WT_perf which equations used to calculate induction factors


Which equations did you use to calculate the axial and tangential induction factors in the WT_perf code? Are it the ones from the Aerodyn Theory manual , from the Hibbs and Radkey document small wind energy conversationsystems… or some completely other ones.

I used the equations from the Aerodyn Theory Manual for my code. My induction factors do not completely match with the WT_perf outcomes but they are almost the same.

If I regard the Thrust/length and the Torque/length it is the same curve.

Thanks and Kind regards


The AeroDyn Theory Manual is a combination of what AeroDyn is now and the way we want it in the future. The BEM equations documented in it are what we use in WT_Perf. There is a small error in the implementation in AeroDyn when including both tip losses and tangential induction. If you disable either option, AeroDyn and WT_Perf give virtually identical answers. There is an error in the Hibbs document in how the tip loss is applied. The second equation on page 17 should have only one F in it. You can see how I marked up the document to remove the second F.

There is also an issue of using the drag term in the either the axial or tangential equations. I made it an option to select either or both in WT_Perf and it’s an undocumented feature in AeroDyn. Please be sure you are consistent when doing comparisons.

I have found that changing the iteration algorithm (the algorithm itself or the constants used in it) in any way can make a noticeable difference.

I assume you mean in the BED files. I just now looked at the ones from the certification tests and they differ. By the way, there is an error in the heading for the units in the BED files. The units for two variables is missing. We have fixed that in the development version I am working on now.

Thank you for your response.

What do you mean with:

Can you give me a number,best would be in percent, how big the difference due to the different iteration algorithms is?

I always set the induction factor for the next step equal the induction factor calculated in the last one.
tangential induction factor = tangential induction factor calculated in the last step
and iterate as long that the difference is very small. Do you have papers or documents that deal with different iteration algorithms. I could not find papers on this topic. Only this one:
Damping the fluctuating behaviour and improving the convergence rate of the axial induction factor in the BEMT- based rotor aerodynamic codes . Alireza Maheri*, Siamak Noroozi, Chris Toomer, John Vinney University of the West of England, Bristol, BS16 1QY, UK,Ali2.Maheri(at)uwe.ac.uk
Thanks for your help

Not really. Try changing the error tolerance, ATol, to see how much the answers change.

That’s how they say to do it in the various books, but it doesn’t always work. I spent a couple months years ago trying to come up with a better method, but was told I had to work on something else and never finished. I had a PhD student (Dave Maniachi) come here last summer to finish the job. That resulted in the version I’m trying to finish now.

David wrote up what he did, but we haven’t had time to publish it. If he approves, I’ll send you a copy of the draft. I’ve seen no comparisons.