterize the impact of the flow straightener with various wind speeds on the Tasha To fully characterize the impact of the flow straightener with various wind speeds on the Tasha III To fully characterize the impact of the flow straightener with various wind speeds on the Tasha III rocket, an uncontrolled airframe with the same dimensions as Figure 8b was placed in the wind III rocket, an uncontrolled airframe with the same dimensions as Figure 8b was placed in the wind rocket, an uncontrolled airframe with the same dimensions as Figure 8b was placed in the wind tunnel. III rocket, an uncontrolled airframe with the same dimensions as Figure 8b was placed in the wind tunnel. This airframe was primarily used to test the parachute before implementing the controlled tunnel. This airframe was primarily used to test the parachute before implementing the controlled This airframe was primarily used to test the parachute before implementing the controlled launch, so tunnel. This airframe was primarily used to test the parachute before implementing the controlled launch, so had slightly different back fins as a result of natural manufacturing variations, launch, so had slightly different back fins as a result of natural manufacturing variations, had launch, so h slightly difa fer d s entligback htly fins different as a bac result k fin of natural s as a manufacturing result of natura variations, l manufactbut uring v wasaessentially riations, but was essentially the same rocket. The specific rocket in Figure 8b was not available for this test as but was essentially the same rocket. The specific rocket in Figure 8b was not available for this test as the but was e same rocket. ssentially The the specific same rocket. rocket in The Figur specific e 8b rocke was not t in available Figure 8b wa fors not this av test aias labthe le for back thisfins test a wer s e the back fins were damaged on landing due to swinging into rocky ground with a large gust of the back fins were damaged on landing due to swinging into rocky ground with a large gust of the back fins were damaged on landing due to swinging into rocky ground with a large gust of damaged on landing due to swinging into rocky ground with a large gust of wind, just as it landed. wind, just as it landed. wind, j wind, j ust ust asas it i land t land ed. ed. The canards were set to 0 and roll rate data logging was enabled. Figure 14a plots the roll rate The canards were set to 0 and roll rate data logging was enabled. Figure 14a plots the roll rate The can The can ards ards were set to were set to 0 0 and ro and roll rate ll rate data data log logg ging ing was en was en abled. abled. Fig Fig uu re re 14a p 14a p lots the roll r lots the roll r atea te response for two experiments with and without the flow straightener. The RPM inputs used in each response for two experiments with and without the flow straightener. The RPM inputs used in each response for two experiments with and without the flow straightener. The RPM inputs used in each response for two experiments with and without the flow straightener. The RPM inputs used in each experiment are plotted in Figure 14b. Figure 14a shows that the flow straightener has significantly experiment are plotted in Figure 14b. Figure 14a shows that the flow straightener has significantly experiment are plotted in Figure 14b. Figure 14a shows that the flow straightener has significantly experiment are plotted in Figure 14b. Figure 14a shows that the flow straightener has significantly reduced reduced the the roll roll r rate ate of the of the r rocket. The ocket. The mean mean ab absolute solute stea steady dy sta state te rol roll l ra rate te fofor r the two experiments the two experiments reduced the roll rate of the rocket. The mean absolute steady state roll rate for the two experiments reduced the roll rate of the rocket. The mean absolute steady state roll rate for the two experiments wer were plotted e plotted against againsthe t the co corr rrespondin esponding g mean mean ste steady ady state veloc state velocity ity in F in Figur igure e 15. 15. were plotted against the corresponding mean steady state velocity in Figure 15. were plotted against the corresponding mean steady state velocity in Figure 15. (a) (b) (a) (b) Figure 14. Tasha III results with and without flow straightener (a) RPM inputs; (b) roll rate response. (a) (b) Figure 14. Tasha III results with and without flow straightener (a) RPM inputs; (b) roll rate response. Figure 14. Tasha III results with and without flow straightener (a) RPM inputs; (b) roll rate response. Figure 14. Tasha III results with and without flow straightener (a) RPM inputs; (b) roll rate response. mean wind speed (m/s) mean wind speed (m/s) Figure 15. Mean steady state roll rate with and without flow straightener. mean wind speed (m/s) Figure 15. Mean steady state roll rate with and without flow straightener. Figure 15. Mean steady state roll rate with and without flow straightener. Figure 15. Mean steady state roll rate with and without flow straightener. mean |p | (deg/s) ss -1 mean |p | (deg/s) mean p ss(deg/s -1 ) mean|p | (deg s | ss | ) -1 ss mean|p | (deg s ) mean|p | (deg s ) ss ss Aerospace 2016, 3, 10 14 of 27 As a final analysis of these experiments, the effective steady state fin offset is computed using Aerospace 2016, 3, 10 14 of 27 known values of the damping α and torque constant β of the airframe as discussed in the next & u = 0 section. Specifically, at steady state, the roll rate p , so assuming that , the disturbance in fin,ss As a final analysis of these experiments, the effective steady state fin offset is computed using Equation (2) can be solved to yield: known values of the damping and torque constant of the airframe as discussed in the next section. Specifically, at steady state, the roll rate p, so assuming that u  0, the disturbance in Equation (2) αp f in,ss ss u = (27) fin offset can be solved to yield: βv a pss ss u  (27) f in o f f set bv ss where “ss” refers to the steady state value for each steady state wind speed v which is computed ss where “ss” refers to the steady state value for each steady state wind speed v which is computed ss from the average of the velocity during the steady state period of interest. This analysis allows a from the average of the velocity during the steady state period of interest. This analysis allows characterization of the swirl in terms of the effective canard angle. Note that the canards and extra a characterization of the swirl in terms of the effective canard angle. Note that the canards and extra fin area in Tasha III, as well as a larger diameter airframe would cause significantly more damping in fin area in Tasha III, as well as a larger diameter airframe would cause significantly more damping Tasha III than in the aluminium fin rocket of Figure 12. Therefore, it’s reasonable to assume that the in Tasha III than in the aluminium fin rocket of Figure 12. Therefore, it’s reasonable to assume that very small amount of swirl remaining after the addition of the flow straightener would have a the very small amount of swirl remaining after the addition of the flow straightener would have negligible effect on the Tasha III rocket. The aluminium fin rocket also has a very low moment of a negligible effect on the Tasha III rocket. The aluminium fin rocket also has a very low moment of inertia, so the threshold of torque required to overcome the damping in the fins, would be much inertia, so the threshold of torque required to overcome the damping in the fins, would be much lower lower in this rocket and thus much more sensitive to swirl than Tasha III. in this rocket and thus much more sensitive to swirl than Tasha III. A plot of u versus v for both experiments, is given in Figure 16. This figure shows that fin offset ss A plot of u versus v or both experiments, is given in Figure 16. This figure shows that in ss f in o f f set in the case of no flow straightener, the swirl has a greater effect at the lower velocities. This result the case of no flow straightener, the swirl has a greater effect at the lower velocities. This result was was expected since the vertical component in the wind tunnel would not be sufficiently high to expected since the vertical component in the wind tunnel would not be sufficiently high to overcome overcome the horizontal component induced from the swirl. However, with the flow straightener the horizontal component induced from the swirl. However, with the flow straightener there was there was very little difference in the fin offset over all velocities, which provides further evidence very little difference in the fin offset over all velocities, which provides further evidence that there is that there is negligible swirl in this case. Subtracting the two curves in Figure 16 provides a measure negligible swirl in this case. Subtracting the two curves in Figure 16 provides a measure of the swirl in 1 −1 of the swirl in terms of the effective canard offset. After 20 m·s , there is an average of about 2° of terms of the effective canard offset. After 20 m s , there is an average of about 2 of swirl in the wind swirl in the wind tunnel. This value will need to be subtracted from future tests to get a better tunnel. This value will need to be subtracted from future tests to get a better estimate of the true fin estimate of the true fin offset for flight prediction. offset for flight prediction. wind speed (m/s) Figure 16. The equivalent fin offset versus velocity representing swirl in the wind tunnel. Figure 16. The equivalent fin offset versus velocity representing swirl in the wind tunnel. 4.2. Tasha III—Launch 1 4.2. Tasha III—Launch 1 T Tash ashaa III III fro from m Figure Figure 88b b was was launched launched fr from K om Kaitor aitorete Sp ete Spitit on on 22 22 July July 201 2015. 5. The ai The aim m of t of this his launch was primarily to test the new avionics stack and fibreglass rear fins. In the previous flight launch was primarily to test the new avionics stack and fibreglass rear fins. In the previous flight of of Smokey Smokey [12], the fins we [12], the fins wer re 3D pr e 3D printed. inted. The re The raso eason n for the fibreglass was for the fibreglass was to provide further to provide further strengthening suitable for supersonic flights in future research. In addition, to gain some useful data strengthening suitable for supersonic flights in future research. In addition, to gain some useful data fr from the laun om the launch, ch, a PD cont a PD contr rolle oller r was was implemented implemented d during uring fl flight ight in both the thrust a in both the thrust and nd coa coast st peri periods. ods. Since the vehicle was finished only days before the launch, there was not sufficient time to do a full Since the vehicle was finished only days before the launch, there was not sufficient time to do a full Aerospace 2016, 3, 10 15 of 27 Aerospace 2016, 3, 10 15 of 27 wind tunnel test, analysis of data and rigorous testing of gains. The only wind tunnel test performed was the stability test of Section 3.2. wind tunnel test, analysis of data and rigorous testing of gains. The only wind tunnel test performed For the flight, the gains chosen were k == 1, k 0.1, which were known to give a reasonable pd was the stability test of Section 3.2. response from previous wind tunnel testing of Smokey with the gimbal frame [12]. The reference For the flight, the gains chosen were k  1, k  0.1, which were known to give a reasonable was chosen to be a series of responses starting at 0° for a pre-determined amount after clearing the response from previous wind tunnel testing of Smokey with the gimbal frame [12]. The reference was launch guide, followed by an alternation between −15° and 15° every second. As a precaution, since chosen to be a series of responses starting at 0 for a pre-determined amount after clearing the launch this was the first flight with the avionics, a maximum limit of 6° was enforced in each canard. guide, followed by an alternation between 15 and 15 every second. As a precaution, since this was Unfortunately, there was a significant fin offset in the airframe which was greater than the the first flight with the avionics, a maximum limit of 6 was enforced in each canard. Unfortunately, canards could compensate for with this maximum limit, so only about 1 s of oscillatory data was there was a significant fin offset in the airframe which was greater than the canards could compensate obtained. However, this data set was sufficient to identify parameters and thus analyse the rocket for with this maximum limit, so only about 1 s of oscillatory data was obtained. However, this data set roll response. was sufficient to identify parameters and thus analyse the rocket roll response. The apogee for this flight was 522 m, the time to apogee was 10.2 s and the maximum velocity The apogee for this flight was 522 m, the time to apogee was 10.2 s and the maximum velocity was −1 −1 1 1 was 97 m·s . The wind speed was very low on the day, varying between 1 and 2 m·s on the ground. 97 m s . The wind speed was very low on the day, varying between 1 and 2 m s on the ground. The flight was successful and the rocket safely recovered apart from a couple of broken canards that The flight was successful and the rocket safely recovered apart from a couple of broken canards that were easily replaced. Figure 17 shows video stills from the ignition, take-off, onboard footage and were easily replaced. Figure 17 shows video stills from the ignition, take-off, onboard footage and parachute recovery. parachute recovery. Figure 17. Figure 17. Tash Tasha a II III I lau launch nch 1 1 st stills ills ( (a a) i ) ignition; gnition; ( (b b) take-off; ) take-off; ( (c c) ) onboard v onboard video; ideo; ( (d d)) recovery. recovery. Since there was only one step response from 0° to −15°, the control reference is modeled by a Since there was only one step response from 0 to 15 , the control reference is modeled by single Heaviside function and the proportional derivative (PD) control command is defined: a single Heaviside function and the proportional derivative (PD) control command is defined: uu=− max{min{uu ˆ , }, }H (tT ) (28) cmd cmd max min PD u  maxtmintu , u u , u u Hpt  T q (28) max PD cmd cmd min ˆ ′ uk=− (R(t) φ(t))+− k (R (t) p(t)) (29) cmd p d 1 u ˆ  k pRptq fptqq k pR ptq pptqq (29) cmd p d Rt () = R −−() RR H(t−T −1) (30) Rptq  R00 pR  R1qHpt  T PD 1q (30) 0 0 1 PD 6 p 6 p 15p 66 ππ−−15π u  , u  , R  0, R  , k  1, k  0.1, T  0.42 (31) max min 0 1 p PD uR ==,,uk =0,R= , =1,k d=0.1,T=0.42 (31) max min 01 p d PD 180 180 180 180 180 180 The Heaviside function in Equation (28) provides a delay of T after the launch detect to ensure PD The Heaviside function in Equation (28) provides a delay of T after the launch detect to the rocket is well clear of the launch guide before starting control. For launch PD detection to occur, the on ensure the rocket is well clear of the launch guide before starting control. For launch detection to board accelerometer on the rocket’s vertical axis needs to detect a consistent 2 g or higher acceleration over occur, the on 0.2 s. This board requir accele ement rometer on t prevents sensor he rocket’s v errors oremotor rtical amisfir xis needs to dete es from triggering ct a consistent 2 g or launch control. higher acceleration over 0.2 s. This requirement prevents sensor errors or motor misfires from Once the launch is detected, the rocket’s vertical axis acceleration is transformed to the earth reference frame triggerand ing then launch cont double integrated rol. Once t to he la determine unch is the det rocket’s ected, the rocket’s vertical axis acce height above the launch guide.ler Usi ation is ng the transformed to the earth reference frame and then double integrated to determine the rocket’s height two conditions of launch detection and launch guide clearance enables safe conditions for actuating the above t rocket’s he la canar unch guid ds. e. Using the two conditions of launch detection and launch guide clearance enables safe conditions for actuating the rocket’s canards. The roll rate data including all the key points of the launch are given in Figure 18, where t  0 corresponds The roll to rat 1.5 e dat s befor a incl eudin launch. g all t The he k contr ey point ol was s of t started he launch whenare thegiv rocket en in F height igure was 18, wher 2 m above e t =the 0 4 m launch guide. However, due to the specified 0.2 s delay in the launch detect, the actual altitude corresponds to 1.5 s before launch. The control was started when the rocket height was 2 m above when control started was 7 m which was 0.63 s after lift-off. Aerospace 2016, 3, 10 16 of 27 Aerospace 2016, 3, 10 16 of 27 the 4 m launch guide. However, due to the specified 0.2 s delay in the launch detect, the actual the 4 m launch guide. However, due to the specified 0.2 s delay in the launch detect, the actual altitude when control started was 7 m which was 0.63 s after lift-off. Aerospace 2016, 3, 10 16 of 27 altitude when control started was 7 m which was 0.63 s after lift-off. control end of true starts thrust 100 launch control end of true parachute time starts thrust 100 launch deployment parachute time deployment -100 -100 launch detect -200 launch detect -200 -300 02 46 8 10 12 -300 time (s) 02 46 8 10 12 time (s) Figure 18. Roll rate response for Tasha III launch 1 including key points in the launch. Figure 18. Roll rate response for Tasha III launch 1 including key points in the launch. Figure 18. Roll rate response for Tasha III launch 1 including key points in the launch. The commanded and encoder measured canard roll angle are defined as the average of all The commanded and encoder measured canard roll angle are defined as the average of all canard inputs which is standard in the literature [19]: The commanded and encoder measured canard roll angle are defined as the average of all canard canard inputs which is standard in the literature [19]: inputs which is standard in the literature [19]: cmd++ cmd cmd+ cmd 12 3 4 u = (32) cmd cmd++ cmd cmd+ cmd 12 3 4 u = (32) cmd cmd cmd cmd cmd 1 2 3 4 u  4 (32) cmd enc++ enc enc+ enc 12 3 4 u = (33) enc enc++ enc enc+ enc 12 3 4 enc enc 4 enc enc 1 2 3 4 u = (33) enc u  (33) enc The data is analyzed from just before control starts up to a couple of seconds before the The data is analyzed from just before control starts up to a couple of seconds before the parachute The data is analyzed from just before control starts up to a couple of seconds before the parachute deployment. The roll rate and fin angle u which is computed from Equation (33) enc deployment. The roll rate and fin angle u which is computed from Equation (33) using the encoder enc parachute deployment. The roll rate and fin angle u which is computed from Equation (33) enc using the encoder outputs enc,, … enc for each canard, are plotted in Figure 19, where the time is outputs enc , . . . , enc for each canar14 d, are plotted in Figure 19, where the time is reset to 0. Note that 1 4 using the encoder outputs enc,, … enc for each canard, are plotted in Figure 19, where the time is reset to 0. Note tha for some of the thrust t foperiod r some of andthe thrust peri all of the coast od period and a all ll of the coa the canards st peri are set od a atll the theirca maximum nards are set a values t reset to 0. Note that for some of the thrust period and all of the coast period all the canards are set at thei of 6r m , yet axithe mur m val oll rate ues of stays 6°, yet the rol negative. The l rarte eason stays ne is ther gat eive. is a The fin re offset ason which is there is i lar s a ger finthan offset the wh 6 ich that is their maximum values of 6°, yet the roll rate stays negative. The reason is there is a fin offset which is lthe arger tha canards n the 6° tha can compensate t the can for ar.ds can compensate for. larger than the 6° that the canards can compensate for. -2 -2 -4 -4 -6 -6 0 246 8 time (s) 0 246 8 (a) (time b) (s) (a) (b) Figure 19. Data for analysis (a) Roll rate response; (b) Measured canard angle from encoders. Figure 19. Data for analysis (a) Roll rate response; (b) Measured canard angle from encoders. Figure 19. Data for analysis (a) Roll rate response; (b) Measured canard angle from encoders. To identify the torque constant β, damping α and disturbance ut () from the roll model of dist To identify the torque constant , damping and disturbance u ptq from the roll model of dist To identify the torque constant β, damping α and disturbance ut () from the roll model of dist Equations (2)–(8), the first step is to specify the range in the β and α values as given in Equation (19). Equations (2)–(8), the first step is to specify the range in the and values as given in Equation (19). Equations (2)–(8), the first step is to specify the range in the β and α values as given in Equation (19). These ranges are defined: These ranges are defined: These ranges are defined: <  t1, 2, . . . , 60u , <  t5, 5.5, 6.5, 7, . . . , 15u (34) roll rate (deg/s) roll rate (deg/s) measured canard angle (deg) measured canard angle (deg) Aerospace 2016, 3, 10 17 of 27 ℜ= {1, 2,…, 60} , ℜ= {5, 5.5, 6.5, 7,…,15} (34) α β The next step is to define the time values for the disturbance changes in Equation (7). These Aerospace 2016, 3, 10 17 of 27 values are equally spaced in both the thrust period and the coast period of the data which are denoted in Figure 19a. Let N be the number of time points in the thrust period and N the thrust coast The next step is to define the time values for the disturbance changes in Equation (7). These values number of time points in coast period. The values in Equation (7) are defined: are equally spaced in both the thrust period and the coast period of the data which are denoted in Figure 19a. Let N be the number of time points in the thrust period and N the number of time thrust coast thrust T =ii,1 =…, ,N (35) i thrust points in coast period. The values in Equation (7) are defined: thrust thrust (TT − ) T  i end , i th1, rust . . . , N (35) i thrust Tj = T+=,1j ,…,N (36) N + j thrust N coast thrust thrust coast pT  T q end thrust T  T j , j  1, . . . , N (36) N j thrust coast Since there are no dynamics in the canards during coast, N is set to the minimum possible thrust coast coast value which obtains a reasonable match in the coast period. It was found empirically that higher Since there are no dynamics in the canards during coast, N is set to the minimum possible coast values than 2 do not help identifiability due to the lack of dynamics during this period, and a value value which obtains a reasonable match in the coast period. It was found empirically that higher of 1 gave a consistently large error. Therefore is set to 2 for all the analysis on this launch. The values than 2 do not help identifiability due to the coalack st of dynamics during this period, and a value of 1 value o gave a f consistently was laralso ge err min or.iTher mizeefor d and it was foun e N is set to 2d for that all the analysis was also on this launch. a good The choice. value N N = 2 coast thrust thrust of N was also minimized and it was found that N = 2 was also a good choice. Higher values Higher val thrust ues gave a progressively better match to the da thrust ta in the thrust period as would be gave a progressively better match to the data in the thrust period as would be expected, but were expected, but were much slower computationally. Specifically, the values from gave N =… 2, , 6 thrust much slower computationally. Specifically, the values from N = 2, ,6 gave virtually identical thrust virtually identical results with an improvement in the match to the roll angle by less than 0.1°. More results with an improvement in the match to the roll angle by less than 0.1 . More importantly, the importantly, the identified damping remained unchanged and the torque constant only varied by a identified damping remained unchanged and the torque constant only varied by a maximum of 0.05. maximum of 0.05. The results for N = 2 and are defined: N = 2 thrust coast The results for N = 2 and N = 2 are defined: thrust coast α= 8.5, β = 10.0 (37) best,, OL best OL a  8.5, b  10.0 (37) best,OL best,OL μ ≡ mean absolute error in roll rate = 9.82 deg/s (38) ||pO , L m  mean absolute error in roll rate  9.82 deg{s (38) | p|,OL μ ≡ mean absolute error in roll rate = 1.51 deg/s m  mean absolute error in roll angle  1.51 deg{s (39) (39) || φ|f,OL|,OL The model response is plotted against the measured values for both the roll rate and roll angle The model response is plotted against the measured values for both the roll rate and roll angle in Figure 20. A zoomed in plot of Figure 20a is given in Figure 21a and the identified time-varying in Figure 20. A zoomed in plot of Figure 20a is given in Figure 21a and the identified time-varying disturbance is plotted in Figure 21b. disturbance is plotted in Figure 21b. model -200 data -400 -600 -800 -1000 -1200 -1400 0 246 8 time (s) (a) (b) Figure 20. Model response versus data (a) Roll angle response; (b) Roll rate response. Figure 20. Model response versus data (a) Roll angle response; (b) Roll rate response. roll rate (deg/s) Aerospace 2016, 3, 10 18 of 27 Aerospace 2016, 3, 10 18 of 27 model canard-fin interaction data dominates response -2 Second PD controlled fin offset First PD -10 response dominates controlled -4 (reference -15 deg) response response -20 (reference 0 deg) -6 -30 -8 -40 00.5 11.5 02468 time (s) time (s) (a) (b) Figure 21. (a) Zoomed in roll angle response versus data; (b) Identified disturbance. Figure 21. (a) Zoomed in roll angle response versus data; (b) Identified disturbance. Figure 21a shows that although there is some error in the first controlled response, the overall Figure 21a shows that although there is some error in the first controlled response, the overall trends are captured accurately. For example the data drops 27.2° from the local maximum at t = 0.49 s trends are captured accurately. For example the data drops 27.2 from the local maximum at t = 0.49 s to the local minimum at t = 1.02 s where the model predicts a drop of 26.15° which corresponds to to the local minimum at t = 1.02 s where the model predicts a drop of 26.15 which corresponds to less than 4% error. The model also captures all the coast period, in both the roll angle and roll rate, as less than 4% error. The model also captures all the coast period, in both the roll angle and roll rate, as shown in Figure 20. The disturbance is quite low initially in the first 0.5 s of the data. This behavior is shown in Figure 20. The disturbance is quite low initially in the first 0.5 s of the data. This behavior is caused due to low velocity and therefore the canard–fin disturbance dominates the dynamics, as the caused due to low velocity and therefore the canard–fin disturbance dominates the dynamics, as the fin offset takes some time to take effect. After about 1 s the disturbance rapidly converges to a near fin offset takes some time to take effect. After about 1 s the disturbance rapidly converges to a near constant value around −7° which remains for the rest of the flight with only a minor increase at the constant value around 7 which remains for the rest of the flight with only a minor increase at the end. The results of Figures 20 and 21 and Equations (38) and (39) show that quite a simple model end. The results of Figures 20 and 21 and Equations (38) and (39) show that quite a simple model with with a relatively smooth disturbance function, is very effective in capturing the rocket roll response. a relatively smooth disturbance function, is very effective in capturing the rocket roll response. Note that the second PD controlled roll response in Figure 21a has a very large steady state Note that the second PD controlled roll response in Figure 21a has a very large steady state error, error, since the reference was −15°. The reason for this error is that the fin offset is having a major since the reference was 15 . The reason for this error is that the fin offset is having a major effect due effect due to the increased velocity and the maximum and minimum canard constraints do not to the increased velocity and the maximum and minimum canard constraints do not provide enough provide enough actuation to overcome this fin offset. However, the goal of this launch was not actuation to overcome this fin offset. However, the goal of this launch was not control, but to test the control, but to test the logistics of the new launch vehicle and avionics and provide an initial logistics of the new launch vehicle and avionics and provide an initial proof-of-concept of the model proof-of-concept of the model and methods. and methods. The final validation of the model and methods for this launch is to match the closed-loop model The final validation of the model and methods for this launch is to match the closed-loop model of Equations (28)–(31) to the data. The results are: of Equations (28)–(31) to the data. The results are: α= 7.5, β = 10.0 (40) best,, CL best CL a  7.5, b  10.0 (40) best,C L best,C L μ ≡ mean absolute error in roll rate = 9.76 deg/s (41) ||pO , L m  mean absolute error in roll rate  9.76 deg{s (41) | p|,C L μ ≡ mean absolute error in roll rate = 1.50 deg (42) || φ ,OL m  mean absolute error in roll angle  1.50deg (42) |f|,C L These results are very close to the open-loop response with a mean error difference of 0.06 deg/s These results are very close to the open-loop response with a mean error difference of 0.06 deg/s in the roll rate and 0.01° in the roll angle. However, there are some small differences in the thrust in the roll rate and 0.01 in the roll angle. However, there are some small differences in the thrust period in the roll angle as shown in Figure 22a, but the overall behavior of the two responses are period in the roll angle as shown in Figure 22a, but the overall behavior of the two responses are very similar. In addition, apart from a small period in the thrust, the identified closed and open-loop very similar. In addition, apart from a small period in the thrust, the identified closed and open-loop disturbances are virtually identical as shown in Figure 22b. disturbances are virtually identical as shown in Figure 22b. Hence, in summary, there is no noticeable change in the output responses and identified parameters when using the closed-loop model over of the open-loop model, although the closed-loop model typically takes about 50% longer to simulate. The advantage of the open-loop model computationally is that the roll rate is decoupled from the roll angle which is simpler to handle numerically. Aerospace 2016, 3, 10 19 of 27 Aerospace 2016, 3, 10 19 of 27 closed-loop model measured -10 -20 Aerospace 2016, 3, 10 19 of 27 -30 -40 0 0.5 1 1.5 closed-loop model measured 0 time (s) (a) (b) -10 Figure 22. (a) Roll angle closed loop response versus data; (b) Identified disturbance comparison. Figure 22. (a) Roll angle closed loop response versus data; (b) Identified disturbance comparison. -20 4.3. Tasha III—Launch 2 Hence, in summary, there is no noticeable change in the output responses and identified A new vehicle was manufactured for the second launch including fibreglassing the rear fins and -30 parameters when using the closed-loop model over of the open-loop model, although the closed-loop 3D printing two new canards to replace the ones that were broken during the Tasha III launch 1, see model typically takes about 50% longer to simulate. The advantage of the open-loop model Figure 8c. For this vehicle, a number of controlled step responses were performed in the wind tunnel -40 0 0.5 1 1.5 computationally is that the roll rate is decoupled from the roll angle which is simpler to shortly before the launch. Hence, there is a good amount of data to identify torque, damping and time (s) handle numerically. disturbances and to analyze the capability of the wind tunnel tests to predict flight response. (a) (b) Figure 22. (a) Roll angle closed loop response versus data; (b) Identified disturbance comparison. 4.3. T 4. asha 3.1. Wind III—Launch Tunnel St 2 ep Responses The rocket was suspended from a string, and 8 step responses were performed with a A new vehicle was manufactured for the second launch including fibreglassing the rear fins and 4.3. Tasha III—Launch 2 −1 −1 magnitude of 45°, at a wind speed of 22 m·s . The highest wind speed of 30 m·s was not used in 3D printing two new canards to replace the ones that were broken during the Tasha III launch 1, see A new vehicle was manufactured for the second launch including fibreglassing the rear fins and this case, as it was found that this airframe also had a fin offset, so it was spinning rapidly and Figure 8c. For this vehicle, a number of controlled step responses were performed in the wind tunnel 3D printing two new canards to replace the ones that were broken during the Tasha III launch 1, see starting to swing backwards and forwards, risking damaging the canards. The gains and frequency shortly before the launch. Hence, there is a good amount of data to identify torque, damping and Figure 8c. For this vehicle, a number of controlled step responses were performed in the wind tunnel were reduced and the parameters in Equations (11) and (12) are defined: disturbances and to analyze the capability of the wind tunnel tests to predict flight response. shortly before the launch. Hence, there is a good amount of data to identify torque, damping and 45π disturbances and to analyze the capability of the wind tunnel tests to predict flight response. kf == 0.5, k 0.05, = 0.1,R= ,R= 0 (43) pd 00 1 4.3.1. Wind Tunnel Step Responses 4.3.1. Wind Tunnel Step Responses The rocket was suspended from a string, and 8 step responses were performed with a magnitude The roll angle and roll rate responses are plotted in Figure 23. 1 1 The rocket was suspended from a string, and 8 step responses were performed with a of 45 , at a wind speed of 22 m s . The highest wind speed of 30 m s was not used in this case, as −1 −1 magnitude of 45°, at a wind speed of 22 m·s . The highest wind speed of 30 m·s was not used in it was found that this airframe also had a fin offset, so it was spinning rapidly and starting to swing this ca40 se, as it was found that this airframe also had a fin offset, so it was spinning rapidly and backwards and forwards, risking damaging the canards. The gains and frequency were reduced and starting to swing backwards and forwards, risking damaging the canards. The gains and frequency the parameters in Equations (11) and (12) are defined: were reduced and the parameters in Equations (11) and (12) are defined: 45p 10 45π k  0.5, k  0.05, f  0.1, R  , R  0 (43) p 0 0 d 1 kf == 0.5, k 0.05, = 0.1,R= ,R= 0 (43) pd 00 1 -50 -10 The roll angle and roll rate responses are plotted in Figure 23. The roll angle and roll rate responses are plotted in Figure 23. -20 -30 -100 0 2040 6080 0 20406080 time (s) time (s) (a) (b) Figure 23. Wind tunnel 45 degree step responses (a) Roll angle; (b) Roll rate. Figure 23 shows there are significantly different overshoots and rise times for each step -50 response as well as a major difference in dynamics depending on the direction of rotation, which is -10 likely caused by the fin offset in the airframe. To account for these variations, the model of Equations -20 (2)–(12) is identified for each individual step response. Since the oscillations reduce quite quickly -30 -100 0 2040 6080 0 20406080 time (s) time (s) (a) (b) Figure 23. Wind tunnel 45 degree step responses (a) Roll angle; (b) Roll rate. Figure 23. Wind tunnel 45 degree step responses (a) Roll angle; (b) Roll rate. Figure 23 shows there are significantly different overshoots and rise times for each step response as well as a major difference in dynamics depending on the direction of rotation, which is likely caused by the fin offset in the airframe. To account for these variations, the model of Equations (2)–(12) is identified for each individual step response. Since the oscillations reduce quite quickly u (deg) u (deg) dist dist Aerospace 2016, 3, 10 20 of 27 Figure 23 shows there are significantly different overshoots and rise times for each step response as well as a major difference in dynamics depending on the direction of rotation, which is likely caused Aerospace 2016, 3, 10 20 of 27 by the fin offset in the airframe. To account for these variations, the model of Equations (2)–(12) is identified for each individual step response. Since the oscillations reduce quite quickly after the first after the first peak, only the first half of the data in each step response is used for the parameter peak, only the first half of the data in each step response is used for the parameter identification. The identification. The remaining half is essentially disturbances in the wind tunnel, and there are very remaining half is essentially disturbances in the wind tunnel, and there are very few canard dynamics few canard dynamics so it does not contribute to identifiability. The time points in the disturbance so it does not contribute to identifiability. The time points in the disturbance model of Equations (4)–(8) model of Equations (4)–(8) were chosen to be simply the beginning and end points with N = 1 were chosen to be simply the beginning and end points with N = 1 in Equation (4). Since 5 s is analyzed in Equation (4). Since 5 s is analyzed in each data set, and time is reset to 0 each time, the time points in each data set, and time is reset to 0 each time, the time points are defined: are defined: TT== 0, 5 T  0, T  5 (4(44) 4) 001 1 For the grid search and non-linear regression algorithm, the ranges of the parameters are taken For the grid search and non-linear regression algorithm, the ranges of the parameters are taken from Equation (34). The results identified parameters and mean model response errors for the from Equation (34). The results identified parameters and mean model response errors for the open-loop model of Equation (9) are given in Table 2. An example set of model responses is plotted open-loop model of Equation (9) are given in Table 2. An example set of model responses is plotted in in Figure 24, which is the sixth step response in Figure 23. Both the roll angle and roll rate match Figure 24, which is the sixth step response in Figure 23. Both the roll angle and roll rate match very very closely to the measured data, even with a very simple linear model, for disturbance across the closely to the measured data, even with a very simple linear model, for disturbance across the whole whole data set considered. data set considered. model 40 measured -10 -20 time(s) (a) (b) Figure 24. Open-loop model response versus measured data (a) Roll angle; (b) Roll rate. Figure 24. Open-loop model response versus measured data (a) Roll angle; (b) Roll rate. Table 2. Summary of the identified model parameters for each of the 8 wind tunnel step responses. Table 2. Summary of the identified model parameters for each of the 8 wind tunnel step responses. β [,uu ] [μμ  ,] Step Response α dd 01 ||pO , L |φ|,OL Step Response ru , u s m , m d 0 d 1 |p|,OL |f|,OL 1 13 10.5 [−5.59,−7.71] [1.64,6.23] 1 13 10.5 [5.59,7.71] [1.64,6.23] 2 15 6.5 [−5.82,−6.10] [0.70,2.38] 2 15 6.5 [5.82,6.10] [0.70,2.38] 3 22 10.5 [−6.04,−6.35] [1.13,4.40] 3 22 10.5 [6.04,6.35] [1.13,4.40] 4 15 6.0 [−4.18,−7.16] [0.42,2.08] 4 15 6.0 [4.18,7.16] [0.42,2.08] 5 25 12.5 [−5.90,−6.51] [0.82,2.92] 5 25 12.5 [5.90,6.51] [0.82,2.92] 6 23 10.5 [5.12,6.25] [0.26,1.66] 6 23 10.5 [−5.12,−6.25] [0.26,1.66] 7 15 10.5 [6.11,7.41] [1.43,5.84] 7 15 10.5 [−6.11,7.41] [1.43,5.84] 8 27 10.0 [5.47,5.44] [0.60,2.66] 8 27 10.0 [−5.47,−5.44] [0.60,2.66] Mean 19.4 9.6 [5.47,6.62] [0.88,3.52] Mean 19.4 9.6 [−5.47,6.62] [0.88,3.52] Table Table 2 sho 2 shows ws there there is is a significant a significant v variation ariation of parameters of parameters acrossac the ross the step responses. step respons The average es. The average model error over all tests was 0.88° and 3.52 deg/s for the roll angle and roll rate model error over all tests was 0.88 and 3.52 deg/s for the roll angle and roll rate respectively. The size respectively. of the step r esponse The size of th was e step r 45 , soethe spon average se was 45° model , so the erraverage ors in T able model e 2 vary rrors frin T om a0.6% ble 2 var to 3.6% y from of 0.6% to 3.6% of the change in roll angle. Hence, the model and methods are very effective at the change in roll angle. Hence, the model and methods are very effective at capturing rocket roll capturing rocket roll response in the vertical wind tunnel. The disturbances in column 4 of Table 2 show a trend for a lower disturbance in the first period, which was similar to the flight in Figure 22b, showing that the canard-fin interaction effects can minimize the effect of fin offset in the airframe. The average fin offset across all tests was −6.1°, so taking into account the swirl this value corresponds to −4.1°. The wide range of values of the damping, torque constant and fin offsets in Aerospace 2016, 3, 10 21 of 27 response in the vertical wind tunnel. The disturbances in column 4 of Table 2 show a trend for a lower disturbance in the first period, which was similar to the flight in Figure 22b, showing that the canard-fin interaction effects can minimize the effect of fin offset in the airframe. The average fin offset across all Aerospace 2016, 3, 10 21 of 27 tests was 6.1 , so taking into account the swirl this value corresponds to 4.1 . The wide range of values of the damping, torque constant and fin offsets in Table 2 give the range of uncertainty in the Table 2 give the range of uncertainty in the launch, and will be compared with the flight data in the launch, and will be compared with the flight data in the next section. next section. 4.3.2. Flight Data 4.3.2. Flight Data Tasha III from Figure 8c was launched from Kaitorete Spit on 4 December 2015. The aims of this Tasha III from Figure 8c was launched from Kaitorete Spit on 4 December 2015. The aims of this launch included testing the rocket under a greater amount of actuations and to overcome the fin offset launch included testing the rocket under a greater amount of actuations and to overcome the fin problem that occurred in the July launch as detailed in Section 4.2. Importantly, the launch provided offset problem that occurred in the July launch as detailed in Section 4.2. Importantly, the launch a characterization of the ability of the wind tunnel to predict flight dynamics far outside the wind provided a characterization of the ability of the wind tunnel to predict flight dynamics far outside speeds that can be generated by the fan. Since the wind speed for the wind tunnel data was only the wind speeds that can be generated by the fan. Since the wind speed for the wind tunnel data was 22 m s , this launch provided a rigorous test of how well the model could be extrapolated to higher −1 only 22 m·s , this launch provided a rigorous test of how well the model could be extrapolated to wind speeds. The apogee for this flight was 422 m, and the maximum velocity was 81 m s which −1 higher wind speeds. The apogee for this flight was 422 m, and the maximum velocity was 81 m·s were much lower than the July launch, due to the increased weight from the more robust, supersonic which were much lower than the July launch, due to the increased weight from the more robust, capable avionics stack. The wind speed was reasonably low on the day with an average ground speed supersonic capable avionics stack. The wind speed was reasonably low on the day with an average −1 of 3 m s . Figure 25 shows several stills of the rocket moving up and leaving the launch guide. ground speed of 3 m·s . Figure 25 shows several stills of the rocket moving up and leaving the The launch guide. The over overall launch was aall launch success although was a success the back altho fins ugh the b were damaged ack fins wer on landing, e damaged due on landing, to a sudden gust due to of wind a sudd that en gu pushed st of wi the nd that rocketpushe onto d stony the rocket o ground. nto stony ground. Figure 25. Sequence of stills showing Tasha III rocket moving up and leaving launch guide. Figure 25. Sequence of stills showing Tasha III rocket moving up and leaving launch guide. The controller for this launch was a single step response from 0° to −20°, which occurred 2 s The controller for this launch was a single step response from 0 to 20 , which occurred 2 s after after the controller was switched on. The canard limits were increased to ±9° in this launch to the controller was switched on. The canard limits were increased to 9 in this launch to overcome overcome the fin offset from the first launch. In addition, some open-loop oscillatory inputs were the fin offset from the first launch. In addition, some open-loop oscillatory inputs were included in the included in the PD control signal of Equation (10). This input signal was implemented 0.4 s after the PD control signal of Equation (10). This input signal was implemented 0.4 s after the control started control started and was stopped 5 s after the −20° step response. The input was a modified chirp and was stopped 5 s after the 20 step response. The input was a modified chirp signal defined: signal defined: ut ()tA=+ ( ΔA(t))sin(( ω ( )+Δωt))t u ptq  p A D Aptqqsin() ppw ptq Dwptqqtq (45)(45) 0 0 ininput put 00 4π t 4p t At =ω , ()tA = 2π(2− ),Δ ( ),Δω(t )≡ random variation on signal (46) A  , w ptq  2pp2  q, D Aptq, Dwptq  random variation on signal (46) 0 0 180 10 180 10 A plot of the applied input signal is given in Figure 26. A plot of the applied input signal is given in Figure 26. The roll rate data including all the key points of the launch are given in Figure 27, where t = 0 The roll rate data including all the key points of the launch are given in Figure 27, where t = 0 corresponds to 1.5 s before take-off. For this launch, two accelerometers were used to improve corresponds to 1.5 s before take-off. For this launch, two accelerometers were used to improve the the robustness in the launch detect and the delay threshold was reduced to 0.1 s. In addition, the robustness in the launch detect and the delay threshold was reduced to 0.1 s. In addition, the accelerometer threshold increased to 2.5 g. Similarly to the Tasha III launch 1, the control was started accelerometer threshold increased to 2.5 g. Similarly to the Tasha III launch 1, the control was started when the rocket height was 2 m above the 4 m launch guide. when the rocket height was 2 m above the 4 m launch guide. Aerospace 2016, 3, 10 22 of 27 Aerospace 2016, 3, 10 22 of 27 Aerospace 2016, 3, 10 22 of 27 -2 -2 -4 -4 -6 -6 -8 0246 8 -8 0246 time (s) 8 time (s) Figure 26. Input signal applied to PD Controller (t = 0 corresponds to start of controller). Figure 26. Input signal applied to PD Controller (t = 0 corresponds to start of controller). Figure 26. Input signal applied to PD Controller (t = 0 corresponds to start of controller). Figure 27. Roll rate response for Tasha III launch 2 including key points in the launch. Figure 27. Roll rate response for Tasha III launch 2 including key points in the launch. Figure 27. Roll rate response for Tasha III launch 2 including key points in the launch. For this launch, the data is split into the two PD controlled responses with the set point of 0° followed by −20° which was 2 s later. A sharp change in roll rate can be seen for this second set point For this launch, the data is split into the two PD controlled responses with the set point of 0° For this launch, the data is split into the two PD controlled responses with the set point of 0 at about 4 s in Figure 27. The first period of analysis is started at 2.4 s in Figure 27 which is 0.4 s after followed by −20° which was 2 s later. A sharp change in roll rate can be seen for this second set point followed by 20 which was 2 s later. A sharp change in roll rate can be seen for this second set the control st at about 4 s inarts and Figure 27 corr . Th esponds to t e first period h e imp of analemen lysis ita s st tion arteof d at the i 2.4 s nput si in Fig gna urel from 27 which Figure 26 is 0.4 s aft . Thi es r point at about 4 s in Figure 27. The first period of analysis is started at 2.4 s in Figure 27 which is st the control st arting pointarts and was chosen corrsesponds to t ince there arhee imp signif lemen icant o tasti cil on latof ory dyn the ina put si mics gna in tlh from e canaFi rds which gure 26. will This 0.4 s after the control starts and corresponds to the implementation of the input signal from Figure 26. ensure good identifiability of the model parameters. The second period of analysis starts at 4 s in starting point was chosen since there are significant oscillatory dynamics in the canards which will This starting point was chosen since there are significant oscillatory dynamics in the canards which Figure 27, which is when the set point changes from 0° to −20°. ensure good identifiability of the model parameters. The second period of analysis starts at 4 s in will ensure good identifiability of the model parameters. The second period of analysis starts at 4 s in Figure 27, which is when the set point changes from 0° to −20°. For the first period, a similar approach to the Tasha III launch 1 model is applied, where N Figure 27, which is when the set point changes from 0 to 20 . For the first period, a similar approach to the Tasha III launch 1 model is applied, where N equally spaced points are chosen, and is increased until there is no significantly further For the first period, a similar approach to the 1 Tasha III launch 1 model is applied, where N equally equally spaced points are chosen, and N is increased until there is no significantly further spaced points are chosen, and N is increased until there is no significantly further improvement in the improvement in the fit to the data. Th 1 e values of N investigated were from 1 to 6 points. For fit to the data. The values of N investigated were from 1 to 6 points. For N = 1, ,4, the best model 1 N 1 improvement in the fit to the data. The values of investigated were from 1 to 6 points. For N =… 1, , 4 , the best model fits had average roll angle errors of 2.36, 2.15, 0.57 and 0.26° fits had average roll angle errors of 2.36, 2.15, 0.57 and 0.26 respectively. There was no significant N =… 1, , 4 , the best model fits had average roll angle errors of 2.36, 2.15, 0.57 and 0.26° respectively. There was no significant improvement for N = 5 and 6 and the parameters remained improvement for N = 5 and 6 and the parameters remained virtually identical for N = 3, ,6. Hence 1 1 respectively. There was no significant improvement for N = 5 and 6 and the parameters remained a value of N = 4 is chosen for the final model. The results ar 1 e defined: roll ra rolte ( l radeg/ te (deg/ s) s) Aerospace 2016, 3, 10 23 of 27 Aerospace 2016, 3, 10 23 of 27 virtually identical for N =… 3, , 6 . Hence a value of N = 4 is chosen for the final model. The virtually identical for N =… 3, , 6 . Hence a value of N = 4 is chosen for the final model. The Aerospace 2016, 3, 10 1 1 23 of 27 1 1 results are de results are defined fined: : α= 23.0,β = 9.0 α= 23.0,β = 9.0 (4 (47) 7) bbeest st,, ,, O OLL be best st O OLL a  23.0, b  9.0 (47) best,OL best,OL μ ≡ mean absolute error in roll rate = 4.10 deg/s μ ≡ mean absolute error in roll rate = 4.10 deg/s (48) (48) ||pO , L ||pO , L m  mean absolute error in roll rate  4.10 deg{s (48) | p|,OL μ ≡ mean absolute error in roll angle = 0.26 deg/s μ ≡ mean absolute error in roll angle = 0.26 deg/s (49) m  mean absolute error in roll angle  0.26 deg{s (4 (49) 9) || φ ,OL || φ ,OL |f|,OL The The model re model response sponse fo forr the roll an the roll angle gle and and roll rate roll rate ar are e shown in shown in Figur Figure e 28 28 an and d the offset an the offset angle gle is is The model response for the roll angle and roll rate are shown in Figure 28 and the offset angle is plotted in Figure 29. plotted in Figure 29. plotted in Figure 29. model model 4 measured measured 2 2 0 0 -2 -2 -4 -4 -6 -6 -8 -8 00.5 11.5 00.5 11.5 time (s) time (s) (a) (b) (a) (b) Figure 28. Figure 28. Mod Mode elled lled roll roll angle angle ( (a a) and roll rate ) and roll rate ( (b b) ) versus versus the measured data the measured data for for first first analysis perio analysis period d. . Figure 28. Modelled roll angle (a) and roll rate (b) versus the measured data for first analysis period. -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 -6 -6 -7 -7 -8 -8 0 0.5 1 1.5 0 0.5 1 1.5 time (s) time (s) Figure 29. Identified time-varying offset angle u for first analysis period. offset Figure 29. Identified time-varying offset angle uu for first analysis period. Figure 29. Identified time-varying offset angle for first analysis period. offset offset The results of Equation (47) are close to the average wind tunnel predicted values of 19.4 and 9.6 The The r re esu sulltts of Eq s of Equa uati tion (4 on (47) 7) a ar re c e cllos ose to e to the the a av ver erage age wind wind ttu unnel predicted nnel predicted values values of 19.4 and of 19.4 and in Table 2, with errors of 15.7% and 4.4%, respectively. The offset angles in Figure 29 are all within the 9.6 in Table 2, with errors of 15.7% and 4.4%, respectively. The offset angles in Figure 29 are all 9.6 in Table 2, with errors of 15.7% and 4.4%, respectively. The offset angles in Figure 29 are all range of values of the wind tunnel tests as well. There is also a similar trend of lower offset angles for wi withi thin n the range of the range of v va alues of the wi lues of the wind nd tunnel tunnel test tests s as we as well. Ther ll. There e is is also also a sim a simiilar lar trend o trend off lower lower the smaller fin movements as was the case in the wind tunnel. The mean offset angle of Figure 29 was offset angles for the smaller fin movements as was the case in the wind tunnel. The mean offset angle offset angles for the smaller fin movements as was the case in the wind tunnel. The mean offset angle 4.9 which is 0.8 greater than the average of 4.1 predicted in the wind tunnel. This value corresponds of Figure 29 was 4.9° which is 0.8° greater than the average of 4.1° predicted in the wind tunnel. This of Figure 29 was 4.9° which is 0.8° greater than the average of 4.1° predicted in the wind tunnel. This to an error of 16.3% but well within the expected variation of Table 2. value corresponds to an error of 16.3% but well within the expected variation of Table 2. value corresponds to an error of 16.3% but well within the expected variation of Table 2. A similar procedure was applied to the second period of data corresponding to a reference angle of 20 . In this case, a value of N = 2 was sufficient for the modelling and the identified parameters are defined: a  23.0, b  9.0 (50) best,OL best,OL Aerospace 2016, 3, 10 24 of 27 Aerospace 2016, 3, 10 24 of 27 A similar procedure was applied to the second period of data corresponding to a reference A similar procedure was applied to the second period of data corresponding to a reference angle of −20°. In this case, a value of was sufficient for the modelling and the identified N = 2 angle of −20°. In this case, a value of was sufficient for the modelling and the identified N = 2 parameters are defined: parameters are defined: Aerospace 2016, 3, 10 24 of 27 α= 48.0,β = 8.0 (50) best,, OL best OL α= 48.0,β = 8.0 (50) best,, OL best OL μ ≡ mean absolute error in roll rate = 8.32 deg/s (51) ||pO , L m  mean absolute error in roll rate  8.32 deg{s (51) μ | p|,OL≡ mean absolute error in roll rate = 8.32 deg/s (51) ||pO , L μ ≡ mean absolute error in roll angle = 0.99 deg/s m  mean absolute error in roll angle  0.99 deg{s (5 (52) 2) || φ|f,OL |,OL μ ≡ mean absolute error in roll angle = 0.99 deg/s (52) || φ ,OL The model responses for the roll angle and roll rate are shown in Figure 30 and the offset angle is The model responses for the roll angle and roll rate are shown in Figure 30 and the offset angle The model responses for the roll angle and roll rate are shown in Figure 30 and the offset angle plotted in Figure 31. is plotted in Figure 31. is plotted in Figure 31. model 0 m mode easur l ed measured -5 -5 -10 -10 -15 -15 -20 -20 -25 -25 -30 012 345 -30 012 345 time (s) time (s) (a) (b) (a) (b) Figure 30. Modelled roll angle (a) and roll rate (b) versus the measured data for second analysis period. Figure 30. Modelled roll angle (a) and roll rate (b) versus the measured data for second analysis period. Figure 30. Modelled roll angle (a) and roll rate (b) versus the measured data for second analysis period. -8.5 -8.5 -9 -9 -9.5 -9.5 -10 -10 012 34 5 012 34 5 time (s) time (s) Figure 31. Identified time-varying offset angle u for second analysis period. offset Figure 31. Figure 31. Iddentified entified time-var time-varying ying offset angle offset angle uu for for secon secondd analysis analysis peri period. od. offset offset The modeled torque constant in Equation (50) is reasonably close to the wind tunnel predicted The modeled torque constant in Equation (50) is reasonably close to the wind tunnel predicted The modeled torque constant in Equation (50) is reasonably close to the wind tunnel predicted value of 9.6 with an error of 16.7%, however the damping is significantly larger than all the damping value of 9.6 with an error of 16.7%, however the damping is significantly larger than all the damping value of 9.6 with an error of 16.7%, however the damping is significantly larger than all the damping values of Table 2. This extra damping is likely due to the rocket pitching over with an increasing values of Table 2. This extra damping is likely due to the rocket pitching over with an increasing angle values of Table 2. This extra damping is likely due to the rocket pitching over with an increasing angle of attack as well as the higher velocity. On the other hand, the average identified offset of of attack as well as the higher velocity. On the other hand, the average identified offset of Figure 31 angle of attack as well as the higher velocity. On the other hand, the average identified offset of Figure 31 is −4.7°, which is even closer to the wind tunnel average of 4.1°. Hence, although the is 4.7 , which is even closer to the wind tunnel average of 4.1 . Hence, although the damping is Figure 31 is −4.7°, which is even closer to the wind tunnel average of 4.1°. Hence, although the damping is less accurate in the post-thrust period, the torque constant and the offset angles are both less accurate in the post-thrust period, the torque constant and the offset angles are both accurately damping is less accurate in the post-thrust period, the torque constant and the offset angles are both accurately predicted for all stages of the flight, which are more important for control design. A predicted for all stages of the flight, which are more important for control design. A similar analysis has accurately predicted for all stages of the flight, which are more important for control design. A been performed for the closed-loop responses, but since the results were very similar to the open-loop analysis above, these results are not shown. Note that the torque constant values of = 8 and = 9 in this second Tasha III launch are reasonably close to value of = 10 identified in the first Tasha III launch. However, both of the values of damping in the second launch are considerably larger than the damping from the first launch. Aerospace 2016, 3, 10 25 of 27 This result is probably because there were a lot less dynamics in the first launch so the damping was less identifiable. 5. Conclusions A vertical wind tunnel has been designed and built at the University of Canterbury. This wind tunnel has been specifically customized for sounding rocket research and has a unique feature of allowing the rocket to be suspended by string for accurate prediction of roll dynamics. It is also very useful for testing stability before flight. The flow of the wind tunnel was analyzed in detail and turbulence intensity was estimated to be less than 0.04%. However, there was a reasonable amount of swirl equivalent to 2 of canard fin. This swirl was dramatically reduced to a negligible amount by using an egg crate at the bottom of the wind tunnel near the fan to straighten the flow. Two new airframes were developed in this research with a supersonic capable avionics stack in the second vehicle. Both rockets had reinforced fiberglass to give strength to the fins, but it was found that they had significant fin offset, with post-thrust average values of about 7 for the first vehicle and 5 for the second. Wind tunnel tests on the second vehicle revealed a high roll rate, which suggested a combination of swirl and fin offset. After the second flight, tests with and without the flow straightener using a similar airframe, showed that swirl could be modeled by the equivalent canard offset. This value was then used to compare the wind tunnel tests of the second vehicle to the flight data. A minimal modelling approach for roll dynamics was developed using a velocity dependent model and a piecewise-linear time-varying canard offset function. Open and closed loop models were considered with PD control, with encoders used to measure the canard movements. A combination of a grid search and non-linear regression provided a rigorous way of identifying the parameters. The models identified gave an excellent match to the flight data in both launches, with quite a smooth varying canard offset profile. It was found that with high dynamic movement in the canards the identified fin offset was lower, showing that canard–fin interaction dominates during these periods. This phenomenon occurred in both the wind tunnel tests and flight. A significant outcome of this paper was proving that wind tunnel tests give accurate predictions of the torque constant and fin offset and importantly, the resulting minimal roll models predict flight behavior closely. The damping is typically underestimated in the wind tunnel so a greater uncertainty should be included in this parameter for future control design. In summary, the vertical wind tunnel at the University of Canterbury is a unique facility and a key part of the success of UC Rocketry. A combination of wind tunnel tests and rocket launches have allowed a thorough understanding of rocket flight and control. Acknowledgments: Funded by the Rutherford Discovery Fellowship, Royal Society New Zealand; Callaghan Innovation PhD Fellowships; and Rocket Lab Ltd. Author Contributions: Hoani Bryson, Hans Philipp Sültrop, George Buchanan, Christopher Hann, Malcolm Snowdon, Avinash Rao, Adam Slee, Kieran Fanning, David Wright: developed the hardware, did the experiments, analyzed the data, developed models and wrote the paper. Jason McVicar, Brett Clark, Graeme Harris and Xiao Qi Chen: helped to construct the wind tunnel including setting up the fan and controller, provided expertise and advice on the flow quality and instrumentation and sensors for the wind tunnel tests, and contributed to writing the paper. Conflicts of Interest: The authors declare no conflict of interest. Notation I Inertia in roll axis (kg/m ) r Air density (kg/m ) a Damping constant (m ) b Torque constant (m) u Roll fin angle (rad) f in Aerospace 2016, 3, 10 26 of 27 A Cross sectional area (m ) p Roll rate (rad/s) v velocity (m/s) k , k Proportional and derivative gains Rptq Reference angle (rad) u , . . . , u Time-varying disturbance offset angle parameters (rad) d,0 d,N f Measured roll angle (rad) data f , f Open and closed loop numerical solutions to roll equations (rad) OL C L < ,< Ranges for , in the grid search for parameter identification a b G Turbulence intensity (m/s) s Standard deviation of wind speed (m/s) u Commanded canard angle (rad) cmd u Measured canard angle by encoder (rad) enc cmd , . . . , cmd Individual canard commands (rad) 1 2 enc , . . . , enc Individually measured encoders (rad) 1 2 u , u Minimum and maximum canard limits for actuation (rad) min max m , m Mean absolute roll rate for open loop and closed loop controllers | p|,OL | p|,C L m , m Mean absolute roll angle for open loop and closed loop controllers |f|,OL |f|,C L u Open loop input signal into PD controller in put Abbreviations PD Proportional-derivative NASA The National Aeronautics and Space Administration UC University of Canterbury CFD Computational Fluid Dynamics RPM Revolutions per minute OL Open loop CL Closed loop References 1. 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Published: Mar 29, 2016

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