# Determining thrust equations for a custom UAV

I have been tasked to mathematically model and simulate a 2 propeller, 2 motor UAV. But I am struggling with determining the thrust equations, of the propeller, for my design.

I know that:

Ft = Ct * rho * (w/(2*pi))^2 * D^4

Where rho is the density of air ;

D, the diameter in meters of the propeller;

Ct, the thrust coefficient;

And w is the angular velocity of the propeller.

However, I was not given Ct although it is necessary for this equation.

I have been told I can use something called the "experimental propeller force-thrust constant" or Kf (units: N/V) to calculate Ct however, after multiplying Kf by the voltage of the motor driving the propeller, I am at a total loss as to how to do so.

I used dimensional analysis in an attempt to receive a clue to the equation:

Ct = Ft/(rho*(w/(2*pi))^2*D^4)

Therefore Ct's units are

N/((kg/(m^3))*(rev^2/sec^2)*m^4)

Which is equivalent to:

(N * sec^2)/(kg * rev^2*m)

Using the definition N = Kgm/s^2 the units of Ct are rev^-2.

Using the last two unit expressions I have arrived at this equation:

Ct = Kf * V / ((w/(2*pi))^2 * D * m)

Where V is voltage and m is mass.

The units work, but I know that doesn't mean its correct.

Can anyone kindly verify if this equation is actually correct? Otherwise can someone please explain how to achieve the equation for Ct using Kf?

Any constructive comments are much appreciated. Please forgive my visually unfriendly web math notation.

• Plane or 'copter type? Hovering and slow advance for 'copters is fairly tricky. – Phil Sweet Feb 25 '19 at 0:59
• Hi, Thanks so much for your response. This is for a helicopter style UAV. At this point I am not too concerned about that. I merely need it off the ground. Any input would be highly appreciated. – gunter Feb 25 '19 at 6:16