Hi,

Eric, we know that every geometry in moving air has aerodynamic forces acting on it. They can be summed up in one total force vector, having a length and an angle. It is now just a question of definition, how we decompose this total force vector. The Lift (Cl) and Drag (Cd) concept decomposes the total force vector into one part parallel to the flow direction and one part normal to the flow direction. Useful for different cases, i.e. aviation. Now, there is no objection in decomposing the total force vector into different directions: for example into the boat’s course direction and lateral direction. Useful, as well. However, just because we decide to use another convention of representing the forces on the geometrie does not change the actual total force vector. The conclusion we can draw from both conventions are the same!

Cl is the Lift, Cd is the drag, just written down in dimensionless form to get comparable coefficients instead of specific forces.

Arne, I repeat: the aim of my 2D profile simulations is not to find the perfect AoA of a real sail to the wind. This information could simply not be drawn from my 2D simulations. I chose the LDmax point to have a variable on which to compare the different profiles. I take it on my head, that this preliminary choice of mine (to use LDmax as the comparable variable) was not the best. That’s why I suggested to open up from one variable to an interval of AoA for comparison between different profiles. It would also be possible to just compare max Cl between for different profiles, but I think it won’t be good as at max Cl the profile is already stalling.

What is sure from Marchaj’s diagrams here, is that the  5° AoA, with the lowest drag angle, is not the setting which will get a boat fastest to windward. One needs some brute force as well. Don’t forget the boat. – Arne K.

Yes, exactly! I do not argue on this one.

In the end, I want to compare profiles to each other. A hull does not have an effect on this comparison. To give a real-world example: think about Ilvy, being rigged as she is now, cambered, and next year rigged as SJR. Given the same weight of the hull (plus 2-3 kg gained body weight from Christmas), the hull can be ruled out when comparing those two rigs.

To compare the profiles, my suggestion is to compare the ClCd curve, at the interval between deflating luff and fully stalling flow (which is about 5° to 15° AoA). Anyway, I’m not emotional on this: Any suggestions or better ideas on how to compare the performance of profiles in this case are very welcome!

Telltales at the leech  -  useful or not. – Arne K.

Arne, I think leech telltales are very useful, indeed! They have been in use with junk rigs as well as Bermuda rigs, airfoil flow visualizations as well as kites. I’m not debating on their usefulness, when I try to investigate what exactly they are showing, and question if they show the most efficient sheeting angle. Regardless if they do or don’t point to the most efficient angle, they depict a very effective, practical and proven way of feedback from the sail – which works!

(Btw. when watching videos on Youtube, showing stall-tests of aeroplanes, the tufted wings clearly indicate that separation starts at the trailing edge...) – Arne K.

I assume you watched stall-tests of thick profiles – at least thicker than a single-ply sailcloth can ever be. That nose radius on an airfoil has a significant effect: i.e. the luff is detaching way later when the nose is not sharp but has a radius. Slieve nicely described it in his “Some thoughts” writeup, and also David must have thought about it a lot when designing his wingsail – and for a good reason. The thickness of the nose, the nose radius, does the trick! Regarding performance, a single-ply sheet, even if cambered, can not be as good as a profile with a nose radius.

Cheers,

Paul

Paul, I am having a bit of trouble understanding your interpretation of these diagrams.

Take these two, for example:

The model of AoA = 2 dgerees shows a bubble of detached flow on the pressure side of the luff - then the model of AoA=10 degrees shows a bubble on the "suction" side?

I must be misinterpreting the images.

I presume the detached bubble is the part in dark blue/violet?

Then, could you please mark on the diagram, or describe the boundary between the pressure and "suction" sides? (Or put it another way, which part of the diagram depicts the sail section?)

Hi again,

Now to the critics part. Thanks, Arne, for your good rethinking and critics. I hope to be able to convince you, that the simulation results are not faulty – we just do need to know how to interpret them. Let’s see:

L/D maximum

Marchaj operates with alpha angles between 5 and 20 mostly, and for upwind work these are 10-15°. The resulting lift/drag will then only be 6/1 on a High-AR sail, that is, very far from the 20:1 and thereabouts as you find. – Arne K.

Now, you compared the L/D ratio of Marchaj at 15°, which is 6.4, with my L/Dmax, which is about +-20 at 4-5°. That is comparing apples with bananas. Either you compare L/Dmax of Marchaj with L/Dmax of me, or you compare L/D at 15° from Marchaj and L/D at 15° from me.

L/Dmax is achieved where the tangent to the Cl/Cd curve has the highest slope (which is at 5° in Marchaj’s graph). I added that line to the drawing, have a look:

it gives L/Dmax = 12, which is double of what you wrote. It is of course still lower than my value, but then, Marchaj’s data comes from measurements with a real model sail, including 3D effects like tip vortex, while mine is a 2D-section which cannot include 3D effects like the tip vortex (resistance from the tip vortex is substantially high). Thus, the L/D ratios of Marchaj can only be lower than mine.

In Addition: the Cl/Cd line has quite a high slope at 5°. Marchaj did only put one measurement point at 5°, the next one at 10°. I do not know of the accuracy of his setup, but chances are that this one measurement point can have a little measurement deviation, which would have a huge effect on L/Dmax due to the high slope of the curve.

Better AoA for L/D reference

However, I definitely see your point about me using L/Dmax at 4-5° is faulty (more to that later). If we compare Marchaj and me at, let’ say, 10°, it looks like this: L/D_Marchaj = 9 and L/D_Paul = 13. Pretty close together, given that my 2D simulation does not include induced drag/tip vortex and thus naturally has to be higher than Marchaj’s measurements!

Choice of AoA range

You are absolutely right in claiming that my fixed geometry is not real at low AoAs. In reality, at AoAs too small, the sail would simply collapse at the luff – which my fixed geometry can’t do.

A simple solution to this is to have a look at the airflow around the luff. If the flow on the pressure side of the luff is detaching, then this simulation run is not modelling reality and has to be discarded. Only the suction side of the luff is allowed to show detached flow. Have a look at the following series:

(this image is also attached, hopefully in better quality.)

It can be observed, that for very low AoA’s < 4° the flow is detaching on the pressure side. This would not happen in a real sail, instead the sail would collapse. Conclusion: Those runs have to be discarded.

Next observation: the flow starts detaching at the suction side of the luff at AoA’s > 7°. That would happen in a real sail. You could see it by the lee telltale (at the luff part of the sail) starting to wobble. à if racing, you try to keep both telltales, windward and leeward, streaming in parallel. The simulation shows, this is the case for 4° < AoA < 7°. What a narrow interval! However, it matches my practical experience: I have to be quite focused at the helm if I want to keep windward as well as leeward telltale streaming in parallel. Now we are talking about alpha-tolerance.

4° - 7° AoA, keep that in mind when looking again at Marchaj’s or my Cl/Cd curves! It is right on that steep slope. That’s where we want to operate our sail.

The max peak in the Cl/Cd graph of Marchaj (my graph shows the same) is not the most efficient one! That peak, at 15° for the sail “2” in Marchaj’s fig. 83, is the point where the detached air bubble on the suction side reaches the leech. From about 7° to 15°, the detached bubble gets longer and longer, starting from the luff, before it finally reaches the leech. At this very point, when the detached bubble reaches the leech, the leech telltales start to wobble – a situation that Arne does not get tired of to sensitise people, and he is right doing so, in my opinion. However, it can now be seen very clearly, that just at the point where the leech telltales start to wobble, it is already “too late”. The sail is more efficient when the AoA is lower than at that point.

Summed up: From all my simulation runs between 0 to 20° (for each tack), the ones below 4° and the ones above the first max peak (about 10-15°) can be discarded. A good learning for the next series of simulations!

No patience with a stalling profile

I should mention, that with a fully stalled flow around the profile (any profile), the simulation isn't static anymore but gets into a periodic state: A Karman Vortex Trail builts up behind the profile, and does not let the simulation converge. Convergence is essential for numerical simulation (there are many books written about this topic). However, as my computational power is quite limited, I stopped the simulation runs at 15 sec simulated time. That is enough time to converge for partly stalled flow, but as soon as the profile is fully stalling, this strategy of me aborting the run “before it is finished” gives faulty results. But, good thing is, it doesn’t matter. We are not interested in fully stalled situations. I just need to find the max peak in Cl/Cd, everything beyond is of no interest (for now). Having explained that, you can observe that effect when looking at the diagram below: after the max peak, moving towards higher Cd, the lines go down and then up again. This second rise is faulty. It is due to me stopping the simulation before it was finished (if it ever would finish).

Cl/Cd plot with equally scaled axes

What I would like to see is a (computer-generated) Lift/Drag diagram with the coefficient of Lift at the Y-axis and the Coefficient of Drag along the X-axes, both to the same scale. – Arne K.

I already posted such a diagram, but without the equal scale on both axes. No problem to do, here you are! Same simulations, same data, different diagram layout:

 How good that it’s nasty outside, otherwise the temptation to go sailing today, instead of sitting at the laptop, would have triumphed :-)

Hope to have you convinced and on board, Arne!

Cheers,

In the last line of that posting I wrote:

The next diagram shows a more realistic sail with AR =3.

Thanks Arne

I misunderstood that sentence.

Hi Arne, I am not sure if we are maybe talking past each other here.

What I meant was - I was referring strictly to “comparative” data. For example, for a given AoA the model can make a comparison between the numbers arising from port tack and starboard tack (the effect of the mast). The numbers themselves may not be absolute, but the comparison is still well made, and we have learned something – or at least verified something.

That was all I meant, but it is only a small point, I suppose.

Having made that one small point, and assuming the AoA figures are not so far out that the conclusion would be reversed, I don't have enough knowledge in theory or practice to question what you are suggesting.

(By the way, just to correct the written record, should you not edit your previous post referring to Marchaj's AR=3 ? Or, am I missing something? I know it's not an important point).