The formula for calculating the angle of bank for a specific true airspeed (TAS) in SI units (or other coherent system) is:[3]
where is the angle of bank, is true airspeed, is the radius of the turn, and is the acceleration due to gravity.
For a rate-one turn and velocity in knots (nautical miles per hour, symbol kn), this comes to
.
A convenient approximation for the bank angle in degrees is
For aircraft holding purposes, the International Civil Aviation Organization (ICAO) mandates that all turns should be made, "at a bank angle of 25° or at a rate of 3° per second, whichever requires the lesser bank."[4] By the above formula, a rate-one turn at a TAS greater than 180 knots would require a bank angle of more than 25°. Therefore, faster aircraft just use 25° for their turns.
One might also want to calculate the radius of a Rate 1, 2 or 3 turn at a specific TAS.
Where is the rate of turn.
If the velocity and the angle of bank is given,
where g is the gravitational acceleration. This is a simplified formula that ignores slip and returns zero for 90° of bank.
In metres (where gravity is approximately 9.81 metres per second per second, and velocity is given in metres per second):
Or in feet (where velocity is given in knots):