Cp Controversy

According to Betz the Cp of a HAWT can not exceed 59.3%. Yet the Vortec 7’s Cp was measured at 200%. The Vortec 7 is not an over-unity device. It cannot extract more energy from the wind than exists in the wind. The reason we get this odd result is that the Cp formula can only calculate the percentage of kinetic energy extracted from the wind. The DAWTs and TWECS use both kinetic energy and flow-pressure energy to produce power. And by doing so, they violate the fundamental assumption underlying the Cp calculation: that all the energy in the wind is kinetic energy. So they produce Cps that make no sense.

In science, when you violate one or more of the assumptions upon which your calculations are based, any conclusions based on those calculations must be looked upon as suspect. So, in short, there is no scientific justification to use Cp as a basis to compare the efficiency of a kinetic WES with a kinetic + flow-pressure WES.

If you wanted to compare the efficiency of these two systems, you would need to derive a new Betz-type limit that takes both the kinetic energy and the flow-pressure energy of the wind into consideration. Since this “Total Energy” limit does not yet exist, there is no calculation we can use to directly compare the efficiency of a kinetic WES to the efficiency of a kinetic + flow pressure WES.

Or, to put it more prosaically: Efficiency is a concept that is useful when comparing apples to apples, but is not very useful (and can be misleading) when comparing apples to oranges.

What do we really want from wind turbines? We want the same thing from wind turbines that we want from any other method of generating electricity: low cost per kilowatt hour. So, the ideal comparison (from an economic standpoint) among all forms of electrical power generation, including wind turbines, is Levelized Electricity Cost (LEC). This is where the rubber meets the road. A system that is twice as efficient as a HAWT but costs so much to build that the LEC is twice that of a HAWT doesn’t really advance the state of the art.

LEC, however, can be a hard number to calculate. You first have to optimize your design, build prototypes, settle on construction materials, make lots of assumptions, etc.

With the appropriate software and adequate data it is fairly easy to generate a power curve for any wind turbine. All things being equal, the turbine that produces more power at the same wind velocity is the better machine.

Yes, I know that all things will not be equal when comparing TWECSs to HAWTs. However, I believe reasonable extrapolations can be made from power curves to LEC that will possess a fair degree of face validity; enough validity, anyway, to determine if further research on The New Approach TWECS is warranted.


Gavhane, K. A. (2009). Introduction to Process Calculations: Stoichiometry, Pub: Nirali Prakashan, ISBN# 978-81-906316-6-8.

Phillips, D. G., Flay, R. G. J., Nash, T. A., (1998). Aerodynamic Analysis and Monitoring of the Vortec Seven Diffuser Augmented Wind Turbine. Proceedings of the Annual Conference of the Institute of Professional Engineers NZ, Auckland.