Energy Utilization for Single and Multi-Stage Rockets in Atmospheric Flight

Methodology is developed for the comprehensive analysis and quantification of energy utilization in chemical rockets, based on the overall thermochemical and kinetic energy availability of the stored propellant. The energy utilization balances for both single and two stage rockets operating in a gravitational field and with external atmospheric drag are derived and discussed in terms of contributors to that balance, including irreversibility occurring in the rocket engine and external to the vehicle, work required to lift expended propellant to altitude, and the productive utilization of energy as realized by kinetic and potential energy changes achieved by the final rocket mass. For multiple stage systems, additional contributors are the energy utilizations associated with kinetic and potential energies of discarded structural masses at staging. The energy utilization balance can be tracked in time through a given mission. Calculation of the thermochemical availability for chemical rockets necessary for a complete thermodynamic analysis of energy utilization is described. A case study for 1st and 2nd stage operation of the legacy Saturn V access-to-space launch vehicle using Apollo 11 data is performed. Details of the time evolution and final balance of energy utilization are provided for this system using the methodology developed.