What Is the Radius of an Arc for a Pilot Experiencing 5G at 700m/s?

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SUMMARY

The discussion focuses on calculating the radius of a circular arc for a pilot experiencing a 5G force while traveling at a speed of 700 m/s. The key equations involved are centripetal acceleration, expressed as a = v²/r, and the normal force, where the total acceleration is 5 times the gravitational acceleration (5G = 5 * 9.81 m/s²). The correct approach to find the radius involves substituting the known values into the equation r = v²/a, leading to a definitive calculation of the radius based on the given parameters.

PREREQUISITES
  • Understanding of centripetal acceleration (a = v²/r)
  • Knowledge of normal force and gravitational force concepts
  • Familiarity with basic physics equations involving force (F = ma)
  • Ability to manipulate algebraic equations for problem-solving
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  • Calculate the radius using the formula r = v²/a with v = 700 m/s and a = 5 * 9.81 m/s²
  • Explore the implications of G-forces on pilot training and aircraft design
  • Research the effects of high G-forces on human physiology
  • Learn about circular motion dynamics and its applications in aviation
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Aerospace engineers, physics students, pilots, and anyone interested in the dynamics of flight and the effects of acceleration on pilots.

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Homework Statement


Im having trouble figuring out which equation to use for this problem. The problem states: "Consider a pilot at the lowest point of a circular arc banking upward. Find the tightest radius arc that an untrained individual can fly ( a total of +5 G, G standing for the normal force the accelerating aircraft is exerting on the pilot. For example, 6G force would be exerting a normal force 6 times the persons weight.). They are traveling at 700m/s.


Homework Equations


Since this involves normal force, I thought I could somehow use: the sum of F=ma and Fw=mg
In addition I tried using a=v squared/r and/or v=2(pi)r/T


The Attempt at a Solution


In an attempt to try to solve this problem I tried using Fn= 5N in the equation Fn-Fw=ma By finding acceleration I could then use a=v squared/r to solve for r, but I don't have enough variables to plug into the first equation.
So I tried using v=2(pi)r/T giving me 700m/s=2(pi)r/T so then I could find r this way, However I do not know the value for T.
Am I using the completely wrong equations? If not, what am I doing wrong?
 
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Welcome to PF.

I'd suggest drawing a diagram and making sure how much acceleration the plane will impart and how much is just a result of gravity.

As to your equation, you want to consider the centripetal acceleration here.
 
I could then use a=v squared/r to solve for r
I think you have it here. r = v^2/a
Your acceleration is 5 times 9.81.
 

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