I want to create a virtual quadcopter model, but I am struggling to come up with a satisfying model for the brushless motors & props.
Let's take an example, based on the great eCalc tool:
Let's say I want to know how much current is consumed by the motor in a hovering state. I know the mass of the quad (1500g), so I can easily compute the thrust produced by each motor:
Thrust = 1.5 * 9.81 / 4 = 3.68 N per motor
Thrust is produced by moving a mass of air at an average speed of
Thrust = 0.5 * rho * A * V²
rho (air density) is 1.225kg/m3 and
A (propeller disk area) is
PI * Radius² = 0.073m² (12" props). So I can compute
V = sqrt(Thrust / 0.5 / rho / A) = 9.07 m/s
All right, now I can calculate the aerodynamic power created by the propeller:
P = Thrust * V = 3.68 * 9.07 = 33.4 W
All right, now I can calculate the mechanical power actually produced by the motor. I use the
PConst efficiency term from eCalc:
Pmec = Paero * PConst = 33.4 * 1.18 = 39.4W
Here, eCalc predicts 37.2W. It's not too far from my number, I imagine they use more sophisticated hypotheses... Fair enough.
From this post, I know that this power is also equal to:
Pmec = (Vin - Rm * Iin) * (Iin - Io)
Where I know
Rm (0.08 Ohms) and
Io (0.9 A). So, finally, my question: How do you calculate
Iin from here? Of course, if I knew the rotation speed of the engine I could get
n = Kv * Vin
Kv = 680 rpm/V. But unfortunately I don't know the rotation speed...
(Note that Vin is assumed to be averaged from the pulse-width-modulated output produced by the ESC)
Thanks for your help!