Assume D=.5C(rho)AV^2 gives the drag force on a pilot plus ejection seat just af

Question

Assume D=.5C(rho)AV^2 gives the drag force on a pilot plus ejection seat just after they are ejected from a plane traveling horizontally at 1500 km/h. Assume also that the mass of the seat is equal to the mass of the pilot and that the drag coefficient is that of a sky diver. Assume the pilot's mass is 82 kg and using vt = 60 m/s for a single sky diver estimate the magnitudes of (a) the drag force on the pilot + seat and (b) the ratio of the horizontal deceleration to g, both just after ejection. (The result of (a) should indicate an engineering requirement: The seat must include a protective barrier to deflect the initial wind blast away from the pilot's head.)

Explanation / Answer

vt = sqrt(2Fg/Crho*A) = C*rho*A = 2mg/vt^2

here vt = 60 m/s

m = 77 kg

v = 1300km/h = 361.11 m/s

D = 1/2 * C*rho*A*v^2 = 1/2 * ( 2mg/vt^2) *v^2 = mg(v/vt)^2

D = 27333.38 N = 2.73 x 10^4 N

part b )

apply newtion seond law in horizontal direction

m = 2m

a = D/2m = g*(v/vt)^2/2 = 18.11 g

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