High Camber hydrofoil section for wingfoiler

I posted this in a facebook group for hydrofoil builders, and commenters suggested I post it also in a forum where it will hopefully remain discoverable for longer than a week.

As an introduction: I build hydrofoils for wing-foiling and kite-foiling for myself as a hobby. After many iterations my builds are working well, I think they perform on par with the best commercial offerings.

I have been trying to find better wing sections for my next front wing. My last design has a straightforward wing section, with 10% thickness, 2.9% camber and shaped like a very normal wing. I created this section with Xflr5/XFoil mostly through iterative inverse design. I have made a 930cm2 front wing with it that is now my go-to wing for wing foiling. It's fast and it transitions well. It glides through tacks as long as it keeps some speed. But pumping is not easy, it probably can be better. And I do have a feeling that this wing does not handle tip-out situations very well. I find it very hard to avoid falling when a tip breaches the surface, I think it easily ventilates (but a lack of skills is another possible explanation). So I mostly want to improve glide and tip-out ventilation for my next design.

How do I improve glide and ventilation? I think I need different foil sections that provide that. Finding better foil sections with Xflr5 is pretty hard, and I felt like I could not get much further. It is easy to optimize for one thing (performance at one speed/angle) but optimizing for multiple objectives is more art than science.

So I figured I'd try doing it the modern way, specify the objectives and let AI figure it out. I read all scientific articles I could find about this (I'm not the first one having this idea) and then wrote a Python program to implement it. The program uses the differential evolution optimization algorithm (so it's not really AI) to evolve foil sections from a set of parameters and runs XFoil to measure the generated foil over a range of speeds. At ten different speeds it calculates:
- Lift coefficient needed to carry the weight (type 2 polar essentially)
- Drag (maximize speed/distance)
- Glide (maximize power/flying time)
- Ventilation (minimize pressure peak)
- Pitch stability (have a stable center of lift)
It throws those measurements in a magic weighted formula to calculate a final score for the foil section. It also calculates the variation of the pitching moment, for a "dynamic" behavior score.

Making this program was not easy. XFoil is finnicky (it's written in Fortran some 30 years ago) and numerically sensitive (flow is physically sensitive too). And published parametrization methods turned out to be either unsuited for hydrofoil sections (Bezier-Parsec) or too compute-intensive (NURBS) to be practical. I had to invent a new parametrization method. The weighed scoring also has a tendency to go off into extremes (like making a "torpedo" foil with very low drag and pressure, giving up completely on everything else). Technically it needs to use multithreading and communicate in-memory, or it'll still be very slow.

After lots of tweaking I now have arrived at a version that works well. It's sort-of magic to see a foil section morphing from a random start shape into something that is highly optimized for its objectives. The program runs for one to two hours and then spits out the best foil it found. The video attached is a sped up recording from a run that took a bit over one hour.


I also wrote a feature to find "matching" sections that match a reference section, but for other chord lengths and with different settings. This lets me optimize sections of the wing separately, from the root to the tip and also calculate with a realistic trailing edge thickness. This makes it possible, for example, to optimize the root for glide, the middle part for speed and the tip for ventilation. I still have to add a feature for scoring stabilizer sections, that have other requirements but as my current stab is fine I'll get to that later.

So what did I learn? I learned that the sections that I used before weren't so bad. I can improve on them by a few percent, but not spectacularly more. Every improvement comes at a cost somewhere else. However I did find many interesting foil sections outside of my previous bounds. Which is where I hope to get some input from this community.

I found that between glide, speed and pitch stability, you can only have two. When optimizing for speed, the thickest point moves backwards and the leading edge gets sharper. Optimizing glide moves the thickness forward and creates a thicker leading edge. Improving one always worsens the other. The only way to get both is by allowing the pitching moment to go very negative, making a "high cambered" foil section. That will improve both, the improvement in speed mostly comes from a smaller wing area made possible by a higher lift coefficient. Btw: there is no added benefit from the higher AR of such a high-lift wing, as the CL is on the opposite side of the induced drag formula cancelling out the gain. Only wingspan can change induced drag.

I have now made two concept designs for my new front wing. One is an optimized version of what I have now, with sections that look normal, it has about the same surface area and the pitching moment is low and flat. The outline is a bit different and each section is individually optimized, the tips should have better ventilation behavior as they are optimized for cpmin. I might add a small fence on the top surface around the transition point to block air flowing in.

The second concept uses a high camber airfoil. It is 50cm2 smaller, has substantially higher end speed, and also lower takeoff speed and better glide, and the wing tips are also optimized for ventilation. The mid range is slightly worse than my old design.

I'm very much in doubt which one to build. I don't want to build both, as they should do essentially the same. I'm inclined to build the high camber version, but have doubts about its pitching moment: how will it behave? At top speed, the center of lift will be near the trailing edge and the flow will push down hard on the leading edge! I did build a high cambered foil once, and it behaved awfully. But I knew a lot less then and it was much larger. Does anyone here have opinions on, or experience with using high cambered / aft loaded hydrofoil sections?

 

Hi Maarten,
I don't see any attached video.
Do others?

 

Sorry, I had hoped the forum would offer some way to upload it, but it doesn't. I have uploaded it to Youtube now and edited the post to show it.

 

What "fitness functions" do you use for optimizing the glide, speed and pitch stability ? From what I read, I assume that you're using a 2d potential flow formulation for the section, and some kind of integrated formulas for elliptical wing configuration. If so, you may be interested in swapping to a full 2d navier-stokes solver to calculate CLs, CDs, CMs, and integrate them using something like a lifting line to take into account some more complex wing shapes. The result of your optimization runs will be influenced by other physical phenomenon, like multi-stable flow patterns and cavitation.

 

The fitness function first calculates a "score" for every variable at every speed that gets multiplied by a constant, or squared, or offset to come out somewhere between 0 and 1 in a way that I feel corresponds to relative performance (lower being better). Then there is a weight table how heavy this score gets counted at every speed, i.e. glide score (cd / (cl^3/2 * sqrt(re))) is only weighed nonzero for low speeds, the speed score is weighed spread over the upper half of the range. I can vary with this weight table, increasing a weight even slightly will result in a section that really scores better at that measurement. I weigh cpmin mostly at medium speeds, because that speed range is where I'd do sharp corners in waves and tip out ventilation would cause me to fall. If you'd want to avoid cavitation you'd weigh this at high speed. Then finally these scores for each score get combined with weights again to a single number.

The wing shapes, stability calculations etc I do in Xflr5, which uses VLM. Xfoil is used mostly in (model) airplane design, it is based on 2D potential flow theory but it's used for hydrofoils too. Is there a practical way for a non-professional to get better results with a 2d navier-stokes solver?

 

Of course. There are quite a lot of "less than 200 lines of code" in C, Python, or Julia for anyone who needs some insights on 2D flow around a profile. As it seems that you are quite capable of programming, you could take advantage of some of the existing programs. If you feel too much limited by your actual optimization loop, which is normal, since your model is quite simplified, then it would make sense for you to reconsider the use of VLM methods, for you to get "better results", in your own meaning.

VLM methods are usefull to study the general configuration of a given wing, or, a combinaison of lifting surfaces and non-lifting surfaces. VLMs have un-steady formulations, can handle supersonic flows, are very fast in term of computing time, and give an excellent quality over investment ratio. However, non-linear effects, like Z+flow coupling, recirculation, cannot be solved with such codes. In aeronautics, you use the code to make the general architecture of your airplane, (lifting surface, weight balance, engine power estimate) and, depending on the amount of money you have to develop a full solution (able to take off, to land, to avoid buffeting....), you either make additionnal studies (CFD, wind tunnel), either rely on general backgrounds, but also being unable, that way, to perform any optimization.
For an hydrofoil application, VLM can be used to compute surface areas, stability given a certain weight distribution, and an idea of the power required if you work on propelled crafts. But you already see that, given a certain domain of practical constraints, the output of your optimization chain tends to always be the same. Not to mention that, if you're using a single wing, almost the same results can be obtained by hand or with an Excel file with 5 cells. Publishers of VLM software are selling dreams, but one shall not forget that NASA has developped the F15 and F16 and VTOL configuration using such codes, with no more than 50 panels in the model. Of course, you understand easily that not the whole flight domain of these planes have been studied that way.

My opinion is that it's the same for you. At this point, your work is amazing, and can surely helps you in your design work, also being able to explain to your clients that you rely on solid numerical models. If you wish to get higher, and if you are not a professionnal CFD guy, than the best thing is to find a true one. This is solution one.
The other solution is perhaps easier for you : Build / Test / Redo. Skip the Navier-Stokes, instabilities, potential flow sh.t. Focus on true experience. So why don't you built these high cambered / aft loaded hydrofoil sections?

 

Hi Maarten88
How did you get on with your foil? Did you get good agreement between your analysis and real world?

 

I built it and have tested it well now. I did find good agreement between the expected behavior and practice.

The positives: it has very early lift, and is very efficient at low speed. So it is very easy to do transitions, it's also very good riding waves. It turns extremely well, in a very short radius. Also tip ventilation was what I hoped for, I can breach the surface and I don't even feel it.

Regrettably, my fear for the high pitching moment did turn out to be real. When going faster, at some speed I notice the center of lift shifting back, making it hard to keep going level. In practice I could not reach the speed that I had hoped and optimized for (40 kmh). I topped out around 37.
Another issue I had was loud whistling. I could not get rid of it: the trailing edge is probably too thin.

My previous (2.9% camber) design feels much more predictable at higher speed, and is a bit faster, even having a bit more surface area.

For wing foiling, speed is important. I decided I don't like this design in the end. I have optimized my software further, and made a new design that is optimized at the mid-speed range and that has lower camber. I have also changed the way I distribute optimization properties over the wing span and hope I can retain the good ventilation performance in this new design. This wing is just finished, I'm waiting for wind to test it.

I think that high camber foil sections are more suited for foiling disciplines where the average speed is just above the takeoff speed, such as downwind foiling and prone foiling.

 

I would be interested in using your optimization algorithm to suggest a profile for my use case, but can't seem to send any private messages (I assume since I have just joined the forum). Can you possibly send me a DM?

 

I can't send you a DM from my end too, probably for the same reason.
You can send an email to my gmail.com spambox at maartensikkema

 

Can you share the findings on the lastest design ?
I want to build a foil for windfoiling, so probably a little higher speed than wingfoil foils.

See the end of this post for information
Foil section? For foil board https://www.boatdesign.net/threads/foil-section-for-foil-board.63233/page-2#post-967629