Bank angle for a chosen turn rate
Instrument flying is built on the standard rate turn, three degrees per second. The bank angle that produces it depends on how fast you are going, and at higher speeds it becomes impractical.
Calculator
This is an educational and planning aid. Use current official weather, your aircraft flight manual, and the rules that apply to your flight before you act on any figure here. See the aviation disclaimer.
What the result means
The bank angle is what a coordinated level turn needs to sweep through your chosen rate. At 100 kt a standard rate turn needs about 15 degrees. At 250 kt it needs about 35.
The familiar cockpit rule of true airspeed divided by ten plus seven is shown alongside, so you can see how close the approximation is at your speed.
Load factor is included because at high rates and speeds the bank angle, and therefore the g, climbs quickly.
When this is useful
- Instrument flying, where procedures are built around the standard rate turn.
- Understanding why faster aircraft limit turns to 25 degrees of bank rather than a rate.
- Setting up a holding pattern or a procedure turn.
How it is calculated
The turn rate in radians per second multiplied by the velocity, divided by gravity, gives the tangent of the bank angle. Taking the inverse tangent gives the angle itself.
This is the same relationship as the turn radius calculation, rearranged to solve for bank angle from a rate rather than for radius from a bank.
bank angle = atan(turn rate in radians per second x velocity / 9.80665)
Worked example
- True airspeed
- 100 kt
- Desired rate of turn
- 3 degrees per second
A standard rate turn at 100 kt needs about 15.4 degrees of bank, at a load factor of 1.04 g.
Check: The rule of thumb of airspeed divided by ten plus seven gives 17 degrees, about 1.6 degrees high. A second common rule, airspeed divided by ten multiplied by 1.5, gives 15 degrees, which is within half a degree of the exact answer.
Limitations
- It assumes a coordinated level turn at a constant true airspeed.
- At high speeds the bank angle needed for a standard rate turn becomes impractical, which is why instrument procedures above a certain speed limit bank angle instead and accept a slower rate.
- It gives geometry, not a recommendation. Whether that bank angle is appropriate depends on the phase of flight and the aircraft.
Common mistakes
- Using indicated airspeed at altitude. Mach and true airspeed diverge from indicated considerably up high, and this needs true airspeed.
- Assuming a standard rate turn always means the same bank angle. It changes with every speed.
- Applying the divide by ten plus seven rule to a rate other than three degrees per second, where it does not apply at all.
Sources
- Instrument Flying Handbook (FAA-H-8083-15), basic flight manoeuvres , US Federal Aviation Administration