Question

Consider the modified rocket equation that takes into account the parasitic weight of the nuclear reactor and its associated shielding. Where, ML = Payload mass M0 = Initial mass âˆ†v = total change in spacecraft velocity for a given engine firing (burn) ue = propellant exhaust velocity tb = duration of a given burn Î± = specific power (Mass of reactor and supporting equipment divided by available reactor power, P) typically in kg/kW or its equivalent Î· = thrust chamber efficiency: Determine the relative impact of the specific power and the efficiency on the delivered payload mass. (This is likely most easily done by differentiation and/or plotting the equation as a function of one or the other. In plotting, be sure to use reasonable values for both Î± and Î·) Discuss ways in which Î± and Î· are coupled and also how one might be optimized without degrading the other.

          Consider the modified rocket equation that takes into account the parasitic weight of the nuclear reactor and its associated shielding.

Where,
ML = Payload mass
M0 = Initial mass
âˆ†v = total change in spacecraft velocity for a given engine firing (burn)
ue = propellant exhaust velocity
tb = duration of a given burn
Î± = specific power (Mass of reactor and supporting equipment divided by available reactor power, P) typically in kg/kW or its equivalent
Î· = thrust chamber efficiency:

Determine the relative impact of the specific power and the efficiency on the delivered payload mass. (This is likely most easily done by differentiation and/or plotting the equation as a function of one or the other. In plotting, be sure to use reasonable values for both Î± and Î·)

Discuss ways in which Î± and Î· are coupled and also how one might be optimized without degrading the other.

Added by Scott W.

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