Express 27 Polar Curves

by Carl Schumacher, N.A.

Polar Diagram

Polar Diagrams are used to determine the optimum course to sail, given existing wind conditions. They are plotted using polar coordinates, (hence the name) with true wind angle and a vector of actual boat speed. The vertical scale shows speed made good (VMG) straight upwind or down. The wind angle and boatspeed numbers can come from actual sailing data, which is very time consuming, or a velocity prediction program. The information for this diagram came from the latter. The upper curve is for sailing without a spinnaker and the lower curve is for sailing with one. As you would expect these curves are discontinuous.

More important for the readers than how to construct the diagram is how to use one. Let's say the wind is 10 knots in strength and the next mark is dead downwind. Look at the 10 knot curve and see where it is farthest down. For you mathematical types it is where the tangent to the curve is horizontal. In our case it is at 151 degrees. Assuming there are no windshifts, if you were to sail at that true wind angle, and then jibe for the mark and sail the same wind angle, you will arrive at the mark sooner than if you were to sail any other course. The extra distance sailed is offset by the increase in speed. I have conveniently marked the points of optimum VMG for both upwind and downwind.

There are a couple of interesting things to notice about these curves. One is how high you need to sail when going downwind in light air. It then changes abruptly starting between eight and ten knots. Also notice the crossover between spinnaker and jib. Crews are always arguing about this call. Remember, these curves are for smooth water and don't take waves into account. It also assumes you have your instruments calibrated.

Most of us don't have instruments that give true wind readings which makes it difficult to use the information. In the chart, I have given optimum apparent wind angles for various true wind speeds. This will give you an idea of what Windex angle and boat speed to try and reach (no pun intended).

Wind Speed True Wind Angle Apparent Wind Angle Boat Speed
6 140 94 3.1
8 142 100 4.0
10 151 121 4.8
12 165 150 5.8
14 170 161 6.3
16 170 162 6.8
20 169 161 8.0