The really nice thing about advance ratio is that now we can evaluate propeller performance by simply plotting it against another variable.
At any given flight condition, a propeller is producing some amount of thrust. We can turn that thrust into a thrust coefficient, CT. And if you do that for a bunch of airspeed and RPM combinations, you get a nice cloud of data.
Now, instead of comparing that coefficient data to either airspeed or rotational speed—where either choice leaves out the other critical variable—we can plot our thrust coefficient against advance ratio.
This is borderline magical.
Why? Because advance ratio takes into account both airspeed and RPM, we can use it to find the corresponding thrust coefficient. Like I said, it doesn’t matter what the exact airspeed and RPM were. It’s the ratio that counts.
Trying to explain this feels a bit convoluted, so here’s a more concrete explanation:
Say you take your UAV to a wind tunnel for some propulsion testing. While there, you’re able to operate your propeller at a whole range of airspeeds and RPM settings.
At each of those airspeed and RPM combos, the balance measures the thrust generated by the propeller. You also measure the power consumed by the motor spinning your prop.
Because you know all of the inputs and outputs, for each test point you calculate advance ratio J and thrust coefficient CT. You can plot CT versus J for your cloud of data and it makes a rough curve; highest at J = 0, and lowest at larger advance ratios.
Now you pull out a file of flight telemetry. At each timestamp you have the airspeed and propeller RPM for your bird.
For regions of flight you’re interested in, you can use the reported airspeed and RPM to calculate advance ratio. You can then look at your CT vs J curve and find the thrust coefficient that corresponds to this telemetry data point’s advance ratio.
And by re-dimensionalizing, you now know the amount of thrust the propeller was making in this point in flight, without having to directly measure it.