PIMS/Shell Lunchbox Lecture: Some Mathematical Issues in Wind Turbine Aerodynamics

  • Date: 12/04/2014

David Wood, Dept. Mechanical and Manufacturing Engineering, University of Calgary



Dr. Wood's main research interests are in small wind turbines and other forms of renewable energy. His book Small Wind Turbines was published by Springer in 2011.
Prior to joining the University of Calgary in February 2010, he was part-owner and technical director of Aerogenesis Australia, a company commercializing the small wind turbine technology he helped to develop over many years at the University of Newcastle.
At the University of Calgary, he has started a project to monitor, model, and predict the urban wind resource to support the installation of small wind turbines in Calgary and other urban areas in Alberta.
Other research areas include generator and control system modeling and development, multi-dimensional optimisation of turbine design, solar and wind resource forecasting, and remote power systems. He has a strong interest in renewable energy for developing countries and is currently working on three projects in Nepal: on novel methods of controlling micro-hydro turbines, performance monitoring of hybrid remote power system, and the use of bamboo for small wind turbine towers and blades. In 2012 and 2013 he lectured on renewable energy in Ethiopia.




Calgary Place Tower (Shell)


Some Mathematical Issues in Wind Turbine Aerodynamics


Mathematical models of wind turbine blade aerodynamics have provided valuable limits on the performance for actual wind turbines. The simplest and best known is the Betz limit on power production. It is less well-known that this limit applies only at very high tip speed ratio (TSR) defined as the circumferential velocity of the blade tips divided by the wind speed. The mathematics for finite TSR is complicated by the helical geometry of the vortices in the wake of the blades. The talk will describe a “lifting line” analysis of wind turbine blades similar to the classical analysis of aircraft wings where the trailing vortices are straight and easy to quantify. The analysis involves solving a Cauchy singular integral equation whose integrand, for helical vortices, contains Kapteyn-like infinite series of products of Bessel functions and their derivatives. These series do not have closed-form summations but some simplifications and approximations are possible for some important practical cases. These will be discussed along with continuing work to extend the analysis to more complex vortical structures.

Other Information: 

Location: Calgary Place Tower 1 (330 5th Avenue SW), Room 1104


Time: 12:00-1:00 pm





PIMS is grateful for the support of Shell Canada Limited, Alberta Enterprise and Advanced Education, and the University of Calgary for their support of this series of lectures.