rocket trajectory

AAE 251 Aerospace DesignSpace Vehicle Flight Mechanics: 

AAE 251 Aerospace Design Space Vehicle Flight Mechanics References: Griffin, M.D. and French, J.R. 'Space Vehicle Design' AIAA, 1991 Vinh, N.X. 'Optimal Trajectories in Atmospheric Flight' Elsevier 1981 http://www.jpl.nasa.gov/basics/index.html http://www.ae.utexas.edu/design/mission_planning/main_links/mp_resources.html

Slide2: 

Newton’s Second Law w/r to an inertial system

Nonrotating Planet: 

Nonrotating Planet

Numerical Integration: 

Numerical Integration

Trajectories: 

Trajectories Constant pitch rate Constant Flight Path angle 'Gravity' turn

Constant Pitch Rate: 

Constant Pitch Rate Solve Equation (1) for angle of attack

Constant Flight Path Angle: 

Constant Flight Path Angle Solve Equation (1) for angle of attack

“Gravity” Turn: 

'Gravity' Turn Angle of Attack =0 Lift = 0 No thrust applied normal to the flight path Solve Equation (1) for pitch rate

Launch Trajectory Losses: 

Launch Trajectory Losses Integrating Equation (1) from ignition to burn out

Techniques for Reducing Velocity Losses: 

Techniques for Reducing Velocity Losses Gravity Lost Keep burn time short (burn at high acceleration) Strive for small flight path angle as early as possible to still achieve mission altitude Drag Force Loss Ascend as slowly as possible. since drag force is proportional to square of relative velocity Ascend as nearly vertical as possible to minimize time spent in dense air  Angle of Attack Loss Keep angle of attack near zero (align vehicle with velocity vector ‑ sometimes called a gravity turn) Propulsion Pressure Loss Ascend to near vacuum (low ambient pressure) as quickly as possible