PPRuNe Forums - View Single Post - Separation Of 2 Planes W/ Different Turn Radiuses
Old 17th March 2025 | 04:26
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MechEngr
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One solution is they collide almost immediately, with the tighter radius plane to the starboard of the larger radius plane.

Neglecting that the tighter radius will descend slightly faster if no trim or power changes are made ...

2.5 seconds * 800 fps = 2,000 ft.

Plane #1 will turn (2,000 ft/35,000 ft) radians
Relative to the start position it will go:
along the original direction 35,000 ft *sin(2/35) = 1998.9 feet
sideways from the original direction (35,000 ft - 35,000 ft * cos(2/35)) => 35,000 (1-cos(2/35)) ~= 57 feet

Plane #2 will turn (2000 ft/55,000 ft) radians
along the original direction 55,000 ft *sin(2/55) = 1999.56 ft
sideways from the original direction (55,000 ft - 55,000 ft * cos(2/55)) => 55,000 (1-cos(2/55)) ~= 36.36 ft

subtracting the second delta from the first:

along the original direction = 1998.9 ft - 1999.56 ft = -.648 ft, so plane #1 lags plane #2
sideways to the original direction = 57 ft - 36.36 ft = 20.8 ft so plane #1 moves sideways more than plane #2.

Neglecting the original offset, the change in the distances between the CGs = 20.78 ft and their paths will be diverging, instantaneously, by (2/35-2/55) radians or 1.19 degrees.
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