For a coordinated turn at constant altitude with a fixed angle of bank and airspeed, for a given bank and airspeed, the rate and radius of turn will do what?

For a coordinated turn at constant altitude with a fixed angle of bank and airspeed, for a given bank and airspeed, the rate and radius of turn will do what?

• A. The rate will increase with airspeed; the radius will decrease
• B. The rate and radius depend on bank and airspeed
• C. For a given bank and airspeed, the rate and radius do not vary
• D. The rate will decrease with bank angle

Answer: (C)

In a coordinated level turn, lift provides the centripetal force needed to bend the flight path, while the vertical component of lift balances weight. From balancing vertical forces, L cos φ = mg, so L = mg / cos φ. The horizontal component L sin φ then provides the centripetal force: m v^2 / R = L sin φ = mg tan φ. Solving gives the turning radius R = v^2 / (g tan φ). The rate of turn is the angular rate ω = v / R, which simplifies to ω = g tan φ / v. Therefore, with a fixed bank angle and a fixed airspeed, both the radius and the rate of turn are fixed and do not vary during the turn. If either bank angle or speed changes, those quantities would change according to the relationships above.

In a coordinated level turn, lift provides the centripetal force needed to bend the flight path, while the vertical component of lift balances weight. From balancing vertical forces, L cos φ = mg, so L = mg / cos φ. The horizontal component L sin φ then provides the centripetal force: m v^2 / R = L sin φ = mg tan φ. Solving gives the turning radius R = v^2 / (g tan φ). The rate of turn is the angular rate ω = v / R, which simplifies to ω = g tan φ / v. Therefore, with a fixed bank angle and a fixed airspeed, both the radius and the rate of turn are fixed and do not vary during the turn. If either bank angle or speed changes, those quantities would change according to the relationships above.