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)

 

[rwisz]

I would approach this problem by first understanding the concept of angle of bank and its relation to turning radius. Angle of bank refers to the angle at which an aircraft's wings are tilted in order to make a turn. This angle is also directly related to the turning radius of the aircraft.

Next, I would use the given information of the aircraft's speed and turning radius to calculate the necessary angle of bank. This can be done by using the formula for centripetal force, which is necessary to maintain a circular motion. By equating the centripetal force to the weight of the aircraft, we can solve for the angle of bank.

Finally, I would also consider other factors such as air resistance and the aircraft's weight in order to ensure that the calculated angle of bank is feasible and safe for the aircraft to perform.

Overall, the angle of bank of a plane is an important factor to consider when making turns and it is essential for pilots to have a good understanding of this concept in order to safely maneuver their aircraft.