1. CRITICAL DESIGN REVIEW Michigan Rocket Engineering Association USLI 2011-2012

2. Final Vehicle Dimensions Total Length: 103 in Can Length: 52 in Airframe Diameter: 5.5 in Can Diameter: 2.5 in

3. Key Design Features Butterfly valves – Varies airflow through cans 4 Public Missile D-07 fins – Preserves dual-axis symmetry Fin-through-can configuration – Eases construction – Allows for fillets

4. Vehicle Sections Main Chute Avionics Bay Access Cut To nose To tail Motor/Fins

5. Final Motor Selection Manufacturer: Cesaroni Motor Designation: L2375 Total Impulse:1093 lb-s Mass:Pre-Burn:9.4 lb Post-Burn:4 lb Retention System: Aero Pack RA75

6. Rocket Flight Stability Unaltered margin of test rocket: – CP: 74.5 in (RockSim) – CG: 71.5 in (experimentally measured) – Stability Margin: 0.55 Altered margin of test rocket: – CP: 74.5 in (RockSim) – CG: 66 in (measured after adding ~4lb to nose) – Stability Margin: 1.55 Aiming for ~1.5 pre-launch – Conservative because of unorthodox design

7. Static Margin Diagram CP: 74.5665in from nosecone CG: 65.9427in from nosecone

8. Thrust to Weight Ratio Average thrust of L2375 Average weight of rocket Average Thrust-to-Weight Ratio

9. Rail Exit Velocity Assuming – 6’ x 1” x 1” rail – Cesaroni L2375 Exit velocity = 81 ft/sec Test launch used 12’ x 1” x 1” rail Final vehicle may use a similar rail

10. Mass Statement and Margin PartDiameter [in]Length [in]Unit Mass [g]QuantityNet Mass [g] BODY TUBES Tube 1 [body]5.518461.31 Tube 2 [body]5.521538.11 Tube 3 [body]5.56153.81 Tube 4 [body]5.510256.31 Tube 5 [body]5.534.8891.81 Tube 11 [Coupler]5.512301.43904.2 AVIONICS BAY Tube 6 [Av Bay]418271.91 Centering Rings [Av Bay]5.5o,4.0i0.25306180.0 Old Av Bayn/a 9051 Can flap axle0.510.51051 Av Bay Parts [rods/bulkheads]n/a 328.11328.125 Av Bay Aluminum Partsn/a 11401 MOTOR [dry] Centering Rings [motor mount]5.5o,3.0i0.2540.14160.4 Motor Retention System5.5o,3.0i1.31451145.0 Motor Thrust Plate5.50,3.0i0.251001 Tube 7 [Motor Mount]324228.71 CANS Tube 8 [Top Can Section]2.5881.73245.0 Tube 9 [Mid Can Section]2.510102.13306.3 Tube 10 [Low Can Section]2.534.8355.331065.8 MISC Nose Cone5.513" + 4" Sleeve360.01360 Shock Cordn/a[package]1901190.0 Fins [Missile Fin-D-07 ]SA per fin:80.4313.5641254.2 Sub Total [dry] Mass:10190.6 Total [dry] Mass [5%wt Epoxy]:10700.2 Total [dry] Mass [10%wt Epoxy]:11209.7 MOTOR Motor Case320124511245.0 Total Dry Mass 25.254 lbs w/ L2375 34.454 lbs w/ new AvBay ~35 lbs +6 lbs before predicted apogee comes within 100 ft of a mile

11. Recovery Specs Harness type – 3 sections tethered with shock cord Size – Shock cord 1” in width Length – 20 feet of cord at apogee, 10 at main chute Descent rates – Maximum of 25 m/s with drogue/streamer – Maximum of 6 m/s with main chute

12. Parachute Sizes Test Launch used 62” domed chute – Too fast for KE of all sections to be < 75 ft-lb Using this equation for parachute diameter: For a parasheet (C d =.75) – Final vehicle needs ~123” chute For a true “dome-shaped” chute (C d = 1.5) – Final vehicle needs ~87” chute

13. KE During Flight At test launch, note: 75 ft-lb = 101.68 J Must cut down KE both during fall and chute – Implement a drogue or streamer – Bigger Parachute Post-BoostFallChute Motor Section231 KJ2.73 KJ181 J AvBay3.08 KJ92 J Nose Cone111 J

14. Estimated Drift Distance Subscale Test Launch: – 65 Second Fall Time – Altitude of ~5150 ft According to the formula for drift: Wind Speed (mph)Drift Distance (ft) 5477 10953 151430 201907

15. Payload Design Overview

16. DART Control System Dynamic Target : Used to aid in assuring the mean energy path solution is followed Restrained Controller : Proportional Integral Derivative (PID) derived controller with physical limits Physics Plant : Simulation of vehicle-environment interaction given controller commands Instrument Uncertainty : Propagation of instrument uncertainty into system values Alt. Projection : Projection of rocket apogee altitude with same physics plant model for consistency

17. Dynamic Target Effect

19. Heuristic Flight Simulation Scoring Launch across 6 initial conditions for every controller constant combination – IC: [0.80 1.00 1.20] x0 @ [1.00 1.00 1.00] v0 – IC: [0.80 1.00 1.20] v0 @ [1.00 1.00 1.00] x0 – No need to simulate across all permutations because x0 or v0 will be a initialization trigger Simulate 20 seconds post motor burnout If any 1 of the 6 simulations does not attain within 2% of goal altitude, the controller combination fails

20. Heuristic Flight Simulation Scoring If all 6 combinations attain within 2% goal altitude, wellness of fit to mean energy path is judged Average divergence from the mean energy path is multiplied by 1*10^19 and cast as a 64 bit unsigned integer This divergence, and this divergence plus the current loop index are minimized with respect to there values last loop iteration The difference between these two indexes is our best flight

21. Hardware Communication

22. Software Implementation Arduino C++ architecture STL “Servo”, “SPI”, “I2C”, “Serial” libraries and functions used for much of the device communications Custom mrea cont class with DART implementation – Additional data filtering not included in DART – Data redundancy and controller safeguards – Flexible implementation

23. Data Sources & Redundancy Altitude (xc) – Primary: SL100 – Secondary: ADXL 345 Velocity (vc) – Weighted ADXL 345 & SL100 data Acceleration (ac) – Primary: ADXL 345 – Secondary: SL100

24. Controller Logic Majority of state variables are expressed in a global scope and modified via the mrea_cont class where they are defined as externs Very little data transfer overhead in function calling due to scoping SD card provides SLI dump to allow data to be discarded immediately after use

25. Logic Diagram

26. Recovery System Tests Raven2 flight computer – Specified certain ejection charge altitudes – Ran various flight simulations – Observed spikes in current at these altitudes Ejection charges – Sealed actual chambers with shear pins – Ignited ejection charges – Observed (non)separation

27. Test Plans Drag servo – Function generator and power source – Arduino board with simple PWM code Drogue parachute / streamer – Next Test Launch (February) Drag values – Computational Fluid Dynamics simulations – Wind tunnel testing Center of Gravity – Suspension of rocket by string

28. Full Scale Test Launch Successes – Exhibited stability – Separated at apogee and 500 feet AGL – Sustained no major damage – Achieved an altitude of 5150 feet – Landed < 150 feet from pad Setbacks – Zippered about 5” down Blue Tube at 500 ft AGL Impacts on design – Verified integrity and functionality – Necessitated drogue chute or streamer at apogee

29. Full Scale Test Flight

30. Full Scale Test Flight Data Measured MinPredicted MinMeasured MaxPredicted Max Average PreLaunch Altitude (ft)357N/A Average PreLaunch Axial (Gs)0.991.00N/A1.00 Average PreLaunch Axial Offset0.94N/A Axial Accel (Gs)-2.25011.9113.9 Baro (Atm)0.82N/A0.991.00 Current Draw (A)000.06N/A Lateral Accel (Gs)-1.46|1.00|2.231.00 Motor Ignition Time (sec)0.1682.6N/A Temperature (F)39.56N/A40.02N/A Time (sec)0016.6317.07 Volts Battery (V)8.2N/A8.32N/A Volts Pyro 3rd (V)0000 Volts Pyro 4th (V)8.16N/A8.34N/A Volts Pyro Apogee (V)0N/A8.32N/A Volts Pyro Main (V)0000 [Altitude (Baro-Ft-AGL)]-12051455023 [Altitude (Baro-Ft-ASL)]345N/A55025380 [Velocity (Accel-Ft/Sec)]00663777 [Velocity (Accel-MPH)]00452530 **Note : these values represent simulation for real rocket mass, not predicted

31. Questions?