Saturday, April21, 2018

Background -- Maximizing Speed to Windward

Without Fancy Instruments



What are Polars?

There are lots of articles on polars around. Polars are a way of presenting boat speed vs true wind angle at a variety of true wind speeds that help you determine the fastest point of sail. They are called polars because they are a plot of boat speed and true wind angle on what is called a polar plot. It is called a polar plot because it looks like what you would see if you looked at a globe and the longitude lines viewed from the poll. In other words, there is a center (the pole) and radial lines going out from the center at various degree increments from 0 all the way around to 360, which is the same as 0. To plot the point when the boat is sailing at 45 degrees to the wind and traveling 10 knots, you find the line going away from the center at 45 degrees and mark off 10 knots away from the center and plot the point. This is a very fast boat, by the way. The same data could be plotted on a normal X-Y graph with X bring the angles from 0 to 360 and Y being the boat speed. In the case of our example, you would find the 45 degree point on the X axis and mark up 10 in the Y direction. You have no more or less information about your point with either plot.

Components of velocity

A boat moving at 45 degrees to the wind traveling at 10 knots would also be described as moving toward the wind at 7.07 knots and moving off at 90 degrees to the wind at 7.07 knots. If you moved both those speeds at the same time, you would obviously be going at 45 degrees and it turns out you would be going 10 knots as well. If one were interested in the velocity the boat was moving toward the wind as well as the velocity at right angles to the wind, you could make two X-Y plots but if you are using a polar plot, you don't need to as you can pick that off the X and Y axis of the polar plot. That is the advantage of the polar plot. For the plot at the right, you can find the point on the boats speed graph that is closest to the top of the page, which is to say closest to the wind. You can then see the angle off the polar plot and the distance from the center. These are the target wind angles and target boat speeds.

Use regular graphs instead of polars

Using regular X-Y (Horizontal-Vertical) graphs and plot both the boat speed and the component of boat speed toward the wind vs the wind angle, we can do the same thing. The maximum value of the component of boat speed to the wind occurs at our target wind angle and the boat speed at that point on the X axis is our target boat speed.

How to convert from Polar to X-Y representation

How do we convert from boat speed and true wind angle to the component of velocity toward the wind? Consider for a moment a thought experiment of a polar of a power boat going at a constant boat speed no matter what the wind angle. On a polar plot that would look like a circle of constant radius from the center. The maximum velocity to the wind would obviously be when the boat was heading toward the wind. The speed would be zero when the boat was heading at right angles to the wind and maximum negative when the boat was heading away from the wind. The component of this power boats velocity to the wind describes a Sine wave (actually a Cosine wave). This is similar to the way the tides go up and down over the course of a day. Let us assume that instead of a constant speed, the power boat changes speed as it changes the angle to the wind. We can take the Cosine wave that described the constant speed component to the wind and scale it (multiply it) by the actual boat speed and get the total component toward the wind. This is what we need to do for our sail boat. Mathematically we just compute VMG to the Wind = Boat Speed * Cosign (Angle to the true wind).

No more talk about polars (almost)

I am not going to talk about polar plots any longer. Well, perhaps a little but mainly I am going to use what are called rectangular coordinates and in specific two rectangular coordinates. First is the raw speed. The second is the VMG to the Wind, one of the two components of the boats speed and direction. The reason I am not using polars is that it is must much easier to plot and understand rectangle X-Y plots than to try and read polars. I have also developed tools that make this easy to do even under way with just a simple 4 function calculator and some charts that this web site can print custom for your boat.

A little more on Polars Buying Polars

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