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Pivotal altitude is the height for a given ground speed at which the line of sight from the cockpit directly parallel to the lateral axis of the aircraft will remain stationary on an object on the ground.

It is also known that bank angle does not change pivotal altitude.

However, increasing bank angle tightens the radius of the turn for a given airspeed, as shown below, so why doesn't bank angle change the pivotal altitude?

enter image description here

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  • $\begingroup$ The math just works out that way. $\endgroup$ Jul 7, 2023 at 2:44

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Assume zero wind. The airspeed $V$, turn radius $R$, gravitational acceleration $g$ and bank angle $\theta$ obey the relation $\frac{V^2}{R} = g\tan\theta$. Meanwhile, at the pivotal altitude $H$, the turn radius, altitude and bank angle obey $\frac{H}{R}=\tan\theta$.

Put the two together and you get that the altitude is $H=\frac{V^2}{g}$. At 50 meter/sec (just under 100 nm/h), this gives $H\approx250$ meters, or about 800'.

At a steeper bank angle you'll fly a tighter turn radius, and also need a tighter turn radius to put the wing on the center of the circle. Those two effects exactly match at the pivotal altitude.

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