You wouldn't give an adult dose of medicine to a baby because the volume is not appropriately scaled for them. A similar thing happens with aerodynamic coefficients. Just because you obtained the coefficients during a wind tunnel test does not mean they automatically apply to a full-scale aircraft. To ensure that the data obtained from a wind tunnel is applicable to a full-scale aircraft, all we need to do is match Reynolds Numbers. To better explain this concept, let’s go back to the wind tunnel.

We’re now standing next to the wind tunnel. Inside the tunnel there is a quarter-scale model of an airplane mounted on a force-measuring device. Let’s call this airplane the Pessna Worrier. The wind tunnel speedometer tells me that the air inside the wind tunnel is traveling at almost 160 miles per hour. Although I’m just a mediocre pilot, I know this airplane could never go that fast. So I ask the operator about this speed discrepancy and he says, “Oh, we’re just trying to match the Reynolds number to full scale.”

Huh?

~flashback~

The world of engineering is filled with special numbers named after people long dead whom you and I will never meet. One of these people was Osborne Reynolds, an Englishman from the late 1800’s. Mr. Reynolds was obsessed with watching colored dye flow through pipes. He was especially interested in how the dye would start out flowing as a smooth streak (Laminar) and invariably break down into eddy-filled craziness (Turbulent); the same phenomenon can be seen with cigarette smoke rising from an ashtray. Reynolds didn’t know it, but he was really studying the concept of boundary layer growth; a subject that is of paramount importance in aerodynamics. In the absence of boundary layer phenomena, aerodynamics is downright simple. Unfortunately, major things like top-speed and maximum lift are very dependent on boundary layers.

At the beginning of the 20th century, long after Osborne Reynolds, a German researcher named Ludwig Prandtl formulated the equations needed to describe how boundary layers grew. In short, they get thicker and messier as they progress downstream. Prandtl used a subset of the previously known Navier-Stokes equations for his methodology. Very complicated stuff, but Prandtl was a very smart guy.

The thing to know is that the Reynolds Number (Re) contains a summary of flow information. It conveys nearly everything you need to know about a certain flow condition and it doesn’t even have any units. No feet. No inches. No pounds. Nothing. It is a product of the fluid density, fluid velocity, important length, and the reciprocal of the fluids’ viscosity. Think of it as a meat grinder where you pour all the environmental flow conditions in one end and the unitless Reynolds Number plops out the other end...