Pilots of high-performance fighter planes can be subjected to large centripetal

Question

Pilots of high-performance fighter planes can be subjected to large centripetal accelerations during high-speed turns. Because of these accelerations, the pilots are subjected to forces that can be much greater than their body weight, leading to an accumulation of blood in the abdomen and legs. As a result, the brain becomes starved for blood, and the pilot can lose consciousness ("black out"). The pilots wear "anti-G suits" to help keep the blood from draining out of the brain. To appreciate the forces that a fighter pilot must endure, consider the magnitude of the normal force that the pilot's seat exerts on him at the bottom of a dive. The plane is traveling at 205 m/s on a vertical circle of radius 745 m. Determine the ratio of the normal force to the magnitude of the pilot's weight. For comparison, note that black-out can occur for ratios as small as 2 if the pilot is not wearing an anti-G suit.

Pilots of high-performance fighter planes can be subjected to large centripetal accelerations during high-speed turns. Because of these accelerations, the pilots are subjected to forces that can be much greater than their body weight, leading to an accumulation of blood in the abdomen and legs. As a result, the brain becomes starved for blood, and the pilot can lose consciousness ("black out"). The pilots wear "anti-G suits" to help keep the blood from draining out of the brain. To appreciate the forces that a fighter pilot must endure, consider the magnitude of the normal force that the pilot's seat exerts on him at the bottom of a dive. The plane is traveling at 205 m/s on a vertical circle of radius 745 m. Determine the ratio of the normal force to the magnitude of the pilot's weight. For comparison, note that black-out can occur for ratios as small as 2 if the pilot is not wearing an anti-G suit.

Explanation / Answer

draw the free body diagram for the pilot at the bottom of this vertical circle

we write newton's second law for the pilot

sum of forces = ma

the forces are the normal force (acting up), the weight(acting down), and these combine to produce a centripetal force which acts toward the center of the circle, in this case, that is up

so we have

N - mg = mv^2/r

or N=m(g+v^2/r)

the ratio is: N/mg = (g+v^2/r)/g =(1+(v^2/(rg))

for the values v=205m/s, r=745m and g=9.8m/s/s

we have

N/mg =(1+(205^2)/745x9.8)) = 4288.265

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