CRITICAL DESIGN REVIEW Michigan Rocket Engineering Association USLI

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

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

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

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

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

Static Margin Diagram CP: in from nosecone CG: in from nosecone

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

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

Mass Statement and Margin PartDiameter [in]Length [in]Unit Mass [g]QuantityNet Mass [g] BODY TUBES Tube 1 [body] Tube 2 [body] Tube 3 [body] Tube 4 [body] Tube 5 [body] Tube 11 [Coupler] AVIONICS BAY Tube 6 [Av Bay] Centering Rings [Av Bay]5.5o,4.0i Old Av Bayn/a 9051 Can flap axle Av Bay Parts [rods/bulkheads]n/a Av Bay Aluminum Partsn/a MOTOR [dry] Centering Rings [motor mount]5.5o,3.0i Motor Retention System5.5o,3.0i Motor Thrust Plate5.50,3.0i Tube 7 [Motor Mount] CANS Tube 8 [Top Can Section] Tube 9 [Mid Can Section] Tube 10 [Low Can Section] MISC Nose Cone5.513" + 4" Sleeve Shock Cordn/a[package] Fins [Missile Fin-D-07 ]SA per fin: Sub Total [dry] Mass: Total [dry] Mass [5%wt Epoxy]: Total [dry] Mass [10%wt Epoxy]: MOTOR Motor Case Total Dry Mass lbs w/ L lbs w/ new AvBay ~35 lbs +6 lbs before predicted apogee comes within 100 ft of a mile

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

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

KE During Flight At test launch, note: 75 ft-lb = 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

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)

Payload Design Overview

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

Dynamic Target Effect

Heuristic Flight Simulation Scoring Launch across 6 initial conditions for every controller constant combination – IC: [ ] [ ] v0 – IC: [ ] [ ] 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

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

Hardware Communication

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

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

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

Logic Diagram

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

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

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

Full Scale Test Flight

Full Scale Test Flight Data Measured MinPredicted MinMeasured MaxPredicted Max Average PreLaunch Altitude (ft)357N/A Average PreLaunch Axial (Gs) N/A1.00 Average PreLaunch Axial Offset0.94N/A Axial Accel (Gs) Baro (Atm)0.82N/A Current Draw (A)000.06N/A Lateral Accel (Gs)-1.46|1.00| Motor Ignition Time (sec) N/A Temperature (F)39.56N/A40.02N/A Time (sec) 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)] [Altitude (Baro-Ft-ASL)]345N/A [Velocity (Accel-Ft/Sec)] [Velocity (Accel-MPH)] **Note : these values represent simulation for real rocket mass, not predicted

Questions?