Reentry Air Data System for a Sub-orbital Spacecraft Based on X-34 ...

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2007 USU Industry Day Angle of Sideslip Solution • Once we know Angle of Attack, we can calculate Angle of Sideslip using any combination of ports exclusive of sets with all ports on the vertical meridian 2 A'tan β + 2B'tanβ + C'= 0 where a b ind ind ( ik 2 j ji 2 k kj 2 i ) ( ik j j ji k k kj i i ) ( ik 2 j ji 2 k kj 2 i ) A'= Γ b +Γ b +Γ b B'= Γ a b +Γ a b +Γ ab C'= Γ a +Γ a +Γ a = cosα cos λ + sinα sin λ cosφ ( ijk ) ind ( ijk ) ind ( ijk ) ( ijk ) = sin λ sinφ ( ijk ) ( ijk ) ( ijk ) 12
2007 USU Industry Day Altitude & Mach calculation • Three unknowns left in system, 5+ pressure measurements => over determined system. Solved with pseudo inverse −1 ⎡ ⎡Θ1 1⎤⎤ ⎡ ⎡p1⎤⎤ q ⎢ ⎥ ⎢ ⎥ ⎡ c ⎤ ⎢ 2 1 2 n 2 1 ⎥ ⎢ 1 2 n p ⎥ ⎢⎡Θ Θ L Θ ⎤ 2 [ Q] ⎢ Θ ⎥⎥ ⎢⎡Θ Θ L Θ ⎤ [ Q] ⎥ ⎢ ⎥ = ⎢ ⎥ ⎢ n× n n× n p 1 1 1 ⎥ ⎢ 1 1 1 ⎥ ⎣ ∞ ⎦ ⎢⎣ L ⎦ ⎢ M M⎥⎥ ⎢⎣ L ⎦ ⎢ M ⎥⎥ ⎢ ⎢ ⎥⎥ ⎢ ⎢ ⎥⎥ ⎢⎣ ⎢⎣ Θn 1⎥⎦⎥⎦ ⎢⎣ ⎢⎣pn⎥⎦⎥⎦ where 2 2 Θ = cos θ + εsinθ [ Q] i i i n× n ⎡q10 L 0 ⎤ ⎢ 0 q2 0 ⎥ ⎢ M = ⎥ ⎢ M 0 O 0 ⎥ ⎢ ⎥ ⎢⎣0 L 0 qn ⎥⎦ This can be simplified to ⎡ ⎢ n ∑qi n n ⎤⎡ ⎤ −∑qiΘi⎥⎢∑pq i iΘi⎥ i= 1 i= 1 i= 1 ⎢ ⎥⎢ ⎥ n n n ⎢ 2 ⎥⎢ ⎥ − qiΘi qiΘi pq i i ⎡qc⎤ ⎢ ∑ ∑ ⎥⎢ ∑ ⎥ 2 ⎣ i= 1 i= 1 ⎦⎣ i= 1 ⎦ ⎢ ⎥ = n n n 2 ⎣p∞⎦ ⎛ 2 ⎞⎛ ⎞ ⎛ ⎞ ⎜∑qiΘi ⎟⎜∑qi ⎟−⎜∑qiΘi 13 ⎟ ⎝ i= 1 ⎠⎝ i= 1 ⎠ ⎝ i= 1 ⎠
Page 1 and 2: Reentry Ai
Page 3 and 4: 2007 USU Industry Day Background co
Page 5 and 6: 2007 USU Industry Day X-34 Trajecto
Page 7 and 8: 2007 USU Industry Day Solution: •
Page 9 and 10: 2007 USU Industry Day Pressure Mode
Page 11: 2007 USU Industry Day Angle of Atta
Page 15 and 16: 2007 USU Industry Day Mach calculat
Page 17 and 18: No system Noise Demonstrat es solve
Page 19 and 20: 2007 USU Industry Day How do we red
Page 21 and 22: 2007 USU Industry Day Noise reducti
Page 23 and 24: 2007 USU Industry Day FADS
Page 25 and 26: 2007 USU Industry Day X-34 FADS <st
Page 27 and 28: 2007 USU Industry Day Questions? 27
Page 29: 2007 USU Industry Day Mach Number -

Reentry Air Data System for a Sub-orbital Spacecraft Based on X-34 ...

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