Electric and Nuclear Propulsions: Dependence of Cost of Payload from a Specific Impulse

Abstract

Work develops ideas of [2] for nuclear and electric propulsions. Unlike the considered in this work of the single-stage rocket with chemical propulsions the presented paper take into account the cost of engines and their mass separately. Received complex dependences determine of the minimum of the specific cost of the launching of payload. The obtained formula links the specific cost of the launching of payload with the specific impulse Isp, with the thrust of rocket engine is P, with the time of its functioning τ, with the terminal increment in velocity ∆w of launching payload with mass mp, with specific cost of propellant mass pf, of structure of spacecraft ps, of engine pe, with total propellant mass flow rate • m . Investigation of this formula on extremum give possibility to discover the optimal magnitude of additional new cost criterions. As shown, that the minimum the specific cost of the launching of payload takes place. The calculations give the magnitude of pe and pf as minimum of cost of launching payload with use Electric Rocket Propulsion (ERP) or Nuclear Rocket Engine (NRE). The proposed supplementary criterions must take into consideration at comparison of the different rocket propulsions and spacecrafts from standpoint of an decreasing of the cost of payload.