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 330 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 gravitythat causes this problem.)

Explanation / Answer

Let a = non-gravitational centripetal acceleration
=> a - g < 2.5g
=> a < 3.5g
=> 3.5g < v^2/r
=> r < v^2/3.5g
=> r < (330000/3600)^2/(3.5 * 9.81)
=> r (minimum) = 244 m

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