MAE142_Lecture6

MAE142_Lecture6 - Translational Velocity Local Velocity...

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Translational Velocity Local Velocity Trajectory Simulation Plotting in KML MAE 142 SR-71 (NASA Image)
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2 MAE 142 Ellipsoidal Earth Model The time rate-of-change in vehicle position over an ellipsoidal Earth model (such as the WGS-84 reference ellipse) is computed using the following equations: ˙= V N R x h ˙ = V E R y h cos ˙ h =− V D R x = a 1 e 2 [ 1 e 2 sin 2 ] 3 / 2 R y = a [ 1 e 2 sin 2 ] 1 / 2 = latitude = longitude h = altitude above ellipse V N = velocity north V E = velocity east V D = velocity down a = Earth semimajor axis e = eccentricity a Rx Ry Equator 6378 km 6335 km 6378 km Poles 6378 km 6399 km 6399 km
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MAE 142 Spherical Earth Model An average Earth radius (R E ) is typically used for the spherical Earth approximation. ˙= V N R E h ˙ = V E R E h cos ˙ h =− V D = latitude = longitude h = altitude above ellipse R E 6367 km V N = velocity north V E = velocity east V D = velocity down
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MAE142_Lecture6 - Translational Velocity Local Velocity...

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