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Calculation of Lift

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ahh, good ol aerodynamics.

T= Pi / 4 *D^2 * (v + deltaV / 2) * p * deltaV

T = Thrust in Newtons (N)
Pi = Pi (3.1415926...)
D = Prop diameter in meters (m)
v = initial velocity in meters per second (m/s) Initial velocity is the velocity of the incoming air flow
deltaV = change in initial velocity in meters per second (m/s). This is the change in inital velocity of the incoming air flow created by the thrust of the prop.
p = density of the fluid in kilograms per cubic meter (Kg / M^3) Air is approximately 1.225 Kg/m^3

Calculating the lift or thrust created by a prop (rotor) is pretty complex because the physical design and airfoil of the prop comes into play. As you might have noticed, most props (rotors) don't have the same airfoil throughout the length of the blades. Commonly, a design called "washout" tapers the pitch closer to 0 degrees as you look further toward the end of the blade. Although this design is most common with propellers than it is with rotors. My point here is that because the airfoil shape of the blade is ever changing as you near the tip of the blade, it is difficult to approximate the thrust coefficient of the blade. Now if you're working with a professionally created rotor (prop), the manufacturer might supply the thrust coefficient given a specified RPM and fluid density. Notice that the above equation doesn't account for the thrust coefficient of the airfoil, thus the entire calculation is more of a guess than a calculation. Without a thrust coefficient, you're pretty much left with a broad guess.

Aside from the airoil challenges and approximating the thrust coefficient, we need to consider the velocity of the incomming flow of air. In your case, this may not be so complicated, but in a circumstance where a rotor (prop) is used to accelerate an object, the incomming velocity changes as the object accelerates (the incomming velocity usually increases).

Additionally, the prop (rotor) will cause an additional increase of incoming velocity as the prop (rotor) creates more thrust. This adds another approximation to our calculation.

As you can see, there are too many unknowns to approximate the thrust from an unknown rotor (prop).

Electrically speaking, we need to figure out the RPM's of your motor at a given voltage and current. This calculation in iteself is difficult without knowing a RPM measurement. Of course this RPM measurement will change when a prop is added to the motor, so we need a way to measure the RPMS of the motor with the prop added to the motor.

A simpler way of approximating the thrust would be to hang the motor from a scale, then zero out the scale due to the effects of gravity, then start the motor with the prop and measure the amount of thrust the motor creates. Of course, the motor would need to be hung from the central axis point so that the prop thrusts straight down toward the ground, rather than twisted off to some angle. (This is the approach that we took to gather "real-world" data on prop mechanics in physics class) We inserted the motor into the end of a PVC tube, which fit the motor snugly, then hung the PVC tube and motor from a scale. We zerod the scale then slowly added power to the motor to reduce the amount of torque movement (P-factor). Then took several readings from the scale. Of course, the measurements were nowhere near exact, but were a good way to approximate.
 
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