How much lift will a wing section produce?

Many smart people asked this same question in the late 1800’s and early 1900’s. They wanted a simple formula. The main difficulty was that the lift force was not just a function of one thing; it was a function of many things. Here are some of the facts they knew:

• As the density of air increases, the lift force also increases.
• As the wing area increases (birds-eye view), the lift force also increases.
• When airspeed is doubled, the lift force is quadrupled!

With these characteristics in mind, those smart guys stated that lift was proportional to the air density, proportional to the wing area, proportional to the square of the velocity, and was somehow related to the wing cross-section itself. But even after they figured all this out, there still wasn’t an exact formula. For example, they couldn’t say that lift was exactly equal to the product of speed, density, and wing area. The best they could do was say that lift was sort of equal. Kind of equal. But not exactly equal to a combination of all those things.

In this situation, engineers often state a problem in outline form using a proportionality symbol called tilda, or "~".

To fix this lack of exactness, they did what any good engineer would do; they used something called a proportionality constant, also sometimes called a coefficient. Generally, these are special numbers used to make our answers agree with what we expect, measure, or predict; especially with natural phenomena where many of the lesser influences are lumped into that single special coefficient. Non-engineers can think of this as a fudge factor. You can represent this coefficient with any letter of your choice; historically we've used the letter C with a little "L" as a subscript: C_l

Stop the presses! You may wonder where the one-half (0.5) came from. That's actually a result of developing the formula using something called dimensional analysis. Trust me on this; it belongs there (I won't talk about it here, but it allows for a shorter version of the formula using a term called Q, or "dynamic pressure.")

Similarly, we can create formulas for the drag force and pitching moment as well. The only real difference is...