VMG plus a tack or a gybe

I have a question out of my experience in the Volvo Ocean Race Game in which a number of Footy sailors participated. As most will be aware, this was essentially a navigational exercise. My question here is not totally related to Footy sailing, but applies to all sailing.
When running or beating with the aid of a polar diagram, and the desired destination will require a tack or a gybe to reach it, is there a method, a tool, or a principle upon which a decision can be made about the optimum True Wind Angle to employ, and the position or time at which the tack or gybe should be made, so that the total sailing time is at a minimum?
I realize that this could be obtained by trial-and-error, but I have never seen amy method described by which these points may be calculated. The same problem arises in standard around-the-buoys racing, although one might not have enough time to sit and calculate the TWA or the Tack-Gybe point. I realize that one can utilize the obvious lay-lines, and the TWA which gives the greatest Velocity (VMG), but do these nescessarily give the shortest time to the destination or buoy?

I think you are on the right idea. Without any variables, shortest time to the next mark would occur when you reach the opposite tack/gybe lay line. In other words, tack or gybe when the course for your best vmg on that heading intersects with the next mark. (You will lose about 2 boat lengths for a tack, and maybe one for a gybe).

However, there are several variables that make this point a guestimate. Will the wind shift? By how much? Will it be a persistent shift or oscillating? Will the wind velocity change? Is the wave angle on the other heading going to affect your VMG? The great imponderables. . .

Hi Rod,
For the volvo game and games like it VMG is the answer.
take the losing board first…opposite to real sailing as in these games there is no possibilty for the wind to shift during your time in each wind square.
My strategy generally was to put markers on the course to where I wanted to head then plot best VMG to each marker.In times of uncertainty of what the next weather update will bring try to be on the edge of squares so you can dive into a better square easily if caught out.

My racing is with a Soling 1M these days, so currents and waves are not a factor. What I was visualizing was something like a protractor with a pivot in the middle to allow it to be set for any wind angle, with each leg marked with a scale. I could see it being used mainly downwind, so you could calculate the elapsed time to any point. In a way, The VRTool and the Polar diagrams for each wind speed are doing much the same thing, but you don’t always have the VRTool to help. The question really becomes–Is it faster to pinch a little, or run free a little–go faster or travel further. it seems intuitive that this should be something that is calculatable rather than being just an exercize in judgement or an ‘educated guesstimate’.

No guessing…http://easyrouter.free.fr/EN/Trucs_VMG.htm

To Brett;
Precisely! “sometimes it is better to go slower…etc”
That is the exact point I was getting at. Surely there has been a method developed to do what intuition would suggest. I realize such a thing would be very difficult to calculate in the brief time of an R.C. race, but is there a ‘principle’ to keep in mind while in the heat of the action?
I use tell-tales on both sides of both sails on my Soling 1M and sail upwind with all tell-tails streaming evenly, and all the sail angles set according to best practice for Solings,…but!!!–. Down wind, I have never seen anybody run at an angle to the wind and then gybe to get to the mark. I have never seen a polar diagram for a Soling 1M, and short of using some sort of miniaturized GPS with a record function, I don’t know how a polar diagram could be made.

collect the data and make your own polar for the soling for each windspeed.
set a mark and others around it in a circle,time the boat from the centre of the circle to the outside of the circle at various angles and over time different windspeeds,plot the data …theres your very own polar…time consumming and differcult yes it is,put if you want a polar for your boat you need to do this.
pretty much what many of us did in the VORG game…collected speed and heading data to create our own polars.

Unfortunately the pond we use is fairly deep and already contains permanent buoys for the power boat club members, and setting up, and removing, a circle of buoys such as you suggest within one day would be a practical impossibilty. I did attempt to make a “speedometer” for my Soling, which involved towing a very light plastic tube, with shaped foam ends, on a short nylon strand with a spring loaded pointer on a scale. The resistance to towing moved the pointer and the scale could be read from shore, with binoculars. I attempted to obtain speed measurements using a stopwatch and the aforementioned buoys, but they were too far apart, so that the pointer position fluctuated far too much to reach even a basic estimate of speed. Minor wind fluctations didn’t help either and the buoy to buoy distance had to be measured from shore with a tape and a protractor.