# How to calculate the efficiency of a rubber powered propeller

I made a simple test rig together with a stopwatch to measure the thrust (in grams) with respect to time of a rubber powered propeller. This enabled me to compare the performance of different propellers in terms of duration and average thrust. However, I cannot determine how efficient these propellers are. What could be the missing data that I should take into account to calculate its efficiency?

• I think first you have to define efficiency to determine what you're measuring. The canonical definition is $\eta = \frac{P_{out}}{P_{in}}$, and since your prop isn't moving forward on the thrust stand, there is no work being done and thus $P_{out} = 0$ and $\eta = 0$. The upshot is that if you are measuring thrust for the purposes of choosing the best propeller for flight, then you have to test the prop across the airspeed range. If you're only testing static thrust, then your definition of efficiency and your test conditions are wildly in disagreement. Jul 31, 2021 at 12:32
• Since an actual model airplane wouldn’t be standing still while flying, I’m wondering if the data you’re taking is relevant. Jul 31, 2021 at 14:16
• What a great start to your work! As others suggested, measure torque to wind the prop (plotting resistance to winding per turn). First see how consistent the rubber band is at storing energy (does it fatigue after say 20 windings)). Next you need to test efficiency at the desired cruising speed of your airframe. So: take it to the hill and see which prop makes you plane fly farthest at the speed you want (if you don't have a wind tunnel). For these types of aircraft, a larger slower prop is generally more efficient, but a faster one may work better due to Reynolds number factors. Jul 31, 2021 at 20:05

You should avoid dated units, such as the gram-force. Now, the area under your graph is in $$MLT^{-1}$$ units, force x time. These correspond to the variation of momentum $$∆MV$$ imparted to the air by the prop. Perhaps you could use that area as a reference, when testing other props...

In order to compare efficiency, you would need some way of measuring the torque exerted by the rubber band, and compare (thrust generated/torque required). You could construct a second arm&scale mechanism at 90º of the existing one that is loaded by the wound up rubber band.

Momentum theory has a glossary efficiency term, the Figure of Merit. Basically, for helicopters, it is defined as (Ideal power to hover/actual power required to hover), with the actual power being the power from induced drag + power from profile drag.

Chapter 2.8 of Principles of Helicopter Aerodynamics by J. Gordon Leishman contains a detailed explanation, The figure above is Fig 2.8 of the book, with thrust coefficient $$C_T$$ defined as

$$C_T = \frac{T}{\rho \cdot A \cdot (\Omega R)^2}$$

With T = thrust[N]; A = disk area [m$$^2$$]; $$\Omega R$$ = blade tip speed [m/s].

Fig 2.8 shows the dimensionless thrust coefficient $$C_T$$, and the chapter mentions that only rotors (or propellers) of equal area should be compared. Or compare $$C_T$$ with $$C_Q$$ for different propellers, with $$C_Q = \frac{Q}{\rho \cdot A \cdot \Omega^2 \cdot R^3}$$ with Q = torque in [Nm].

The above should get you going, more detailed info in the reference books.