lecture_33

lecture_33 - 16.512, Rocket Propulsion Prof. Manuel...

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16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 33: Performance to LEO V Calculations for Launches to Low Earth Orbit (LEO) Ideal Earth-to-orbit launch α ∆= ' 12 E Vco s R vR µµ =− 2' 2 22 E VV RR µ ⎛⎞ = ∆− ⎜⎟ ⎝⎠ 2 1 1 2 E R Vcos 2 1 2 2 2 1 V R cos R 1 2 2 1 2 1 E E E R R V R R cos R = c v R αα −− ∆= − = = 2 2 2 2 11 '2 2 E E EE c E E E R Vvv c o s c o s R R R R cos cos VVV ∆+ () η ηη =+ 21 1 / V cos cos cos R R R = ηα + + 1 1 / Vc o s cos R (increasing f.of ) + 2 1 2 1 / MIN E V R For 0 = 16.512, Rocket Propulsion Lecture 33 Prof. Manuel Martinez-Sanchez Page 1 of 9
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Note: Max at 0.064178 99,260 Rk m η =→ = (worst altitude) 1.5363 / MIN F MAX V R µ ⎛⎞ ⎜⎟ = ⎝⎠ 7910 / ms R = ε −= 1 1 = + 1 1 + 1 1 + += + 2 1 1 () εε + + ± 2 2 1 2 1 ++ = + 22 13 3 3 1 ... 1 ... 1/ 21 28 4 2 3 1 ... 4 0 α = 0.9 1.05128 = (approx. 1.05093) // VR V 0.15095 = (GEO, R=42,200Km) 0.23951 = = 1 , 26,580 2 day Km 0.87620 = ( ) = 900 ZK m 0.91392 = ( ) = 600 m 0.95502 = ( ) = 300 m 0 0 = 1.50775 (11,918 m/s) 1.45534 (11,504 m/s) 1.06387 (8,409 m/s) 1.04399 (8252 m/s) 1.02275 (8,084 m/s) 0 15 = 1.51366 (11,965 m/s) 1.46373 (11,570 m/s) 1.07960 (8,534 m/s) 1.05952 (8375 m/s) 1.03748 (8201 m/s) 0 30 = 1.53109 (12,102 m/s) 1.48854 (11,766 m/s) 1.12032 (8,856 m/s) 1.09755 (8676 m/s) 1.06953 (8454 m/s) +− ± 2 1 5 1 43 2 / E V R ± 2 2 7 2 / E V R NOTE: So, for LEO, mainly (apogee kick) 1 V Sticking to 0 = , variation with R 16.512, Rocket Propulsion Lecture 33 Prof. Manuel Martinez-Sanchez Page 2 of 9
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1 1.05 R R η == 1.1 1.05 2 4 6 10 15.6 / V R µ 1.02041 1.04651 1.18164 1.28446 1.44868 1.49934 1.52978 1.53626 Effects of Earth’s Rotation (a) reduction V = 463 / sec Rm β is launch azimuth w.r.t East ( 0 α = , near-horizontal launch) 1 V = rocket-imparted V Starting velocity (abs.) is now ( ) () ∈∈ =∆ +Ω +∆ Ω 22 11 1 2 v V R cos L V R cos L cos So,
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This note was uploaded on 11/07/2011 for the course AERO 16.512 taught by Professor Manuelmartinez-sanchez during the Fall '05 term at MIT.

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lecture_33 - 16.512, Rocket Propulsion Prof. Manuel...

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