G Force vs Speed


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.


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=v2/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=v2/800, or v2=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
This is also the magnitude of the force of the pilot on the seat by Newton's third law.

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