Stunt pilots and fighter pilots who fly at high speeds in a downward-curving arc

Question

Stunt pilots and fighter pilots who fly at high speeds in a downward-curving arc may experience a “red out,” in which blood is forced upward into the flier’s head, potentially swelling or breaking capillaries in the eyes and leading to a reddening of vision and even loss of consciousness. This effect can occur when the non-gravitational part of the centripetal acceleration exceeds 2.5g's.

For a stunt plane flying at a speed of 390km/h , what is the minimum radius of downward curve a pilot can achieve without experiencing a red out at the top of the arc? (Hint: Remember that gravity provides part of the centripetal acceleration at the top of the arc; it’s the acceleration required in excess of gravity that causes this problem.)

Explanation / Answer

centripetal accleration a = 2.5 g plane speed v = 390 km/h ( 5/18 )                          =108.33 m/s minium radius of curve r = v2/a                                         = ( 108.33 m/s)^2/ 2( 9.8 m/s^2)                                        = 478.99 m

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