*2.2. Tip Loss Correction*

Tip loss effect was first described by Prandtl who noted that the induced velocity tends to zero exponentially when approaching the blade tip and then the tip loss correction was introduced to BEM to make the simulation more realistic. For ALM, although the relationship between velocity and force is correct, a tip loss correction is suggested by Shen [19] due to the inconsistency between 2D airfoil data and attack angle of the 3D blade. This tip loss correction is employed in this study to compensate for the tip loss effect of wind turbine blade as shown in Equations (7) and (8).

$$F\_1 = \frac{2}{\pi} \cos^{-1} \left[ \exp \left( -g \frac{B(R - R\_i)}{2R\_i \sin \phi\_i} \right) \right] \tag{7}$$

$$g = \exp\left(-0.125\left(\frac{B\Omega R}{lI\_{\text{ov}}} - 21\right)\right) + 0.1\tag{8}$$

Here, *B* is the number of blades, Ω is the angular velocity, φ*<sup>i</sup>* is the inflow angle for the *i*th blade element. *R* and *Ri* are the radius of the rotor and the radial position of the *i*th blade element, respectively.
