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VMC revisited

Hi, I’m going to give the concept of Velocity Made Course, or VMC in short, another look. Hopefully easier to understand, let’s go.

With routing, we are dealing with three issues.
1. Wind changes over time. Here VMC gives the perfect solution.
2. Wind is different in space. Think weather map. VMC is sorta OK I guess.
3. Forecasts change over time. VMC is actually useful here.

Anyway this post is all about the first point.

It’s really basic vector math. I start by picking a somewhat arbitrary target bearing, in this example 280 degrees. In the Optimum Angles Tool [1] we pick this option:

TBH the waypoint option os pointless. [2]

I can express the boatspeed as the sum of two vectors. A forward, or ‘made course’ vector, in this case 280 degrees. And a sideways (or normal, lateral etc) vector, in this case 10 degrees (280+90=10).

VMC_vector [3]

We can now look at a moving boat in the SOL client. Because the point is to maximize the ‘made course’ vector, the orange line must be a tangent of the polar.

VMC_boat [4]

Next we look at the course the boat would take to the first mark. The boat will tack at TWD 280. As a practical matter it’s easier to guess the TWD at the tack and use that as the VMC target.

VMC_Route_280 [5]

How is it fastest?
There’s two points here. First there must be a unique VMC target to get to any particular point. Aim wrong, you miss.

VMC_Route_Comparision [6]

Second it is simply impossible for a different course to get ahead of the orange line. To reach the line all boats have to travel the same distance in the ‘made course’ direction, and pink has optimized speed in this direction. When the pink boat reaches the mark, all other boats must be behind the orange line, thus pink is leading. Hence a perfect solution.

And that’s all there is.

What’s next?
We now have a perfect solution for short distances. Unfortunately the whole ‘perfect solution’ walks the plank as soon as we deal with a weather map. There are some upsides. There are some patterns, that are easier to understand with VMC. And the VMC curve is overall smoother than the alternatives. If one were to plot course and VMC one might get something like this:

VMC_course_plot [7]

The VMC curve is smooth and easy to work with. And when tactics matter, it becomes massively important again. But that’s for another day.