I'm thinking about how a quadcopter flight controller works, and I usually see that each motor speed is determined by a formula like:

speed_motor_1 = throttle + pitch_pid + roll_pid + yaw_pid

This looks fine, but one thing I was considering is throttle -> thrust is not so straightforward. For instance, a quadcopter in horizontal position have propellers pointing up and the thrust may be X. If you pitch this quadcopter by 30 degrees, now the propellers vector force is inclined and thrust it is X*cos(30 degrees)

Does that make sense? Is that something that must be taking into consideration when calculating "throttle" in the aforementioned formula?


  • $\begingroup$ what are you looking to get? throttle is an input. thrust is a vector that's impacted by all 4 parameters, yes. throttle here is in effect an absolute offset from the other things the copter is trying to manage (roll, pitch, and yaw, specifically). you don't need to calculate throttle as it's provided, and you don't need to calculate thrust as its just the speed of the motor (in effect). are you looking for velocity? $\endgroup$
    – kolosy
    Feb 8, 2019 at 17:30
  • $\begingroup$ My point is that it looks like "throttle" should change depending on the angle of the quadcopter (if you want to maintain level flight) even if the input doesn't change. For instance, if I need "throttle=40%" to keep the quadcopter stable at a level and I put some pitch (let's say 30 degrees) to it, this means I should increase the throttle if I want to keep level flight. $\endgroup$
    – Lem0n
    Feb 9, 2019 at 1:51
  • $\begingroup$ No, again - throttle is the input (or one of them). Motor speed, and, by extension, thrust is the output. What you're trying to do is ask whether thrust will vary as a function of y/p/r, with the same throttle. The answer is yes, it will. $\endgroup$
    – kolosy
    Feb 10, 2019 at 6:29

2 Answers 2


The simple answer is yes, to maintain level flight when pitched forward you need more throttle than when not moving forward.

This can be seen from the a simple force diagram. Thrust vs weight vs drag

A corollary to this is that the maximum forward speed is when full trust at the angle of the quad matches the weight.


Typically max-thrust will be bigger than vehicle weight, so that the quadcopter can accelerate upwards.

  • $\begingroup$ Welcome to Robotics robotno. Thanks for your answer but we are looking for comprehensive answers that provide some explanation and context. Very short answers cannot do this, so please edit your answer to explain why it is right, ideally with citations. Answers that don't include explanations may be removed. $\endgroup$
    – Chuck
    Feb 17, 2019 at 7:58

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