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Aeronautical Engineering. Rocket Motion. Objectives. Define axes of motion Relate center of pressure and center of gravity Derive equations for predicting velocity and altitude. Three Axes of Motion. Roll, Pitch, and Yaw. Lift Force. Lift Force. Center of Pressure. Center of Pressure.
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Aeronautical Engineering Rocket Motion
Objectives • Define axes of motion • Relate center of pressure and center of gravity • Derive equations for predicting velocity and altitude
Altitude Prediction • The peak altitude (apogee) is the altitude at burnout plus the coasting distance • The burnout altitude depends on the thrust, duration, and weight of the rocket • The coasting distance depends on the burnout velocity and the weight of the rocket
Altitude Calculation • The weight of the rocket is changing during flight, as the propellant is being expended! • Use “average weight” in the calculation • Average weight is the weight at liftoff minus half of the propellant weight
Average Mass • Mavg = average mass • mi = liftoff mass • mf = mass at burnout • mr = no-motor mass of rocket • mm = mass of rocket motor • mp = mass of propellant
Weight • Weight is a force • Newton’s second law
Velocity Calculation • The maximum velocity occurs at burnout
Velocity Calculation • So, another way to write the velocity is • Find the altitude reached with this velocity
Burnout Altitude • Use the average velocity and the time to find the distance
Peak Altitude • The combined distances equal the peak altitude
