Post by iconPost by BGSteMarine | 2020-04-25 | 16:13:51

Hi there !
I noticed a phenomenon that I can't explain to myself, so I'm going to need a few more effective brains than mine to help me understand!
In the polars, as displayed by toxcct, in the Transat AG2R, at TWS of 10 knots, and with the Light Gennaker, the optimal VMG is showed at TWA 146.6 without the Hull Polish, but at TWA 147 with the Polish !!
I can't understand how the Polish, which increases the speed by a homogeneous factor of 1.003, can influence the optimal TWA ...
If someone has the explanation, I am interested ;-)

commenticon 11 Comments
Post by iconPost by zezo | 2020-04-25 | 16:22:27
Probably a rounding error. The numbers at 147 and 146.6 are 5.529 and 5.53 when truncated for display, but multiplying them by 1.03 gives the same (truncated) result of 5.546.

The actual numbers are with infinite length because they involve a trigonometric function.

Post by iconPost by BGSteMarine | 2020-04-25 | 17:33:45
Hum ! Yes, probably something like that. depending on the TWS, the gap with and without polish seems to be between 0 and 0.3
Anyway, my understanding is that it should be always 0 as the factor 1.003 is always the same in any direction ...
BTW, same effect with the foils, even in TWA area where they deliver 100% of speed increase.
Post by iconPost by zezo | 2020-04-25 | 18:08:05
It's just the third or fourth digit randomly being larger. I haven't looked at the code, but javascript is not exactly the type of language defining strict math rules, although it probably follows the underlying C library with single precision math.
Post by iconPost by YourMomSA | 2020-04-25 | 18:31:35
In absence of rounding, the difference is indeed zero.

Toxcct's polars are showing one and only one optimal TWA angle... Even though a range of angles (in tenths of degrees) will all be within a couple thousandths of a knot of the optimal angle. Using the example being discussed... AG2R TWS 10 downwind...

Without hull polish...
145: 5.521 VMG
146: 5.530
147: 5.529
148: 5.525

So the optimal is somewhere between 145.5 and 147.5. You could be running any angle between 146 and 147 rather than fine-tuning (see the "xxx.o TWA" topic), and can figure you're running at the optimal VMG. Sometimes fine-tuning is worthwhile, but not in this case.

With hull polish...
145: 5.538
146: 5.546
147: 5.546
148: 5.542

So once again, anything between 146 and 147 is fine. Both scenarios agree on that, per your expectation.

The specific answer would require Toxxct to explain...
-How many decimals does he round the VMG to before identifying which angle is "optimal"?
-When multiple angles produce the same rounded "optimal" VMG, how does he determine which to show as the optimal?

Let's say, for example, that the rule is to round off to 3 decimals and then show the highest angle among those that produce the optimal VMG. It seems that in this example, the true optimal VMG is somewhere between 146 and 147. If that's the logical rule, then it would show the highest angle that rounds up to 5.530 (without polish) or 5.546 (with polish). So... perhaps 146.6 without polish is producing 5.5295..., barely rounding up to 5.530. And then perhaps 146.7 produces 5.5294..., which rounds down to 5.529. So 146.6 would be presented as the optimal angle. The best angle, with 6 decimals of accuracy, is probably more like 146.3, but if a range of angles all rounds off to 5.530 and it shows the highest such angle, then it would show 146.6. Then with polish, the true optimal angle would be the same... somewhere in the 146's, but the 4-digit accuracy wouldn't drop below 5.5455... until 147.1. So, if I've guessed the rule correctly, that would result in 147 being shown.

With that said... I want to be clear that I don't worry about thousandths of a knot while racing... I find this to be an interesting question, and I'm guessing it was asked as a curiosity rather than for strategic reasons. I wouldn't encourage people to spend hours trying to perfectly optimize VMGs. There ARE cases where sailing precise angles can be important. If you're doing a long stretch of several hours at TWA 120 where TWA 120 is the optimal speed, then it can be worthwhile to try to get 120.0 instead of 119.6 or 120.4. If you're sailing upwind VMG where optimal is 36.0, then 36.3 might be fine but 35.7 might actually hurt. (The upwind VMGs tend to drop off fast when sailing slightly too high). So... precision is worthwhile in specific cases, but I wouldn't want people to think you have to spend hours trying to be perfect to do well.

Post by iconPost by zezo | 2020-04-25 | 18:47:32
Thanks. Good write-up.

There are very sharp points indeed where it matters, and flat spots where the speed or VMG is exactly the same for few degrees.

Without looking at the code I can tell you that the indicated value is either the first or the last point of the equal values, depending if you search the optimum from 0 or from 180, and if you compare with >= or > of the last best value.

An optimum range within 0.1% of max would be nice addition to the polars.
Post by iconPost by BGSteMarine | 2020-04-25 | 19:45:37
Thanks YourMom. You are right ! That was definitely a curiosity question! I don’t feel much stressed by the decimals of degrees, even if I know that a couple of guys from my team are spending quite a lot of time with that ;-)
I also like Cvetan’s idea of the range, even if the difficulty of the precision of calculation for the boundaries of the range would probably be same as we have today.

Post by iconPost by zezo | 2020-04-25 | 19:54:24
In proper computer math A never equals B. It's always |A-B| < epsilon.

You don't usually pay much attention to that unless you are doing serious stuff like launching things into space. But sometimes it shows up.
Post by iconPost by toxcct | 2020-04-25 | 21:19:19
The specific answer would require Toxxct to explain...

-How many decimals does he round the VMG to before identifying which angle is "optimal"?
==> 3 digits used internally to compare values (even if only 2 are sometimes displayed).

-When multiple angles produce the same rounded "optimal" VMG, how does he determine which to show as the optimal?
==> The smallest angle for the upwind best VMG, and the greatest angle for the downwind best vmg. that allows to handle "flat spots" where a range of angles share the same twa (between a tolerance range).

Thanks BTW for your nice post, YMSA ;)

Post by iconPost by BGSteMarine | 2020-04-26 | 09:12:05
Thanks much tox for these explanations :)
Post by iconPost by YourMomSA | 2020-04-25 | 21:43:00
Ah, the minutia that we discuss when we are stuck at home with no sports on TV...
Post by iconPost by BooBill | 2020-04-26 | 01:18:29
The Ocean Race has been releasing roughly hour long episodes of the past Whitbread races, starting with the first, every few days. If you really need something sailing related to occupy yourself. Or you can go back to polishing your hull.

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