Optimal Windmill Theory by Dr. Simon P. Farthing

After completing the technical development of the Wing’d Mill, my research from 2004-2011 was into windmill theory generally which produced 6 original papers with many original ideas. In 2011 I built a windmill model to test one outstanding problem in Hawt theory and tested it in the wind tunnel of the Danish Technical University at considerable personal and carbon expense. The model validated the BEM and provided the first–ever visualization and then analysis of the process by which the kinetic energy of the torque reaction flow is lost.

I have now extensively edited my working book of windmill theory into a textbook, both an easy introduction for university mechanics students with at least one fluid mechanics course and a theory update for wind turbine engineers and researchers. A publisher is sought, and sample electronic drafts (also paper reprints) are available by request to me spfd@cantab.net. Click for the table of contents or look at these highlights. Or download Chapter 1 and send me your edits and comments please. Please acknowledge me as the author if you reproduce any part of the Chapter.

Highlights of Optimal Windmill Theory by Dr. Simon P. Farthing

Complete 2D momentum analysis showing no rotortube force and windpower lost by mixing

First visualisation and analysis of flow process in Hawt loss of torque reaction kinetic energy

Simple analytic solution of Glauert’s Optimal Hawt including analytic drag correction

First solution and thorough explanation of robust optimality for windmills, including near stall

Simple Trisection solution for Robust optimal Hawt blade elements

Best (unyawed) annual power through optimum blade twist and chord for typical winds & tides

Clear derivation of Prandtl tip loss and connection to isolated wing tip loss

First correct (analytic) solution for Contra-rotating Hawts

First sensible perturbation treatment of Hawt boundary layers, with higher Coriolis stall delay

Inclusion of Tidal Stream Power in analysis

Clear and throrough explanation of Hawt yawed power and moment and momentum balance

Constant circulation vortex analysis of Vawt’s & tangent blade oscillating & Schneider windmill

Analysis of Vawts in common with Hawt for fair comparisons

First clear proof of why for fixed blades Vawt has a narrower, lower peak C_p vs X than a Hawt can

Optimal variable and Robust cyclic pitch found for Vawt’s