# Does the Reynolds number on a smaller model need to match the one of the original aircraft?

1.Airbus 380-800 : The overall length of it , is 72.72 m and its cruise speed is 903 km/h. Based on the mean chord of wing , its Reynolds number in cruise phase is around 75 millions. Now , a 1/18 scaled model is built for the purpose of wind tunnel testing. Assuming similar flow condition , the Reynolds number of wind tunnel tests would be around 4.15 millions. This is great difference. Is Reynolds number , as a very important similarity variable, is so different for wind tunnel testing comparison with free flight condition, what is the advantage of performing such tests? 2.do we always need to match Reynolds number exactly?

• I have no idea if this is relevant but one thing stands out to me: 903 km/h would be cruise groundspeed, but the wind tunnel would only be testing airspeed.
– Ben
Oct 13, 2017 at 11:48

In wind tunnel testing you need to match several similarity parameters; the most well known are the Reynolds number and the Mach number.

Since the Reynolds number depends on flow speed, viscosity and physical size while the Mach number also depends on flow speed, it looks like both can only be matched when the physical size of the model remains unchanged. But when fluid pressure and temperature are also changed, it is indeed possible to get both close to the real value. This requires an actively cooled, pressurized wind tunnel.

Such tunnels are expensive and have a long waiting list, so other tunnels exist which match both parameters less well. In that case, the researcher needs to pick which is more important and select one of the many facilities in existence.

For preliminary development, it is in most cases sufficient to test at a much lower Reynolds number and then apply correction factors, just as it has been done in the early days of aviation. If, for example, you need to find the lateral stability of a design or test its spin behavior, a smaller Reynolds number is not critical. In order to trip the boundary layer where it would have its natural transition between laminar and turbulent flow, the flight surfaces of such models have artificial roughness applied at the right chord location, so the flow is made as similar as practical.

This will depend on what you are testing for and how accurately you want to test.

It can be sufficient just to match flow regimes. Such that if the actual aircraft has a turbulent boundary layer then your model needs to have one as well. This is easier to do than exactly matching Reynolds numbers.

If the accuracy or type of test demands it you need to match Reynolds and Mach numbers for the model this will ensure your results are the same as they would be in a flight test. In order to match these numbers you will most likely need a pressurized wind tunnel. Or use something like a water tunnel.