Fastest route to the finish line

4 05 2010

This situation presented itself during one of the increasingly popular practice races that a dedicated group of SOLers are organising in the time before the official race starts. Races are arranged on the fly, and usually use some interesting courses and are of relatively short duration. Everyone is welcome to join in – it’s a good opportunity to test out setting Delayed Commands, work on boat handling and ask some questions!

In last night’s race, the finish line was defined as the beach just East of the island shown below. The length of the line and the angle of the wind made for an interesting decision at the turn – which angle will get you to the finish fastest? The shortest distance is straight to a point perpendicular to the line, a little ways above where the fleet has gathered for the next race, but sailing lower might give more speed.

One way to approach this problem is to use the steering tool to measure distances and speeds to each end of the line, and do some quick math to find out which end is favoured. (distance is shown with more precision in the upper right corner of the map window, and speed in the lower right of the polar) This works most of the time, but for long lines, the best point might be somewhere in the middle. We can use the VMC concept to pretty accurately pick the fastest angle straight from the polar diagram without any math.

In the screen capture above, I’ve laid in a line defining the finish line and extending a ways beyond the edges of the beach. The beach is angled slightly @184°. The shortest distance is to the point perpendicular to the beach, or a CC of 94° from the boat, and defines our VMC target direction. You can eyeball this angle – use the steering tool to lay in this line and the resulting TWA will be shown on the polar diagram.

The black line on the polar above is the TWA for the shortest distance, and the windcurve we’re on is the black one just outside the red 20kn line. We want to pick the point that is “furthest forward” along that line. If you visualise a line at right angles to the target direction, the point where it touches the windcurve is our fast VMC angle. If you have a small piece of card or tear the corner off a sheet of paper, you can hold it up to the screen and use it like a little set square. In the example, the solution works out to around 93°.

Use the steering tool to set your TWA to your fast angle, and if the predictor hits the beach (or the finish line) enter that course and click “send” 🙂 In this example, the landing spot is marked by the red dot in the first picture.

We can also do the math as a double-check and to see how much we stand to gain: The shortest distance option gives us a speed of 8.36 knots over 4.89 nm, while the second results in a speed of 8.77 knots over 4.98 nm. This gives us times of 35m 6s and 34m 4s. The VMC method gains just over a minute, or  0.15nm – not a lot, but more than enough to decide a race. The top 5 boats finished inside that window last night!

What if your fast VMC angle ends up missing the line? Then you target the pin at that end of the line. This is much more common.



4 responses

4 05 2010

You have a talent to put things in a simple logical manner, another great hint for the novice.

4 05 2010

Hi 76, I believe I’m getting closer to understanding the concept, but I do have a problem regarding the final leg of tonights extra-race. Using rounding time=start+2hours – twd=6deg; tws=17,85 kt average and interpolated BS from detailed xls-file, I do not get a “minimum” time. Graphically it could indicate cc=95-96 degrees, but calcs do not.

19 01 2011

Hey 76T…. nice article.

I have written a small tool that calculates both max VMG (for upwind & downwind) for a given TWS – , and also maximum VMC given input of TWS, TWD and a CC to the waypoint and hey, when I input 20.3kt@12 degrees and CC of 94, it outputs “Max VMC = 8.57kt @ 105.95 [8.76kt]”, where actual BS is in the square brackets, and VMC is 8.57kt…
No more sliding around bits of cardboard! 😉

PS: I was quite surprised by how much even the upwind max VMG angles can change for different TWSs… Some more than others of course, like mini 6.5 varies greatly- with a critical point around 11kt.

3 05 2012
Using the VMG/C Calculator to Determine Favoured end of the Finish Line « Tools

[…] a more visual discussion of this topic, read 76Trombones’ excellent article: Fastest Route to the Finish Line (actually read all his articles!) The first polar image in that article also gives you a clue on a […]

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