They would like a spreadsheet to calculate the true wind, given the readings from the boat's instruments of the apparent wind speed and apparent wind angle. They'd also like a spreadsheet to calculate what the boat's instruments should read as an apparent wind, in order to sail a certain course to the true wind. Both of these calculations are made a little awkward by the boat's leeway.
The downloadable Excel spreadsheet (about 19kb) that I've developed has two worksheets. One worksheet runs the "reverse" calculation for apparent wind, while the other worksheet provides an estimate of what the boat instruments should be reading for a given position on the boat's polar diagram. Both worksheets make a stab at correcting the calculations for the boat's leeway. Unfortunately, leeway is not a value which can be obtained from common instruments, so it has to be estimated. The worksheet calculations simply use whatever leeway values you enter as appropriate. (By the way, the spreadsheet is still useful if your total boat instrumentation consists of a mast-top burgee; you can still get an idea of the sort of apparent wind angle needed for maximum effect with your asym.)
The following diagrams show the triangle of velocities involved in the speeds of the true wind, apparent wind, and the boat. Blue is the true wind, and green is the apparent wind. The boat always sails the red course as the actual course. If she makes leeway, she sails an apparent course shown in purple. (Please note that the purple, apparent course of the diagram is the apparent course as recovered or implied by the boat's instruments. The boat's actual course, with leeway, is different from that shown in the diagram, and is of course lower than the red course, not higher.)
The first diagram shows the boat on the beat, making no leeway and sailing her actual, red, course. Taking some example figures, we have the 20 knot true wind (true wind speed, TWS) at an angle of 45 degrees (true wind angle, TWA) to the boat, while the boat speeds along at 14 knots (boat speed, BS). This gives rise to an apparent wind of about 31.5 knots (apparent wind speed, AWS) at an apparent angle of about 26.5 degrees (apparent wind angle, AWA). This situation does not occur in practice, of course. Instead, we have the boat making leeway, as illustrated in the next diagram. For the sake of argument, a leeway angle of 5 degrees is shown, and the diagram has been exaggerated to show the effect this leeway has on the boat's instrument readings.
The diagrams show a leeway that has been exaggerated to about 15 degrees. This exaggeration is purely for effect, to make it easier to see what happens to the boat's instrument readings when the boat makes leeway.
We assume (reasonably, I hope, and subject only to a relatively small error) that the boat's speed as shown on the instruments is not much affected by moderate leeway angles. If it is, you will need to make whatever corrections seem appropriate.
We also assume that the apparent wind speed is not affected by the leeway. This should be a better assumption, since most mast-head anemometers are designed to take wind speed readings regardless of wind direction.
What is very much affected by leeway, however, is the reading of the apparent wind angle. If the boat's centre-line is taken as the zero datum for the AWA instrument, then the instrument's reading of AWA is underestimated by the angle of leeway. Put another way, the instrument tells you that the boat is pointing somewhat higher than her actual course. If the details of the true wind are "recovered" from these raw instrumented readings, then you would incorrectly think that the true wind was closer to the bows than in reality, and that its strength was a little less. Assuming a leeway of 5 degrees for argument, the instrumented AWA would be about 21.5 degrees, leading you to think the true wind was at an angle of 37.5 degrees off the bows and blowing at about 19 knots, when in fact the true wind was angled at 45 degrees and blowing at 20 knots. (The spreadsheet assumes that the AWA instrument readings are not corrected for leeway.)
On the run, the situation is similar. The next two diagrams show the boat running without leeway, and with leeway. Without leeway, we imagine the boat making 14 knots before a true wind of 20 knots at a true angle of 135 degrees. The resulting apparent wind is pretty much square on the beam at an apparent angle of about 90 degrees, and has an apparent speed of about 14 knots. Again, the boat makes leeway in practice. The last diagram shows this leeway, exaggerated for effect as before, and we see that the AWA is again underestimated by the instruments. If we assume 5 degrees of leeway, the instrumented AWA would be about 85 degrees. If this was used as raw data to recover the true wind details, we would find the true wind angle was underestimated, not as seriously, to a value of about 132.5 degrees, and the true wind speed would again be underestimated at about 19 knots. (Again, note that the leeway shown in the diagram is the course that would be implied by the boat's instruments. The actual leeway made by the boat would be lower than the red course, not higher.)
The spreadsheet provides a better estimate of the true wind by accounting for the leeway. It does this by simply adding your estimate of the leeway into the instrumented AWA, and calculating from there.
Using the spreadsheet with polar diagram data is intended to help you find the right apparent wind angle to sail according to your instruments. For example, you might know that, from the polar for your boat, she makes her best VMG at a broad reach flying her asymmetrical spinnaker with the true wind at 135 degrees. You might know that, if the true wind was about 20 knots, the polar predicts some good surfing at a boat speed of about 14 knots. Putting these values into the spreadsheet then tells you that your instruments, your mast-top burgee, or your hair, should be reading an apparent wind angle of about 90 degrees with 0 leeway, or about 85 degrees assuming 5 degrees of leeway. I hope that's useful...
©2011 Lester Gilbert