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

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Homework Help Overview

The problem involves determining the required angle of bank for a jet fighter executing a turn at a constant speed and a specified radius. The context is related to circular motion and forces acting on the aircraft during the maneuver.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the relationship between lift, gravity, and centripetal force in the context of a banked turn. There are attempts to derive equations related to the banking angle and its dependence on speed and radius.

Discussion Status

Some participants have provided equations relating to the forces involved in the turn and are exploring the relationships between these forces. There is an ongoing exploration of the expressions for the banking angle, but no consensus has been reached on a final approach.

Contextual Notes

Participants are working with assumptions about the forces acting on the jet fighter, including lift and gravity, and are attempting to relate these to the conditions of the turn. The discussion reflects a need for clarity on the definitions and relationships between the variables involved.

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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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