# Viterna extrapolation

The Viterna method is used in Ashes to compute aerodynamic coefficients (Cl, Cd and Cm) that are missing for certain angles of attack. Typically, when generating aerodynamic coefficients (for example with XFoil, see Airfoil database ), only coefficients for a limited range of angles of attack are produced (for examples for angles going from -20 to 20 degrees). The Viterna methods enables extrapolating these coefficients to the full 360 degrees, taking into account the shape of the ful blade. Therefore, this method can only be applied to airfoils that are part of a blade.

The Viterna method in Ashes has been implemented based on the description in Tangler et al. (2004b)

In this document, we detail the equations implemented in Ashes. For this example, we assume that we have aerodynamic coefficients for a given airfoil, for angles of attack going from -20 to 7 degrees, as shown in the picture below. We use the NREL 5-MW blade.

## 1 Estimation of Cd max

The maximum drag coefficient
$$Cd_{max}$$
is taken as the maximum of all drag coefficients of the polar and
$$Cd_{max,1}$$
, defined as
$$Cd_{max,1} = 1.11+0.018\cdot AR$$

where
$$AR$$
is the Aspect ratio, which is a characteristic of the blade.