The fundamental relationship between entropy and aerospace vehicle and mission performance is analyzed in terms of the general availability rate balance between force-based vehicle performance, available energy associated with expended propellant, and the overall loss rate of availability, including the vehicle wake. The availability relationship for a vehicle is analytically combined with the vehicle equations of motion; this combination yields the balance between on-board energy rate usage

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... rates of changes in kinetic and potential energies of the vehicle and overall rate of entropy production. This result is then integrated over time for a general aerospace mission; as examples, simplified single-stage-to-orbit rocket-powered and air-breathing missions are analyzed. Examination of rate of availability loss for the general case of an accelerating, climbing aerospace vehicle provides a powerful loss superposition principle in terms of the separate evaluation and combination of loss rates for the same vehicle in cruise, acceleration, and climb. Rate of availability losses is also examined in terms of separable losses associated with the propulsion system and external aerodynamics. These loss terms are cast in terms of conventional parameters such as drag coefficient and engine specific impulse. Finally, rate losses in availability for classes of vehicles are described. Nomenclature A frontal = frontal cross-sectional area of vehicle, m 2 a veh = instantaneous acceleration of vehicle (linear), m=s 2 = loss rate of availability per unit mass of vehicle, W=kg C D = vehicle drag coefficient based on A frontal C PP = specific heat at constant pressure of propellant, J=kg K D = external drag of vehicle, N f = final mission state f = fuel/air ratio for propulsion system (stoich denotes stoichimetric) F xengine = net axial force on engine wetted surfaces, propulsion system thrust, N F xflight = overall (net) fluid-dynamic force component on vehicle in direction of flight, N g, g 0 = gravitational acceleration at altitude, sea level, m=s 2 h = altitude, m h i;l = static enthalpy per mass of species l on inflow to global control volume, J=kg K H oP = reference enthalpy of propellant at T ref H P = heating value of propellant, J=kg I sp = engine specific impulse, s L = vehicle lift, N M = flight Mach number _ m i = mass flow rate at entrance of global stream-tube (Fig. 1), kg=s _ m P = propellant mass flow rate, kg=s m veh = vehicle mass, kg _ m w = mass flow rate at exit of global stream-tube (Fig. 1), kg=s NS = number of chemical species considered P i = ambient pressure, N=m 2 _ Q flow-path , _ W flow-path = heat and work rate interaction to main flowpath (excluding propellant subsystem) from vehicle, W T = temperature, K T i = ambient temperature, K _ S = entropy rate, W=K _ S irrtotal = total entropy rate due to irreversibility and nonideal heat transfer (vehicle and wake), W=K s l = entropy per mass of species l, J=kg K T = temperature, K T i = ambient temperature, K u i , V = freestream velocity, vehicle flight velocity, m=s V inj = propellant injection velocity vector, m=s W = vehicle weight, N l;i , l;i = species mass and mole fractions of species at entrance i of global stream-tube (Fig. 1) l;w , l;w = species mass and mole fractions of species at exit w of global stream-tube (Fig. 1) = second-law effectiveness = climb angle = vehicle mass fraction