Mental maths for best VMG

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TallBuoy

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TallBuoy said:
Its some decades since I performed badly at A'level maths, and I have been trying to find a simple way of deciding best AWA on the go, without having to resort to doing sums at the chart table.
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If you already have a polar diagram for your boat its easy to work out your optimal AWA for a given windspeed upwind - it is the furthest point forward on the polar for that particular wind strength. To save actually trying to read graphs whilst going along most race boats have a laminated card with the optimal AWA and a target boat speed upwind and downwind in 2 knot increments of wind speed so that you can quickly glance at it to tell you what angle you should be sailing.
 
Ingwe said:
If you already have a polar diagram for your boat its easy to work out your optimal AWA for a given windspeed upwind - it is the furthest point forward on the polar for that particular wind strength. To save actually trying to read graphs whilst going along most race boats have a laminated card with the optimal AWA and a target boat speed upwind and downwind in 2 knot increments of wind speed so that you can quickly glance at it to tell you what angle you should be sailing.
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I get that but maximum boat speed does not necessarily mean best VMG. Sailing higher but slower MAY be better.
Therein lies the challenge.
 
TallBuoy said:
Its some decades since I performed badly at A'level maths, and I have been trying to find a simple way of deciding best AWA on the go, without having to resort to doing sums at the chart table.

Just looking at Wikipedia I find this article


the table gives an example:

Degrees From Destination True VMG (kts) Rate of VMG per Degree away from Destination (VMG (kts) / degree)
40 14.64 -12.28
45 13.51 -13.51


I am somewhat confused how the Rate of Change is shown as a double digit value per degree!

Are there any better brains than mine that can put this into plain english?

Better still, how do I calculate best VMG in my head? I can remember cosines for 30 45 and 60 degrees
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Nahh, that math looks very suspect....

= No Go Zone Limit ( given by manufacturer )
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The first term, wind speed/no go angle from manufacturer is just wrong, that should be and should be * not /
Maths got muddles....
 
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If you are racing what matters to you is the speed at which you get to the next mark. You get an idea of that from the VMG to waypoint shown by your GPS. Unlike the wiki article, that takes into account tide and leeway. And also the fact that most boats sail ever so slightly different on the two different tacks. But that still doesnt tell you when to tack nor does it tell you which is the best tack unless you keep tacking and comparing.

I find in our racing that the mark is very rarely dead upwind, the tide is never directly from the mark to us, and the wind strength varies depending on how close inshore we are. So we usually can guess the best tack quite easily
 
dunedin said:
If the instruments don't calculate automatically, perhaps bang a waypoint in to windward and just read off the VMG to waypoint from the GPS (or tablet/phone)
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Please don't follow this advice, it does not work. For the pretty simple reason that you only have to be a degree or two off directly to windward for there to be a very large discrepancy between tacks. And even if you are using it as a tuning aid on one tack a wind shift of 5 degrees (which is hardly uncommon) will have a much, much bigger effect than anything you just did to the trim.
 
birdseye said:
If you are racing what matters to you is the speed at which you get to the next mark. You get an idea of that from the VMG to waypoint shown by your GPS. Unlike the wiki article, that takes into account tide and leeway. And also the fact that most boats sail ever so slightly different on the two different tacks. But that still doesnt tell you when to tack nor does it tell you which is the best tack unless you keep tacking and comparing.

I find in our racing that the mark is very rarely dead upwind, the tide is never directly from the mark to us, and the wind strength varies depending on how close inshore we are. So we usually can guess the best tack quite easily
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I have never sailed on a race boat where VMG to waypoint has been displayed on the instruments, and can see no practical reason why you would need this information.

The information the helm and crew need is simply speed and TWA, and target speed and TWA to compare to, either upwind or down. Provided the Nav has done his job of keeping the boat within the cone, then this is all the helm and crew will ever need.

The Nav will need to know where the next mark is, and together with info on TWD and the tidal situation will decide the best course to the mark. Whether that is to favour a side, or to tack on the shifts up the centre.

Upwind, VMG to waypoint is simply a bi-product of the crew maxing the boat's performance on speed and TWA and the Nav making sure they have not overstood the mark and are in phase with the shifts. It is not always a good indicator, as I can think of many situations where I would choose to come of the start line and tack onto the tack that gives me, at that point, the worst VMG to waypoint.
 
flaming said:
The information the helm and crew need is simply speed and TWA, and target speed and TWA to compare to, either upwind or down. Provided the Nav has done his job of keeping the boat within the cone, then this is all the helm and crew will ever need.

The Nav will need to know where the next mark is, and together with info on TWD and the tidal situation will decide the best course to the mark. Whether that is to favour a side, or to tack on the shifts up the centre.
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What you have described is an excellent example of K.I.S.S !

It just gets a little more complicated when as skipper on the corporate gigs, one is doing everything including nav, tactics, helm, coach and crew boss !

Flaming will know this but others might not: One more thing to take into account is that any True Wind readings are entirely dependant on the boat speed measurement being correct. i.e. clean paddle wheel, properly calibrated etc. This is because the wind instrument can only measure Apparent, and uses the boat speed to calculate True.
 
TallBuoy said:
It just gets a little more complicated when as skipper on the corporate gigs, one is doing everything including nav, tactics, helm, coach and crew boss !
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Yep, been there, done that, got (many) T-Shirts! I did tend to find that at that level boatspeed was King, and I just kept the Nav super simple.
 
Playing wind shifts will give you a much better advantage than trying to calculate VMG. Go out a bit early, don't just rock up for the start, and keep an eye on the course you're getting on each tack whilst warming up. You could write it down, and there's probably an advantage in that, but even doing it mentally will give you an idea of the range and 'norm' on each tack.

Then just take account of that during the race. If a shift heads you on one tack then it'd be lifting you on the other, so you might want to tack - if you're going to tack do it immediately, so usually an idea to have it in your head beforehand whether you want to tack or not on the next shift.

Of course, don't let it overrule what you see with wind strength variations across the course or what you know about tidal differences or local shifts caused by the topology etc. And sometimes the wind is changing rather than shifting back and forth, so do be open to that possibility. A forecast will give you a slight hint of a systematic change, but they're usually so large scale that it's rarely sensible to believe the forecast rather than your own eyes.
 
Remember that "playing the shifts" will shorten the course that you sail to a windward or leeward mark, but sailing optimum VMG let's you sail a particular leg of the course 'faster' or more efficiently than a boat that does not sail optimum VMG. The most powerful combination is sailing optimum VMG while playing the shifts. For most boats, there will be an optimum VMG for every wind speed, and it may be different depending on sea conditions (e.g., rough water v. smooth water.) In shifty conditions, it may be better to "foot" if you are going toward a favorable shift or better pressure, even if you are not making the best VMG in the meanwhile. Usually, it is pretty easy to tell whether or not you are sailing the best VMG, based on relative performance against other boats in the vicinity.
 
Just taking the cosines
40 degrees pointing, 6knots, VMG 4.6
42 degrees 6 knots VMG 4.46 3% different. You need 6.2knots to get VMG 4.6
44 degrees 6 knots VMG 4.32 6% 6.4

Offwind
0 degrees up, 6knots is 6 knots VMG
10 degrees up 6.1 knots is 6 knots VMG
20 6.4
30 6.9
35 7.3
40 7.8
45 8.5

Some people might find that more useful than changing the subject to polars or tacking on shifts.
The downwind numbers seem to be counter intuitive to a lot of people. It costs you virtually nothing to come up 10 degrees, but once you are up at 30 degrees, coming up any more needs a big speed increase to pay for it. (some boats, and some kites, wil deliver this!)
This is as relevant to the cruising sailor who wants to arrive as it is to racing.
Upwind, the boat sailing free may make less leeway and all that.
 
TallBuoy said:
Its some decades since I performed badly at A'level maths, and I have been trying to find a simple way of deciding best AWA on the go, without having to resort to doing sums at the chart table.

Just looking at Wikipedia I find this article


the table gives an example:

Degrees From Destination True VMG (kts) Rate of VMG per Degree away from Destination (VMG (kts) / degree)
40 14.64 -12.28
45 13.51 -13.51


I am somewhat confused how the Rate of Change is shown as a double digit value per degree!

Are there any better brains than mine that can put this into plain english?

Better still, how do I calculate best VMG in my head? I can remember cosines for 30 45 and 60 degrees
Click to expand...


I am all for mental arithmetic but in this case the result will never be that accurate or indeed sensitive enough to variation. You dont need the cosine at 30 and 45 but at every degree interval in between. How is your memory?

Just use the VMG from your hand held gps or fixed gps. Ignore your wind instruments which only tell you VMG to windward - fine if your destination is directly upwind but NBG if it isnt
 
wotayottie said:
I am all for mental arithmetic but in this case the result will never be that accurate or indeed sensitive enough to variation. You dont need the cosine at 30 and 45 but at every degree interval in between. How is your memory?

Just use the VMG from your hand held gps or fixed gps. Ignore your wind instruments which only tell you VMG to windward - fine if your destination is directly upwind but NBG if it isnt
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It's always a joy to race againt people who use this sort of logic....
 
Well go on then Flaming. You round the last mark and your next one is 20 degrees off the wind. Why wouldnt you say on the best vmg until it starts to drop sharply and you can make the mark by tacking.
Forget wind shifts.
 
wotayottie said:
Well go on then Flaming. You round the last mark and your next one is 20 degrees off the wind. Why wouldnt you say on the best vmg until it starts to drop sharply and you can make the mark by tacking.
Forget wind shifts.
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If you forget windshifts. And I don't... do you really expect to beat me to the next mark?

I've said this to you multiple times, and I'll say it once more. If your next mark is in the cone, then best VMG to wind is the way to go. You may be able to increase your VMG to waypoint by cracking off a bit at the start of your longer tack, but if it's not your best VMG to wind, when you tack you won't cross me.
 
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