Under mentorship of Prof. Earl Dowell
After reaching out to Prof. Dowell about my interest in aerodynamics, he pointed me towards an interesting problem through his notes that were provided for Aeroelasticity (ME 775). The main principle was the discussion of the conditions in which the flow around a wing section would result in moments that were precisely extreme for the given arrangement.
The hypothetical apparatus of this analysis was the introduction of a torsion spring that would counter the moment (if rotated) of the forces of lift produced on the wing. If, with the spring countering the moment produced by lift, we see that there is a large angle of attack is observed, the moment is extremely large.
A diagram explaining the setup briefly is as follows:
We're interested in the airflow conditions that would make TR point to the right edge of your screen. What could possibly be the characteristics of the windflow that would allow for a force to overcome the force of a spring.
Here L is lift force, e is the distance from the edge to the aerodynamic center, and M is the moment about this point. The k \alpha term is the term that accounts for the spring. When this equation is true, equilibrium occurs. We then decompose these terms and find the relation between the angle of attack and the flow of air and the spring. This is the part at which I would point you to these notes.
By numerically solving for the dynamic pressure conditions that would satisfy these results, we find:
Those high values of Q on the vertical axis are what we are seeking. The air velocity, chord length, and the torsional spring constant conditions with which this occurs is what we wish to study. We can make approximate guesses, of course, but the testing is where the real magic occurs.
Experimental Testing
We can be honest: most of the above was gibber-jabber. To test the above criterion, we need an apparatus. To attach a wing section to a torsional spring is not a standard task. It required the construction of a new CAD drawing. The following image, courtesy of eMachineShop, may give an idea about the thought process:
A more interactive 3D viewer can be found here: https://grabcad.com/library/wing-mounted-to-torsion-spring-1
Building this out is the next step, and I'm excited to do so!
