What exactly is a Reynolds number?

What does X-Plane do with the high and low Reynolds number that you can enter in PlaneMaker?

Reynolds number is air density x true airspeed x wing chord divided by the air's viscosity. (Viscosity is a measure of the "stickiness" of a fluid. Alcohol has a lower viscosity than honey.)


More to the point, the Reynolds number is a measure of how "fine grained" the turbulence of the airflow is. At very low speeds, fluid flow is laminar, that is, it flows in smooth layers. At higher speeds (i.e., higher Reynolds numbers) the flow becomes increasingly turbulent at increasingly smaller dimensions.

Aifoils behave differently at different Reynolds numbers; in general you get a higher stall angle and correspondingly higher lift from an airfoil at higher Reynolds numbers. You can see this from most airfoil performance charts, like those in Theory of Wing Sections.

Each .AFL file has a Reynolds number. When you create a .AFL, you should enter the Reynolds number that's given for the airfoil chart you're using. X-Plane computes the Reynolds number for each airfoil section as you fly. If you've specified two different airfoils for the high and low Reynolds number entries (PlaneMaker Special -> Foils), X-Plane will compute airfoil performance from the two airfoils by interpolating according to the current Reynolds number. For example, if your current Reynolds number is halfway between the Reynolds numbers of the two airfoils, X-Plane will take the average of their performance.

How do I assign Reynolds numbers when I create an airfoil?

Here's the ideal way to do it:
  1. Point your web browser at the Stanford Standard Atmosphere calculator.
  2. Enter the altitude and airspeed for which you want to compute a Reynolds number. For the Reference Length, enter the wing chord. Reynolds numbers will be lower at higher altitudes. (Remember - the Reynolds number represents your flying conditions; it is not a property of the airfoil.) Compute Reynolds numbers at the plane's stall speed and at maximum speed.
  3. Take the two Reynolds numbers you've found and match them up with their Cl and Cd curves in the airfoil chart. Create two different airfoils from the two sets of curves, entering the appropriate Reynolds number for each airfoil. The airfoil chart may not have performance data for a Reynolds number that you computed. (This is likely to happen with larger aircraft like heavies, where the operating Reynolds number are much higher than what's in most available airfoil charts.) In that case, just choose data for the nearest number that's available. Enter the Reynolds number corresponding to the chart, not the one you computed!
  4. In the PlaneMaker Foils menu, enter the two airfoils for the Low RN and High RN airfoil positions.
  5. Now, when you fly the plane, X-Plane will compute the current Reynolds number and then select the correct airfoil data. If your current Reynolds number is in between those of the two airfoils, X-Plane will interpolate the airfoil performance data.

OK... How important is this? Not very, in my opinion. It's a lot of work, and it requires the actual airfoil data. Further, some of the regions of the airfoil performance range where the difference matters will never be used in most circumstances. The most obvious example is stall angle. You are likely to stall the aircraft at low speeds. However, high speed stalls are unlikely, especially in a passenger plane. (You'll get the passengers seriously upset, and you risk ripping off the wings.) Conversely, low AOA drag is more of an issue at the higher speeds. Meanwhile, the lift curve for moderate AOA values is normally independent of Reynolds number.

So in most circumstances you're just as well off with a single airfoil for the entire speed range. Use the high speed Cd values for the low AOA area, and set up the stall region to match the low Reynolds number. The Reynolds number you enter for the airfoil is unimportant when there's only one airfoil for the entire range.

Back to the Theory page