What Angle of Bank Is Required for a Jet Fighter's Turn?

[skyisthelimit]

Homework Statement

The turning circle of a jet fighter when flying at a constant speed of 650m/s has a radius of 850km. What angle of bank must the plane have to achieve this manouevre?

Homework Equations

Angular velocity? Centipetal Force? I'm assuming.

The Attempt at a Solution

Well, I've calculated the angular velocity, now what?

 

[RTW69]

This is similar to a car making a banked turn. The lift is normal to the tilted wings. The angle between the vertical and the lift force is the bank angle. Force due to gravity acts down. The component of the lift acting toward the center of the turn equals the centripetal force L*sin(theta)

 

[rl.bhat]

What is the expression for thew angle of banking?

 

[RTW69]

L*sin(theta)=m*v^2/r (1) where L is lift, Theta is angle between vertical and lift force

L=mg/cos(theta) (2)

2 eqns/2 unknowns

tan(theta)=v^2/(r*g)