# Propeller Efficiency calculation different by two methods

Please refer to this MIT page which I used for my calculations: https://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node86.html

I calculated my aircraft propeller's prop, thrust, and torque curves, and subsequently the efficiency at a certain operating point (given the input thrust requirements and airspeed), by dividing the useful power (=Tu_0) by the input power (torqueRPS), where u_0 is the flight speed.

Now, in the propeller plane, the airspeed is u_disk according to Actuator Disk Theory, and can be calculated using the formulas and the known info. When I calculate the input propeller power according to another formula on that page [Power in = Thrust * u_disk], I get an answer not equal to the one using the torque*RPS formula. Where did this extra power go? I was expecting them to be the same, and the aerodynamic losses to be factored into the useful power being lower.

In my example, the flight speed is 3 m/s. Due to the conditions of the aircraft and environment, this requires 42N of thrust, which requires 4.5N-m of torque at 1503 RPM. This is all due to the propeller characteristics. Now, the useful work is T * airspeed = 42 x 3 = 126W.

Using the calculations on that page, we can get the accelerated speed at the disk is 11 m/s. So the input power (According to the page) is 42 x 11 = 464 W. This is different from the conventionally calculated input power of Torque * RPS = 4.5 * (1500/60) = 700 W.