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September 22nd 2013.

# Sailing 101: Understanding Polars Through Animation

With interactive animation technology, we can take seemingly incredibly complicated systems and break them down to simple.

Today I’m going to explain a basic concept of sailing that even most sailors don’t understand. Even if you’re not a sailor or never want to be one, at least you’ll know how those pesky things that powerboaters have to give way to can move through the water without a propeller, and why the heck they’re zigzagging all over the place. And I’ll do it all without even once mentioning an airplane wing (besides this one time, of course).

In the animation below, you can click on the numbers on the green vertical stripe. The numbers represent the angle that a sailboat is sailing to the wind. For example 90 means that if you are looking in the same direction as the sailboat, the wind would be coming over your left shoulder.

First, just to get the feel of things, try a few random clicks and watch the boat move on the graph. As you do this you’ll also notice that the wind meter at the bottom shows changing display numbers of True Wind Angle (TWA) and boat speed.

Once you’ve done this, click on 0 to point the boat back directly into the wind.

Right, now back to the explanation. The graph with the funny looking backwards C curve is called a Polar Plot, and it usually scares most people away because of it potential complexity – but thanks to the graphic, now it is simple to explain. A properly trimmed sailboat will track this C curve. You can read the Polar Plot by placing the boat on the C curve and tracing around the concentric arc to determine the speed of the boat. For example, click on 60, this will point the boat so that it is sailing at 60 degrees off from the wind direction. Now trace around the arc to see that the boat is achieving 8 knots. Similarly, click on 120 and see that the boat is achieving 8.4 knots. You’ll see that this is the fastest speed that this boat can attain. No other intersection with the C curve produces a higher number when following the arcs around to the vertical line.

Now click on 30 degrees, and you’ll see the boat speed has dropped significantly to 5.1 knots. 20 degrees:3.1 knots and 10 degrees:1.5 knots. And in the animation on the wind meter, you’ll see the sails flapping wildly (called luffing) at 0, 10 and 20 degrees. This indicates that the wind is not able to fill the sails properly and thus can not produce any significant forces on the sails. At zero degree (directly into the wind) the boat is making zero speed.

So, then from this polar plot, to find the speed of your boat towards your destination at a specific angle to the wind, just follow the arc around at a point where the angle to the wind meets the C curve. Where it hits the vertical line, that’s your speed towards your destination.

But, you say – I want to drive my boat in the direction of the wind. If I can’t sail directly into the wind, do I just turn on the engines? Here’s the little known secret that the polar plot reveals. First, obviously if you were going across the wind then you’d not be making any speed towards a windward destination. The polar plot also shows this. The horizontal line at 90 degrees originates at zero knots. IE zero knots towards a windward destination. So if you drew a line horizontally across from the intersection of the angle 80 and the C curve, you’d get about 2 knots. This means you’re making 2 knots in a windward direction even though your boat is travelling at 8 knots as shown on the wind meter (and by tracing the arc around). It is said then in this case that the VMG (Velocity Made Good) is 2 knots.

So now the question begs then – at what is the best angle should I sail in order to make my windward destination in the fastest time? I mean 30 looks pretty good. The boat speed from the wind meter is 5.1 knots and it’s only 30 degrees off my destination. Or what about 20? While the boat has slowed, now we’re heading closer to the destination. The answer lies by drawing a horizontal line that touches the apex of the C curve. i.e. click on 40. The boat speed is 6.9 knots but coming horizontally across you’ll see the boat is making 5.2 knots in the direction of the windward destination. No other higher horizontal line touching the C curve can be attained. Thus the answer is, head 40 degrees off the direction from the wind. Your boat speed will be 6.9 knots but what is important is that you’re making 5.1 knots towards the windward destination – your VMG is 5.1 knots. Sail trimmers will use the 6.9 knot number from the polar plot to ensure that the sails are trimmed to their optimum angles. You can follow the sail positions on the wind meter to see how they should be trimmed to optimize your speed for a given wind direction.

So now, what about a direct downwind destination? It would seem like that since the boat can physically sail downwind that you should just head right for the destination, right? Well, not so fast. Let’s look at the polar plot again. We want a horizontal line that produces the biggest number that touches the lower apex of the C curve. Hmmmm that looks like at about 140 degrees. So now you’re saying “Wait, are you telling me it’s faster to head 40 degrees (180-140) off my target?” Yes – let’s look at it. Click on 140. The boat speed is 8 knots, and drawing a horizontal line across gives us a 5.7 knot component in a direction dead downwind. Alternatively, if you click on 180 degrees the boat speed has dropped to 5.1 knots. In a 10 mile downwind race if you elected the 140 degree course, you’d come in 12 minutes ahead of any opponent who elected to head directly for the downwind finish line. (Of course we mean here that you zigzag downwind by sailing 140 degrees clockwise, then gybe over to sail 140 degrees counter clockwise.)

Caveats: This polar plot shown is for a specific boat at a specific wind speed. Each manufacturer produces a series of polar plots for each specific model and for specific wind speeds.

So the next time you’re out on the bay seeing sailboats zigzagging all over the place, you’ll understand that they are actually making way towards their destination—hopefully helped by a polar plot. Many sailboats have electronics that use polar plots to optimize VMG.