Back to **Aerodynamic Design of Aircraft with Computational Software**

Back to overview: **Preamble Exercises and Projects**

Chapter 11[pdf]: 11.1 Introduction 11.2 Model of Wing Section in Torsion 11.3 Aeroelastic Configuration Model 11.4 Modular Framework for Aeroelastic Loop 11.5 Case Studies: Elastic-Static Wing Effects

**Tutorial: **Under Construction**Exercises and Projects **– software here `pyTornado` and `Framat.`**Review questions to consider before doing calculations**

- Explain the terms static and dynamic aero-elasticity

- What does “divergence” mean in this context? Why is a forward-swept wing more prone to divergence than an aft-swept wing?

- How can the divergence speed be estimated? What data is necessary?

- Explain the transfer operators from CFD to structures and vice versa. Why and how might a structural model with shell elements on the skin be easier than the classical “elastic axis” beam model?

**Computations for static aero-elasticity**

- The example in Ch 11 on a straight wing in a wind-tunnel is modeled by the script
`WTexample`which runs the aero-elastic loop between VLM and an “elastic axis” beam model. Look into the script and make it plot the deformed wing at each iteration.

- HALE configurations are very flexible and have very long wing span to reduce the induced drag. The HALE model from Ch 10 has a straight, rectangular wing which can be modeled easily by a beam with constant cross section from root to tip. The beam bending equation says

EId^{4}w/dy^{4}=Qwithw(0) =w'(0) = 0,w''(b/2) =w'''(b/2) = 0 (*)

where* Q*(*y*) [N/m] is the lift force distribution, so the *deflection/EI* can be computed easily. If *Q* were constant across the span even by a simple degree 4 polynomial. Since the total lift equals the weight you can do that and plot the deformed wing. Choose *EI* to make the tip move up 10% of the half-span.

Then investigate the “results” returned from VLM (see `../Ch3Docs` for information about the octave `Tornado`), figure out how to extract* Q*(*y*). Then use a simple difference scheme to solve (*) with the correct distribution. The “elastic loop” can now be put in motion by editing the geo file and running VLM on the deformed geometry. Do that manually once.