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.
Defining "useful" as moving the plane forwards, the rate at which useful work can be done is equal to whatever power which has been imparted to the fluid, i.e thrust x velocity at disc. This is propeller power. The rate at which useful work is done which is equal to whatever power which has gone into actually making the plane move forward, i.e thrust x freestream velocity (since freestream velocity and airspeed are interchangeable depending on the frame of reference). This is propulsive power 

Consequently there are two different measures of efficiency, the propulsive efficiency which is a measure of how efficiently the plane uses the propeller power and the propeller efficiency which is a measure of how efficiently the propeller uses shaft power. The equation on the MIT webpage is for propulsive efficiency but you want to know how efficiently your shaft power (2π x torque x RPS) was used, therefore you have to calculate propeller efficiency so you don't use that equation.