# Yaw rate of a multi-rotor

Is there any type of relation that limits yaw rate of a multi-rotor (i.e quadcopter)?
Something like this relation for fixed wing aircraft: $$R = \frac{v^2}{g \tan(b)}$$, where $$R$$ is the minimum turning radius and $$b$$ is the maximum bank angle.

• note that that formula is for a coordinated turn. you might get a higher yaw rate if you remove this constraint. what kind of constraints are you interested in for your answer?
– Federico
Nov 17 '20 at 13:47

A conventional quadcopter yaws by speeding up two rotors and slowing down the other two. Once those two have slowed down to zero RPM, it can't yaw any faster.

A formula for this would involve the rotational moments of inertia of each motor+rotor and of the quadcopter's chassis, and the distance from the quadcopter's center of mass to each rotor's axis. (If the rotors aren't coplanar, it gets messy.)

If those two rotors can be reversed, then they are (inefficiently) thrusting up instead of down. The limit then may be when they overpower the thrust of the first two, forcing the quadcopter to descend. Or, if the rotors are spectacularly inefficient when reversed, the limit is when the rotors reach maximum RPM.

• this is true for yawing without banking, but a quadrorotor can still turn like a fixed wing would do
– Federico
Nov 17 '20 at 18:54
• But a coordinated turn yaws much slower than a pirouette, and yaw rate is what the question is about. The coordinated turn formula is merely incidental. Nov 17 '20 at 19:57
• it depends, I have worked with multirotors that have a pirouette faster than a coordinated turn, and ones that don't. they're not all the same
– Federico
Nov 17 '20 at 20:29