THE APPLICATION OF NEWTONIAN PHYSICS IN SIMULATED AND EXPERIMENTAL MODEL ROCKETRY Tarung Bhimnathwala, Colette Bilynsky, Cara Giovanetti, David Hua, Katie Liu, Anand Nanduri, Max Nezdyur, Vineeth Puli, Grace Stridick, Farhan Toddywala, Meghan Wilmott, Jason Xu Advisor: Robert Murawski Assistant: Sam Zorn
Introduction ● Model Rocketry and Flight Simulations ● Theory and Rocket Equations ● OpenRocket and Experimental Launch ● Study 1: Apogee ● Study 2: Thrust ● Study 3: Effects of Payload ● Conclusions
Theory ● Newton’s 1st, 2nd, and 3rd Law 1. Law of inertia 𝑒𝑞 2. F net = 𝑒𝑢 3. Every action has an equal and opposite reaction ● Momentum-Impulse Equation: o Fdt = dp ● 4 forces acting on a rocket Drag → Friction o Thrust → Change in momentum from engine o Lift → Wind (Center of Pressure) o Weight → Gravity (Center of Mass) o ● Center of Mass must be above Center of Pressure
Theory ● Dynamics of the rocket system and Tsiolkovsky’s rocket equation* o Start: Definition of momentum p t = mv o After some time dt p t + dt = (m - dm e )(v + dv)+ dm e ( v +dv - v e ) o *Assumptions, valid only in deep space, no external forces 𝑒𝑞 F net = 𝑒𝑢 = 0 o Further simplification and division, dm e = - dm −𝑤 𝑓 dv = 𝑛 dm o Finally, integrating…Tsiolkovsky’s Rocket Equation Δv = v e ln ( m o 𝑛 )
Theory ● New equation accounting for gravity and drag o Assume gravity/mass/thrust constants o Integrate for velocity as a function of time o Integrate for position as a function of time of rocket flight
Theory ● Calculations for post-thrust motion, only gravitation and drag o Integrate for time as a function of velocity o Take second integral for function of position after the thrust force is exhausted
Model Construction ● Used three Estes model rocket designs Alpha Viking Generic E2X ● Viking: unique fin arrangements
OpenRocket ● Flight trajectory simulation ● Allows for specific rocket design parameters ● Considers all physics and flight ● Utilized in ideal conditions – no wind or turbulence ● Guideline prior to field testing
Experimental Procedure ● Apogee comparison: launch experiment vs. OpenRocket simulation ● Data collection o “Anglers” and trigonometry o Apogee o Time of flight
[Video]
Study 1: Model Comparisons Apogee vs. Mass
Study 1
Study 2: Thrust Tracker Software Mathematica
Estes A8-3 Engine Thrust Profile maximum thrust point: (.226s, 9.73N) equation of thrust vs. time: T(t)=bt b=9.73N/.226s b=43.05 N/s
Example Launch — Viking cubic regression using Mathematica : y(t)=905.613t 3 905.613 ft/s 3 =276.031m/s 3 In this case T>>W and D is negligible, so the equation can be simplified to: = 276.031m/s 3 payload: .02929 kg b =6(.02929)(276.031)=48.51 N/s T(t)=48.51t 12.68% error
Study 3: Payload
Study 3cont.
Conclusion ● Implications of Results ● OpenRocket o Sources of error ● Tsiolkovsky’s Equation ● Newtonian Physics
References 1. Niskanen S. 2009 May 20. Development of an Open Source model rocket simulation software [Internet]. Helsinki University of Technology; [2009 May 20, cited 2015 Jul 29] . Available from: http://openrocket.sourceforge.net/thesis.pdf 2. Benson T. 2014 Jun 12. Brief History of Rockets [Internet]. NASA; [2014 Jun 12, cited 2015 Jul 24] . Available from: https://www.grc.nasa.gov/www/k-12/TRC/Rockets/history_of_rockets.html 3. Timeline: 50 Years of Spaceflight [Internet]. 2012 Sep 28. Purch; [2012 Sep 28, cited 2015 Jul 24] . Available from: http://www.space.com/4422-timeline-50-years-spaceflight.html 4. Timeline - Brief History of Rockets [Internet]. 2011 Nov 30. University of Waikato; [2011 Nov 30, cited 2015 Jul 24] . Available from: http://sciencelearn.org.nz/Contexts/Rockets/Timeline#top 5. James D. Balloon Staging [Internet]. NASA; [cited 2015 July 24] . Available from: http://quest.nasa.gov/space/teachers/rockets/act7.html 6. Redd NT. 2013 Feb 27. Konstantin Tsiolkovsky: Russian Father of Rocketry [Internet]. Purch; [2013 Feb 27, cited 2015 Jul 24] . Available from: http://www.space.com/19994-konstantin-tsiolkovsky.html 7. Loff S. 2015 Jul 16. Apollo 11 [Internet]. NASA; [2015 Jul 16, cited 2015 Jul 25] . Available from: https://www.nasa.gov/mission_pages/apollo/missions/apollo11.html 8. Garcia M. 2015 Jul 23. International Space Station [Internet]. NASA; [2015 Jul 23, cited 2015 Jul 25] . Available from: http://www.nasa.gov/mission_pages/station/main/index.html
References (cont’d) 9. Garber S, Launius R. 2005 Jul 25. A Brief History of NASA [Internet]. NASA; [2005 Jul 25, cited 2015 Jul 25] . Available from: http://history.nasa.gov/factsheet.htm 10. Brown D. 2015. Tracker: Video Analysis and Marketing Tool [Internet].comPADRE; [cited 2015 Jul 29] . Available from: https://www.cabrillo.edu/~dbrown/tracker/ 11. Wolfram Mathematica [Internet]. 2015. cited 2015 Jul 29] . Available from: http://www.wolfram.com/mathematica/ 12. Estes A8 [Internet]. 1998. NAR Standards and Testing; [ cited 2015 Jul 29] . Available from: http://www.nar.org/SandT/pdf/Estes/A8.pdf 13. Kluger J. 2010 Feb 02. No Liftoff: Obama's Plan Grounds NASA [Internet]. Time, Inc.; [2010 Feb 02, cited 2015 Jul 20] . Available from: http://content.time.com/time/health/article/0,8599,1958230,00.html 14. Junod T. 2012 Nov 15. Elon Musk: Triumph of His Will [Internet]. Hearst Communications Inc.; [2012 Nov 15, cited 2015 Jul 25] . Available from: http://www.esquire.com/news-politics/a16681/elon-musk-interview-1212/ 15. Howell E. 2015 Jan 09. SpaceX’s Elon Musk to Reveal Mars Colonization Ideas This Year [Internet]. Purch; [2015 Jan 09, cited 2015 Jul 25] . Available from: http://www.space.com/28215-elon-musk-spacex-mars-colony-idea.htm 16. Wall M. 2015 Jul 20. After Epic Pluto Flyby, What's Next for New Horizons? [Internet]. Yahoo!; [2015 Jul 20, cited 2015 Jul 20] . Available from: http://news.yahoo.com/epic-pluto-flyby-whats-next-nasas-horizons-164533597.html
Acknowledgements Team Elmer would like to give a special thanks to: ● Dr. Robert Murawski and Sam Zorn, team project advisors ● Dr. Adam Cassano and Dr. Steve Surace, Governor’s School co -directors ● AT&T ● Bayer Healthcare ● Independent College Fund of New Jersey/Johnson & Johnson ● The Overdeck Family Foundation ● NJGSS Alumnae, Parents, and Corporate Matching Funds ● The State of New Jersey ● Board of Overseers, New Jersey Governor’s School ● Sir Isaac Newton and Konstantin Tsiolkovsky
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