Prandtl's lifting-line method for sails

I developed a software to calculate and optimize the sail forces for jib and main:
New software to calculate and optimize sail forces https://www.boatdesign.net/threads/new-software-to-calculate-and-optimize-sail-forces.67844/
I would like to discuss the theoretical background, see attached paper. I modified the lifting-line method to take care of the specific flow conditions around sails. The validation of the program was not very successful, because useful experiments are scarce. I found that the accuracy of the results is comparable to CFD-methods. Please let me know your thoughts.

 

Hi Remmlinger,

this is very interesting. Do you manage also the position and value of the max camber on the chord along the height of the sails ? ? What vertical variation of the twist du you use ?

 

Perhaps I missed it (I’m working out on my elliptical) - are you including differences between tandem morphing to biplane arrays ( as the boat falls off the wind), including stagger, decalage, & how far the sails are apart in the cell?

(If I did miss it, please advise?)

 

Alan, the information is linked in the paper. The NACA-mean line is described in: http://www.remmlinger.com/2D aerodynamics.pdf
The alternative profile, the parabola, has its max. draft always at 50% chord.
A diagram of the vertical distribution of the sheeting angle can be found in the excel-file that is contained in the zipped folder that you can download from my website: 3D Sail aerodynamics http://www.remmlinger.com/3D%20Sail%20aerodynamics.html
There is also a diagram depicting the camber.
Uli

 

Paul, I hope, I understand your question. For each of the 62 panels, I calculate the position of the chord in space. The prescribed sheeting angles and twist define this position. Then I sum up all induced velocities at a control point inside the panel, using Bio-Savart law. A change in the sailed course will also change the sheeting angles, the distances between the control points and the direction of the trailing vortices. Therefore, the induced velocities will also change and the interaction of the sails will be different.
Uli

 

Thanks for the response- we have a boat with a jib (see avatar), and this subject is one I am very interested in, so your paper, which deals with specific sailboat sails rather than airplane wings, is excellent, coupled with CFD by our excellent sailmaker here, upon whose images, and others, I spend a fair amount of time. (Translating between that and a lot of telltales on our sails and shrouds….)

Example of the stuff I usually read below:

https://www.politesi.polimi.it/bitstream/10589/93619/1/2014_07_Minardo.pdf

plus a lot of recent low Reynolds number stuff

Looking forward to more, especially understanding intellectually and hopefully intuitively the differences in the aero of jib/main sail plans as they transition between tandem arrays vs biplane arrays.

 

Just a point I think needs to be made. In some CFD codes the "D" in dynamics means that the fluid is moving, not the surface. Lifting line and lifting surface theory is based upon a "fixed" "line" or "surface". It predicates a "moving" fluid to determine the force on the line/surface. It does not consider a vessel surging. pitching, or yawing to weather and how that changes the flow in each (or any) timestep. The whole concept of 3-d integrated flow and motion is a really big bite to chew and not usually addressed (especially as far as I can see in this paper ). This paper (correct me Remmlinger if I am wrong) looks at a single specific geometry relative to inflow per each run.

Now back to your regularly scheduled discussion.

 

Dear Uli,

Thanks for your additionnal precisions. Please allow me some times to go through your papers & sources, litlle by little. I use such combinaison between X-foil and the lifting line theory to produce CL-CD curves of thick foils, or wings. As I understand, the methodology is quite the same : Rely on X-foil to estimate the transition point of sections and their viscous drag & lift coefficient, "integrate" them along the span. In the end, this approach gives excellent results compared with CFD calculations.

For this concept to be apply to soft sails, I've conducted a study with North Sails, some years ago, applied on the sails set of our racing catamaran. I've seen the in-house software used by this company, which is doublet source panel code coupled with a structural finite element code (FSI). Given some materials for the sails, the operator has to make the tuning of the sails manually, because 2d optima sections do not appear naturally, but instead, tension-constrained shapes, with which the operator has to compose.

At first glance, I wonder if the modeled sails, in your approach, are not too much "optimized" and too much rigids. Comparaisons with CFD results may be excellent, but how far a real sail set will differ from the model that you choose ?
Alan

 

I may have missed this, but how do you deal with the vertical gradient of the wind? This affects both velocity and direction of the apparent wind, and the effect depends on the boat speed.

regards

krzys

 

Correct! The code is just one module in my genetic search for the optimal yacht.

 

Thank you, Alan, for sharing your experience. Your last sentence points to an important weakness of my method. The initial aim of my work was the genetic search for the optimal overall design, as explained on my website. The aerodynamic forces are only one module in the workflow. With genetic algorithms, thousands of different designs have to be evaluated. It is not possible to spend too much computing time for each module. The calculation of the sail forces must be fast, and it must converge to a useful result. I guess, the best way is to introduce a "real world factor" that reduces the computed sail forces to a more realistic value. The currently computed value is indeed for a sail, where the profile and the sheeting angles are all at the optimum, the sail has no wrinkles and the trailing edge has no curvature in the direction of flow.

Unfortunately, this explanation does not fit to the comparison of my results with full size measurements on the water. The measured forces were higher than my prediction, see page 7/8.
Uli

 

Krzys, the vertical gradient of the wind is described in chapter 3 at the end of page 5.
Uli

 

A real world factor could indeed a convenient way for the computations results to come closer to reality. Nevertheless, the correction methodology may also depends on the reason why computations on the sails are intended. If an aerodynamic model is to be derived, to be used in a VPP, or if design loads on the rigging are to be estimated, you probably choose a way or another to fit the computations before them to be used.

Regarding the comparison in quantity, between your computations on the Dehler and those found in your reference, and withouth having myself read this reference, I would say that explanations can be found in a large spectra of influencing parameters. One central question that I have, for instance, is : What do you mean by optimum and optimization ? Especially with genetic algorithms, a unique optimum is not to be found, but Pareto boundaries, on which particular solutions are taken, according to additionnal criteria, brought on top of the objective function that is used in the optimization loop itself.

For instance, I create a genetic optimizer of the planform of the daggerboards of racing multihulls, being used on the transatlantic speed records. Requirements are quite simple, since no tack or gybe is allowed for this record to be broken. A long transatlantic downwind stretch... The objective function choosen was the Liftt/Drag ratio, and the additionnal criteria was the variation of this Lift/Drag ratio of the neighbouring solutions. Trying to select robust solutions among all.

Depending on the boat type (monohull-catamaran-trimaran) and the hull's shape, the maximum driving force of the sailplane may not correspond to the best VMG. So. What is your definition of an optimum sailplane ? What objective function, or fitness function do you use in your loops ? What are the additionnal criteria that guide the final selection of the optimum ?

 

I guess I have to supply more information and put the module UliSail into perspective.

In 2006 I presented an idea at the HPYD2 in Auckland. I used genetic algorithms to find the optimum overall dimensions of a sailing yacht. The figure of merit was the VMG and the constraint was the cost of the yacht. The only available data at that time to calculate the VMG was the Delft-method.

In the years to follow, a lot of new tank test data became available, and I realized that the delft-method was too simple, and it led the optimizer into a wrong direction. I developed a new regression and a new hydrodynamic model that is now contained in the program UliTank.

In a next step, I thought about new and more accurate methods to calculate the aerodynamic forces. I included trim parameters, used XFOIL and the new optimizer IFFCO. The result is the module UliSail.
In the near future, I will combine UliTank and UliSail into a real VPP. Only with this VPP it will be possible to maximize the VMG. UliSail alone can only maximize the driving force on a given course.

The last step will be the combination of the VPP with the lines plan UliLines. With this package, I can go back to my initial genetic optimization of 2006. Hopefully, the new and more accurate prediction of the speed potential of the design will lead to more realistic results of the genetic algorithms.

It is all work in progress and I publish intermediate steps to get an early feedback. Good questions force me to rethink my theoretical assumptions, and I might get new ideas.
Uli

 

Thanks for your kind answer, Uli. I see that this sail module is the result of a very serious work, and understand the whole plan. Coupling the VPP with an optimizer is an excellent idea. I will keep digging into your papers with a real interest, since you've given so much detailed on your method. Great work.

Alan