lecture1b

lecture1b - 16.522, Space Propulsion Prof. Manuel...

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16.522, Space Propulsion Lecture 1b Prof. Manuel Martinez-Sanchez Page 1 of 6 16.522, Space Propulsion Prof. Manuel Martinez-Sanchez Lecture 1b: Review of Rocket Propulsion The only practical way to accelerate something in free space is by reaction. The idea is the same as in air breathing propulsion (to push something backwards) but in rockets the “something” must be inside and is lost. Here is a revealing derivation of the thrust equation for vacuum : () () () ( ) ( ) ( ) t 0 Mom .t=Mtvt+ mt ' vt '-ct ' d t '=Con s tan t ⎡⎤ ⎣⎦ i () dMom =0 dt dv dM M+ v + m v - c = 0 dt dt i But dM dv m=- M =mc dt dt ii call this thrust, F. Notice dMv =F-vm=m c-v dt which can be (+) or (-) Using the same technique, the kinetic energy of the system rocket-jet is () () () t 2 2 0 11 KE = Mv + m t' v t' - c t' dt' 22 i So, 2 2 dKE dv 1 dM 1 1 =Mv + v m v +c -2vc mc dt dt 2 dt 2 2 += mcv i m i So, if thermal (or electrical) energy is expended internally at the rate E, i and converted to total kinetic energy with efficiency th e1. (or ) η η ; i.e., no drag, no interaction of molecules with ambient air
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16.522, Space Propulsion Lecture 1b Prof. Manuel Martinez-Sanchez Page 2 of 6 () th dKE =E , dt η i then 2 1 E= mc 2 η ii jet kinetic power Note that we counted both vehicle and wake KE as produced by E i , and this is unambiguous. If we try to define “useful Propulsive work” as Fv = mcv, i then we find that the “propulsive efficiency” prop 2 th F.v mvc 2v == 1 c E mc 2 = η η i i i is arbitrarily high!
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lecture1b - 16.522, Space Propulsion Prof. Manuel...

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