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Posted by Roddo 

Hi All,
I'm really keen to understand VMC a lot better, in fact any understanding would be better than I know at the moment. I've read a few posts on VMC and sort of understand that if you expect a shift on the course then you need to sail to a point to take advantage of the shift and get on a higher rung. I'd very much like to understand the mathematics of arriving at the number. So I've attached a screen shot of AGage's optimum angles tool for the current tallships race and wonder how the VMC TWA is calculated. I'm also wondering why there is noone on that VMC course  and in general in any of the races and consequently how I can use it to assist with which heading to take. Cheers Rod 

Posted by kroppyer 

outlaw wrote a couple of posts about VMC on solfans, if you haven't read them, be sure to do so.
There are two parts to this VMC thing: 1. understanding VMC, how to calculate and guesstimate it, understanding the relation between the polar, TWA, BRG, VMC and isochrones. 2. figuring out the BRG to use during the race. 1. understanding VMC It's a very geometric/graphic concept. Go to a race where you're currently racing. Zoom in all the way to max zoom. Double click the steering wheel button. You'll see a polar drawn around your boat. Your pink predictor line cuts this polar right in front of you. Imagine you're standing at the crossing of your predictor line and the polar, you're looking in the direction of your predictor line. Now raise/straighten you arms, (like you're an airplane ). Turn a little so that your arms align with the polar line. When you've done that, you're no longer looking in the direction of the predictor line. You're looking in a different direction. This is a special direction since all of the polar is "behind" you. Whatever other angle people right next to you would be sailing, they can't get across your stretched arms. This is the whole point of sailing with VMC. Make sure that while sailing you don't turn too much (your boat may change course, but your arms should stay out aligning with the polar, and you should stay looking in the same direction). As soon as you start turning your body, to the left for example, people on the left have a chance to get ahead of your stretched arms. You have to keep them behind you. Now let's say the wind changes, both in angle and speed. This means if you don't turn you boat, you have to turn your body in order to align your arms with the polar again. We've just said that when you turn your body, you lose. So you need to change the course of your boat, but where to? Enter the direction you're looking at into AGages opt.angles tool, press "VMC" and there you go, it says what angle you should sail. Now this is a very effective way to keep people behind you. But the other thing is that you need to get to the finish... This is where you need to choose the correct initial BRG to start. If you choose well, you shouldn't need to turn your body (change your BRG) too much to get to your next waypoint (the finish, the next mark, some cape you need to round, etc.) 2. figuring out the BRG to use The screenshot shows "VMC to next waypoint", which (to the knowledge of AGages optimum angles) is the next mark to round. The good new is that the bearing to this "next waypoint" is usually no more than 90 degrees off. The bad news is that it is usually off. I'm racing in the tallships race (CiC  Cadiz to A Coruna) using VMC. VMC only. I'm using my own program SPINNACER for that. It has an autopilot that send commands automatically based on a bearing the user enters. For the duration of the race, I have entered values between 290 and 295. I'm not sure if these turn out to be the correct bearings, maybe I should'be used a bearing of 300, or 280. The difficult part is determining what bearing to use, but there is a thing that can help you:  Your bearing should not change too much over time. How much is changes over time depends on how much the wind speed changes spatially.  When you tack, your bearing is equal to the TWD, when you gybe its equal to TWD+180⁰. In the tall ships race there was a tack after the start (if you went north first). I determined roughly when and where I wanted to tack, and found that the TWD was between 290 and 295. So I used some bearings between 290 and 295. In a couple of hours there's a new tack coming up, I'll tack when the wind shifts to somewhere between 290 and 295. And then later I'll tack back when the TWD shifts back to an angle larger than 295. Hopefully I'll end up exactly at the next mark using bearings close to 295, as that means I've been sailing roughly the correct bearing up to that point. But it may very well be that when I don't change my bearing, I'll end up too much north or south. In general (without a router): eyeball a route to your waypoint. Determine the BRG at different points along the route. If they differ too much, adjust your route to have a more constant BRG. Once you have a route with a roughly constant BRG and you end up at your next waypoint, you're good to go. The only way for people to get past you now is when they are in a position where they have more wind or a better TWD than you have.  Last Edited by kroppyer at 20160801 10:11:01  

Posted by Schakel 

So, that's what they were doing.
Who knew. 

Posted by Roddo 

Kroppyer  thankyou. I've been looking at your SPINNACER  amazing. I reckon the hardest thing for you was the acronym  haha. I've been reading over and over as well as outlaws post and I reckon I'm nearly there.
Just don't quite get how to arrive at the bearing. Agage's Optimum Angle uses the bearing to the next mark but you seem to use the average TWD and Outlaw seems to use the TWD later in the leg. So trying to find my own answer; Tacking (inside upwind VMG) Bearing=TWD perhaps with a skew towards the TWD later in the leg Reaching Bearing=Bearing to Mark Gybing (inside downwind VMG) =same as tacking VMC=VMG when bearing is 0,180 Once this gets us to the VMG laylines then we're on the layline?? Am I close?? PS  does your autopilot have land avoidance? Schakel  hahaha  Last Edited by Roddo at 20160805 13:28:07  

Posted by outlaw 

Hi I've actually gone and made another post on the topic. Tell me what you think, maybe it's easier to understand.
http://solfans.org/blog/sailingbythenumbers/vmcrevisited/ Two comments on the last post. VMC to waypoint is pointless on a fundamental level, that's just some random bearing with no real meaning. It does matter for DTF purposes. DTF is of course also pointless. Once this gets us to the VMG laylines then we're on the layline?? If I understand this right, VMG layline is when you barely make it to the mark on VMG? With a proper VMC course you will tack a bit later than that. 

Posted by Rod 

It needs to be pointed out that VMG is merely two special cases of VMC, where you need to go either up or down wind. If you need to go somewhere else, then VMC is needed.
If you look at the geometry of VMC, you will find that VMC is the point that is tangent to the Polar curve. (This is the point where a line at right angles to your desired destination is the tangent to the polar curve (VMG is exactly the same, where your desired destination is just the general direction up or down wind)). It should be added that it is no use plotting a VMC that is closer to the wind than the VMG'pinching' is not the way to greater speed! VMC (and of course VMG) merely shows you the fastest speed your boat is capable of, in any direction. VMG and VMC in SOL ___________  Last Edited by Rod at 20161016 03:03:54   Last Edited by Rod at 20161017 04:15:57  If it breaks, it's not strong enoughif it doesn't, it's too heavy. 

Posted by JB 

Dear Rod, Huib and Roddo,
Let’s clear this a bit, I hope. “Velocity Made Good” represents the module of the vector projection on some chosen direction. In the sailing world “VMG” or ”Velocity Made Good” is (wrongly) used as “VMG” on “Wind”. For “VMG” the projection of the BS vector (“BS” = Boat Speed”) is in the direction of the Wind. For “VMC” the projection of BS vector is on the “Course” (different from “Heading” = “HDG”) you want your boat to take or on the “Course” the boat is already sailing. Formally speaking “VMC” is the same as “VMG” as, again, both represent a vector projection on some chosen direction. “VMG” only depends on the boat Polar via the BS, it is something intrinsic to each boat. VMC depends on the BS and on the “Course” you want to take. With a constant pair (TWA ; TWS) to sail and a simple and clear sailing course from “A” to “B”, the “VMC” calculation is easy because there’s only one target point for reaching: “B”. The issue with “VMC” starts when you have a variable pair (TWA ; TWS), or Nature at work, you have land crossed by the boat path, well, also Nature, and/or also compulsory race marks to be rounded. In this case you have several target points to achieve (better wind zones and geometric constrains) and so different “VMC’s” all along the boat course. To get the things a little nasty, you can even think of “VMC” calculated in relation to the initial race Orthodromic line between Start and Finish and/or between the initial race Loxodromic line (or rhumbline) and duplicate that calculations for the actual Orthodromic line and/or the actual Loxodromic line, assuming the boat has already moved from the Starting line (#4 different calculations for “VMC”, depending on the precision you want/need). Hope I’ve made some light on those two definitions. Big Hug to all. Sail Fair. 

Posted by Rod 

Dear JB
I read your Forum entry, (above), with interest and puzzlement: 'module of the vector projection on some chosen direction' left me scratching my head in the aforementioned 'puzzlement'. The next sentence also puzzled mewhat about down wind? Again in the third sentence. What exactly do you mean by the term 'projection of the BS vector'? I would reverse the expression that VMC is the same as VMGrather VMG is just a pair of special cases of VMC,(directly 'up and 'down' wind). I agree totally with your paragraph "With a constant pair (TWA : TWS) to sail from A to B", but am puzzled by the next paragraph. Obviously if the wind varies along your desired route, several recalculations of your course would be required. Your next paragraph about the 'nasty' caused much scratching of my headI do not understand what you are writing about. It is possible that my math terminology is outofdate with increasing age, but it does seem to me that this is a simple geometric problem. The speed in any direction is shown by the line of the polar. In an ideal boat which made the same speed in all directions, the polar curve would be a perfect circlebut sailboats have polars with variable curvature. This means that a greater speed in the desired direction will be at an angle to the direct course. This angle is chosen as the point where a line at right angles to the desired direction touches (is at the tangent to ) the curve of the polar. This has nothing to do with Orthodromic, Loxodromic, Rhumb or Starting lines, and the precision of the calculation is whatever you desire. One point that has not been discussed (to my knowledge) is that, on any VMC course, the angle to the desired 'destination point' is constantly changing, and that therefore the calculation (or geometric estimation) of the VMC course must also be constantly repeated. Also, I have never seen any discussion about the situation where the VMCcalculated course is closer to the wind than the VMGcalculated course. Personally, I am more "visually" oriented than "mathematically" inclined, so I do all of my VMG and VMC determinations with a small plastic setsquare and a small plastic protractor, directly on the surface of my computer screen. It is quick, direct, and prevents arithmetic and multiplication errors, which creep in with the previously mentioned advancing age.... Likewise, as Trump says, big hugs to all who permit that sort of thing...  Last Edited by Rod at 20161020 14:11:09  If it breaks, it's not strong enoughif it doesn't, it's too heavy. 

Posted by outlaw 

There's two big problems in this discussion, one being linguistic. That is Angle, Bearing, Course & Direction meaning approximately the same thing. Just how it is. Work it out yourself.
Second is the extremely unfortunate fact that "bearing to the next mark" is somehow the default course for VMC calculations. As Rod correctly observes ...on any VMC course, the angle to the desired 'destination point' is constantly changing, and that therefore the calculation (or geometric estimation) of the VMC course must also be constantly repeated. Just don't do that. VMC to the next mark, and by extension DTF is as important as the weather in Shimane two days from now. My assertion is simply that if I make up some number, say 152 degrees, then express the boat speed as a course (152) vector and a normal (62) vector, then always choose the point of sail that maximizes the course vector. I call that VMC152. If I sail VMC152 for six hours I expect to be the 152degreemost boat in the fleet. The corrolary is if I happen to end up at the mark, I will round the mark first. That leaves two minor issues, first while this works over six hours, it absolutely will not over six days. And second the need to get the VMC direction right, where estimating TWD at the next tack is the most obvious approach. 

Posted by kroppyer 

For the people familiar with geometry this shouldn't be too difficult to understand. For a lot of others, this may be impossible to understand without some clear visuals (which should also solve the linguistic problem outlaw mentioned). Still images may not be enough.
I have had the intention of creating a number of animations explaining, in order: 1. The polar; 2. VMG (upwind and downwind); 3. VMC (360 degrees); 4. How using VMC to determine you course is fastest when TWS/TWD change over time (possibly including the slow/fast wally concept); and 5. How to change the bearing you use for your VMC calculation, when TWS/TWD vary over space. I made the first two animations two years ago (see attached files), but it took me too much time to continue with the slightly more complicated ones. If you have experience with creating animations and the time to create these animations, PLEASE let me know. I think it would be very valuable to have these animations, especially the fourth one. SOLers now and in the future will thank you, and possibly the odd IRL sailor wandering on the internet as well. 
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