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E. Refueling Mass Savings The propellant required for a spacecraft mission depends exponentially on the total V required for the mission ∆𝑉 𝑚𝑝 =𝑚0(𝑒𝑣𝑒 −1) (7) For n stages, it is convenient to treat each stage as the payload of the stage that precedes it. So, stage 0 is the payload, stage 1 is the last stage used, and so on. In this case, m0 of the vehicle for each stage is m0 of the vehicle at the next stage, plus the expended propellant mass and dropped dry mass 𝑚𝑑 of the current stage. Therefore, the propellant mass for each stage is: 𝑗 ∆𝑉𝑗 𝑚𝑝,𝑗=(𝑚0,𝑗−1+∑(𝑚𝑝,𝑖+𝑚𝑑,𝑖))(𝑒𝑣𝑒 −1) (8) Thus, the total propellant required is: ∆𝑉𝑗 𝑀𝑝=∑(𝑚0+∑(𝑚𝑝,𝑖+𝑚𝑑,𝑖))(𝑒𝑣𝑒 −1) (9) 𝑗=0 𝑖=0 Refueling saves mass over staging, because there is no redundant dry mass, e.g. engines, that must be carried by previous stages, driving up the effective payload mass for each. Also, . If the spacecraft is refueled prior to each maneuver with only the propellant required for that maneuver, then: 𝑛 𝑗=0 In the limit of 𝑛 → ∞ filling operations, the spacecraft approaches continuous refueling, with no propellant mass ever carried, and thus approaches the minimum theoretical propellant mass required to produce a given V. The result is a simple momentum transfer from which the minimum propellant mass for the total V can be found: 𝑀𝑝,𝑚𝑖𝑛 = ∆𝑉𝑚0 (11) 𝑣𝑒 The propellant mass found in Eq. (11) cannot be achieved in practice, but can serve as a benchmark for comparing the effectiveness of staging and refueling strategies. Consider a 63.1 t vehicle, 58 t payload with a 5.1 t solar array as selected in Section II.C, and a 6 t dry mass for each propulsion stage, making a round trip to and from Mars orbit. In the baseline trajectory, it requires 4 km/s V LEO to trans-Mars injection, 1 km/s V for Mars orbit injection, and 1.6 km/s for trans-Earth injection.. For the case of a single load of propellant at the outset of the mission, and a single 15 t propulsion stage, Eq. 7 determines that 270 t of propellant is required. For three stages with only 5 t of dry mass each, Eq. 9 shows that only 253 t of propellant is required. For refueling for every maneuver with a single 15 t propulsion stage, Eq. 10 allows one to conclude that only 169 t of propellant is required. For the theoretical ideal of continuous refueling and a 15 t propulsion stage, Eq. 11 identifies 116 t of propellant as the requirement. Table II-11 contains these results with more detail, including the propellant mass required for each maneuver, and the results of refueling only once (for TEI) and for refueling three times (at GTO from LEO, before MOI, and before TEI). These results show that refueling reduces the required amount of propellant used in the vehicle significantly, compared to the example staging used. Refueling at Mars prior to TEI uses only 69% more propellant than the theoretical minimum, while the example staging in the table uses 117% more. Refueling more often improves this, with refueling at GTO (after transfer from LEO), and then before MOI and TEI reducing to only 24% more propellant than the theoretical minimum. However, this does not account for the task of delivering the refueling propellant to its destination, which requires a separate launch vehicle. In practice, frequent refueling offers diminishing returns or even becomes counterproductive, as long as propellant must be delivered from Earth. Section III considers different architecture options, including the Mars DRA-5, and multiple alternatives that refuel an electrolysis propulsion system at different stages in the round trip to Mars. Because the payload being delivered is very similar in all cases, it is possible to compare these architectures in terms of the number of launch vehicles required for each, counting both the launches to assemble the crew vehicle itself, as well as any launches used for propellant delivery. 11 American Institute of Aeronautics and Astronautics 𝑖=0 𝑛𝑗 ∆𝑉𝑗 𝑀𝑝 =∑𝑚0(𝑒𝑣𝑒 −1) (10) Downloaded by NASA LANGLEY RESEARCH CENTRE on January 30, 2018 | http://arc.aiaa.org | DOI: 10.2514/6.2018-1537PDF Image | Water Electrolysis for Propulsion of a Crewed Mars
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