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.

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Again: my simulation is of a section/profile! The Cl/Cd-curve gets distorted when 3D effects get into play. Still, comparing a 2D profile with another 2D profile gives absolutely valid, comparational results.
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,

Paul