Min Radius and Max Rate of Turn

Minimum Radius

R=(1/CL.Sin @).(W/S).(1/d).(2/g)

Where CL = Coefficient of Lift
@ = Angle of Bank
W = Weight
S = Surface Area of Wing
d = Density of the air
g = Force of Gravity

It should be able to be seen then that to minimise the radius of turn the aircraft must be flown with the maximum coefficient of lift (ie. on the buffet) with an angle of bank as close to 90 degrees as possible. Light weight and therefore low wing loading (W/S) and high density (ie. low level) are also required.
This equation also reveals that radius of turn is independent of the speed that is flown, providing the aircraft is on the buffet. This occurs because at higher speeds higher load factors (ie. 'g') are possible.

Maximum Rate

RT=CL.V.Sin @.d.(S/W).(g/2)

Where CL= Coefficient of Lift
V = Airspeed
@ = Angle of Bank
W = Weight
S = Surface Area of Wing
d = Density of the air
g = Force of Gravity

To maximise the rate of turn (ie. the number of degrees per second the aircraft turns through the sky) the aircraft must be on the buffet (ie. maximum CL), flying as fast as is possible to sustain, at an angle of bank as close to 90 degrees as possible, at low level (ie. maximum density), large wing surface area and low weight.

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