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Reacher

Reaching v Running

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This thread is an offshoot of the Velocity Made Good (VMG) discussion in the Everglades Challenge 2019 thread.

 

I always want to reach downwind rather than running wing and wing. But, I never really know how much faster I have to reach to have a better vmg. I thought the vmg function on a GPS would give the answer but it doesn't.

 

Feel free to correct my trig calculations, it's been awhile. 

Course deviation of 10 degrees gives a 2% longer course.

20 degrees gives a 6% longer course.

30 degrees gives a 15% longer course.

40 degrees gives a 31% longer course.

45 degrees gives a 41% longer course.

 

If you can do 5 kts straight down wind, then:

10 degrees off is 5.1 knots to stay even

20 degrees off is 5.3

30 degrees off is 5.8

40 degrees off is 6.6

45 degrees off is 7.1 kts.

 

Once the ice melts I will check this out. 

 

 

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Reacher: What you need is a polar plot of your boat's performance on all points.  For a boat with zero friction at the "interface" (which an iceboat approaches because steel on ice friction is very very low) -- the polar plot approximates a circle.  It looks like this:

 

image.thumb.jpeg.ed7ddfbd97db5d6034a7cc274d21b76c.jpeg

 

The vector W is the wind velocity and V is the boat velocity (showing speed and direction with respect to the wind vector -- which is straight up the page).  The circles represent the boat's performance expressed as a function of its heading and the L/D (lift to drag) ratio of its sail (ignoring the boat's windage).  So, an iceboat with a sail having an L/D of 3 (typical) or 5 (high performance) can, on a broad reach make V = 3 X W (typical) or V = 5 X W (high performance).  Note that directly downwind the polar plot shows that V = W no matter what the L/D is.

 

The horozontal L/D of a keel-less boat is quite poor, but is vastly improved by a centerboard, especially one with a hydrofoil with high aspect ratio (length to width).  For steel on very smooth ice, the "L/D" is probably close to the inverse of its coefficient of friction.  The velocity polar plot is affected by these performance figures (in each medium) for the vehicle traveling in this "ancient" interface -- water/air for boats, hard sand or Tarmac for land yachts, Gravity/air for airplanes, air/string/anchor or surfboard (gravity) for kites.

 

Note that iceboats always sail "close hauled" even when on a broad reach -- and, because they are going much faster than the wind, the sail luffs and a gibe is quite tame.

 

The polar plot shown above was in an article that I wrote back in 1974:

image.thumb.jpeg.d1339006899c0ff50cb07a6604506cc7.jpegimage.thumb.jpeg.d2e345dbd2d0331fd77de14cfe42a282.jpeg I don't know the link, but the article is available on the Internet

 

If you had a compass, a good GPS plotter, a steady wind, and a lake with no tide or current, you could easily create your own polar plot and determine the best point to sail in order to fetch any destination in minimum time.

 

 

 

 

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The "polar plot" shown previously is not for a "water" boat, but for an idealized iceboat (steel on ice friction & windage, both) = zero).  The plot is with respect to a wind-speed of unity.  A water Catamaran would have a polar plot looking something like this:

 

image.thumb.jpeg.b7550a1294dcf62c456f79d3fe31c4a7.jpeg 

 

And it would look different for various wind and wave conditions.

 

Years ago I had an Auqua Cat with an A-frame rig holding up a lanteen loose-footed sail.  On smooth water in a good wind it made better progress downwind by tacking as opposed to going directly downwind.

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Here's an example of a polar plot for a keelboat, a Hunter 34 in this case.  These are not always public info.  They are usually from mfg. prediction software not experimental.  Note that the little boat symbols show optimum downwind angle and associated speed for various true wind strengths (shown at the left end of the lines for each wind speed, 8, 10, etc.post-105471-0-96823000-1452952972.jpg

 

http://forums.sailinganarchy.com/uploads/monthly_01_2016/post-105471-0-96823000-1452952972.jpg

 

Here's one for a J105, which can plane at higher wind speeds.  You'll see the lopsided nature of the plot as wind goes up:

 

post-40815-127727855708.jpg

In this case, there are separate lines for flying a jib or an asym spinnaker. You can tell by the kinks in the boat speed curves.

 

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Pete, Alex, Brad, thanks for the polar plots. When a sailing friend saw my page of calculations he said, "there's charts for that."

 

I'm thinking that the CS-20 polar plot is like the J-105, especially when the wind is up.  The best downwind tactic is to sail 135 to 140 degrees off the wind in lighter air and then sail deeper off the wind as wind speed picks up to 20 kts. Or, on a typical day, sail 40 degrees off of dead downwind, then head more downwind in the puffs.

 

Pete, my experience in ice boating is that you can't really go downwind, and you think you can't pull the sheet in hard enough going upwind.

 

Alex, that is a very interesting link. Good find.

 

Brad, good choice to show the difference between the Hunter (beam reach is fastest) and the broad reaching J-105.

 

 

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On ‎3‎/‎16‎/‎2019 at 9:25 AM, Reacher said:

I thought the vmg function on a GPS would give the answer but it doesn't.

It will give an answer through trial and error as you sail a downwind leg if you put in a waypoint where you're headed, then try different headings and speeds until you maximize the vmg.  It's essentially telling you if your actual speed exceeds the distance penalties you've worked out through trig (5.1, 5.3, 5.8, etc.).  But if you mean will it statically predict a vmg for a given boat or wind condition, no.  That's where the polars come in, and as noted they are highly individualized.    Also, I think most racing skippers will tell you that they "know" they can beat or can't quite make the polar numbers in certain areas of the graph:  they remain estimates, especially when a boat model is new and there is little experience to feed in.  Finally, sea state can have a huge effect on the polar performance.  There is a lot of difference between sailing in flat water vs reaching hard into a head sea (which may not be the same on each tack) and vs. broad reaching on waves sufficient to provide a surfing boost.  For fun, you could throw in the difference between salt and fresh waveforms.  Our relatively light CSs may take a huge hit on upwind performance in a chop, but could pick up a huge lift from a fairly modest following sea, especially if the skipper and crew can "ooch" it right.  The onboard vmg reading will give you that, where a polar can only give a predicted estimate.

 

All obvious, maybe.

 

--pb

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My DN iceboat (sail #2141) could definitely make way downwind faster than the wind -- but not directly downwind.   To do that we had to tac (jibe?) -- during which we had the [apparent wind in our faces].  Here's a link to a wind-powered machine that goes much faster directly downwind than the wind:

https://www.google.com/search?q=going+downwind+faster+than+the+wind&oq=going+downwind+fas&aqs=chrome.1.69i57j33l3.38470j0j4&client=ms-android-verizon&sourceid=chrome-mobile&ie=UTF-8#imgrc=_

 

An iceboat sail performs just like a propeller blade with a very large radius.

 

The skipper of an ice boat is always pulling hard on the sheet (usually with x6 purchase) on any heading mainly to flatten the sail which improves its L/D ratio.

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When I was doing the calculations in the first post I was thinking that the destination was directly downwind.  But I realized that it is more likely that a downwind mark might be 20 or 30 degrees off of dead downwind.  In those situations the temptation might be to sail directly to the mark. But, if a 10-20 degree course deviation (sailing 40 degrees off of dead downwind rather than 10-20 degrees) adds only 2-6% to the length of the leg, it might be well worth it to sail the higher course if boat speed rises accordingly. So important to find the sweet spot for boat speed.

 

Pete, my favorite ice boat is the Class A stern streerer aptly named The Menace. 

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