**Aerodynamic profile optimized for AWE, the Venturato Airfoil**

The power production of AWE generators depends heavily on the aerodynamic forces on the wing. The development of a wing that is optimized for Airborne Wind Energy power production is a field almost completely unexplored. From Loyd's model, we know that the power output is proportional to the factor:

\[\frac{C_L^3}{C_D^2}\]

where $C_L$ and $C_D$ are the lift and drag coefficients, respectively. Maximizing this factor (hereafter referred to as fitness factor) means directly maximizing the power output of an AWE generator. This fitness factor is a close relative of the aerodynamic efficiency, therefore a real prototype of an AWE wing should certainly have a high aspect ratio (the most important parameter when determining the aerodynamic efficiency). However it is interesting to see what is the 2D airfoil that maximizes the value of the fitness factor $C_L^3/C_D^2$.

An optimization of such factor was performed in [1] using a genetic algorithm. The profile was defined as a set of Bezier control points. The genetic algorithm started from the Clark-Y profile, then randomly changed the geometry, then computed the fitness factor for the new profile and determined whether the geometry changes were to be kept or discarded, then started over with another change in geometry until an optimal airfoil was found. The fluid-dynamics simulation was run at a Reynolds number of 300000, and all the solver parameters were chosen to best fit the experimental data available for the Clark-Y airfoil.

The optimal geometry found in [1] is elegant and looks as follows.

**Figure 1: Venturato Aerodynamic Profile.**The picture shows an airfoil optimized for AWE generation. It was computed with a genetic algorithm maximizing the power output.

The optimal profile (hereafter referred to as Venturato profile) is better than the Clark-Y from various points of view. As shown in Fig. 3, the fitness factor is better for a very wide range of angle of attacks, improving the power output by more than 50%. Moreover the pressure distribution for the Venturato profile (available in [1] pp. 65) shows a lower gradient on the low-pressure side which suggests a better stability in terms of flow separation.

Figure 2: Venturato profile vs Clark-Y, geometry. The Clark-Y airfoil is slightly rotated. |
Figure 3: Venturato profile vs Clark-Y, fitness factor. |

**What is next?**

This analysis does not take into account the cable drag which unfortunately accounts for most of the drag in an AWE generator. However it is a good starting point, especially for a prototype. A further analysis that takes into account the cable drag [2] would have a different fitness factor that is likely to be:

\[{\left( \frac{C_L}{C_D+\frac{ n r d C_\perp}{4A}} \right)}^2 C_L A \]

where $C_\perp$ is the cable perpendicular drag coefficient, $n$ is the number of cables, $r$ is the length of each cable, $d$ is the cable diameter, and $A$ is the wing area.

I would like to conclude this post with a citation from [3]: "Obtaining raw lift on a body is relatively easy. Even a barn door creates lift at angle of attack. The name of the game is to obtain the necessary lift with as low a drag as possible."

**References**

[1] A. Venturato, Analisi fluidodinamica del profilo alare Clark-Y ed ottimizzazione multi-obbiettivo tramite algoritmo genetico, MSc Thesis, Università degli studi di Padova (2013)

[2] B. Houska, M. Diehl, Optimal control of towing kites, Proceedings of the 45th IEEE conference on decision & control, San Diego, USA 2693-2697 (2006).

[3] John D. Anderson, "Fundamentals of Aerodynamics", McGraw-Hill, New York, Third Edition (2001).