# How to account for propeller (fixed pitch) in model aircraft performance calculations?

I'm working on performance calculations for a plane I'm building. By setting the sum of my drag formulas (one for the wing, one for the fuselage, both with predicted drag coefficients) equal to the thrust at a given power setting, I'm able to come up with some predictions for speed. They seem unrealistically fast, given my experience with previous builds for which I did not do performance calculations. I figure that this is because of the prop, but I do not know how prop performance varies with different air speeds.

My questions are:

1. As airspeed increases, does the propeller produce drag similar to a wing while producing the same amount of thrust, or does it produce less thrust?
2. How do I take the prop into account in these calculations?

I'm using a 1550 Kv motor, for calculations I am using 7.4v at full power with an APC 8x4 prop, produces 468 grams/4.59 newtons at 8,620 rpm (rpm from data sheet).

• If you don't get a good answer here eventually, you may have better luck at rcgroups dot com-- they have subforums dealing with motors, power systems, etc, and also their "modeling science" subforum has some very sharp folks in it. Several other similar forum sites exist as well. Might also browse drones SE to see if you think this sort of question is likely to attract quality answers (I'm not sure if yes or no.). But maybe you'll get what you are looking for right here too-- good luck-- PS yes the edit helped- Oct 5, 2022 at 21:36
• (Some insight about meaning of "1500 Kv" -- astroflight.com/explanation-of-motor-terminology.html ,. rotordronepro.com/understanding-kv-ratings ) Oct 5, 2022 at 21:49
• Belongs on Drones.SE, not here.
– Ralph J
Oct 6, 2022 at 5:26

The easiest way to account for propeller thrust, is just by using basic physics.

Being $$P$$ the power supplied to the propeller, the propeller changes this power in a thrust $$T$$ moving the airplane at a speed $$V$$. In this process, some 20% of the power (at the design point) is lost in inefficiencies which are incorporated in an efficiency factor $$\eta$$:

$$T=\eta \frac{P}{V}$$

$$\eta$$ depends on the speed, with a typical trend visible in the following plot taken from McCormick B.W. Aerodynamics, Aeronautics & Flight Mechanics. John Wiley & Sons, Inc.:

As visible, $$\eta$$ depends on the blade pitch as measured at 75% of the span and on the advance ratio $$J=\frac{V}{nD}$$, where $$n$$ is the rotating speed and $$D$$ the diameter. The theory behind this plot and therefore the plot itself is valid for a more or less broad range around the peak: at $$V=0$$ it gives $$\eta=0 \Rightarrow T=0$$ which is not realistic since also at zero speed the propeller provides thrust. For that part of the thrust (so called static thrust) you can refer to this answer.

Note that this plot refers to "real size" propeller, I can't say if those values are also valid for an RC propeller due to the lower Reynolds number i.e. higher viscous-related effect. Design point for propeller is normally around their $$\alpha$$ for max $$L/D$$ and this latter value reduces a lot at lower Reynolds numbers. Anyway propeller's manufacturer should provide that plot.

• 0.8 is overly optimistic for a fixed pitch propeller. That value will only be approached near the design advance ratio.
– Peter Kämpf
Oct 6, 2022 at 17:35
• @PeterKämpf: correct, 0.8 might be valid only for the design point. I'm trying to find a decent plot for $\eta$ Oct 6, 2022 at 18:12
• Well, the plot isn't so poor when you understand the x axis to show the speed in the propeller plane. Even at rest the prop will accelerate air, so its efficiency does not go down to zero. The linear increase with speed and the sharp drop above the design advance ratio are rather realistic.
– Peter Kämpf
Oct 6, 2022 at 20:03
• @PeterKämpf: I implemented your comments, now it should be correct, thanks Oct 7, 2022 at 5:52