Section 4 Reynolds Number

This section might properly be titled air viscosity effects. Of most importance to free flight, R/C gliders, and propellers, the Reynolds number (R_e) represents the ratio of inertia forces to viscous forces in the airflow around the aircraft. Variations in R_e can have a profound effect on the boundary layer and flow separation. The R_e values for model flight range roughly from 100 for indoor models and control line wires, to 1,000,000 in R/C pylon racing. The rule of thumb is: low Reynolds numbers are bad for aerodynamics. Wind tunnel data are classified according to R_e so if you make reference to these data it is important to be able to estimate R_e .

Wakefield flier Fred Pearce pointed out the practical importance to me. His thoroughly tested model was flown at a contest in “high and hot” conditions and had to be re trimmed to recover anything like the expected performance. When he got home he computed the horizontal tail R_e at the flying site conditions and found it was low enough to have become sub critical.

The formula for R_e found in model magazines is almost always based on sea level standard, yet R_e can vary by up to 40% from sea level standard conditions, and is almost always lower than it would be in the ’standard’ atmosphere. Atmospheric temperature has the largest effect on R_e , density differences due to altitude and humidity will also change Reynolds number.

For power model propellers there is an important R_e effect. Low R_e reduces critical Mach number, which can vary from 0.5 to 0.7 depending on section and R_e. The drag rise starts at this Mach number accompanied by shock-induced separation. Some racing propellers operate close to or over the critical Mach number, some are even slightly supersonic, and take a big hit in efficiency. Military R/C drones also have had trouble with the combination of high tip Mach numbers and low Reynolds numbers. Other than geared engines, propellers with lower diameter, more and/or wider blades are the only fix for this problem.

The formula to calculate R_e is given below. In this relation is the velocity, is a length (for airfoils the chord is usually chosen), and the Greek letter nu () is called the kinematic viscosity.

Either low density or high temperature will reduce the R_e. If is measured in feet, and in feet per second, Figure 2 shows the value of kinematic viscosity to use.

An example, using the Figure, follows:

Velocity 70 mi/hr= 102.7 feet/sec.

Chord 10.0 in. = 0.833 feet.

Pressure 29.00 in. Hg

Temperature 85 ^oF.

From Figure 2 find standard pressure dynamic viscosity = 1.725 x 10-4 = 0.0001725

Correct for pressure (29.92/29.00)*0.0001725 = 0.000178

Compute R_e = 102.7.0 x 0.833 / 0.000178 = 480,000

Note that R_e can vary over a larger percentage range than density. In the example given in the previous section (the “Colorado Springs” example), the kinematic viscosity in the high/hot condition is 1.56 times what it is in the low/cold situation.