Bill Cummings wrote:A wind speed of 2 mph going to 4 mph the lifting force isn't just doubled the force jumps to 16.
That's exactly right. All aerodynamic forces depend on the velocity squared. Twice the speed ... four times the forces. Three times the speed ... nine times the forces. Four times the speed ... sixteen times the forces. That's true for lift and drag, and it's what limits the upper speed of your car. Eventually the drag gets so great that it equals 100% of your engine's power.
I worked in a wind tunnel for a couple years in college. The primary results we produced were lift and drag coefficients. What are they? I'm glad you asked.
A lift coefficient (CL) is just a number that describes the amount of lift for a given wing of a given size at a given speed in a given air density:
Lift = CL x 1/2 x density x velocity x velocity x wingarea
You'll note that I included velocity twice because the lift force goes up with velocity squared.
The cool thing about that equation is that you can ask questions like:
How much larger does a wing have to be to carry twice the weight at the same speed in the same air density?
Well, if you're requiring twice the lift and keeping everything else the same, then you're going to need twice the wing area.
How much would your speed go up to carry twice the load at the same conditions?
Since the lift depends on the velocity squared, you'd need to double your squared velocity. That means your velocity would have to up by the square root of 2 ... which is about 1.4.
If you understand that equation it can help answer a lot of questions. But it does leave out an important point. Does CL depend on anything else? The answer is a big YES!! CL depends very directly (and nearly linearly) on alpha - the angle of attack. And that's what we control directly with pitch. But as we increase alpha, we also increase drag ... which reduces velocity.