Mass Driver Design Traveling Earth to the Moon

Received September 26, 2019, accepted October 25, 2019, date of publication November 1, 2019, date of current version November 14, 2019. Digital Object Identifier 10.1109/ACCESS.2019.2950882 Mass Driver Design Traveling Earth to the Moon ERK INGER Airframe and Powerplant Maintenance Department, Atılım University, 06830 Ankara, Turkey e-mail: [email protected] ABSTRACT In this article, the flight of a mass driver was designed for launch from the Earth with Electro Magnetic Space Launching System (EMSLS). Then the orbit exit from the Earth at 185 km and orbit entry the Moon at 100kmwere examined with respect to change of trajectories by using chemical fuel and the engine in the mass driver. Electromagnetically launched mass drivers should orbit with a specified orbital velocity at a designated altitude. In this paper, the energy is transferred externally to a mass driver throughout the flight path the electromagnetic coil system called multistage (EMSLS) designated in order to achieve the specified orbital velocity. The mass driver is synchronously accelerated by a voltage through the capacitors which are used for storing energy. This energy is transferred through a switching inductor to the circuit of the mass driver so that the mass driver is launched into the orbit with a muzzle velocity. However, this fact creates high air drag energy losses due to atmospheric conditions and high velocity obtained in EMSLS. Thus, in the mass driver at 21km altitude an engine starts to increase the velocity of the system to reach orbital velocity. The final aim of this article is to capture the transfer of 1v cost for traveling to the Moon. At any given arrival time in order to guide the system, designers only consider the gravity of the Earth and gravity of the Moon by using a Direct Lunar Transfer Trajectory for the Earth to the Moon approach. Finally, EMSLS was evaluated as a more advantageous and complimentary alternative to chemical propulsion systems for space transportation. INDEX TERMS Mass driver, electro magnetic space launching system (EMSLS), muzzle velocity, lunar transfer trajectory from earth, useful payload, 1V cost, perigee, apogee. I. INTRODUCTION Electro Magnetic Space Launcher Systems (EMSLS) create a propelling force using electromagnets in a magnetic field. The energy stored by a voltage through the capacitors is transferred through an inductor to a driver so that the mass driver is launched into the orbit with a muzzle velocity. EMSLS launched mass driver carries higher useful load with a very high acceleration value in comparison to chemical rockets. They can be used at a faster rate, are more cost effective, less hazardous and safer than chemical launcher systems [1]. In the very near future, hundreds of tons of supplies are planned for interplanetary transportation using EMSL systems [2]. EMSLS transportation is evaluated as more cost efficient when economic, commercial and technical aspects are considered. The direction of trajectories was generated for travelling from the planar circular restricted three-body system of parking at 185-km in the inertial frame of Earth to 100-km lunar orbits. The Sun’s gravity is also taken into account, but only The associate editor coordinating the review of this manuscript and approving it for publication was Xiaodong Liang 161034 . as a perturbation to the transfer and a very short duration of transfer departs from the Earth. In the Direct Lunar Transfer Trajectory, only the gravity of the Earth and the gravity of the Moon are considered for evaluation of the trajectory from the Earth to the Moon. The most efficient direct transfers typically require 4–5 days, depending on the location of the Moon in its elliptical orbit, similar to the Hohmann transfers. Corresponding total 1V values and total amount of fuel required are used in the design of the mass drivers. The rest of the mass belongs to structural mass and useful payload. Design Specifications for a Space Mass Driver and EMLS system are calculated using a simulation program which will be explained below. Additional velocity changes required to reach orbit velocity, its elliptical orbit for the Hohmann transfers and the amount of chemical fuel are calculated for a vehicle travelling from Earth orbit of 185km altitude to lunar orbit of 100km altitude. II. THEORY A. ELECTROMAGNETIC LAUNCHING THEORY A cylindrical armature (projectile) with payload starts to accelerate through the surrounding segments of equally This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see http://creativecommons.org/licenses/by/4.0/ VOLUME 7, 2019 E. Inger: Mass Driver Design Traveling Earth to the Moon Acceleration of mass driver is presented in (8). η (PE) (8) mw where η is efficiency of the whole system and m is mass of the projectile. Launcher length, s, is calculated by using (7) and (8) as in (9) a= FIGURE 1. Dimensions of a multi segment electromagnetic launching system. spaced coils without contacting wires. In the conceptual design model, required velocity is calculated mathematically by using different voltage, magnetic field and multiple coil dimensions [3]–[5]. Launching velocity (1) can be determined by 2w distance on Fig. 1 by discharge time of the capacitance, τk , (2) and replacing an average of β = 1/2, inductance area factor [4] vL = 2w √ π Nk βLC (1) Discharge time of the capacitance τk , was been taken as the rise time of coil segment and expressed as, π τk = Nk (βLC)1/2 (2) 2 here Nk is the k th segment of coil and Ik is corresponds to the current. Inductance of wire coil equation used for calculations in this article are evaluated (3), Lcircle = µ0 rln[1.39ω̄] B2 w2 rln[1.39ω̄] 4µ0 Finally, current strength, is expressed as in (5).  Nk Ik = Bw µ0 B. ORBIT VELOCITY CALCULATION (4) (5) B is the magnetic field and w is the width of the related segment which is considered as the design parameter. Capacitance (6) is calculated as: C= w2 B2 rln[1.39ω̄] 2µ0 V 2 (6) The launching velocity (7) can be found below; vL Nk = 4V π rBln[1.39ω̄] (7) In terms of design and performance, parameters are tabulated as presented in Table 2 and Table 3. VOLUME 7, 2019 Electrical potential energy is converted to kinetic energy and all calculations are based on this conversion. In order to calculate launching velocity, inductance, current strength and capacitance are calculated for input values of the given magnetic field and voltage and the physical dimensions of coil radius, segment height and width. Besides these; acceleration, velocity, launcher length and number of coil segments are also calculated. Acceptable orbital velocity equivalent launching velocity for a specified altitude is calculated and presented in Table 3. (3) where L is the inductance, µ0 is the permeability, r is the mean radius and ω̄ is the ratio of external and the internal radius of coil. Electrical potential energy multiplication of capacitance and voltage square capacitance re expressed by using (5), (6). PE = v2L (9) 2a Number of segments, k, is calculated by using web thickness of the coil, w and launcher length, s as in (10). s k= (10) w Elapsed time for the launching period is evaluated in (11). r 2s t= (11) a s= The orbital velocity [6] of a space vehicle at 185km is calculated below. s

6.67 × 10−11 Nm2 /kg2 5.98 × 1024 kg vOR = 6378000 + 185000m = 7796m/s MEARH = 5.98 × 1024 kg rEARHH = 6378km  Nm2  G = 6.67 10−11 kg2 According to the calculations, electromagnetic velocity at 185 km altitude should be equal to orbital velocity of 7796m/s. 1 1 2 mvOR + mgh = 1500 (7796)2 + 1500g185000 2 2 r p 1E v= 2 = 2(32.204)MJ = 8025m/s m 1E = The velocity of mass driver is reduced by aerodynamic drag loss with very high muzzle velocity and with high air density at low atmospheric altitudes. The energy loss due to air drag is calculated by (12) under average conditions of flight altitude. ELOSS = D.1h/g = 1 ρair .σ .CD .A.v2 .1h/g 2 (12) 161035 E. Inger: Mass Driver Design Traveling Earth to the Moon TABLE 1. 1V cost figures from p.232 in [7] (low-energy transfers require trans-lunar injection C3 values of about −0.6 km2 /s2 , compared with typical direct transfers that require C3 values of about −2.0 km2 /s2 ). FIGURE 2. Earth origin, low lunar orbit. FIGURE 4. Different trajectories for transferring to a low lunar orbit [7]. FIGURE 3. Flowchart of 1V cost needed to transfer to a low lunar orbit is presented below [7]. TABLE 2. EMLS input specifications. The velocity loss (13) is found by using ELOSS in (12) r 2.ELOSSS (13) VLOSS = m The mass driver should have at least 8025 m/s of velocity to start orbiting at 185km altitude. The plan is to activate the engine in the mass driver before entering orbit. The next step is to reach lunar orbit as shown in Fig. 2. TABLE 3. Performance parameters. C. DIFFERENT LOW-ENERGY LUNAR TRANSFER ITINERARIES AND 1V VALUES There might be several alternative low lunar transfer itineraries for determining the velocity changes used for calculation of fuel amount for space flight from the Earth to the Moon. Fig. 3 illustrates several direct lunar transfers that have varying transfer durations. 1V costs taken from p. 232 [7] are shown in Table 1. Five examples are given for direct transfers from 185 km Earth circular orbits to 100 km prograde lunar orbits within in inertial frame. Parker and Anderson [7] state that those trajectories were generated in the planar circular restricted system. The following information applies to the labeled trajectories (See Fig.4). III. SPACE VEHICLE DESIGN A. EMLS DESIGN Performance parameters for the space vehicle are calculated by using engine specifications given in Table 2. Structural 161036 weight and payload for space projectile mass are assumed to be 1500kg. Table 3 summarizes results for a 1500kg space projectile with design parameters of mean coil radius 0.35 m, electromagnetic field 25 T, coil web length 0.25 m and voltage 130000 V to generate 8473 m/s of electromagnetic muzzle velocity which is required for 8025 m/s orbital velocity at 185 km without considering the drag energy loss. VOLUME 7, 2019 E. Inger: Mass Driver Design Traveling Earth to the Moon TABLE 4. Results of simulation program. TABLE 5. Energy loss due to the drag of mass driver. TABLE 6. Summation of structural weight and payload for space projectile, ISP = 1000s. Table 4 shows the simulation program used in the calculation of performance parameters for EMLS. TABLE 7. Engine specifications. B. CALCULATION OF FUEL WEIGHT As observed in Table 4, due to the very high muzzle velocity energy loss at each altitude segment of flight, mass driver velocity is reduced from overall driver muzzle velocity. Table 5 presents this energy loss phenomena for each 3 km and how the muzzle velocity of the mass driver is reduced to 2803 m/s at 21km flight altitude. Starting from this altitude of 21 km to 185 km, the engine operates to increase the velocity of the mass driver to 7590 m/s by considering the energy loss in almost vacuum conditions of flight. All average air density values were transferred from ‘‘Engineering Science Data Sheets [8]. Building launcher at the equator and launching the rocket towards the east will receive another big boost from the Earth’s rotation and rotating in the direction of the Earth adds extra 460 m/s velocity [9] gain to mass driver final velocity at 185 km. Therefore, theoretically the launcher can reach up to 8050m/s which may be acceptable to enter orbit. Fuel weight required to reach 185km altitude from 21 km altitude, 5000 m/s 1vLOSS and for changing orbits 1vTLI with 1vLOI are used to find the total 1v (14) and total fuel amount are calculated by using fuel 1000s when ISP is specific impulse, and g is gravity in (15) (15) as −1.976, then a short-duration direct transfer departs the Earth and encounters the Moon in 6 days and the total velocity change is 3.966 km/s according to Table 1. Using these values in the formula (15), required fuel mass is calculated as 409 kg and total fuel mass is shown in Table 6 as 900 kg [7]. The space mass driver will be redirected towards the Moon at 100km orbit. The low amounts of fuel and small engine types are presented in Table 7 and selected with ∗ to enter elliptic orbit at perigee and to enter lunar orbit at apogee. Pre-calculations of LEO-LLO low-thrust transfers with constant thruster power levels (5 kW, 10 kW and 15 kW) in a range of specific impulses for propellants in Table 8 varying from 1500 s to 5000 s are investigated in [9], [10] and listed in Table 8. Direct transfer depends on the location of the Moon in its elliptical orbit and resembles Hohmann Transfer. It can be achieved by taking C3, launch injection energy parameter, Basically, the amount of payload, rate of launches and required mass transportation determines the cost of EMSLS. 1v = 1vLOSS + 1vTLI + 1vLOI   − gI1v mp = m 1 − e SP VOLUME 7, 2019 (14) IV. RESULTS AND DISCUSSION 161037 E. Inger: Mass Driver Design Traveling Earth to the Moon TABLE 8. Specific impulse and propulsion types. TABLE 10. Terminology, symbols and units. TABLE 9. Comparison of engine specifications and performance values according to Kolm. In an spacecraft EMLS design targeting 1000 kg useful load to be used from Earth to Space with 1000 ‘‘g’’ acceleration and 12.3 km achieved velocity studied by Kolm [11], the launcher formed of copper, steel and concrete layers cost 24 million dollars. For a 24 GJ energy storage system consisting of capacitors and generators, the cost was $ 11 billion on condition that conventional generators and capacitors are used. However, it was calculated that half of this value is reflected in depreciation with 120 launches per day for 10 years cost paying a depreciation cost of $ 12 per kg of payload. In the same application, the energy cost per kg was calculated. At a speed of 12300 m per second for a useful load of 1000 kg, the system will draw a total of 150MW power by calculating 22% losses. It was calculated that with 1000MW power capacity and assuming the system will use 1.5 minutes of electricity for each shot, the energy cost will be $ 2.5 per kg for each launch. In Table 9 the results of Kolm and the present author are presented as much as possible and the results are evaluated in comparison with each other. Similarly, in the EMSLS in this study very high switching voltages are necessary to energize the drive coils rapidly while the projectile package is nearby. Assuming a total mass driver of 1500 kg and selecting an engine mass of 246 kg, leaves about 200 kg for useful payload and about 150 kg for structural mass in this design study. 161038 According to the results of our EMSLS system cost parameters, investments [3] and energy costs are calculated as $27 per kg fire amortization of the launcher for a period of 10 years, 365 days per year, assuming 120 launches per day. For 3s fire duration, 1000 kwh/kg energy cost is calculated for launching the system to 2800m/s which is equal to extra fuel of 372 kg. Electromagnetic launching has advantages as far as the amount of payload is concerned. Finally, it is concluded that the energy and investment costs per unit mass are reduced by increasing the useful mass of the space vehicle which will lead to a reduction in acceleration and increase in unit mass of the space vehicle. However if input values in Table 4 are examined, in simulation table, the magnetic field value of 25 Tesla is very high. The voltage which is directly proportional with linear velocity is very high at 130000volt as well. The weight of the mass driver is limited to 1 meter diameter so that it provides very high accelerations but shorter launcher length. Finally, it is concluded that the energy and investment costs per unit mass are reduced by increasing the useful mass of the space vehicle which will lead to reduction in acceleration and increases in unit mass of the space vehicle. EMLS unit cost per kg is in the order of tens, the same figures are in the order of thousands whereas for chemically propelled space vehicles. EMLS is the only item that can be compared to chemical propellant systems as far as cost of the flight economies are considered. It is assumed that the rest of the orbital flights work similarly in both systems. Design of a space vehicle for Lagrange Colonization might be planned for a much heavier vehicle to reduce acceleration to 3 g and VOLUME 7, 2019 E. Inger: Mass Driver Design Traveling Earth to the Moon involving with 2000 km launcher length to transport human beings. Improvements and application of superconductors, magnetic levitation and related EMSLS technologies will be studied further. [10] P. A. Czysz and C. Bruno, Future Spacecraft Propulsion Systems: Enabling Technologies for Space Exploration. Chichester, U.K.: Praxis Publishing, 2006, p. 496. [11] H. Kolm. (Sep. 1980). Mass driver up-date. L5 News. Accessed: Sep. 23, 2019. [Online]. Available: https://space.nss.org/l5-news-massdriver-update/ V. TERMINOLOGY, SYMBOLS AND UNITS See Table10. REFERENCES [1] Lunar Base Applications of Superconductivity, Eagle Eng. Rep., NASA, Washington, DC, USA, Oct. 1988, nos. 88–218. [2] Electromagnetic Launch of Lunar Material, document NASA SP-509, May 2011. [3] E. Inger, ‘‘Electromagnetic launching systems to geosynchronously equatorial orbit in space and cost calculations,’’ IEEE Trans. Plasma Sci., vol. 45, no. 7, pp. 1663–1666, Jul. 2017. [4] B. Marder, ‘‘A coilgun design primer,’’ IEEE Trans. Magn., vol. 29, no. 1, pp. 701–705, Jan. 1993. [5] S.-W. Kim, H.-K. Jung, and S.-Y. Hahn, ‘‘Optimal design of multistage coilgun,’’ IEEE Trans. Magn., vol. 32, no. 2, pp. 505–508, Mar. 1996. [6] Accessed: Sep. 13, 2019. [Online]. Available: http://www. physicsclassroom.com/class/circles/Lesson-4/Mathematics-of-SatelliteMotion [7] J. S. Parker and R. L. Anderson, Low-Energy Lunar Trajectory Design. Pasadena, CA, USA: Jet Propulsion Laboratory, Jul. 2013. [8] C. Matthews, Aeronautical Engineer’s Data Book. Oxford, U.K.: Butterworth-Heineman, 2002. [9] C. Casaregola, K. Geurts, P. Pergola, L. Biagioni, and M. Andrenucci, ‘‘A VEGA dedicated electric propulsion transfer module to the moon,’’ in Proc. 30th Int. Electr. Propuls. Conf., Florence, Italy, Sep. 2007, pp. 1–10. VOLUME 7, 2019 ERK INGER graduated from the Faculty of Mechanical Engineering, Middle East Technical University (METU), in 1971. He received the M.S. degree from METU, in 1976. He started his professional career at Gazi University as a Research Assistant. He joined the TUBITAK Centre for Measurement Works of Guided Equipment, thereby becoming involved with military projects as a Research Engineer. In TUBITAK, he worked on ballistics and guidance control of missiles and rockets. He was a Project Supervisor in the BAIKS Project, concerned with software for fire control computers of artillery batteries. In 1985, he was with the private sector LAMAŞ, as a Factory Manager, producing tail wings for 500 lb. shells and T1, T2, and T3 targeting systems for mortars. In later years, he joined the TAFICS—Turkish Military Telecommunication Network Master Plan—Project. He was also with MKEK as an Investment Planning Manager. In 1990, he was appointed to the Board of Management and as a General Manager at ROKETSAN, until 2003. He also taught at the Faculty of Aeronautics, METU, as a part-time Lecturer in flight dynamics and stability control, aircraft performance, automatic control, and rocket and missile engineering, from 1983 to 2013. He was appointed as the Chairman of the National Boron Research Institute (BOREN), from 2004 to 2013. Since 2013, he has been with Atılım University. 161039