Deriving thrust and torque from the blade element perspective. Equating with momentum theory to solve for the axial and tangential induction factors. Showing how to solve more efficiently with a 1D residual. Overview of the implementation for computing across the whole rotor. Nondimensionalization.

For more detail see the following two references:

Ning, A., “Using Blade Element Momentum Methods with GradientBased Design Optimization,” Structural and Multidisciplinary Optimization, Vol. 64, No. 2, pp. 994–1014, May 2021. doi:10.1007/s00158021028836

Ning, A., “A Simple Solution Method for the Blade Element Momentum Equations with Guaranteed Convergence,” Wind Energy, Vol. 17, No. 9, pp. 1327–1345, Sep. 2014. doi:10.1002/we.1636