Tack angles

Moderator: GreenLake

Tack angles

Postby talbot » Mon Dec 22, 2014 3:16 pm

Watching it rain, fretting about pending job proposals, can't even work on the boat, and this is what happens: Escape into pondering tack angles. We all know the boat goes faster if you fall off from close-hauled, but how much faster do you need to go to make it worth the longer tacks? I'm sure this is published someplace, but I put together my own display of how much speed you need to gain in a Day Sailer to keep your arrival time the same for each 10 degrees you fall off from apparent wind angle of 45 degrees. The table at the top of the image is what I plan to cut out and laminate for the boat. The highlighted cells indicate knots well above the DS theoretical hull speed (5.4kt). That is, if you are already going 5kt at 45 degrees into the wind, you would only gain an advantage in falling off if you could get the boat onto a plane. I trust that people will scramble to check my math, and I'll revise as needed. Higher resolution version available on request. Happy holidays!
tackanglesm.jpg
tackanglesm.jpg (58 KiB) Viewed 11826 times
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Re: Tack angles

Postby GreenLake » Mon Dec 22, 2014 8:35 pm

Interesting subject.

Your math is fine. I checked :) (You might want to put a slightly larger version of the graph with the curves. The legends aren't quite readable. :( )

But you are showing true wind, not apparent wind. Your calculation is based on the course over water (or, in the absence of current) also course over ground. So the angle you are describing is the angle against the wind as measured over the water (or true wind angle).

At different wind vs. boat speeds, the apparent wind angle that corresponds to a true wind of 45° would be different.

The relation between these angles depends on the ratio of the true wind speed to the boat speed. Here's what I calculated.

ApparentWindAngle.png
ApparentWindAngle.png (7.28 KiB) Viewed 11811 times


If the ratio of wind speed to boat speed were constant (for a given wind speed) then we could take this calculation, apply it to your table, and express things in terms of apparent wind (or what we see on the windex). It's not, so, things are a bit trickier. If we had the information (from a velocity prediction program, or from measurements) we would also be able to determine whether it's realistic to achieve the higher boat speeds needed at a larger angle.

For example, if 1.0 knots is the best I can get at 45° TWA for a given wind, is it realistic to get to 1.7 knots at a different point of sail? In other words, is a course of 65° ever realistic? What about 55° at 4.0 kn close hauled?

More generally, can we tell what wind ranges sailing any non-planing angle will get us there faster? These are interesting questions.

Same can be worked out for gybing angles, that is DDW versus reaching.

Using the TWA has the advantage that it can be approximated by compass headings. Not fully because of leeway. Assuming 5° of leeway, one would use your table for headings of 40° to 70° off the direct course to an up-wind target. Perhaps I'll try to measure some actual speed ratios for these angles.
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Re: Tack angles

Postby K.C. Walker » Mon Dec 22, 2014 11:14 pm

I agree, this is an interesting subject. Frank Bethwaite writes about this in his books. He says unless you have true upwind planing conditions, you are better off sailing close hauled at what he calls "target speed". Because we really don't see upwind planing with our DaySailers I think we can safely assume that close hauled at target speed is the best we can do. There's a simplified version of these theories in the manual for the Frank Bethwaite designed Taser. I found it interesting to read. http://www.tasar.org/the-tasar/tasar-manual/
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Re: Tack angles

Postby talbot » Tue Dec 23, 2014 12:00 am

Thanks for the clarification of apparent and true wind. That "simplified" article cited by K.C. is something it will take me a while to work through. So glad I don't have to read the unsimplified article.

I didn't put the chart in full size because, as Greenlake and KC pointed out, the continuous functions are really too precise for our needs. In practice, the only change we are likely to make is falling off 10 degrees or less from close hauled (i.e., the first line of the table is the most important one).

I will start next season with the rule of thumb that when my compass shows me falling off 10 degrees from close-hauled, I want to see the GPS pop up 25% (e.g., from 4 to 5 knots). We'll see what happens. The local yacht clubs maintain an Olympic circle of bouys on our lake, which often has the wind out of the north, so I could actually sail a course just like my diagram.
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Re: Tack angles

Postby Swashbuckley » Tue Dec 23, 2014 2:20 am

FWIW - take this with a serious grain of salt. When I raced 22's this was a perpetual topic at the docks. On the water head to head racing I never saw a boat bear off of close hauled by 5, 10 or more degrees and pass or overtake another boat on the coarse. That is distance made good or over ground. The only time I ever experienced anyone overtaking another boat was to achieve a higher tack angle. The year we moved up in the ranks my skipper estimated we were getting about a 1/4 of a degree better tack angle than our competitors. The pros (ok, they just traveled the US sailing circuit, that is pro to me) that sailed with us, would tell us to only bear off of close hauled to search for better wind. 2 cents. I really like your chart, it makes it much easier to discuss the subject.
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Re: Tack angles

Postby GreenLake » Tue Dec 23, 2014 7:10 am

This discussion is only getting more interesting.

Here's another wrinkle on this: there appears to be penalty in the DS if you point too high, a place where you might think you are still sailing close-hauled but effectively you are almost or already "pinching". The result would be a higher leeway angle, so that while your heading looks optimistic, the course isn't that great and the speed falls off below the optimum as well.

The difference is not 10 degrees, but much less. I'm not sure I've seen differences of a 1/4 of a degree, but 10 degrees is huge. I'm not sure I know how to reliably tell when I am in that condition, the lack of opportunity for comparison with a like boat leaves the GPS as a poor substitute.

For keel boats it's common to have a so called "polar diagram" where you can read off the theoretical best boat speed for each wind angle (at a constant true wind speed). The maximum boat speed upwind is usually at some close hauled angle, with a steep fall off as you "pinch" but before you stall the sails. This curve would be different for each wind speed.

Something like Talbot's calculation could then be used to translate the curve from boat speed to VMG (or effective speed to an upwind destination). The conventional wisdom is that this curve still has its maximum at the close-hauled angle (the same angle where speed through the water is maximized). However, again, you need to draw one curve for each wind speed.

The question is then whether in light or very light winds, for example, it remains the case, that the maximum boat speed and maximum VMG continue to coincide for a displacement hull.

Part of the reason they should is that, especially in light airs, the boat speed contributes so much to the apparent wind speed, and more if you point higher. At the same time, at the relatively low boat speeds you might have the best chance at driving the boat noticeably faster with a correspondingly smaller increase in power (as you get near hull speed, fat chance to get faster at all). Light air racing is definitely different, but there are many other aspects besides pure tacking angle that drive success there. (Where you are and which wind you have trimmed your sail for matters a lot when a puff finally comes -- I remember once being surrounded on all four sides by boats just a few boatlengths away to find myself accelerating and sailing away from them, while they appeared to stand still -- you'd sworn I was using a motor...)

One interesting effect is cited in the article linked by K.C. - the transition between laminar and turbulent flow over the sails around 5 kn of apparent wind, with its corresponding strong increase in driving force (and ability of the air flow to stay attached to fuller sail):

The technique is to sail the lulls with "Light Air" settings. At
the onset of a puff, accelerate by sailing a little full, so that the leeward jib tuft is
just on the point of agitating. ... As the boat accelerates, the sails will suddenly begin to
"pull" -when you feel this, sheet jib and main in smoothly towards their "Moderate Air"
settings, ... and point as high as possible while retaining speed through that puff.

As soon as the puff dies, return to Light Air" settings... This is a "flat water
only" game: it won't work in waves.


Here the "win" is not in getting a higher speed over the total leg by sailing fuller, but just to get a higher initial boat speed, which can then be "converted" to higher wind speed by pointing higher, for a final win providing both higher speed and high pointing angle -- as long as the puff lasts. Playing this game requires control of sail shape with vang etc. that not every DS is set up for. Also, whether this works as quickly as needed to take advantage of a light air 'puff' is a question, because the DS is heavier and accelerates less quickly.

The "sailing a little full" that is mentioned here, I would guess, is something on the order of at most 5° probably much less; I've never measured the angle needed to get the jib telltale to rise, perhaps someone has a more accurate answer.
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Re: Tack angles

Postby K.C. Walker » Tue Dec 23, 2014 9:40 am

Right, "simplified" :-) maybe I should've called it condensed. For our purposes, the Taser manual has most of what we could use from his teachings. I found his books also interesting, though. His books mostly deal with "apparent wind boats", meaning boats like the 49er or the Sydney Harbour Skiffs that regularly plane to wind.

There really is a lot of good stuff to think about in those articles. What I particularly like about this is that he is trying to teach people to sail by the seat of their pants (get good boat feel). Yes, it seems very technical and is, but he's trying to teach us to sail with our heads out of the boat and not look at the GPS or compass all the time, but to feel how the boat's moving and the tug on the sails, look at the water, and what it means.

Finding that just right angle for us as sailors is really what it's all about. It's like hitting the ball perfectly in tennis or golf, it's so satisfying. And because it changes continuously and we don't get it all the time, actually very little of the time, even when we concentrate, it keeps us interested. To think that basically anyone can get in the sailboat and have the wind make it move but that there are people who are national champions, world champions, Olympic champions of being able to get these angles just right is pretty amazing. And, that at each level it can be very satisfying.
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Re: Tack angles

Postby talbot » Tue Dec 23, 2014 3:29 pm

Great discussion. I think the GPS is useful at those marginal transitions (such as trying to sail just a little too high), where the increase in speed from falling off a degree might be apparent to the satellites before you feel it through the cockpit coaming. Yeah, 10 degrees is probably too big in increment. 5 degrees would be more realistic, and is the smallest gradation on my steering compass.

I think my chart might also be a motivator in situations where our boat handling is sub-optimal. For instance, if we are heeling more than 15 degrees close hauled, but can bring the boat down close to 10 degrees (either by steering or hiking), we very well could get the speed increases my chart requires.

I would imagine the easier a boat planes, the more sense it make to fall off. I understand that NZ took the early lead in San Francisco by realizing that foiling at lower tack angles was much faster than having any water contact with the hulls. Oracle had to fall off and beat NZ at its own game to win the cup.
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Re: Tack angles

Postby GreenLake » Wed Dec 24, 2014 3:35 am

Talbot. Having played with a GPS for a while now I'm not really convinced that it's more sensitive than telltales.

For one, it only updates the display every so often, and subjectively that seems to me less often than the boat state changes due to wind or waves.

For the other, when sailing upwind, the most relevant thing is the direction of the apparent wind. If that changes due to speed change or wind shift, I'm better off adjusting to that than to an average course. Bethwaite, in his books, discusses how the wind oscillates about a medium direction. Stuart Walker also mentions that in detail in his books on both racing and weather.

Where the GPS (as replacement for a compass) comes in handy is in tracking such shifts, especially when it comes to realizing that a shift is no longer oscillating but that some permanent wind shift has happened. The other place were the GPS comes in handy is in recording a trace of where I sailed (including actual tacking angles over ground). Combined with some direct recollection of how the afternoon's sail went, the trace lets me observe things afterwards, from a bit different perspective. Sometimes it's even possible to see a "wind shift" in the trace (because while I remember sailing a long leg nicely to the telltales, the track shows a kink, for example).

My GPS does not record the speeds it calculates, but there are programs that will do that from the distance over time between track points. Curious fact is that the two do not agree !!

I consistently remember seeing peak speeds on the GPs a few tenth of a knot higher than what is later read off from the track. One factor appears to be that track points are recorded less frequently than each change in the speed value, so that the speeds read off later would be averaged over slightly longer intervals (hence miss the peak speeds).

Tricky tool that, the GPS.
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Re: Tack angles

Postby talbot » Wed Dec 24, 2014 4:58 pm

My suggested use of the GPS was simply as a knot meter. Is is not really necessary for my experiment, because on the 1-mile-diameter race course, the distance between any two buoys is known. I guess it would be useful for recording the exact amount of leeway.
I've also had to learn to ignore bogus GPS accelleration. If we hand the GPS unit forward from the helm for someone to return it to its mount on the bulkhead, the satellites will add the velocity of the handoff to the speed of the boat, and the GPS memory may even retain it as the recorded top speed.
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Re: Tack angles

Postby GreenLake » Wed Dec 24, 2014 6:31 pm

I created a mount for the GPS so it can be read from anywhere in the boat (avoids moving the GPS relative to the boat). I also mount it in the back so it doesn't distract me too much :D

Ideally, one should be able to get to the "best" upwind angle and sail trim and then use the GPS to experiment with small changes. Your experience may be different, but I've found so far that the wind speed and direction are too unsteady for me to run an experiment based on it. Whenever I thought I had some useful result, I could not be sure that it wasn't attributable to a gust or a wind shift. The "instantaneous" speeds as displayed on the GPS seem to rarely stay fixed for long.

Curiously enough I've seen it done on larger boats, to some moderate success.

Bethwaite, in his books, goes into measurements he did on some performance characteristics, like differences in drag between different prototypes. He essentially had to resort to towing both boats on a beam so that they would experience the same external influences (waves, wind on the hull portion above the water, small fluctuations in towing speeds) so he could eliminate those influences. That's why it's normally so advantageous to compare like boats.

Those of us that can't measure ourselves directly against another DS on the water are at a disadvantage. However, even having a friend in a similar boat sail along can be very revealing. For some reasons, I would get "tricked" occasionally in thinking I was sailing close-hauled, when I was in fact sailing 10° off the wind (and I really mean 10°, a "huge" angle). Telltales and all other indicators pointed to the heading being a close hauled one. At that time, having him sail behind and asking "where are you going? (and why)" helped me locate the problem. If I had been cruising by myself I may not have noticed it.

I still encounter situations where I feel the boat should point better than I can manage; either the wind is really screwy (such that the Windex at the top reads at an angle to the wind felt lower down at the sails - not in itself impossible) or I'm doing something wrong without realizing it (incorrect sail trim, what have you). I don't know if a GPS would help me in those situations, as much as direct observation and comparison with any reasonably compatible boat would. I do use the GPS trace to later determine whether tacking angles over ground were in fact worse that day. This is on a lake, so no appreciable current or wind-driven surface currents that would cause SOG to be different from speed over water.

The leeway is of course factored in with the GPS, so the angles are based on the course, not the heading (the latter is the tacking angle you'd measure with a compass).

Speaking of leeway, I should try that measurement, to see whether it's sensitive enough. All it would take is to make a tack (so there's a fixed point on the GPS trace) then sail a fixed heading based on compass for a bit, make another tack (to again mark it on the GPS trace). Later, one could compare the heading with the course angle.

I guess you could record the apparent wind angle and speed and with the average boat speed from the trace figure out what true wind angle you were sailing.

Perhaps you'll succeed in generating a polar diagram for the DS. Would be fun. Keep us in the loop with what you come up with.
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Re: Tack angles

Postby Windnsails » Sun Jan 25, 2015 12:24 am

I am new to this sailing board.

I first began sailing in 1972 on a Cal40 on Puget Sound, WA.

Fast forward though almost 3 dozen years of sailing small boats in Lk Michigan, San Diego's Coronado Bay and Lk Washington in Seattle, and I wound up in the big boat racing on Puget Sound for a few years. I specialized in jib and spinnaker trimming.

Then in about 2010 I called it quits on racing after losing feeling in my hands after a white knuckle experience in high winds with dropping temps below freezing and driving snow on Puget Sound.

I regained feeling after 3 weeks but considered my sailing days over until a friend gave me his Daysailer III a few days ago.

So here I am with a boat that I want to get to know and one of my first thoughts was that this boat needs a Windex.
That is what brought me to this thread. I am impressed by the thoughtful points and experience shared here. From my racing, and even my USNavy days where we calculated required ship's speed and course to provide a mandatory relative wind speed and direction for helo operations, a lot of this discussion brings back memories.

So here's a question for you seasoned Daysailors. What is optimal relative wind angle for close hauled? Put another way, what can I reasonably expect from a Daysailer?
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Re: Tack angles

Postby talbot » Sun Jan 25, 2015 4:47 pm

Welcome to the forum, and congratulations on your DS III.
I get lost in the true/apparent wind relationship as speed increases, so I generally think in terms of tack angles. That is, I compare headings on my steering compass before and after a tack. I have not been able get higher than 90 degrees, which translates into 45 degrees off true wind. Higher than that, the sails might appear to be full, but the speed falls way off and I'm clearly about to stall. That's in optimal conditions, maybe 8kt under full sail, Barber haulers and traveller trimmed. Once I start reefing, the tack angle falls. Not too bad with a single reef, but very shallow for a double reef with no jib. The DS can't sail into the wind under jib alone in anything but a very light zephyr (and why would you only have a jib in those conditions?)
Given your experience, I would welcome your thoughts on ways to improve upwind performance, since the previous discussion ended with the conclusion that a DS is unlikely to make up in speed what it loses in distance by falling off the wind. Right now, I'm inclined to think it would depend on money. That is, new sails.
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Re: Tack angles

Postby Windnsails » Mon Jan 26, 2015 1:25 am

You mentioned new sails and it prompted me to share the following website.
http://www.sailcare.com/
I have in mind to look into the sail cleaning and repair and resin treatment services after I have time to see what I've got here. Being in the middle of winter now, I'm not too enthusiastic about spreading out sails on the wet moss, I mean grass! :?
Last edited by Windnsails on Mon Jan 26, 2015 10:48 am, edited 2 times in total.
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Re: Tack angles

Postby talbot » Mon Jan 26, 2015 2:43 am

Thanks for the link. Not sure my current sails are worth restoration, but I'll see what the cost is. BTW, we have family in the Puget Sound area, will probably drag the boat up from Oregon again this summer. There are a couple of other northwest sailors on the forum. Maybe we can put together some kind of group sail.
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