G Force vs Speed

## Question:

Determine the maximum constant speed at which a pilot may travel
in a vertical curve with a radius of curvature of 800m, so that
the maximum force he experiences is 8 gs. If he has a mass of
70kg, what is the maximum normal force he exerts on his seat at
this speed.
## Answer:

The maximum gs the pilot will experience will be at the bottom of
the curve where gravity is pulling him downward and his seat is
pushing him upward due to his circular path. The centripetal
acceleration due to the circular path is
ac=v^{2}/r where v is the tangential velocity
(speed) of the aircraft and r is the radius of the loop. In this
case 7gs are allowed for centripetal acceleration, with 1
resulting from the Earth's gravitational attraction for a
total of 8. So 7*9.8=v^{2}/800,
or v^{2}=54880, or v=234m/s. The force required to hold the 70kg
pilot in this circular path (provided by his seat) at the bottom
of the loop is

Fs=8*9.8m/s/s*70kg=5488N.

This is also the magnitude of the force of the pilot on the seat
by Newton's third law.
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