Cost viability of coilgun-style kinetic launch system to place satellites in low earth orbit

Barker College

Purpose: This paper aims to explore and compare the cost viability of utilising high-velocity kinetic systems to send various-sized payloads into Earth's orbit against traditional rocketry propulsion. Design/methodology/approach: A model was developed to provide costing for high-velocity kinetic systems which considered the required velocity of a projectile (numerically calculated considering the effects of gravity and air resistance), construction, and energy costs. The cost of various sized payloads was then compared to the cost of current rocketry programs using traditional propulsion. Findings: The results of the investigation show that while the coilgun may potentially be a viable option later on due to the increasing abilities of technology, however, currently the available technology does not make this technique a viable or cost-effective method compared with traditional rocketry. Research Limitations/implications: Individual cost estimates are from validated sources, however, they are only estimated when applied to this alternative technology and there is a high degree of complexity in producing the technology. Further research needs to further evaluate the model for comprehensiveness and does not comment on the practicability of the system, only the costing. Practical implications: As the results indicate that according to this model it is very cost inefficient to use high-velocity kinetic systems, using these systems from the ground level is not a likely practical alternative. The increased combination of these values incurs a greater chance of error, either disassociating key variables from equations or incorrectly estimating values. Social implications:Through any system, the cost of the launch of objects into Earth's orbit remains prohibitive to all but large governments or corporations. Rocketry and high-velocity kinetic systems can also be unethical technologies. Originality/value: To the author's knowledge, the costing of high-velocity kinetic systems to traditional rocketry has not been done before. Keywords: Rocketry, Kinetic launch systems, Alternative launch methods

The use of rockets and traditional launch systems have been tested since late in World War II (WWII) with the German V2 rocket (Reuter & GermanCanadian Museum of Applied History, 1998). This has allowed us to develop sophisticated methods to achieve our goals, often reducing cost and risk (Jones, 2018). Modern-day technologies have significantly increased the efficiency of the creation and usage of fuels in traditional propulsion systems (Mercado, 2019). However, traditional rocketry requires a vehicle to contain all of its fuel required onboard, during flight this creates empty mass which only reduces the rocket's efficiency throughout the burn period, requiring more fuel (Zimmerman, 1966). Furthermore, the most common rockets use a singleuse hull and engine, increasing the general cost of launch. However, modern advancements toward reusable boosters and hulls have been explored (Reddy, 2018).

The use of mass accelerators to launch projectiles has been considered since before the idea of using a traditional rocket, however, due to the large-scale requirements and limiting factors they have not been invested in as significantly (Klyushnikov, 2020). Certain mass accelerators such as explosive projection incur diminishing results as the scale of the system grows, and the rate of expansion of the gas remains relatively the same, therefore the system becomes ineffective at the scale required to achieve even LEO. However, electromagnetic systems have a technical indefinite limit, therefore allowing them to be effective even at great scales. Mass accelerators all incur the issue that all the kinetic energy required must be generated at the point of launch, making it unusable for multistage designs without the incorporation of hybrid systems, and air resistance is

a major factor that affects the ability of the system to reach its goal.

New technologies that were predicted to exist have been created and suggest that newer technologies are potentially on the horizon and could make the process significantly easier or cheaper (Marshall, 1981). Furthermore, the arrival of Spin Launch as an electromagnetic propulsion system, proposes that these technologies may be under development (Klyushnikov, 2020). Electromagnetic systems work purely on electric input, this allows them to run on many energy systems. However, as the majority of electromagnetic propulsion systems fall under the mass accelerator category, they possess similar, or the same problems imposed in their usage. Current electromagnetic systems are of small scale, used for particle research. The Hadron Collider uses a coilgun-based system to accelerate particles. These guns allow for a low friction environment, as projectiles are suspended within a field, this reduces friction and heat, allowing for fewer fatal malfunctions (McMillan, 1945).

For a projectile to sustain orbit, there is a horizontal velocity that it must attain, dependent on the orbital radius and gravitational acceleration of the projectile. (Farr et al., 2018)

How would the cost of a coilgun-style velocity-based launcher compare to the cost of traditional thrusterbased rocketry when launching varying satellites/payloads into Low-Earth-Orbit (LEO)?

For heavier payloads, traditional rocketry will be cheaper than coilgun acceleration. For lighter payloads, traditional rocketry will be more expensive than coilgun acceleration to achieve a low earth orbit (LEO).

This experiment seeks to propose costing models of two methods of launching payloads, to compare the costs required to get payloads of various masses to an altitude of 1,500,000 m above mean sea level (AMSL) with a horizontal velocity of 6,956.59 m/s. The altitude was selected as it is the midpoint between the ‘edge’ of the atmosphere (1,000,000 m AMSL) and the upper limit of low earth orbit (LEO) (2,000,000 m AMSL). The velocity was calculated by evaluating the gravitational force to the centripetal acceleration to maintain the orbital altitude:

Published data were used to estimate the cost of payload launch with traditional rocketry. (Jones, 2018)

Figure 1: Experimental Launch Method Payload Mass vs Cost (25kg payload removed due to 5350% increase in cost)

To determine the cost of the alternative method of acceleration, the muzzle velocity of the gun must be established. A computational program written by a research supervisor with support from the author was used to iteratively work backwards in time from the final orbital velocity. This program is can be requested via the author, and the process is described below. Due to the constraints of the coil gun system, the launches must occur in packets. This is because of the exponential growth in cost as packet size increases, see Figure 1.

To simulate the path of the projectile, step back in set time frames (1s) and calculate the acceleration acting on the projectile for that period, to calculate the velocity before the step. To calculate the radius from the centre of gravity before the step, use the formula, �������� =����������������+ 1

2

����������������2, this produces a displacement for the time step, which is used to find the new radius.

The calculation of the effects of air resistance on the projectile is determined by using the velocity from the current step and the formula ���������������� =

1

2����������������2������������������������. The formula solves for the force acting on the projectile (����������������), by taking the fluid density (��������), velocity (��������), drag coefficient (����������������) and area cross-section (��������). Fluid density is sourced from the International Standard Atmosphere.

The muzzle velocity of the projectile from the launch apparatus is used to calculate the kinetic energy required. The energy is converted to watt seconds, with the time required to achieve the muzzle velocity with the set acceleration (1000G | 9810m/s/s).

The watt seconds converted to kilowatt hours is used to estimate the energy cost based on local retail (0.4 cents/KwH) (Energy Australia)

Table 1: Comparison of Traditional and Experimental Launch Methods of Equal Payload Sizes

9 Vanguard $8,052,300 $88,039 $21,516 $135,653 122 Scout $13,639,600 $1,193,418 $291,662 $1,838,856 443 Pegasus XL $19,270,500 $4,333,475 $1,059,068 $6,677,157 540 Delta E $90,612,000 $5,282,340 $1,290,963 $8,139,199 632 Start $10,554,400 $6,182,294 $1,510,905 $9,525,877 820 Athena 1 $25,994,000 $8,021,331 $1,960,351 $12,359,524 1380 Taurus $28,152,000 $13,499,314 $3,299,128 $20,800,174 1500 Kosmos $12,000,000 $14,673,167 $3,586,009 $22,608,885 1500 Cosmos $18,600,000 $14,673,167 $3,586,009 $22,608,885 1850 Rockot $19,240,000 $18,096,906 $4,422,744 $27,884,291 2065 Athena 2 $34,279,000 $20,200,060 $4,936,739 $31,124,898 2177 Titan II $67,487,000 $21,295,656 $5,204,494 $32,813,028 2315 Delta 3910 $64,820,000 $22,645,588 $5,534,407 $34,893,046 3200 Long March 2C $32,000,000 $31,302,756 $7,650,152 $48,232,288 3630 Atlas-Centaur $101,640,000 $35,509,064 $8,678,141 $54,713,502 4400 Dnepr $21,560,000 $43,041,290 $10,518,959 $66,319,396 5144 Delta II $78,703,200 $50,319,181 $12,297,619 $77,533,403 7000 Soyuz $53,200,000 $68,474,780 $16,734,707 $105,508,130 8292 Delta III $97,016,400 $81,113,268 $19,823,456 $124,981,916 8618 Atlas IIA $170,636,400 $84,302,236 $20,602,815 $129,895,580 9200 Long March 2E $70,840,000 $89,995,425 $21,994,187 $138,667,828 10060 H-2 $265,584,000 $98,408,040 $24,050,165 $151,630,255 10200 Ariane 44 $182,580,000 $99,777,536 $24,384,859 $153,740,418 13600 Long March 3B $85,680,000 $133,036,715 $32,513,146 $204,987,224 13740 Zenit 2 $60,456,000 $134,406,210 $32,847,840 $207,097,386 15875 Zenit 3SL $120,650,000 $155,291,018 $37,951,926 $239,277,366 17700 Titan-Centaur $198,240,000 $173,143,371 $42,314,903 $266,784,842 17700 Titan IV $437,190,000 $173,143,371 $42,314,903 $266,784,842 18000 Ariane 5G $235,800,000 $176,078,005 $43,032,105 $271,306,619 18600 Saturn IB $321,780,000 $181,947,272 $44,466,508 $280,350,173 19760 Proton SL-13 $81,016,000 $193,294,521 $47,239,688 $297,834,378 22800 Falcon 9 $62,016,000 $223,032,139 $54,507,332 $343,655,051 27500 Shuttle $1,697,300,000 $269,008,063 $65,743,493 $414,496,224 63800 Falcon Heavy $89,958,000 $624,098,706 $152,524,904 $961,631,240 140000 Saturn V $728,000,000 $1,369,495,593 $334,694,147 $2,110,162,596

Figure 2: Comparison of Traditional and Experimental Methods (Payload Size vs Cost)

Figure 3: Comparison of Traditional and Experimental Methods (Payload Size vs Cost) – Zoom in

The results illustrate that while generally, the experimental method is more cost-effective, the more modern traditional systems outperform the experimental method. As seen in figure 2 the Falcon Heavy (63800 kg Payload) outperforms all variants of the coilgun, however, the Saturn V (140000 kg Payload) only outperforms the coilgun in 2.5 kg and 10 kg packages. This suggests that this method may be viable, as it is only beaten by much heavier rockets designed for longer voyages. The 10kg has a higher cross-section, increasing the drag during the launch. However, both the 2.5kg and 5kg packs use the same cross-section, allowing the 5kg packs to before better than the 2.5kg.

The outlier that is apparent in figure 2 is the Space Shuttle Program (27500 kg Payload), this is due to

the high experimental efforts of the program and did not have technologies that are now available to us. Figure 3 shows a more refined view of the data, showing a greater comparison between the experimental method and traditional methods. The Falcon 9 (22800 kg Payload) is a common rocket used today, as seen in figure 3 the 5 kg variant is slightly more cost-effective. However, these are estimations that do not include the addition of errors between launches. For this data to be of greater accuracy and value additional factors must be considered, such as maintenance, cost of the sabot, and potential costs due to excessive usage. The data is far from perfect, but still grants a relatively accurate representation of the costs of launching a projectile into LEO.

The data, in general, supports my hypothesis, however, the values in comparison to the modern-day standards do not vary significantly.

The data illustrates that the usage of experimental coilgun designs to achieve Low-Earth-Orbit (LEO) is either less or not significantly more cost-effective compared to traditional rocketry. The experimental method may become more viable due to the discovery of technology, however, I would suggest against investing our time into following these methods. This is because the value that would potentially be achieved within this context would be drastically less than if we invested the same value into traditional rocketry methods. The technology could be used for tools of destruction, therefore, there is still a potential use for this technology, however, would not have the clearest of ethics as utilised in my report.

I would like to acknowledge Dr Matthew Hill for his support as my supervisor and the author of the program I used to generate an appropriate muzzle velocity with a correlation to air resistance and gravitational acceleration.

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