Up-wind sailing
- Thread starter La Bestia
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Forget about the sail for a moment. If you sail straight from A to B at 1 length/time (just imagine it), and then sail from A to B taking one tack, that is, two course lines 45 degrees to the first. The total distance in that case is \sqrt{2}. So, if your speed on that course is between 0 and \sqrt{2}, then it will take longer. If your speed on that course is \sqrt{2} or greater, then it will be faster. So, for each course angle, the angle determine two things, then length of a one tack, two leg trip, and the speed of the boat along that course (given the polar for the boat/wind speed and the hull characteristics). As you bear off from close hauled, the course length increases, but the speed along the course line goes up faster, at least at first. Eventually, the increased speed does not make up for the increased length, and the Vmg starts to go down again. I can do better examples/illustrations, or find explanatory web sites, if you'd like.
\sqrt{2} \approx 1.4
Another way to look at it is as follows. Take a very long rubber band and tie it at point A and point B. Grab it in the middle and pull perpendicular to the line from A to B. As you do so, you make a triangle. After a little bit, that triangle will describe your best course for close hauled. The time you take to go from A to B on this course is the total distance divided by the speed along the course. Now, keep pulling the rubber band. The triangle now describes the course you take when falling off. The distance is increasing, which by itself makes the time go up. But the speed is increasing. You can see that on your polar. If the time is Length/Speed, then the increasing speed will decrease the time. The overall time will continue to go down as long as the speed is increasing more than the length is increasing. The optimum course for Vmg is therefore somewhere between close hauled and close reach for monohulls with conventional sails.
\sqrt{2} \approx 1.4
Another way to look at it is as follows. Take a very long rubber band and tie it at point A and point B. Grab it in the middle and pull perpendicular to the line from A to B. As you do so, you make a triangle. After a little bit, that triangle will describe your best course for close hauled. The time you take to go from A to B on this course is the total distance divided by the speed along the course. Now, keep pulling the rubber band. The triangle now describes the course you take when falling off. The distance is increasing, which by itself makes the time go up. But the speed is increasing. You can see that on your polar. If the time is Length/Speed, then the increasing speed will decrease the time. The overall time will continue to go down as long as the speed is increasing more than the length is increasing. The optimum course for Vmg is therefore somewhere between close hauled and close reach for monohulls with conventional sails.
Thanks for your thoughts on VMG. The question I still have is what did you mean by:
--Tom.
In theory VMG max is as good as it gets, why would it be better to have it "starting to go down" (ie. less than max) in theory? What theory?
--Tom.
Really? Phil is that what you mean?
If so there is a problem that we discussed earlier in the thread -- you need to take very long averages on each course or you'll find yourself pinching to death... (ouch!
) This is because it takes time for the boat to speed up or slow down. So each time you head up it seems that you are going closer to the wind but not going any slower. So, your instantaneous VMG rises. The opposite happens when you slow down. One solution to that is to calculate your VMGs over time and from them read a target speed for each true wind. So, if you're sailing too fast for the wind speed head up and if you're sailing too slow head down. The speed signal points the right way immediately. --Tom.
Because if you start from close hauled, Vmg goes up first. If you continue to fall off, eventually Vmg stops going up, and starts going down.
Exactly Ron, that's it, very simply.
My theoretical analysis depends only on the wind and the characteristics of the boat. Detecting that optimal state using actual instruments on the boat is a whole other ball of snot. I would say sailing is more like VFR flying than it is like IFR, that is, trust your instruments, but trust your senses too. It's certainly true that changes in attitude of the boat and sail (or wind in a real situation) must be given time to stabilize, as does any instrument that works by sampling position.
So, are you saying that if you start out pinching and head off until the vmg starts going down that you will end up at VMG max? And, you're doing this theoretically on paper. Why? It is trivial to find VMG max on paper. And, VMG max is a single point* (the one where the slope of VMG function is zero). If you scan the function until VMG starts going down you have gone to far.
VMG as calculated by sailing instruments does not sample position. Sailing instruments provide immediate readings by vector summation from the wind indicator and knot meter. But, VMG is not useful until the boat is in equilibrium. If you know your target speed then you can take instant action based on your knot meter -- you do not have to, nor should you, wait for equilibrium.
It is important to see that the delay in VMG is not a result of instrument error or inadequacy. Even with perfect theoretical instruments you would have to wait for the boat to come to equilibrium before your VMG was valid. In theory you should instantly sail towards your target speed. So, no snot [sic], these ideas, too, depend "only on the wind and the characteristics of the boat.
--Tom.
*There may be two significantly different courses that give virtually the same VMG max for planing boats and multi-hulls in some conditions.
Be careful not to make claims about both distance and time. People can argue time because there are so many factors, but you can't argue distance in any significant way. Your quote was surely meant to claim distance only.
Your wording "straight up and then turn 90 degrees" isn't ideal for me. It took me awhile to realize that you did _not_ mean "sail until you are 90 degrees from target B relative to the line of the original A-B course, which would mean sailing the hypotenuse and one side of a right angle triangle, where the third side of the triangle is the direct A-to-B track. You are talking about sailing the two equal sides of an isosceles triangle, where the third side is the direct A-B track. In other words, "Starting at A and looking at B, sail at 45 degrees until the target B is on the beam and then tack once through 90 degrees".
I would say it more like this:
If you can get from A to B by traveling on 2 tacks (tacking once), the distanced traveled would be the same if you tack once, twice, 3 times, 4 times, etc, as long as the angle turned during each tack is the same.
The reason is that if you draw a simple picture (of 45 degree angles to the wind and 90 degree tacks), you can see that you just have a series of triangles which are one half of a bunch rectangles if you complete the shapes symmetrically. It doesn't matter which sides of these rectangles you travel on; the distance is the same. If the tack angles are not 90, you have parallelograms but the same holds true. No matter how many parallelograms you split the traveling into, the total distance traveled is always the same.
Said yet another way, the length of a bunch of short tacks is the same as the length of fewer longer tacks, if the tacking angle is the same every time.
One last time:
If I build a staircase with 3 steps with rise=run=2 feet, or 12 steps with rise=run=6 inches, I need to buy 12 feet of carpet for my stairs in either case.
Because the original thread post expressed confusion on the matter that didn't seem to be cleared up by the first page of posts. Close-hauled is not the best point of sail for max Vmg, as many beginning sailors wrongly believe. The theoretical point of sail for max Vmg is as I described. The practical problem of finding the point of sail where Vmg is max on the boat in real conditions is a very different matter.
All GPS devices (such as those discussed earlier in the thread) determine speed and direction by sampling position. If you are using the knot meter to test and/or experiment with Vmg, do it in an area where there are no substantial currents.
I'm not sure what you are driving at here. Let's suppose you've worked a given boat in many wind and sea conditions and charted max Vmg point of sail for each condition. In this case, after equilibration, you could tell (in a known current and a little calculation) from the knot meter and wind indicator whether you were on the max Vmg course. On the other hand, if you had all that data, you would simply set course to the appropriate heading and trim accordingly. Maybe that's what you meant towards the end.
Yes, I agree and stated so in my last. Time is required following changes made to trim and course before speed can be reevaluated for the new conditions. That is to say, boat speed through the water will continue to change until it stops changing. Whether you can predict how close or far to optimal you are and whether or not to make another adjustment is a different story and a matter of experience.
How so? Is that coming from the shape of the polar?
That would be ideal (only 8.49 feet of carpet), but that's akin to sailing directly into the eye of the wind. :naughty:How about a ramp?
It's not the distance that makes hard the traveling, it's the traveling that makes hard the distance.
Phil,
I don't know how many posts you looked at on your "first page" of posts. It is obvious that you didn't read my posts there. I believe I've dealt with most of your questions already.
--Tom.
Have you considered
that the second page of all these topics repeats the initial post?
It took me a while to figure that out and thought that questions had been copied again, but they aren't.
Great answer, BTW, Tom. Thanks,
Stu
that the second page of all these topics repeats the initial post?
It took me a while to figure that out and thought that questions had been copied again, but they aren't.
Great answer, BTW, Tom. Thanks,
Stu
With all due respect, I think your posts on page 1 make sense, if you already know the answer. Those details were buried in a discussion of instrument usage. It's all good stuff, I just thought my post added something in simplicity that was lost in the shuffle. If you'll notice, the original poster dropped out.
Ouch! That bad, huh? It would be lovely if the OP would provide some feedback.
Anyway, your goal of simplifying this for folks who are new to it is a great one. I wonder if a diagram might be easier to understand than the the textual efforts so far. For me, a clear definition of terms would help, too. I think you are using "close hauled" in a way that is different from the one I use. And, it isn't clear to me if you are looking at VMG with respect to the wind or a waypoint.
--Tom.
Close-hauled is a point of sail that is literally as close to the direction the wind is coming from as possible without stalling the sails. I was looking at Vmg w.r.t the wind, as La Bestia indicated a destination directly upwind, though the other problem is interesting too.
This site has some relevant diagrams, though I haven't read the article yet.
http://knol.google.com/k/john-navas/why-vmg-matters/qefv1b2dsnit/2#
This site has some relevant diagrams, though I haven't read the article yet.
http://knol.google.com/k/john-navas/why-vmg-matters/qefv1b2dsnit/2#
Good link. Thanks.
Again, it would be neat to know if the OP or similar target audience finds it helpful. I have a feeling that because the article simply assumes we know the geometric proofs of VMG (both wrt the wind and the mark) that it might be hard for the true novice to follow. I'm pretty sure it was that geometry that you were working towards. Maybe the old fashioned "upwind ladder" diagram might be helpful. Also, while the article makes note of the problem of momentum and steering to VMG he does not provide any useful methodology for steering the boat to VMG. Steering to True Wind angle is implied but not proved. And, it would be hard to prove it since it doesn't work
... I've just got two words: "target speed". "Close hauled" is an interesting term. The racing rules of sailing strongly imply that it is the point of sail that would get you to the layline fastest (ie. your proper course upwind) but they don't actually define it. I've always thought that it included all upwind courses. That is, courses from as high as you can point without stalling (pinching) through pointing (a course somewhat above VMG) and VMG and down to a faster but non-optimal course (footing). In racing having a "high" mode and a "Low" mode are tactically important. But, I notice that the online dictionaries use your definition. I'd love to know how others are using the term.
--Tom.
Tom,
By Vmg I mean velocity made good. It has a value on every upwind course. I think you use it that way too, but it wasn't clear in this last post. My understanding of pinching/footing is also that they are relative to a given course and wind. If you are sailing on the course for max Vmg, with sails properly trimmed, and you head up a bit without retrimming, then you are pinching. If you bear off and don't retrim, you're footing. Those terms are used with respect to sail trim, not course.
There is another great figure in a book called "The Symmetry of Sailing: The Physics of Sailing for Yachtsman" by Ross Garrett. It's in the section where he is taking apart the polar diagram for a given boat/sail/wind and explaining all the forces. I'll try to scan it and post it, if it's ok to do that on this forum.
By Vmg I mean velocity made good. It has a value on every upwind course. I think you use it that way too, but it wasn't clear in this last post. My understanding of pinching/footing is also that they are relative to a given course and wind. If you are sailing on the course for max Vmg, with sails properly trimmed, and you head up a bit without retrimming, then you are pinching. If you bear off and don't retrim, you're footing. Those terms are used with respect to sail trim, not course.
There is another great figure in a book called "The Symmetry of Sailing: The Physics of Sailing for Yachtsman" by Ross Garrett. It's in the section where he is taking apart the polar diagram for a given boat/sail/wind and explaining all the forces. I'll try to scan it and post it, if it's ok to do that on this forum.
Right, just to be clear about my lack of clarity
, there is a VMG for every course but typically only one VMG max for any condition. Sometimes I get lazy and drop the max and assume that the context will make it clear when I'm talking about VMG max and when I'm talking about VMG. The "high, low, slow, fast, pinching, footing" thing is culturally dependent. FWIW, I use the terms this way when sailing upwind:
Pinching is usually a pejorative for sailing too high in error (sails can be luffing of not).
High is a term for intentionally sailing a course above VMG max (eg. to gain height after the start).
Slow can be used to mean either pinching or high depending on the context. It is also used to tell the skipper which side of target speed she is on.
Footing, low and slow are the opposites. Those definitions just reflect my cultural bias. I'm know others have different terms or definitions for the same terms... Because of that, I think it is useful to include a definitions when and exact understanding is key to the dialog.
The Garrett book is wonderful. One of my favorites. Sadly my copy is in Hawaii and I'm in Mexico so I can't look at the diagram you're thinking about... Amazon.com has a somewhat searchable copy. You might be able to link to the page you're thinking of...
--Tom.
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