The Cosine

Haven't had a ton of time to post lately but here's a quick thing you should all know: the cosine.

The cosine curve looks like this:

And it rules your life in sailing, whether you know it or not.

How fast you are getting to someplace (whether that place is a mark or the wind) is a function of your speed and how directly you are pointed at your destination. Your speed multiplied by the cosine of the angle between your heading and the destination is how fast you are getting to the destination.

For example, let's say we are going 10 knots (we're sailing Marstroms today) and we are tacking through 90* (Marstroms can't point very high). That means that our true wind angle (the angle between our heading and the wind's direction) is 45*. The cosine of 45* is .707. That makes our VMG (which is our speed of progress into the wind) 7.07 knots. If we get a 10* wind shift, our VMG is still 7.07 knots.

If the mark is directly upwind, then the speed at which we are heading to the mark is the same as our VMG - 7.07 knots. But if we get a 10* header, then the angle between our heading and the mark becomes 55*, and the cosine of 55* is .573. That reduces our speed to the mark down to .573. Ain't that a kick in the pants? On the other hand, if we get a 10* lift, the angle between our heading and the mark is 35*, and the cosine of 35* is .819. So our closing speed with the mark gets bumped up to 8.19 knots.

This is why I am such a freak about pointing to the mark. You have to have a REALLY good reason to not sail towards your next mark. This is a point on which I will continue to relentlessly hound you.

That is all.