Assume I have a system comprising of an airfoil A immersed in a fluid.
Further assume, that the airfoil is affixed via two bolts at one end, and is untethered at the other end.
The system can be parametised as follows:
- S is the span of the airfoil
- C is the chord of the airfoil
- V (vega) is the relative velocity of the fluid passing over the airfoil
- $\rho$ is the density of the fluid in which the airfoil is is immersed
- $\theta$ is the current angle of attack of the airfoil (in radians)
- L the distance between two bolts affixing the airfoil at one end (< C)
Given a new angle $\theta_i$, what would be the formula for calculating the force required to be exerted on the two bolts to change the current angle of attack of the airfoil from $\theta$ to $\theta_i$? (assuming all other variables held constant)
From the lift characteristics of an airfoil, I think its fair to assume that a greater force will be required to be exerted as the angle of attack increases (up until the stall angle)
Additionally, since the force required is likely to be monotonically increasing (up until stall angle), I would prefer if the function actually returned the supremum of the the forces required to increase the angle of attack from:
$\theta$ $\rightarrow$ $\theta$ + $\delta$$\omega$
where $\delta$$\omega$ is the change in radians divided into an infinitesimal number of steps.
Ideally, the formula should derived from first principles (or the answer be provided as pseudocode for an algorithm), so that I can follow the logic, and apply it to an airfoil of non-rectangular shape.