VMG, Pointing, Rig Setting

by Lester Gilbert

A while back, I realized I didn’t really know whether I was maximizing drive or maximizing efficiency when beating to windward. We’re nearly at the end of quite a journey, having looked at the lift-to-drag ratio as a measure of efficiency, at the course theorem, which explains how our ability to point depends on efficiency, and at VMG and the heading that maximizes our progress towards the windward mark. Finally, we are now ready to pull it all together to find out what we need to do to set the rig for the optimum pointing angle for maximum VMG.

Ross Garrett’s “The Symmetry of Sailing” (1987, Fig. 3.35) tells us that optimal velocity made good (VMG) when beating to windward occurs in a curious and counter-intuitive position on the lift-to-drag curve—when drive is higher than that seen at best efficiency, but not quite as much as when drive is maximized.

Let’s have a look at the lift-to-drag curve Ross uses. Previously, we saw a plot of the lift-to-drag ratio for various boat headings. We now need a version of this, but instead of the ratio, we are going to plot Cl (coefficient of lift) versus Cd (coefficient of drag), and make a note on the resulting curve of the heading that gave us that particular pair of Cl and Cd points. Figure 1 is an example of this kind of lift-to-drag curve.

Figure 1. IOM rig Cl plotted against Cd for a range of headings

On this curve, we have shown two interesting points. One point is where Cl is a maximum, i.e., where this curve peaks; maximum Cl is around 1.6 when the heading is around 39 degrees. Another point on the curve is the place where the Cl/Cd ratio is a maximum. What is important here is how we got to see this—by drawing a tangent to the curve from the point of zero lift and zero drag. The tangent touches the curve at a heading of around 15 degrees, where the Cl is about 1.0 and the Cd about 0.03, giving a lift-to-drag ratio of around 33.

Previously, we noticed that sailing the boat at a heading of 15 degrees is not going to win too many races. We might be maximally efficient, but our VMG would be close to zero. Let’s take a look, though, at what this heading of 15 degrees looks like if we plot it from the lift-to-drag curve. The result is shown in Figure 2. What is important is how we visualize this—by drawing a perpendicular to the tangent line that corresponds to the point of maximum Cl/Cd. This perpendicular conceptually shows us where to point, relative to the true wind direction and the windward mark, if we wish to sail at maximum efficiency. And we can see that it would be pretty hopeless pointing so high.

Figure 2. Suggested heading corresponding to maximum efficiency

Now, let’s draw the heading that was suggested to us by the VMG polar and see where that tangent touches the lift-to-drag curve. The resulting diagram is shown as Figure 3.

It turns out that the point on the Cl-to-Cd curve that corresponds to the optimum VMG heading is somewhere above the maximum efficiency point, and somewhere below the maximum lift point. The lift-to-drag we are seeking is nowhere near the point of maximum lift-to-drag efficiency and is about equally far away from the point of maximum lift. Figure 4 illustrates that, in some sense, it is “halfway” between the two.

Figure 4. Cl/Cd for optimum VMG between maximum efficiency and maximum drive

My takeaway from this is that we are trying to set up the boat so that it is in the VMG groove when beating to windward. We know that a well-behaved boat sails in its groove “by itself”; that is, it sails happily at some heading where it is balanced. The trick is to make its comfortable balanced groove a VMG groove, and not a continually pinching groove or a needlessly footing groove. Our analysis tells us that a VMG groove does not require us to set the rig at maximum efficiency, and it also does not require us to set the rig for maximum drive; but it does require us to set the rig pretty much “halfway” between the two. Good luck with that!

A note on efficiency

From this discussion, some might think that efficiency, or maximum efficiency, is therefore not particularly important. Not so! What we are saying is that you do not need to set up your rig to work at its maximum efficiency in order to achieve your boat’s optimum VMG, but you certainly must have an efficient rig and boat to be able to point at all. According to the course theorem, the more efficient your boat and rig, the better you will be able to point while keeping up boat speed. In this case, your optimum VMG will change because of your improved efficiency to give you a higher pointing optimum heading.