The key performance characteristics of concepts in this category, where the propellant is also the energy source, can be distilled to these two parameters:
• Propellant Specific Energy, Esp (J/kg)
• Propulsion System Specific Power, Psp (W/kg)

A given propellant has its unique specific energy Esp (J/kg), and a given propulsion method has an overall thrust conversion efficiency η (the fraction of the energy in the propellant which appears in the exhaust stream power). Energy which is lost to space, turned in to waste heat for the cooling system, etc., does not appear propulsively and so only that portion of the energy which appears in the exhaust stream is suitable for computing exhaust velocity and subsequent parameters. The amount of waste heat has an important impact on the mass of the spacecraft system (radiators, for example), discussed later.
An overall propulsion system (defined here to include all the spacecraft masses except payload and propellant) has a unique Propulsion System Specific Power, Psp (W/kg), that can be expressed in terms of the jet power Pj (W), propellant mass flow rate, dm/dt (kg/s), thrust force, F (N), and effective exhaust velocity, Ve (m/s).
⎛
⎞
⎛
⎞
Pj = 1
dm
2 = dm
⎠ ⎟ Ve
⎠ ⎟ Espη Eq. 3
⎝ ⎜
⎝ ⎜
dt
dt From this it follows that:
Ve = 2Espη Eq. 4
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Where
⎛
⎞
F = dm
⎠ ⎟ Ve Eq. 5
⎝ ⎜
dt
€
So either the effective exhaust velocity, Ve (m/s), or propellant specific energy, Esp (J/kg) can be used, as convenient.
The relation between the mass of the spacecraft, Mse (kg), and the Propulsion System Specific Power, Psp (W/kg) is:
€ Psp = Pj
Eq. 6
M se where the mass of the spacecraft (empty and without payload), Mse (kg) is defined to include: • Propellant storage • Engine • Nozzle • Radiators • Remaining spacecraft structure and elements (typically insignificant to those other masses)
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For equitable comparisons, any design parameters used to calculate the masses of those subsystems should be identified. When comparing competing concepts that use common systems (tankage, radiators, etc.) they should all use the same design parameters. For example, concepts that use the same propellant should use the same tankage fraction (kg-tank/kg-propellant), and concepts which use the same radiator technology should use the same radiator specific masses (W/kg). The exception to this is when the competing systems that are based on different mission commitment years, Ym, where those design specs might have improved for the later model. Tracking how the design parameters might improve over the years is covered in Section 8.5.3.
Therefore, from this relation it can be seen that the Propulsion System Specific Power controls acceleration:
a = F
= 2
Psp Eq. 7
M se
Ve
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pg 46 of 69

Millis 2018 Grant NNX17AE81G_for_CR.docx The achievable change in velocity in free space, ∆V, comes from the familiar rocket equation (burnout form which assumes thrusting time is << trip time.

Note: Chemical and nuclear rockets usually have very high thrust to weight {high Psp} and hence, the thrusting time is << trip time. This is not necessarily true for other systems.):
⎛
⎞
ΔV = ln M se +M pay +M p
M se +M pay
⎝ ⎜ ⎜
⎠ ⎟ ⎟ Eq. 8 And where:
Mse = Empty Mass of Spacecraft associate with Propulsion System Specific Power (kg) Mpay = Mass of Payload (kg) Mp = Mass of Propellant expended (kg)