Coordinated Turn Radius and Rate

Tan(bank) = V^2/(g x radius), so radius = 0.08854 x airspeed(kt)^2 / tan(bank) -- depending only on speed and bank, not weight or aircraft type. At 120 kt and 30 degrees the radius is about 2,208 ft (0.36 nm) at 5.25 deg/s. Speed enters squared, so doubling it quadruples the radius, which is why a fast jet needs miles to turn while a trainer needs yards; a standard-rate turn is 3 deg/s (a 2-minute 360). Level coordinated flight assumed. A planning aid; the flight manual and the pilot in command govern.

turn_radius_ft = (airspeed_kt x 1.68781)^2 / (32.174 x tan(bank)) = 0.08854 x airspeed_kt^2 / tan(bank); rate_of_turn_deg_s = (v_fps / radius) x 180/pi.

Coordinated-turn radius and rate (FAA Airplane Flying Handbook; classical flight-dynamics balanced-turn relation), by name; the flight manual and the pilot in command govern.

The balanced-turn force balance is first-principles Newtonian mechanics; the airspeed and bank come from the flight instruments.

Estimate. AHJ and licensed professional govern.

Field names used by the API: airspeed_kt, bank_angle_deg, turn_radius_ft, rate_of_turn_deg_s

• Depends only on V and bank radius = V^2/(g tan bank) is independent of weight and aircraft type in coordinated level flightflight dynamics
• Standard rate 3 degrees per second (a 2-minute 360-degree turn)FAA AFH