Scale Effect and Reynolds NumberBy Craig Skinner Its that time of year again when you host the grand unveiling of that master scale project you have been labouring over all winter. You studied pictures, went to the museum to look at the real job, and she's perfectly to scale. Or is it? In January we talked about the problems of building a scale model. If you reduce the linear dimensions by 1/10 then the area will be reduced by 1/100 and assuming you built it out of the same material the mass will be 1/1000. Well that's all fine and dandy (right now the guy who made the lovely scale model is starting to get angry with me), but how will it fly? How do the flight characteristics of a scale model differ from that of its full size brother and what can we do to correct these differences? What happens when a scale model is flown in "full size air"? Good questions, I'm glad you asked. Over 100 years ago, a smart man called Reynolds was studying fluid flowing in pipes and noticed that the velocity at which the flow became turbulent was inversely proportional to the diameter of the pipe. For example, a fluid would become turbulent at 10 m/s in a 20 mm pipe or at 5 m/s in a 40 mm pipe. The formula is: Constant = Velocity * Pipe Diameter When dealing with airplanes we can substitute Wing Cord for pipe diameter. Lets use an example of a fill size Spitfire with a 1 meter cord flying at 500 km/hr. 500 = 500 km/hr * 1 m Now we recreate the Spitfire at 1/5 scale with a cord of 20 cm and fly it at the same speed. 100 = 500 km/hr * 0.2 m If order to get the same aerodynamic results from a scale model, we need to maintain the same Reynolds number. Therefore, we will have to increase the speed to 2500 km/hr. 500 = 2500 km/hr * .2 m Well that's the theory. The reality is that you just broke Mach 2, your plane disintegrated in a blaze of glory and you are the hero of everyone at the club. But seriously, how do we get accurate results from a scale model? How do professional designers working with wind tunnels do it? To start with, we have to expand our formula. Constant = Density of Fluid *
Velocity * Dimension (Wing Cord)
So getting back to the original question, how do we make our scale Spitfire accurately represent a full size version? How about we change the fluid. Water is 815 times as dense as air and only 64 times as viscous. We now have a factor of 12.8. Here goes. 500 = 12.8 * 195 km/hr * 0.2 m Success! All we have to do is submerge our model into a stream of water doing 195 km/hr and we will know how a real Spitfire flies. That is going to be almost as spectacular as the Mach 2 considering that a "water tunnel" of 195 km/hr is a fantasy and the model would be under tremendous stress. Right, one last attempt at solving our dilemma. Lets increase the density of the air and at the same time cooling it to maintain the same viscosity. If we were to pressurize our wind tunnel to 10 atmospheres (10 times sea level pressure or about 140 psi) then we could reduce the air velocity. 500 = 10 * 250 km/hr * 0.2 m Voila! Problem solved. We can properly test scale models if we build a wind tunnel in a pressure chamber. Right now you may be saying "What does this have to do with a model out at the Farr's Farm", and my response to you would be "Absolutely nothing". Now we know why some models come with different airfoils than their full size counterparts. Not only does a scale model not have a disproportionate area and mass as compared to a full size plane, but they fly differently too.
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