Closed-Form Solutions For Optimum Rotor in Hover and ClimbWilliam Luer
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This document presents closed-form solutions for the optimum rotor loading in hover and climb based on Glauert's momentum theory approximations.
The key results are:
1) Glauert's variational approach leads to a quartic equation for the optimum loading in climb. While this has no simple closed-form solution, the document derives an excellent approximation solution in closed form.
2) For hover, the equation reduces to a cubic with a known closed-form solution.
3) Wake contraction behavior is also derived in closed form for the Betz and Glauert loadings, allowing induced velocities to be calculated throughout the rotor disk and wake.
4) Numerical results show the approximation achie
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