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Does anyone know if there is any requirement regarding turning radius during taxi for a normal category aircraft?

I searched both the Part 23 and Part 91 from cover to cover and couldn't find any. If there is no legal requirement but a recommendation from some Advisory Circular or any other document I also would like to know.

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There is no legal requirement. In fact there is no stipulation that the aircraft be maneuverable on the ground.

Good examples of this are early aircraft (often biplanes) with tail skids. In the middle part of the last century there where gliders that had no wheels - just a center skid. Many current gliders have just one wheel and it is not steerable.

"The nose gear of a few aircraft with tricycle-type landing gear is not controllable." FAA Airframe Handbook pg 13-4

These type of aircraft are usually steered using differential braking. Examples are: Grumman (AA1, AA5, AG5), Diamond (DA1, DA4), Rallye except the 235C, early "straight 35" Bonanza, Columbias, T-28, T-34C, Nanchang CJ-6A, HU-16 Albatross, IAR 823, etc.

HU-16 Albatross

The HU-16 Albatross does not have steerable gear

Aircraft without wheels

Aircraft without wheels

Glider without steerable gear

Glider without steerable gear

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You will find some information on assumed turn radii in the ICAO Doc 9157 - Aerodrome Design Manual Part 2. For the purpose of taxiway design, they assume a relation between taxispeed and turn radius according to the following equation: \begin{equation} V^{2} = 127.133 * (f) * R \end{equation} with radius R given in meters, lateral acceleration assumed to be limited to 0.133 g and velocity V measured in km/h

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