Rocket Equation, Dynamics, and LaunchingKen ChenCOSMOS 2013C3 Engineering MechanicsWhy Rockets? Imagine a world where you didnt have these: Cell phones Television Internet GPS Navigation Rockets are used for: Space transportation/exploration Satellite communications Military weaponryThank rockets!Parts of a Rockethttp://exploration.grc.nasa.gov/education/rocket/Images/rockpartifForces on a Rocket On Center of Gravity (CG) Weight Thrust (mostly) On Center of Pressure (CP)(Aerodynamic) Lift Draghttp://exploration.grc.nasa.gov/education/rocket/rktaero.htlThrust Thrust-Newtons third law Rocket pushes on propellant, propellant pushes back on rocket Thrust equation: Ways to increase thrust: Maximize mass flow rate Maximize exit velocity to incoming velocityCorrection term Pressure differencee e e thrustA p p v m F + = ) (0e eA p p ) (0Drag Frictional drag Caused by friction of fluid against the surface of the body Pressure/Form drag Different shapes and sizes Vortices in the wake of the body Wave drag Common at transonic and supersonic speeds Can reach up to 4x subsonic dragDAC v D221 =Control CP below CG stable equilibrium Gimbaled Thrust Nozzle can be shifted/rotated; changes direction of thrust Vernier Rocket Small additional rocket engineshttp://exploration.grc.nasa.gov/education/rocket/rktcontrl.htmlKonstantin E. Tsiolkovsky (1857-1935) Early education impaired by deafness College Moscow Studied mathematics and science Monoplane Wind tunnelhttp://www.allstar.fiu.edu/aero/images/Tsiolkovsky.jpgTsiolkovskys Contributions Rocket equation Still remains the basis of all rocket dynamics today Founder of rocket dynamics Understood dynamics of firework rockets through math and physics Anthropocosmism Humans will dominate space Inspired several other great minds in rocketryRobert H. Goddard (1882-1945) Masterful physicist and inventor Built/tested first liquid fuel rocket in 1926 Patented multi-stage rocket in 1914 German V2 missiles Steering, vaneshttp://www.rugusavay.com/wp-content/uploads/2013/03/Robert-Goddard-4.jpgDerivation: Conservation of momentumTsiolkovsky Rocket Equation||.|

\| = AfeqmmV V0ln0 = =dtdpF ) ( ) ( t p dt t p dp + =v m t p = ) (mdm mdmvev dv v + ) () ( ) ( ) ( ) (ev dv v dm dv v dm m dt t p + + + = +dv v +mv v dv v dm dv v dm m dpe + + + = ) ( ) ( ) (dm v mdv dmdv dmdv vdm vdm mv mv dpe + + + =0 = = dm v mdv dpe0 = + = dm v mdv dpeFlip signTsiolkovsky Rocket Equation (cont.)0 = + = dm v mdv dpedmmvdve =dmmv dvf fmmvve =} }0 01)) ln( ) (ln(0 0m m v v vf e f = ||.|

\|= Afemmv v0lnIdeal Rocket EquationA parallel:Newtons Second LawConstant MassVariable Massa m Fnet =dtdmvdtdvmdtmv dFnet + = =) (Specific Impulse Isp A way to measure engine efficiency Can also be used to determine thrustg mFIsp=What actually happens -Launching Potentially dangerous Astronauts bear about 3 gs of acceleration Requires a high amount of precision Sound energy can cause damage Liftoff process Entire process controlled by computers Increase in air pressure overstressing Need enough thrustFuture Rocket Dynamics Nuclear Propulsion Abandoned in 1972 (Project Rover) Comeback?ANTIMATTER Propulsion Involves the annihilation of matter Efficiency is incomparable interstellar missionshttp://static.ddmcdn.com/gif/antimatter-1.jpgMore on Antimatter Propulsion When combining electron with anti-electron Photons (gamma rays) Proton with anti-proton Pions Decay into muons and neutrinos Eventually all annihilate or decay into massless particles, photons, and neutrinos Facts Exhaust velocity ~0.95 c Storage and production of antiprotons 1 ng/year Comparison Apollo 11 took 4 days to reach the moon In 4 days, a pion antimatter rocket can travel from Earth to Sun 350 times 2 ++ e eon n n p p t t t + + + +References "Basic Rocket Motion." Guided Tours. Ed. Tom Benson. NASA, n.d. Web. 29 J uly 2013. Braeunig, Robert A. "Basics of Space Flight: Rocket Propulsion." Rocket and Space Technology. N.p., 2012. Web. 29 J uly 2013. Brewster, Isaac. "The Physics Behind The Rocket." The Physics of Rockets. University of Alaska Fairbanks, 31 Oct. 2000. Web. 29 J uly 2013. Dunbar, Brian. "Konstantin E. Tsiolkovsky." NASA. NASA, 20 Sept. 2010. Web. 01 Aug. 2013. Dunbar, Brian. "Societal Impact of the Space Age." NASA. NASA, 07 Nov. 2005. Web. 29 J uly 2013. Dunbar, Brian. "What Is a Rocket?" NASA. NASA, 12 J uly 2011. Web. 29 J uly 2013. Garner, Rob. "Robert H. Goddard." NASA. NASA, 28 J uly 2013. Web. 01 Aug. 2013. Hafez, Mohamed M. "COSMOS Engineering Mechanics." COSMOS 2013. Davis, California. J uly 2013. Lecture.References (cont.) Keith, Edward L. "Fundamentals of Rockets and Missiles." Laurel, Maryland. Lecture. Krempetz, Kurt. "Freeflight Trimming." AMA Glider. Academy of Model Aeronautics, May 2006. Web. 29 J uly 2013. Portland State Aerospace Society. "Simple Rocket Science." Simplerockets 1d. Portland State University, 02 Mar. 2010. Web. 29 J uly 2013. Qualitative Reasoning Group. "Propulsion." How Are Rockets Designed? Northwestern University, n.d. Web. 29 J uly 2013. Turner, Martin J . L. Rocket and Spacecraft Propulsion: Principles, Practice and New Developments. Berlin: Springer, 2009. Print. Walter, Ulrich. Astronautics. Weinheim: Wiley-VCH, 2008. Print. Wilkinson, Peter. "Rocket Launch and Reentry." Senior Science. St. Francis Xavier's College, Hamilton, n.d. Web.