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. The mission delta V and the maximum mission/burn duration are key variables; here, the author makes the decision to simplify the analysis by again assuming that the thruster is always on since a reactionless drive doesn’t pay a significant penalty for burning inefficiently at points in its trajectory. The other variable is the ratio of the electric system’s specific mass to the thruster’s specific power, and the ratio can also be expressed as the ratio of the electric system’s mass to thrust; put another way, it is the inverse of how much acceleration the reactionless spacecraft would be able to deliver with zero payload.

This formulation has the incidental effect of substituting in the thrust to power ratio, a finite number for an infinite efficiency term. An efficiency of a reactionless thruster can be defined, however, though it is not useful to do so for this paper; a photon rocket has a power-specific thrust of 1/c or 3.336 nanonewtons per watt. Anything above this is thrust to power ratio is forbidden by the theory of relativity, so one can set that as 100% efficiency; by that definition, the proposed reactionless thrust to power ratio of 1.2 millinewtons per kilowatt (or 1.2 micronewtons per watt) is roughly 360,000%. It can be seen that this number is not a useful one to conduct engineering analysis with. The formulation above has the virtue of being able to analyze infinitely efficient thrusters and spacecraft with useful and finite figures of merit. These two equations allow a parametric analysis of different mission profiles to determine payload mass fractions of current and future mission profiles with both electric propulsion and reactionless drives.

III. Results and Discussion

To compare reactionless and conventional electric propulsion, this paper will perform an analysis of a selected subset of three things. The type of engine, the type of power system, and the desired mission will all be varied to give a good feel of what the comparative design space is like, with examples of each of the three things serving as examples.

A. Analysis of Near-Future Mission Design Spaces

For thrusters, the representative reactionless drive will be one similar to the drive proposed by NASA- Eagleworks, with a beta of 1.2 mN/kW. Its counterpart on the conventional electric propulsion side will be similar to a laboratory-tested high power ion thruster such as the HiPEP ion thruster. Using HiPEP’s tested capabilities as a guide, our conventional electric propulsion thruster will have 9600 s of specific impulse and an efficiency of 80% for a thrust to power ratio of 17.1 mN/kW, or roughly 15 times the reactionless thruster. This implies directly the trade-off that the reactionless drive for an equivalent mission (in terms of delta-V and maximum mission time) will require roughly 15 times as heavy an electrical subsystem but will require no propellant. Note also that as discussed in the prior section one can find a maximum acceleration for a reactionless thruster by setting the payload ratio to 0 and solving. The maximum acceleration is exactly equal to the ratio of beta/alpha. For beta = 1.2 mN/kw and, for example, solar panels with an alpha of 0.0077 kg/W the maximum spacecraft acceleration is 0.16 mm/s^2, or just under 5 km/s per year. Anything that requires more delta V per year is not possible with that thruster and electrical subsystem. For simplicity, this paper is assuming perfect scalability of both thrusters equally, to allow a parametric comparison. Downloaded by UNIVERSITY OF ILLINOIS on July 12, 2017 | http://arc.aiaa.org DOI: 10.2514/6.2017-4843 Three power systems have been chosen. RTGs have insufficient power to be viable, and so are not considered. The first electrical subsystem will be a first-generation in-space fission reactor similar to the TOPAZ-1, at 32 W/kg, or what a solar panel would provide at ~2 AU. The second will be a SOA solar panel system at Earth’s orbit, 130 W/kg; falloff will not be explicitly analyzed for many of these missions. The final assumed electrical subsystem will be a proposed second-generation fission reactor similar to the SAFE-400 reactor, at 200 W/kg. These span the ranges of near-term plausible spacecraft power subsystems at reasonable scales, and should give a good overview of what is and is not possible with these thrusters.

The final piece is which missions will be analyzed. Five representative missions have been chosen to demonstrate this comparison. No trajectory analyses have been performed; instead they have rough estimates of time requirements and low-thrust notional delta-V requirements to span a broad mission space. These can also be assumed to span the set of plausible near and middle-term mission requirements for either a conventional electric propulsion mission or a reactionless thruster using mission.

4 American Institute of Aeronautics and Astronautics  Low Earth Orbit (LEO) at 28.5º inclination – Geostationary Earth Orbit (GEO): 6 km/s in 1 year  LEO – Low Mars Orbit: 15 km/s in 3 years  LEO – Jupiter: 30 km/s in 6 years  LEO – Uranus: 35 km/s in 12 years  Thousand Astronautical Unit (TAU) Mission: 100 km/s, 50 years

A set of 2 engines, 3 power subsystems, and 5 missions has 30 unique data points each representing a spacecraft with the selected subsystems carrying out the proposed mission. Table 1 below shows these 30 point calculations . With first generation nuclear fission reactors, a 1.2 mN/kw reactionless drive cannot accomplish any of the proposed missions; this is because its critical acceleration, or the fastest it can ever go, is 1.21 km/s per year, and none of these missions can be achieved in that time. To be clear, a longer mission at the same delta-V could be done, but that raises other issues with building spacecraft to last for decades, attendant mass costs, and so forth. For comparison purposes, these notional missions allow an apples-to-apples comparison even ignoring engine and structural mass. With solar-power-like power densities, the reactionless drive can conduct long term missions to Uranus and the TAU mission, but is only the best option for the 50-year mission. A second generation fission reactor allows the reactionless drive to be able to do every mission (7.5 km/s/year critical acceleration) but the bulk of the power system is such that still only the 50-year mission is better performed by a reactionless drive. This table demonstrates the paper’s primary contention, that low-thrust reactionless drives are strictly inferior to conventional technology for many missions even if they work as claimed. Table 1 gives these values as the inverse of the payload mass fraction; that is, a 2 on the table below signifies that the initial mass is twice the payload mass delivered at the end of the mission.

Table 1. Initial mass / payload mass for each type of thruster, electrical system, and mission considered inside the design space.

Another way to look at this is to study the ‘critical mission length’, or, for a given delta V, what length of mission is needed before a reactionless drive reaches equivalence with conventional technology. This can be calculated analytically, but is simpler to calculate by curvefitting to data. The breakeven mission durations for the design space considered in this paper are shown below in Figure 1. The result is that mission duration and power system are the critical parameters for a reactionless versus conventional thruster trade study, not delta-V, for

Downloaded by UNIVERSITY OF ILLINOIS on July 12, 2017 | http://arc.aiaa.org DOI: 10.2514/6.2017-4843 a given thruster technology! Each line represents the ‘break-even’ point between conventional and reactionless drives for the three specific power technologies considered in this abstract. With first generation fission power, only 75+ year missions benefit from a reactionless drive of 1.2 mN/kW. With solar panel like specific powers, 20-25 years becomes the breakeven range, while with second generation fission reactors the breakeven point is 12-16 years. Above those numbers, a reactionless drive at the cited specific thrust is a good option; below it, it is not.

5 American Institute of Aeronautics and Astronautics 32 W/kg 130 W/kg 200 W/kg 100

t n ) e l s a r v a i e u y q (

E n

r o i o t f

c h a t r g F n

e d a L

o l n y o i a s P s i

M 10 0 10000 20000 30000 40000 50000 60000 Mission Delta-V (m/s)

Figure 1: Breakeven mission duration of a conventional and reactionless thruster propelled spacecraft for different power systems and required delta-Vs.

These results show that low-thrust reactionless drives have serious issues competing with conventional electric propulsion for a large number of potential missions. They also show that the ways to mitigate this are to be comfortable with longer duration missions and additionally to increase the power density of nuclear reactors or other power-generating subsystems going forward- although to an extent conventional propulsion benefits from both of these as well. Another method is to increase the thrust to power ratio of reactionless thrusters, though that seems to be premature before confirming that the small thrust already measured is real. The relative weighting of each of the possible increases will be discussed in the next section.

B. Sensitivity of Payload Mass Ratio to Parameters

It is of interest to set up a baseline mission and begin analyzing both the sensitivity of our payload ratio figure of merit to our available ‘dials’- attributes of the thruster, mission duration, and power subsystem- as well as see just how much of a change is required to bring reactionless thrusters to a competitive balance with conventional electric propulsion.

Downloaded by UNIVERSITY OF ILLINOIS on July 12, 2017 | http://arc.aiaa.org DOI: 10.2514/6.2017-4843 For our baseline, we choose a near-term plausible mission, that of a Earth-Mars disposable cargo transport. The total required delta-V to go from LEO to LMO with low-thrust propulsion is estimated roughly at 15 km/s, with a total allowable mission duration of 3 years for consistency with the data point above. Both types of thruster have been allowed a 10,000 kg initial mass in LEO, and the payload mass delivered to LMO after 3 years compared.Table 2 gives some key parameters of the baseline mission for both types of thruster, and shows that the conventional HiPEP-like ion thruster is capable of significantly more payload delivered to the destination in the allotted time, and illustrates why. While the conventional system needs over a metric ton of propellant, it is more than five metric tons of electric subsystem mass lighter than the reactionless drive, given that the reactionless thruster needs over a megawatt of power and the conventional craft can get away with less than 100 kilowatts.

6 American Institute of Aeronautics and Astronautics Table 2. Baseline LEO-LMO in 3 years comparison of propulsion systems.

From the baseline, small variations in key design parameters affect the delivered payload mass of the above design case. Using the analysis tool, small variations in thruster, mission, and electric system parameters were made, and the leverage of those changes examined. In this case, leverage is defined as “the ratio of the change in the figure of merit to the change in a parameter”; put another way, for a leverage of 0.1, every 1% change in a variable produces a 0.1% change in the figure of merit being studied. Table 3 gives the results of this simplistic analysis. At a top level, the conventional electric solution is pretty close to ideal, or in other words the design space is ‘flat’ around this point solution. Changes in parameters only slightly affect the amount of delivered payload; a 1% increase in specific impulse increases delivered payload by 0.1%, with increases in reactor efficiency having half as much proportional effect. In contrast, the reactionless drive is extremely sensitive to variations in any of its input parameters. Each percent change in any of thrust to power ratio, reactor efficiency, or mission duration causes an almost 2% change in delivered payload. None of the three parameters has an appreciably stronger effect than any of the others.

Table 3. Leverage of Design Parameters on Delivered Payload

Finally, we examine what changes would have to be made to bring the reactionless drive to equivalence with the conventional electric propulsion system. Significant improvements in all three major design parameters would be needed, with none appreciably higher-leverage than the others. If: Downloaded by UNIVERSITY OF ILLINOIS on July 12, 2017 | http://arc.aiaa.org DOI: 10.2514/6.2017-4843  Acceptable mission duration was increased to 12.5 years, with no assumed impact on other systems, or  Electrical system specific power was increased to 840 W/kg, or  The thruster’s thrust to power ratio was increased to 4.2 mN/kW

Or some combination of those changes occurred in proportion, the reactionless drive would be a competitive propulsion solution for this LEO-LMO cargo mission. This validates the paper’s findings that as presented, reactionless drives are not a particularly compelling technology for many current and near-term misisons.

IV. Conclusion The above results show that as presented to date, reactionless drives with a thrust to power ratio of ~1 mN/kW are not very useful engines for all but the longest-duration missions either currently being conducted or studied, and even then only with advanced second-generation in-space nuclear power. This paper does not offer any judgment on

7 American Institute of Aeronautics and Astronautics whether or not prior reactionless drive experiments were conducted without error or whether they have in reality found a thruster that appears to break conservation laws. The author is deeply skeptical, but that is not relevant to the results presented above. Instead, this paper takes the assumption that the data is real, and examines what that thruster would be able to do; the answer is, not as much as breathless media articles might imply.

Acknowledgments

This paper is dedicated to the memory of Norman L. Dean, who was decades ahead of his time.

References

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White, H., et al. “Measurement of Impulsive Thrust from a Closed Radio-Frequency Cavity in Vacuum”. AIAA Journal of Propulsion and Power, pre-publication. Downloaded by UNIVERSITY OF ILLINOIS on July 12, 2017 | http://arc.aiaa.org DOI: 10.2514/6.2017-4843

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