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

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To determine the angle of bank required for a jet fighter to turn at a speed of 650 m/s with a turning radius of 850 km, the relationship between centripetal force and lift must be analyzed. The lift force acts perpendicular to the wings, and its component directed towards the center of the turn provides the necessary centripetal force. The equations derived include L*sin(theta) = m*v^2/r and L = mg/cos(theta), leading to the expression tan(theta) = v^2/(r*g). This approach allows for the calculation of the bank angle needed for the maneuver. The discussion emphasizes the physics principles involved in banking during a turn.
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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?
 
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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)
 
What is the expression for thew angle of banking?
 
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)
 
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