advertisement

Project Proposal: Evaluation of Electrical Low Thrust-to-Mass Rocket Trajectories Using Numerical Methods Dennis Chandler Updated: October, 21th 1999 Numerical Analysis for Engineers 4960 Rensselaer Polytechnic Institute – Hartford Electrical rockets have very low thrust-to-mass ratios and are only capable of very low accelerations. These rockets are only useful after being placed in orbit by conventional chemical rockets, these devices can be used to accelerate continuously over long periods of time until escape velocity is achieved. Since electrical rockets are power-limited devices, it is best used by at constant power , using variations in thrust direction, and sometines magnitude , to achive escape velocity. The trajectory of the vehicle then becomes a gradual outward spiral until the vehicle achieves escape velocity. The path of the trajectory can be represented by the third order equation: 1 d d 3 d 2 2 d 2 This equation can be written as three simultaneous first-order equations: d A d dA B 2 d 3 dB d With intial conditions: 1, A 0, B 1 I propose to use a Runge-Kutta method with variable step-size and error correction to integrate the equations and to evaluate the time required, free-space velocity increment, and trajectory path for several scenarios. References: Burden & Faires, Numerical Analysis, Sixth Edition, Brooks/Cole Publishing Company, Pacific Grove, CA, 1997 Hill & Peterson, Mechanics and Thermodynamics of Propulsion, Second edition, Addison-Wesley Publishing Company, Reading, MA, 1992