We’ve got this nice little number that apparently tells us everything we need to know about the wing we just tested, and that we can apply to other cases.
But why do we care? How is abstracting the forces on our wing even useful?
Because it allows us to do exactly what the Wright brothers did.
Over 120 years ago when they were first experimenting with heavier-than-air flight, they used data about lifting shapes which had been generated by other experimenters.
When the brothers went to test gliders designed using that data, though, they found that the gliders’ performance wasn’t even close to what they expected. Somehow the way they were using the data, or the data itself, was wrong. So they did their own experiments.
The way they did it is almost the same as we did with driving our wing on the top of a car.
They made a tiny wind tunnel, literally just a wooden box with a fan stuck to one side. They made little rectangles with a constant cross-sectional shape to serve as their test articles. Instead of a modern electronic load sensor, they made an ingenious metal apparatus to measure the lift generated by the wings.
Within the span of about two months, the Wright brothers tested over 200 of these wing shapes, collecting all sorts of data on lift and drag for different geometries.
But of course the tiny wings they tested weren’t nearly big enough for an airplane meant to carry a person. They would need to extrapolate their findings to the size necessary.
So they turned their data into coefficients, similar to how we did. By multiplying these coefficients by the air pressure they expected their aircraft to experience, and by the planned area of the wings, they could accurately calculate their design’s expected lift. This is why their 1902 glider performed so well when the previous ones had failed—and it’s how the brothers became the first people to invent sustained heavier-than-air flight.
This is still how we design wings today. Coefficient data is readily available for thousands of different airfoils. We can compare the characteristics of these airfoils—which one has a higher maximum lift coefficient, or a lower drag coefficient—and pick the one that matches what we need.
We can then multiply by our expected dynamic pressure and wing area, and boom—we have the lift generated by a wing using that airfoil, with the size and flight conditions we gave it.
This is what makes coefficients so fundamental to everything we do. By using a handful of unitless numbers, you can create as many different aircraft as you can possibly imagine.