Mission Design and Trade Study Considerations for Reactionless Thrusters

AIAA 2017-4843 AIAA Propulsion and Energy Forum 10-12 July 2017, Atlanta, GA 53rd AIAA/SAE/ASEE Joint Propulsion Conference Abstract for Mission Design and Trade Study Considerations for Reactionless Thrusters Dr. Shae E. Williams 1 Buffalo, NY 14203 Recent research on the subject of high-thrust reactionless drives have, to date, shown seemingly impossible amounts of thrust for a thruster with no exhaust. There has been significant attention to these claims, both in professional and media outlets, attempting to prove or disprove these reactionless thrusters. To date, nobody has performed a rigorous analysis of what missions these reactionless thrusters could perform in comparison to state of the art electric propulsion thrusters. This paper takes the results from the NASA-Eagleworks paper published in late 2016 of roughly 1 millinewton of thrust per kilowatt of power and shows that a reactionless thruster with these properties would only be superior to ion thrusters with mission durations significantly higher than a decade. To this end, a first-order estimation of the payload mass fraction of a spacecraft with conventional electric propulsion or a proposed reactionless drive is derived, and then applied to a range of mission scenarios with both current and near-term power generation systems and efficiencies. The major result is that a reactionless drive with this specific thrust requires very high specific power electricity generation, such as a 2nd generation in-space fission reactor, or is not competitive for most conceivable current and proposed missions. This paper does not take a position on whether or not the NASA-Eagleworks reactionless drive (or any other reactionless drive) is ‘real’, but treats the recent NASA-Eagleworks findings as though they were correct and applies them to top-level mission analysis. Nomenclature mo = spacecraft initial mass mf = spacecraft final mass mp = spacecraft propellant mass me = spacecraft electrical system mass mL = spacecraft payload mass Isp = specific impulse T = thrust P = usable electric power delivered to a thruster Downloaded by UNIVERSITY OF ILLINOIS on July 12, 2017 | http://arc.aiaa.org DOI: 10.2514/6.2017-4843 tb = total thruster burn time η = thruster efficiency α = Power-specific mass of the electrical system (kg/kW) β = Power-specific thrust of the thruster (mN/kW) ΔV = Mission velocity change required I. Introduction HIS paper discusses the use cases in which a reactionless thruster similar to that described in the recent NASA- TEagleworks paper could be superior to conventional electric thrusters and those cases in which it would not be, without discussing the merits of the thrust measurements in question. This is accomplished by creating a top-level 1 AIAA Full Member, 2012. Work was conducted independently, and Dr. Williams’ current employer was not involved in this research. 1 American Institute of Aeronautics and Astronautics Copyright © 2017 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. parametric model for how much payload mass a given initial mass in orbit could deliver to a mission target. The key mission parameters are delta-V and total mission time, and all results are a function of those two requirements. Second order masses such as thruster mass and structural mass are neglected in favor of splitting a mission into “fuel (if applicable), electric subsystem, and delivered payload” to keep the parametric analysis simple. The general equation for a conventional electric propulsion is rederived first following the usual conservation of momentum based arguments, and then for comparison a similar equation for the ratio of initial mass to payload mass is derived for a reactionless thruster with a given thrust to power ratio and a given mass-specific power of its electrical subsystem. Once the equations are derived and a parametric tool created able to give a first order estimate of payload mass for a given mission, propulsion, and electrical subsystem, it is possible to compare conventional electric propulsion and reactionless drives on a level playing field. This analysis will compare the two propulsion families in two ways. First, sample missions such as a LEO-Mars orbit cargo transfer using solar power will be analyzed with both types of thruster. These missions span from current-day needs to projected needs for decades to come, with the most ambitious being a 50 year mission to 1,000 AU to study the inner edge of the Oort cloud or investigate gravitational lensing. This analysis shows that as a general rule, delta-V is a less significant variable in determining if reactionless or conventional electric propulsion is preferred. Instead, the mission maximum duration as well as a figure of merit for reactionless spacecraft that is the ratio of electric subsystem power (m electric/P) to the thrust to power ratio of the thruster. These two numbers largely determine the success of reactionless thrusters, and for the NASA-Eagleworks level of ~1 mN/kg thrust to power ratios and current and near future electrical subsystems, the breakeven mission duration measures in the decades. Finally, a sensitivity analysis around one of these baseline missions will show what variables have the most impact on delivered payload, both for conventional and reactionless propulsion architectures. This shows that reactionless drives are much more sensitive to input variables for this baseline mission than conventional drives, with a small change in mission duration causing over an order of magnitude more payload change for the reactionless spacecraft than the conventional one. These two analysis methods show the issues that result from a thruster with a very low thrust to power ratio, even with infinite specific impulse- to sum it up, saving a ton of propellant isn’t useful if it requires one to include two tons of solar panels. II. Equations and Derivation To compare a reactionless and a conventional electric propulsion architecture, a convenient mission-level metric is the payload mass fraction; what percentage of the mass of one’s spacecraft, at the beginning of a mission, is payload delivered at the end of it. To use this, we will simplify our notional spacecraft into three subsystems: Required propellant mass, mp Required electrical subsystem mass, me Delivered payload, ml Thus, in this definition, things like tankage mass and thruster weight are included in payload; this is a simplification chosen because the masses involved will likely be small compared to the mass of the overall spacecraft, and would needlessly complicate the below analysis if included. Downloaded by UNIVERSITY OF ILLINOIS on July 12, 2017 | http://arc.aiaa.org DOI: 10.2514/6.2017-4843 A. Conventional Electric Propulsion This result is well-covered in many textbooks as an illustration that the Tsiolkovsky equation is not the only thing that matters for electric propulsion. Starting with that equation, we have the ratio of the final mass to initial mass, mf −ΔV =exp mo ( g⋅I sp ) We know that final mass is the payload mass plus the electrical subsystem mass. We can then write the payload mass fraction as, 2 American Institute of Aeronautics and Astronautics mL mf me −ΔV me −ΔV αP me = − =exp − =exp − , where α= mo mo mo ( gI sp ) mo ( gI sp ) mo P We have now defined the specific mass of the electrical subsystem as the mass of the electrical system divided by the power supplied. We also define the efficiency of the thruster as half the product of thrust and specific impulse divided by the power, and use that to replace P in the equation above. T⋅g⋅I sp mL −ΔV αTgI sp mL −ΔV αgI sp T mp η= , so =exp − and hence =exp − 2⋅P mo ( gI sp ) 2ηmo mo ( gI sp ) 2η mp mo The propellant mass divided by the initial mass is, by our definitions, equal to one minus the final mass over the initial mass, and we can replace the latter term via the ideal rocket equation. Thrust we replace by its definition of mass flow rate time effective exhaust velocity, and we then have a mass flow rate divided by a total propellant mass which becomes the burn time. mL −ΔV αgI sp m˙ gI sp mf =exp − 1− mo ( gI sp ) 2η mp ( mo ) And, finally, the payload mass fraction under our assumptions for a conventional electric-propelled spacecraft is: 2 mL −ΔV α (g⋅I sp ) −ΔV =exp − ⋅ ⋅ 1−exp m g⋅I 2 η⋅t g⋅I o ( sp ) ( b )( ( sp )) This brings forth the familiar behaviors of there existing for a given mission an optimal specific impulse and other well-known phenomena. B. Reactionless Propulsion To get a similar equation for a reactionless drive, the presence of efficiency (as defined here an infinite number) as well as infinite specific impulse makes straightforward calculations unuseful. However, if you make the assumption that the thruster is always firing- a useful assumption, since there is no propellant to ‘waste’- you can simplify things greatly. Now since there is no propellant, the final mass is the same as the initial mass which equals the electrical system mass and the payload mass. m m L =1− e m m Downloaded by UNIVERSITY OF ILLINOIS on July 12, 2017 | http://arc.aiaa.org DOI: 10.2514/6.2017-4843 o o We define the thrust to power ratio as “beta”. We note that the acceleration of the vehicle a equals the thrust divided by the initial mass, but also equals the delta V divided by the burn time: T ΔV βP ΔV βme ΔV a= = and, given our definition of beta, = and knowing P from earlier, = mo t b mo t b αmo tb Rearranging, we get the equation for payload mass fraction for a reactionless drive-propelled spacecraft: mL ΔV α =1− ⋅ m t ( β ) o ( b ) 3 American Institute of Aeronautics and Astronautics It is immediately apparent that this is a relatively simple equation.

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