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Assuming I have a propeller with a given diameter (D), pitch, blade twist, and number of blades, I can theoretically analyze discrete airfoil sections in XFOIL and come up with lift and drag polars for the airfoil sections, for a given Reynolds number. Using the new information along with the pitch and twist (to give angle of attack for each section), the overall thrust and torque for the propeller blade can be solved for given operating conditions (RPM and airspeed). Even more accurately, the induction airflow factors can be accounted for to adjust the velocity vectors and angles of attack experienced by the airfoil sections on the blade, and an iterative solution can yield more accurate thrust and torque data for the propeller. Doing this at different operating conditions (RPM and airspeed) can give many data points, allowing for a generation of a thrust, torque, and efficiency curve vs advance ratio. I have done all of the above for a certain propeller.

However, if I wanted to change my flight altitude (and thus air density would be different), my Reynolds number could be vastly different for the same operating conditions. Does the thrust, torque, and efficiency curves for the propeller still hold up? Or does the different Reynolds number mean that if I solved the airfoil sections thrust and torque data again, they would yield different dimensionless data as a function of advance ratio?

I'm happy to provide more details. Looking forward to figuring this out!

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  • $\begingroup$ Using 2D airfoil data will give too conservative results. The slowing boundary layer is accelerated sideways by centrifugal forces, which means it is shifted to a section of the propeller blade that moves faster. As a result, flow separation is greatly delayed on propellers. $\endgroup$
    – Peter Kämpf
    Commented Nov 12, 2018 at 19:19
  • $\begingroup$ You need to look into blade element theory -- XRotor, JavaProp, and CCBlade are good examples. Before the Reynolds number differences will be important, the density differences will dominate. As you go higher, you will need to spin the (presumed fixed pitch) propeller at much higher RPM in order to make the same thrust. Your power required to produce said thrust will also increase. Look into the definitions of thrust and power coefficient and advance ratio. $\endgroup$
    – Rob McDonald
    Commented Dec 17, 2023 at 6:37

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Your lift and drag polar is Reynolds number dependent. You need to check if you are happy with what XFoil generates for you. Airfoil characteristics are fairly constant over a wide range of Re, so it might not effect you at all.

Also, if you are running high tip speeds, there is another pote increasing altitude drops the temperature as well, so you are increasing the tip Mach number, which you need to make sure stays within the validity limits of your calculation method.

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Regardless of the Reynolds number, momentum theory says that if air density is decreased, the actuator disc has to move air faster in order to provide the same amount of thrust. Threfore the induced velocity across the actuator disc must increase. Going back to an actual propeller, a higher propeller RPM is required to provide this extra velocity therefore the required RPM will also rise.

Conversely, at a set RPM and induced velocity, less thrust will be produced. Since advance ratio is proportional to the ratio of free stream velocity to RPM, advance ratio would stay the same while the thrust at a given advance ratio would decrease. This would result in your advance ratio - thrust curves being "shifted down" along the Y axis.

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  • $\begingroup$ So to clarify, propeller characteristic curves (e.g. thrust, torque, or efficiency vs Advance Ratio), are only valid at a certain density (/altitude)? At any change with density, they also change? Is there a way of quantifying this change without doing the XFOIL analysis from scratch, if the curves for one density are known? $\endgroup$
    – dumbpropnerd
    Commented Oct 5, 2018 at 19:28
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    $\begingroup$ @dumbpropnerd I use thin airfoil theory so that I don't have to manually punch in lift coefficient values from XFOIL for each blade element into my spreadsheet every time I have to re-sum the thrust and torque for the entire blade. $\endgroup$
    – Aviator S
    Commented Oct 5, 2018 at 22:21
  • $\begingroup$ Thank you! I will look into this approach. $\endgroup$
    – dumbpropnerd
    Commented Oct 5, 2018 at 22:27
  • $\begingroup$ You said that the thrust-AR curve moves down. But wouldn't the torque-AR curve move down as well? In that case, is the propeller more or less efficient? It's producing less thrust, but also using less power to do so. $\endgroup$
    – dumbpropnerd
    Commented Oct 8, 2018 at 20:17
  • $\begingroup$ I guess so. This has nothing to do with efficiency, that's a tip vortex thing. $\endgroup$
    – Aviator S
    Commented Oct 8, 2018 at 23:18
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'tis a bit more interesting when it is fully considered. As density alters, to achieve a given thrust level, the AOA of the blade must alter, and while density is a common factor to both lift and drag, the CL/CD for varying AOA alters, a lot. That assumes the torque exists to turn the blender at all altitudes. The difference in AOA can be estimated, for a given thrust output the density delta compared to the base altitude will require a deltaCL to match. Easy. Except that the prop pitch is relative to TAS, so as TAS goes up, so does the geometric blade pitch, to achieve a constant AOA, so there is an additional delta for the tas, proportional to the tip velocity of the blade. As that increases the blade geometric angle to gain a given thrust, that results in a further increase in drag, and more annoyingly, a reduction in lift, as they are vectors dependent on... the relative air flow to the blade. Take it to the extreme, go fast enough, the blade needs to be near feathered angle, and it doesn't give much thrust then, but lordy it gives a force counter to the torque required to turn the whole blender thing.

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