With Persephone still on the hard, I tend to grasp at any sailing-related straw to occupy my mind. I recently went through a little exercise relating sail power to diesel power on my particular boat that you may find interesting (or pathetic). According to Yanmar, at 3200rpm my 3YM30 is putting 15kw into the prop shaft, or about 20hp. (It takes 3600rpm to develop its maximum 29hp.) If the prop can convert 70% of it to axial thrust (blades approximately 45degrees and deflecting aft that amount of the force normal to the axis from shaft torque), that implies forward power of 14hp. (A rule-of-thumb says it takes 2hp per ton of displacement to reach hull speed. My hull speed is 7.4kts, and my displacement is about 15,000 lbs, so that sounds reasonable.) At 3200rpm my boat is doing 7kts in flat water, or 11ft/sec. Converting 14hp at 550ft-lbs/sec/hp yields 7700ft-lbs/sec, which when divided by 11ft/sec yields a forward thrust of 700lbs from the prop. Consequently. if the boat is doing 7kts under sail, instead, it must also be being pushed by 700lbs forward thrust on the sails. On a beam reach doing 7kts my ST60 Wind indicates an apparent wind angle of 60-65 degrees off the bow, and simple trig with the length-vs-offset of my boom indicates that it's at an angle of 18-20degrees off the stern (and jib trimmed to match). Thus, the apparent wind is about 45degrees off the sail area, giving it a normal force push of 70% of what it would be if blowing perpendicular to that area. Consequently, the force generated is equal to that on 70% of my 800sq-ft sail area, or equivalent to about 560sq-ft of sail. Since normal force in pounds is 0.004 times area in sq-ft times the square of wind velocity in knots, that implies an apparent wind velocity equal to the square-root of 700/2.8, or a little under 16kts. That, in turn, is about 14kts of true wind on my beam, which is, indeed about what it takes for me to do 7kts. Of course, it's a lot more fun actually doing it.
