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 270 km/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

F = mg + mv^2 / r ;

ma= mg + mv^2/ r ;

a = g + v^2 / r ;

2.5 g = g + ( 270 e3 / 3600 )^2 / r ;

or 1.5 g =  ( 270 e3 / 3600 )^2 / r ;

or 1.5 * 9.8 =  ( 270 e3 / 3600 )^2 / r ;

r = 382.65 m <------ans

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