# Propeller Curve Modification on Test Rig

this is my first stack exchange question so please bear with me if I have missed a rule: I tried searching for this question to no avail.

I have an off-the-shelf propeller for the purpose of eventual high-altitude flying. I used the airfoil profiles to make an approximate propeller efficiency/c_thrust/c_torque/c_power vs advance ratio curves, as well as the power/thrust/torque/rpm vs airspeed.

My question is: if I had to spin up this prop on a test rig on the ground, there are two major changes I can see - atmospheric air density, and the fact that airspeed is zero. How can I predict how the propeller will behave when the airspeed is held zero (the rig will cancel out the thrust generated). Looking for things like max possible RPM, torque, etc. and how the behavior of the propeller changes.

Thanks a lot, happy to provide more details.

Fortunately, the speed in the propeller plane is not zero once the propeller runs. It will suck in and accelerate the air ahead of it as much as it pushes air out the back, accelerating it further. This was already formulated by Robert Edmund Froude and is called Froude hypothesis. Read this answer for more.

Using the equations from the linked answer you can already calculate your propeller's efficiency and the flow speed in the propeller plane once you run it on your test bench. Most likely your propeller is designed for more than the flow speed achievable with static conditions, so this will help you to calibrate your calculations only for low prop speeds. But since there is a flow speed already, all equations will work.

Your propeller has an advance ratio that tells you how fast it should be spun for a given flight speed. In order to extract more thrust, the propeller should be spun a bit faster, so a positive angle of attack at the blades results over the whole propeller span.

In static conditions, you will not achieve a good angle of attack over the whole span. The faster you spin the propeller, the more it will experience too high an angle of attack, a condition that will be worst at the root and only the tips will exhibit close to proper flow conditions. Since the inner part of the propeller is stalled, it will create lots of drag for little thrust. Therefore, the max. RPM and torque numbers are very hard to predict, and measurements at that point will be of no value for predicting the behavior of the prop once it runs at its design advance ratio. Air density should be less of a problem - it will drive up dynamic pressure and, consequently, the power which is needed to run the propeller at a given speed.

• Thank you so much! I kept seeing your name and answers when learning about propellers, and you've helped a lot in the past as well! Cheers Jun 13, 2018 at 21:38
• @ Peter Kampf I followed your link to your other answer and calculation therein. I encountered a problem, that I asked as a question here, and would appreciate your thoughts: aviation.stackexchange.com/questions/55633/… Oct 3, 2018 at 17:58
• @dumbpropnerd: Your example has 3 m/s airspeed and needs 11 m/s speed in the prop disk plane in order to work. With that massive acceleration, the usual simplifications of simple propeller theory break down (speed increase is small when compared to flight speed), so different equations will give different results. Test your prop at higher speeds and the differences will shrink. Oct 10, 2018 at 3:50
• Kampf Thanks! I suspected this had something to do with this being a simplified theory, as I had done my other analysis using induction factors taken into account, etc. I also realized that the simple propeller theory doesn't even take into account propeller characteristics, just the flight speed, thrust req'd, and air density, before making an efficiency calculation. How is this possible? I understand that its the ideal propeller efficiency, but how is this useful without taking into account propeller geometry? Oct 10, 2018 at 14:08
• @dumbpropnerd: The propeller details are hidden in the prop efficiency. With a poor twist distribution (think fixed prop at the wrong speed, for example), this number will reflect all effects that are caused by the non-ideal nature of the prop. And what you describe sounds just like a fixed prop at the wrong speed. Oct 11, 2018 at 18:06