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Finding the Target Boat Speed and Wind Angle

I have been sitting here trying to figure out how to discuss the process of determining the best boat speed and wind angle for a given wind speed. I think the best way is to do it with a series of graphs.

	The graph to the left is a plot of the boat speed vs true wind. I would have to calculate true wind as I can't read it out directly but I really don't care because I am not going to use true wind for my graphs, just to explain the process so bear with me. What we can see from this plot is that the more we bear off, the faster we go. This is not my boat, by the way, it is a fast Cal-40. Thanks to Timm for some very scrubbed boat performance data. We cannot use this plot to determine out optimum settings but the information in this plot is all that we need to determine our optimum targets. What we need to do is find the component of the velocity in the direction of the wind. We know that to get that we need a Sine or Cosine function.
	We know that if the true wind angle was 0 we would be heading right to the mark and we would want to multiply our speed by 1. Problem is the boat wouldn't be moving. We also know that if we were heading 90 degrees, we would be going very fast but in the wrong direction so we would have to multiple that large velocity by 0. From this we know two things. First is that we want to use the Cosine function and multiply our boat speed by the Cosine of the true wind angle. We also know that if this plot is 0 at 0 degrees and 0 at 90 degrees that when the boat speed is not 0 and the angle is less than 90 degrees there will be some point where this product is largest. That is our maximum VMG to Wind and is shown on the plot to the left as the point of maximum Y value which is at about 46 degrees.
	The plot to the left includes both the boat speed and the VMG to wind on one plot. It could be two plots but here it is one. You can now pick off your target true wind angle (45 degrees) and move up the graph to see your target boat speed (5.9 knots). But what if we don't know the true wind angle. All we need to do is convert the X-axis scale to apparent wind angle, something we can observe on the boat.
	Here is the same plot, but this time it is plotted against the apparent wind. This is actually the plot we want. To make it I just converted the true wind readings to apparent wind as I knew the true wind was 12 knots, and I have the boat speed. I just used the formulas from the section on apparent wind vs true wind to change the axis. This plot is the goal. Once you have this you can see that the optimum angle to the apparent wind is about 30.5 degrees and the optimum boat speed is 5.9 knots. But all these conversions are too difficult. We have a better way. We are going to plot out boat speed vs apparent wind angle directly. That is easy. Then we are going to come up with a number to use instead of the Cosine that converts from apparent wind angle to VMG to wind. That number is dependent on the apparent wind angle and both the apparent wind strength and the boat speed. Wow, sounds like we need a super computer to solve that. Turns out that with a simple trick using a four function calculator, we can do it with a table that we will print out along with our calibration diagram for our masthead fly. That is the subject of the next section

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