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Expand Up @@ -132,11 +132,11 @@ In addition to accuracy vs. speed, another consideration when choosing the right

## Airfoil Shape Optimization using NeuralFoil

NeuralFoil can be used for airfoil shape optimization, in conjunction with [AeroSandbox](https://www.github.com/peterdsharpe/AeroSandbox). An example airfoil design optimization result is given in the [NeuralFoil whitepaper](./paper/out/main.pdf), where we optimize an airfoil shape for a human-powered aircraft application. This is a drag-minimization problem, subject to lift and pitching moment constraints, and manufacturing limits.
NeuralFoil can be used for airfoil shape optimization, in conjunction with [AeroSandbox](https://www.github.com/peterdsharpe/AeroSandbox). An example airfoil design optimization result is given in the [NeuralFoil whitepaper](./paper/out/main.pdf), with [code here](https://github.com/peterdsharpe/AeroSandbox/blob/master/tutorial/06%20-%20Aerodynamics/02%20-%20AeroSandbox%202D%20Aerodynamics%20Tools/02%20-%20NeuralFoil%20Optimization.ipynb). Here, we optimize an airfoil shape for a human-powered aircraft. This is a drag-minimization problem, subject to lift and pitching moment constraints, and manufacturing limits - full details in the paper.

![daedalus_optimization.svg](./paper/TeX/figures/daedalus_optimization.svg)

Here, NeuralFoil achieves performance equal to expert-designed airfoils. The entire optimization process takes roughly 30 seconds on a PC; optimization studies with a lower NeuralFoil `model_size` value can run as quick as half a second. Notably, if the problem formulation is well-posed, NeuralFoil will not "over-optimize" to achieve a solution that performs well at on-design conditions but very poorly when off-design. Compared to optimization by simple wrapping of XFoil with a gradient-based optimizer, the resulting airfoils achieve better aerodynamic performance due to the [ragged nature of XFoil's gradients](https://websites.umich.edu/~mdolaboratory/pdf/Adler2022c.pdf). And, compared to [wrapping XFoil with a gradient-free optimizer](https://github.com/jxjo/Xoptfoil2), NeuralFoil-based optimization is much faster.
Here, NeuralFoil achieves performance comparable to expert-designed airfoils. The entire optimization process takes roughly 30 seconds on a PC; optimization studies with a lower NeuralFoil `model_size` value can run as quick as half a second. Notably, if the problem formulation is well-posed, NeuralFoil will not "over-optimize" to achieve a solution that performs well at on-design conditions but very poorly when off-design. Compared to optimization by simple wrapping of XFoil with a gradient-based optimizer, the resulting airfoils achieve better aerodynamic performance due to the [ragged nature of XFoil's gradients](https://websites.umich.edu/~mdolaboratory/pdf/Adler2022c.pdf). And, compared to [wrapping XFoil with a gradient-free optimizer](https://github.com/jxjo/Xoptfoil2), NeuralFoil-based optimization is much faster.

## Extended Features (transonics, post-stall, control surface deflections)

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