In a level banked turn at a fixed bank angle, what is the effect on turn radius when airspeed increases?

In a level banked turn at a fixed bank angle, what is the effect on turn radius when airspeed increases?

• A. Radius increases
• B. Radius decreases
• C. Radius remains the same
• D. Not enough data

Answer: (A)

In a level banked turn with a fixed bank angle, the lift must both support weight and provide the centripetal force to bend the flight path. Vertically, lift equals weight: L cos(phi) = W. So lift is L = W / cos(phi). The horizontal component, L sin(phi), provides the centripetal force for turning: m V^2 / R = L sin(phi). Substituting L gives m V^2 / R = (W / cos(phi)) sin(phi) = m g tan(phi). Cancel m and rearrange to V^2 / R = g tan(phi), so R = V^2 / (g tan(phi)). With the bank angle fixed, tan(phi) is constant, meaning radius grows with the square of speed. Therefore, increasing airspeed increases turn radius (the turn becomes less sharp at the same bank).

In a level banked turn with a fixed bank angle, the lift must both support weight and provide the centripetal force to bend the flight path. Vertically, lift equals weight: L cos(phi) = W. So lift is L = W / cos(phi). The horizontal component, L sin(phi), provides the centripetal force for turning: m V^2 / R = L sin(phi). Substituting L gives m V^2 / R = (W / cos(phi)) sin(phi) = m g tan(phi). Cancel m and rearrange to V^2 / R = g tan(phi), so R = V^2 / (g tan(phi)). With the bank angle fixed, tan(phi) is constant, meaning radius grows with the square of speed. Therefore, increasing airspeed increases turn radius (the turn becomes less sharp at the same bank).