We now know there are multiple variables that influence our propeller’s performance.
We have rotational speed, as well as forward speed—i.e., our airspeed. We also have to toss air density in there somewhere.
Many engineers’ gut reaction is to use lookup tables in their performance or sim modeling. These usually end up as massive matrices of RPM versus airspeed, providing the thrust output and power required at each combo of conditions.
But using lookup tables requires a number of interpolation steps, which can be computationally slow. And honestly, this method just isn’t very robust: you need to make sure you cover all possible combinations of RPM and airspeed or else your calculations could break.
Thankfully, folks much smarter than me gave us all the tools we need to simplify this problem.
One of the key tools for our simpler modeling method is something called the advance ratio.
This ratio is airspeed divided by the product of the prop’s diameter times the number of rotations it makes per second. That’s a little wordy, so here’s a simpler way to express it:
Here n is the revolutions per second, D is prop diameter, and v is airspeed. For advance ratio, we use the letter J.
What this effectively gives us is how far forward the propeller travels for each rotation it makes. Let’s think of our prop in Jell-O again:
- The first case, where we were spinning without moving forward much, our advance ratio was near zero. No matter how fast it spins, the incoming speed is teeny (only what the prop itself generates) so J is effectively zero.
- As forward speed increases, with our rate of spin staying constant, our advance ratio also increases. We’re moving forward more with each rotation of the prop—again, taking bigger and bigger bites.
We’ve now condensed these two variables into a single value. We don’t have to care as much about the exact airspeed and RPM we’re using—we just have to keep track of the ratio between the two.