Prandtl's lifting-line method for sails

Lucky you! If you go skiing, I wish you enough snow and fun without a crash.

The Fx values are much higher than mine, but the AWA is also larger. I will try to copy your setting.

 

This is interesting! I ran XFOIL at a position halfway up the genoa. In the case with linearly increasing camber the sail has a camber 0f 13.5% at this position and an effective angle of attack of 5.2°. XFOIL shows separated flow at the pressure side directly behind the luff, but the flow reattaches towards the leech. See attachment. This would confirm your picture.
If I prescribe constant camber for the genoa, the optimizer proposes a camber of 9% and an effective angle of attack of 8.5° at the same position. The flow remains attached without separation. See second attachment.
The surprising result is the L/D-ratio. With separation it is 89 and without it is 59.

When sailing upwind on Lake Constance (flat water) I usually trim the Jib to a point where the telltales on the pressure side are slightly pointing upwards. This would indicate a mild separation. It gives the best VMG.

PS: with your wind- and boat data, I get an AWA of 23.2°.

 

I noticed a typo in my wind shear numbers, will rerun your test case when I get back in Office.

 

Also, I’m not using the log law for wind shear, but the power law, hence your coefficient 0.02 would not be correct for me.

 

Reading the manual often helps: You refer the BETATW to the boat axis, while I have my TWA referred to the direction of motion? So 40 deg in Ulisail is 46 deg for me - that would certainly explain the separation on the inside of the genoa in my test run. Also, my Fx is in the direction of motion, while you work in the body axes. I should rotate my coordinate system to the body axes.

 

Thanks for the precision, If not top-secret proprietary research, is the power around 0.60 in your power law ?
I would understand it can be confidential,
Cheers
EK

 

Erwan, no secrets here - I normally use k= 0.12, or between 0.1 to 0.14. The law itself is Windspeed * (H/10)^k. 0.6 would be an extremely stable case, with hardly any vertical mixing, like springtime in Finland with sea temperature 7 degrees & air 15 degrees, and a very light wind of 6kn.

We've measured with the French Olympic team, natural wind turbulence over the sea in the baie de Quiberon, for a week in a rib anchored in place, at the height of 2 m & 6 m. The turbulence intensity is much higher than generally assumed "on a smooth sea", ranging between 5% to 20%, with a maximum of 34% and minimum 4,7%. It varies a lot from day to day, and even during the day from hour to hour, as the wind (and waves) develop. Therefore, I would not count on any laminar flow on sails. In wind tunnels, you usually strive to a minimal turbulence, in the order less than 0,5%, therefore with small models & reynolds numbers, there can be too much laminar flow and the results can be less reliable than CFD.

 

Mikko,
Thank you very much for sharing,

in fact, in 2014, talking with P.I engineer at ENV, I knew you had made this research, but as I guessed you had paid for it, I did not ask any details to Paul, in addition I guessed he was probably tied with a kind of NDA too, so I didn't want to embarrasse him.

I remember that to assume this turbulence with XFOIL, Tom Speer sometimes used to put the transition point at -1% of the wing section chord, in other words at 1% in front of the leading edge. That is probably a good idea I will continue to use in the future.

Thanks again for these very interesting results.

Cheers

EK

 

Hello all. Truly a newbie here. I have been an avid sailor / builder for most of my earlier life But for the last decade been involved in the design / build of experimental aircraft. Imagine my surprise when I found 1/4 chord lift distributions Prandtl span wise lift lines and low range Reynolds number considerations. I plan to do considerable reading here. thank you all

 

As Mikko stated, the flow in the atmospheric boundary layer is turbulent and time dependent. The surface of the earth is rough, and the turbulence scale is large compared to the size of the yacht. It is a chaotic system and can not accurately be predicted. Nevertheless, we need a mathematical expression for the statistical average of the wind profile, if we want to compare our simulation of the sail forces.
The power law for the velocity profile in the turbulent boundary layer is 100 years old and was introduced by Prandtl. Around 1960 the logarithmic law of the wall was generally accepted as a better approach, because it was based on observations of the ruling mechanisms within the boundary layer. Today, the whole meteorological scientific community uses the log-law.
I have compared in the attached picture the profiles. The power law with k=0.088 is practically identical to the log-law. The power law with k=0.12 has a larger gradient at the height of the sails. The right value depends on the surface roughness (wave height, etc.). If we want to discuss the atmospheric boundary layer, we should open a new thread.

 

I love this^!

an amuse bouche:

Clippers, yachts, and the false promise of the wave line https://physicstoday.scitation.org/doi/10.1063/PT.3.3627

 

The input that I got from discussions in this forum and with Mikko, led to an update of my paper http://www.remmlinger.com/3D Aerodynamics.pdf as well as the program: 3D Sail aerodynamics with UliSail http://www.remmlinger.com/3D%20Sail%20aerodynamics.html
Please use the new versions.
Uli

 

Modeling Star in UliSail: results compare nicely with a VPP run of Star, with sailcoefficients based on CFD, despite the Star sailplan being quite different from current fashion.

 

If any haven’t seen this… (and I don’t think anyone here has touched on Prandtl’s ~1933 solution, which is pretty fascinating)



or this



and if you really want to get in the weeds

al bowers prandtle wing spanwise lift profile - Google Search https://www.google.com/search?q=al+bowers+prandtle+wing+spanwise+lift+profile&ie=UTF-8&oe=UTF-8&hl=en-us&client=safari#ip=1

more Al Bowers and Prandtl

 

Yeah, it has been touched on before in the "is circulation real" and "is downwash necessary" threads. A good discussion of it will probably just degenerate into the "all models are wrong, some models are useful" vortex.

Downwash equation for Bell-Shaped spanload distribution https://www.boatdesign.net/threads/downwash-equation-for-bell-shaped-spanload-distribution.63446/