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