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11. Mass Driver Appendices Purdue University Arch Pleumpanya Mass Driver Appendix | 1 11. Mass Driver Appendices Suhas Anand1, Alexander J. Chapa2, Kevin Huang3, Nicholas Martinez- Cruces4, Arch Pleumpanya5, Dylan Pranger6, Peter Salek7, William Sanders8, Erick Smith9, and Natasha Yarlagadda10 Purdue University, West Lafayette, Indiana, 47906, United States 1 Power and Thermal 2 Controls 3 Human Factors, Associate Editor for Mass Driver 4 Mission Design 5 Propulsion 6 CAD 7 Power and Thermal 8 CAD 9 CAD 10 Propulsion Purdue University Arch Pleumpanya Mass Driver Appendix | 2 Appendix. Mass Driver A. Sources: [1] Bilby, Curt R., and Nathan Nottke. "A Superconducting Quenchgun for Delivering Lunar Derived Oxygen to Lunar Orbit - NASA-CR-185161." 1990. [2] Burton, R. R., Crisman, R. P., Alexander, W. C., Grisset, J. D., Davis, J. G., and Brady, J. A., “Physical Fitness Program to Enhance Aircrew G Tolerance,” https://apps.dtic.mil/, Mar. 1988, pg 13, Available: https://apps.dtic.mil/dtic/tr/fulltext/u2/a204689.pdf. [3] C. Frueh, Space Traffic Management, AAE590 course script, Purdue University, 2019 Hall, N. (Ed.). (2015, May 5). [4] Centripetal Acceleration. (n.d.). Retrieved March 3, 2020, from http://hyperphysics.phy- astr.gsu.edu/hbase/cf.html. [5] Davey, K., “Designing with null flux coils,” IEEE Transactions on Magnetics, vol. 33, Sep. 1997, pp. 4327–4334. [6] Elert, G. (n.d.). Equations of Motion. Retrieved January 2020, from https://physics.info/motion-equations/. [7] Green, Michael A. “Cooling Large HTS Magnet Coils Using a Gas Free-Convection Cooling Loop Connected to Coolers.” IOP Conference Series: Materials Science and Engineering, vol. 502, 2019, p. 012100., doi:10.1088/1757-899x/502/1/012100. [8] Guo, Li, and Zhou, “Study of a Null-Flux Coil Electrodynamic Suspension Structure for Evacuated Tube Transportation,” Symmetry, vol. 11, Mar. 2019, p. 1239. Purdue University Arch Pleumpanya Mass Driver Appendix | 3 [9] He, J., and Rote, D. M., “Computer Model Simulation of Null-Flux Magnetic Suspension and Guidance,” Center for Transportation Research, Energy Systems Division, Argonne National Laboratory, Jun. 1992. [10] He, J., Rote, D., and Coffey, H., “Survey of foreign maglev systems,” US Army Corps of Engineers, Jan. 1992. [11] Jokic, M. D., & Longuski, J. M. (2004). Design of Tether Sling for Human Transportation System Between Earth and Mars. Journal of Spacecraft and Rockets, 41(6), 1010–1015. doi: 10.2514/1.2413. [12] Katorgin, B., Chvanov, V., Chelkis, F., Ford, R., and Tanner, L., “Atlas with RD-180 now,” 37th Joint Propulsion Conference and Exhibit, Salt Lake City, UT, 2001. [13] Lunar Reconnaissance Orbiter. (2019, July 11). Retrieved January 2020, from https://solarsystem.nasa.gov/missions/lro/in-depth/. [14] “Maglev: Magnetic Levitating Trains,” Electrical and Computer Engineering Design Handbook Available: https://sites.tufts.edu/eeseniordesignhandbook/2015/maglev- magnetic-levitating-trains/. [15] Mars Atmosphere Model - Metric Units. Retrieved January 2020, from https://www.grc.nasa.gov/WWW/K-12/airplane/atmosmrm.html. [16] Mars Odyssey. (2019, July 23). Retrieved January 2020, from https://solarsystem.nasa.gov/missions/mars-odyssey/in-depth/. [17] Masugata, K., “Hyper velocity acceleration by a pulsed coilgun using traveling magnetic field,” IEEE Transactions on Magnetics, Vol. 33, No. 6, pp. 4434-4438. Purdue University Arch Pleumpanya Mass Driver Appendix | 4 [18] NASA: Lunar Reconnaissance Orbiter. (2013). LUNAR RECONNAISSANCE ORBITER: Detailed Topography of the Moon. Retrieved from https://lunar.gsfc.nasa.gov/images/lithos/LRO_litho8-lunar_topography.pdf. [19] Nasar, S., and Boldea, I, “High-Speed Linear Induction Motors,” Linear motion electric machines, Wiley New York, 1976, pp. 53-133. [20] “New England Wire Technologies,” New England Wire Technologies Available: https://www.newenglandwire.com/application/the-repulsive-attractive-world-of-maglev/. [21] Ohsaki, H., “Review and update on MAGLEV,” European Cryogenics Day 2017 [22] Power. (n.d.). Retrieved January 2020, from https://www.physicsclassroom.com/class/energy/Lesson-1/Power. [23] R., G., P., A., and H., W., “Artificial gravity as a countermeasure for mitigating physiological deconditioning during long-duration space missions,” Frontiers In Systems Neuroscience Available: https://www.frontiersin.org/articles/10.3389/fnsys.2015.00092/full. [24] Redd, N. T. (2017, December 9). Olympus Mons: Giant Mountain of Mars. Retrieved January 2020, from https://www.space.com/20133-olympus-mons-giant-mountain-of- mars.html. [25] “Shape Effects on Drag.” NASA, NASA, www.grc.nasa.gov/www/k- 12/airplane/shaped.html. Purdue University Arch Pleumpanya Mass Driver Appendix | 5 [26] Slemon, G. R., “Linear induction motors,” Encyclopædia Britannica Available: https://www.britannica.com/technology/electric-motor/Linear-induction-motors. [27] Tarantola, A., “Why the Human Body Can't Handle Heavy Acceleration,” Gizmodo Available: https://gizmodo.com/why-the-human-body-cant- handle-heavy-acceleration-1640491171. [28] The Topography of Mars. (2009, January 12). Retrieved January 2020, from https://www.asc-csa.gc.ca/eng/astronomy/mars/topography.asp. [29] Vasantha Kumar, K., and Norfleet, W. T., “Issues on Human Acceleration Tolerance After Long-Duration Space Flights,” NASA Technical Memorandum, Oct. 1992, pg 11-24, Available: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930020462.pdf. [30] Wyrick, B., and Brown, J. R., “Acceleration in Aviation: G-Force,” faa.gov Available: https://www.faa.gov/pilots/safety/pilotsafetybrochures/media/acceleration.pdf. Purdue University Arch Pleumpanya Mass Driver Appendix | 6 B. Coilgun Acceleration Profile Analysis Initially when we were studying coilgun designs for our system, an analysis was done on the acceleration profile delivered by an induction coilgun. An induction coilgun exploits repulsive magnetic force to drive a loop diamagnetic material mounted to a non-magnetic projectile. This is in contrast to the reluctance coilgun which exploits attractive magnetic force to drive a ferromagnetic projectile. The analysis followed the equations outlined by Matsugata [17]. The mutual inductance between the projectile coil and the driving coil (each section within the coilgun) is the main parameter to be calculated. The driving force, 퐹 (and thus the acceleration, if the projectile mass is known), can be calculated using Eq. (A.1). 1 푑푀 2 퐹 = 퐼푝 퐿푝 (A1) 푀 푑푥푐 Figure 5 from Ref. [1] was reproduced to verify the MATLAB script used for this analysis and given here as Fig. A1. Our plot matches the original satisfactorily hence validating the script for further analysis. Purdue University Arch Pleumpanya Mass Driver Appendix | 7 Fig. A1: Force on Projectile by Coilgun. This plot is a reproduced result from Ref [1] of force profile in a single coilgun section. The architecture of our coilgun needed to be immense in scale relative to the original analysis. The dimensions were scaled up to match the taxi vehicle’s size. The launch stack was assumed to be 269 Mg. We chose each coilgun section to be 11 m in diameter and 50 long containing 50 coils. The coils are circular and wound such that no free space is permitted between them, therefore the coil wire is 1 m in diameter. The diamagnetic wire loop that needs to be mounted to the projectile is 9 m in diameter and 1 m long. The driving coil is energized at 785 kA which is 20% the maximum current rating for copper wires (500 A/cm2). The acceleration profile resulting from this design is given in Fig. A2. Purdue University Arch Pleumpanya Mass Driver Appendix | 8 Fig. A2: Acceleration for Single-Stage Coilgun. This plot shows the acceleration profile where coilgun is constantly energized. It can be observed that acceleration only occurs once the projectile has passed through the center of the coil section. From the entrance to the center (corresponding to -0.5 on the horizontal axis in Fig. A2), only deceleration occurs. Downrange of the exit (corresponding to 0.5 on the horizontal axis in Fig. A2), the projectile is still being accelerated at a decaying rate despite not being physically enclosed by the coil section anymore. It can be concluded that constantly energizing the coils will not produce net acceleration in the direction we desire. Once we synchronize the capacitor discharge such that the coil becomes energized right at the instant the projectile passes the center of the coil section, net acceleration can occur reaching almost 4 g at peak, as seen in Fig. A3. Purdue University Arch Pleumpanya Mass Driver Appendix | 9 Fig. A3: Acceleration for Single-Stage Coilgun. This plot shows the acceleration profile where coilgun is energized only when the projectile has passed the center of the section. Thus far, we have examined a single-stage coilgun. To qualitatively assess the acceleration profile of a multi-stage coilgun, we append the acceleration profiles and sum up overlapping portions. Figure A4 is an approximation of the acceleration profile of a multi-stage coilgun with five sections arranged in series. Thrust ripples can be observed clearly as the acceleration peaks near the exit of each section and drops almost instantaneously as it enters the successive section. Purdue University Arch Pleumpanya Mass Driver Appendix | 10 Fig. A4: Acceleration for Multi-Stage Coilgun. This plot shows the acceleration profile of a multi-stage coilgun with five sections arranged in series displaying pronounced thrust ripples. C. Kinematics of Launch A script was written to analyze the kinematics of a constant acceleration motion like the one our mass driver needs to execute. The script plots a value of acceleration and the associated duration of launch for varying track lengths. The analysis was done on both Luna and Mars. If a mass driver were to be constructed on Luna, the track length and launch duration associated with the limit of 2 g constant acceleration are 159 km and 2 minutes 7 seconds. The required forces on Luna and Mars are equal since the gravitational acceleration is almost perpendicular to the direction of launch. Purdue University Arch Pleumpanya Mass Driver Appendix | 11 Fig.
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