Turn Instruments and Angle of Bank

The gimbal in the turn coordinator is set at an angle allowing the gyroscope to sense both rate of roll and rate of turn. This is where it differs to the turn indicator. But... neither of these instruments directly report the angle of bank.

Why not? Because you need to know the airspeed to estimate the likely angle of bank using the turn coordinator. The bank angle necessary for a standard rate turn can be estimated using the following formula:

Bank Angle Required = (Airspeed in knots / 10) + 7

In other words the faster you go the more angle of bank you need to maintain a standard rate turn (which is 3 degrees per second).

For example, to maintain a standard rate turn you need to apply approximately:

For each of the above speed/bank angle combinations, the turn coordinator display should be identical - showing a standard rate turn. This means that your turn instrument is not directly telling you what the angle of bank is.

So, neither the turn indicator nor turn coordinator can directly tell you the angle of bank without additional reference to your airspeed. Furthermore, the formula described above only works for a standard rate turn, meaning that a different formula is required to calculate your angle of bank when you are not in a standard rate turn. So you can see that these turn instruments are not really telling you very much about angle of bank.

It is worth mentioning that recent editions of the AFE (Jeremy Pratt) series of PPL training books suggest that a turn coordinator indicates the angle of bank. As we have shown above, this is only an indirect indication at best. (Feb 06: We wrote to the publishers to advise them of this.)

Atmospheric Picture

FL45, English Channel.