A simple analytic multistage model is presented for combined chemical-electric orbit-raising missions. Expressions for transportation rates and optimum electric specific impulse are derived for two-stage, three-stage, variable-efficiency, and tank-limited missions of up to 100 days duration. The optimum electric specific impulse is shown to depend strongly on the specific impulse of the chemical thruster. A low-thrust-trajectory optimization model is combined with launch-vehicle performance data to derive end-to-end optimized three-dimensional chemical-electric orbit-raising profiles to geostationary orbit. Optimized profiles are derived for the Sea Launch, Ariane 4, Atlas V, Delta IV, and Proton launch vehicles. Optimum electric orbit-raising starting orbits and payload mass benefits are calculated for each vehicle. The mass benefit is shown to be between 6.1 and 7.6 kg/day with two SPT-140 thrusters, or up to 680 kg for 90 days of electric orbit raising. The optimized profiles are combined with the analytic model to a create simple parametric performance model describing multiple launch vehicles. The model is a good tool for system level analysis of electric orbit-raising missions and is shown to match calculated performance to within 13%.
Nomenclatureb = fitting constant c lv = effective launch-vehicle exhaust velocity, m/s c 1 = effective on board chemical thruster exhaust velocity, m/s c 2 = effective electric thruster exhaust velocity, m/s c * 2 = optimum electric thruster effective exhaust velocity, m/s d = fitting constant, m/s g = 9.81 m/s 2 m 0 = spacecraft mass, beginning of orbit raising, kg m 1 = spacecraft mass, end of chemical orbit raising, before electric orbit raising (EOR), kg m 2 = spacecraft mass, end of orbit raising (payload mass), kġ m 2 = electric propulsion mass flow rate, kg/s P = thruster input power, W T 2 = electric propulsion device thrust, N t = time, s v chem = v for all-chemical orbit raising, m/s= v for chemical portion of a C-EOR mission, m/s v 2 = v for electric portion of a C-EOR mission, m/s v 2eff = chemical v effectively replaced by electric v, m/s η p = thruster efficiency η v = mission planning efficiency