# Aerospace Question about Trefftz plane theory?

1. Jul 6, 2012

### mezah

Hello every one
I would like to learn more about trefftz plane theory which is used to calculate induced drag.
Is it an effective method to calculate induced drag?
can i used it with propeller and wind turbine instead of an aircraft wing?

2. Jul 8, 2012

### RandomGuy88

Are you planning on doing experiments or computational work?

Computationally I think Trefftz plane is probably better because it can be difficult to accurately integrate the friction and pressure forces on the surface.

Experimentally the only way you are going to get induced drag without relying on simple theory is through measurments in the Trefftz plane.

Either way a difficulty arises because the simple Trefftz plane analysis requires integrating
(v^2 + w^2) over the entire downstream plane. If there is somewhere far from the actual wake where v and/or w are not zero ( and there is) you have to include that in your computational domain or your experimental measurment plane. ( i am not completely sure how this is done in cfd land but i believe they do something similar to what i am going to talk about)

There has been a lot of work done on this problem most notably by Betz and Maskell who derived expressions to get profile drag and induced drag by only taking measurements in the viscous wake region. I am currently using their results to take experimentally measure the profile and induced drag of my wing in a wind tunnel. This is beneficial because a force balance only gives me total drag while these results give profile and induced drag from measurments of velocity in the wake. In addition they also give the spanwise distributions of these drag components as well as the lift distribution so it is very helpful.

If I was using standard Trefftz plane analysis I would have to measure over the entire cross section of the wind tunnel and it would take forever. But using the results of Betz and Maskell I only take measurments in the viscous wake region. Even if there were no viscosity these methods would still get induced drag by only measuring the regions of nonzero vorticity.

So if you want induced drag then you will need information in the wake. You might be able to get away with standard Trefftz plane analysis in some situations but I think what I just discussed is more typical/practical. This is at least true based on my experiences and from what I have read.

I have seen people use these methods on propellers as well and I plan on doing this with propellers and wings in a few months. There are some difficulties with prop and wing combinations because of wake roll up and distortion so it becomes a little less clear what you are measuring. I haven't looked into this very much yet but I do have at least one reference.

If you are interested I can send you some references and I would be happy to answer any questions. I have working on this suff for awhile now.

3. Jul 9, 2012

### mezah

Thank you for taking time to answer my question

what i am intending to do is measuring the tip losses for wind turbine experimentally and may be verified it analytically, i am not sure what to do yet.

After reading about the subject i found that - as you mentioned - going CFD will give me the drag as single number without mentioning how much the contribution of different drag components, and i read that if i want to calculate specific drag component like induced drag i have two ways to go.

First : using CFD to calculate lift distribution and put the distribution of lift in trefftz plane equation,which will give me the induced drag.

Second: calculate the lift distribution using trefftz plane theory and then calculate induced drag using the same theory.

Since i can't find any references about the subject i am not sure what i should do, and i can't follow you when you are taking about it.

sure i am interested, and appreciate your help.

4. Jul 10, 2012

### RandomGuy88

Sorry if I wasn't clear. I would suggest you go look up the following reference for a description of what I am talking about.

Brune, G.W., "Quantitative Low-Speed Wake Surveys," AIAA Journal of Aircraft, Vol. 31, No. 2, 1994.

Let me know if you can't find the article or if you have any questions. I have been working on this stuff for awhile and have a lot of references if you are still interested.

5. Jul 10, 2012

### mezah

Thank you very much for your help, i will check it out and inform you.