Can Rocket Simulations Accurately Predict the Flight Characteristics of Model Rockets?

Overview

Objectives/Goals My objective was to find out if rocket simulations are accurate. My hypothesis was that rocket simulations would be accurate to 20% of the actual measured values. Methods/Materials Material List: 6 Drafts of Rockets; 1 Calculator; 1 Triple Beam Balance Scale; 6 rockets; 2 Estes Altitude Finders; 1 Estes Porta-Pad# II; 1 Electronic Beam Launch controller; 2 Stopwatches; 6 Estes A8-3 Engines. Procedure: 1. Obtain Materials on Material list; 2. Determine The Mass of rocket by weighing it on scale; 3. Determine diameter of rocket using draft; 4. Determine the Area of rocket in Square Meters using the following equation: A=d*(0.5*(diameter in inches/12)*.3048)2= dr2; 5. Determine engine thrust and impulse from engine specifications; 6. Compute Burn Time for the engine: impulse/thrust; 7. Determine k: k= (0.5*1.2 kg/cubic meter*.75*area); 8. Compute Gravitational force: Mass*9.8 m/sec=M*g; 9. Calculate velocity at burn out : velocity=q[1-exp(-x*(impulse/thrust) / [1+ exp (-x*(impulse/thrust)], where x =2*k*q/Mass; 10. Calculate altitude at end of boost = [-Mass/2*k) * ln[Thrust-mass*9.8 m/sec*velocity2]/mass*9.8 meters/sec; 11. Calculate altitude at end of coast phase: [Mass/2*k]*ln(Mass*9.8 meters/sec+k*velocity2)]/Mass*9.8 meters /sec; 12. Sum steps 9 and 10 to come up with final altitude; 13. Calculate using the following equations: qa = sqrt(M*g / k), qb = sqrt(g*k / M), ta = arctan(v / qa) / qb; 14. Add burn time to ta to come up with time to apogee; 15. Divide altitude by time to apogee to come up with speed in feet per second; 16. Convert feet per second into MPH by multiplying speed in feet per second by .6818; 17. Launch Rocket and measure altitude and speed with altitude finder and stopwatch; 18. Repeat for every rocket used. Results The expected values came within 20% of the actual values. Conclusions/Discussion Rocket Simulations CAN Predict the flight characteristics of model rockets.

Competition history

• CSEF 2002 Mathematics & Software · Entry J1201

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