Post 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.
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