| The Skiff-Catamaran paradox |
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| Created by : Wouter Hijink, 13 july 2001 |
| By : Wouter Hijink Created : 13 july 2001 Last updated : 13 july 2001 Classification :Mathematical analysis Copyright : Freeware Status : Needs a workover. but info is valid Comments : |
| The question : Let say that both a cat and a skiff design are racing one another on a gate course. That means a course with a start and finish line with just the A or weather mark. Both the cat and skiff sail two 45 degrees beats to the weather mark. And after that they both sail back to the start finish line with two 150 degrees beats.(relative to wind direction) because they both have similar design spis. The weathermark and start/finish are seperated by 1000 metres (about 3333 ft.) The cat has a continious upwind speed of 15 knot (7.5 m/s) The Skiff has a continious upwind speed of 11 knots (5.5 m/s). Slower than the cat as this has been experienced by some reliable sailors on this forum. This was also found to be true with respect to 18-foot skiffs and 18 square cats in 1985 in San Fransisco bay. However ! (before skiffers start yelling) The cat has a continious downwind speed of 20 knots (10 m/s) And the skiff has a continious downwind speed of 35 knots !!! This is also the experience of the same reliable cat sailors. The skiffs smoked the non genaker cats downwind. Or as a cat sailor that was there put it : we smoked them upwind and they smokes us downwind ! A pretty good picture for the skiff guys when looking at the given speeds, I imagine. Now they both make one tack and one jibe and they both are sailing in clean air all the time. The cat loses 5 seconds on both the tack and the jibe relative to the skiff. Now the question is : WHO WILL WIN THIS RACE ? Or more precise who has the best average speed around this race course. If anyone is willing to make a bed out of this than I'm willing to go with you. Later a catsailor forum member calculated the results correctly. The resuts are presented : Assuming both the cat and skiff make one tack and one jibe CAT DATA Cat upwind VMG = 7.5 m/s x cos 45 = 5.3 m/s Cat downwind VMG = 10.0 m/s x cos (180-150)= 8.7 m/s Cat upwind time = 1000 m / 5.3 m/s = 188.6s Cat Downwind time = 1000 m / 8.7 m/s = 115.5 s + tacking loss = 2 * 5.0 s = 10 seconds. --------- TOTAL CAT TIME = 314.1 s SKIFF DATA Skiff upwind VMG = 5.5 m/s cos 45 = 3.9 m/s Skiff downwind VMG = 17.5 m/s cos (180-150) = 15.2 m/s skiff upwind time = 1000 m /3.9 m/s = 257.1 s skiff downwind time = 1000 m / 15.2 m/s = 66.0 s --------- TOTAL SKIFF TIME = 323.1 s THE CAT WINS BY 9 seconds And the skiff never comes near the cat. Apart from on the start line. The 9 seconds difference at a finishing speed of 10 meters a seconds still makes up a distance of 90meters or 300 ft. And why does it happen? Since these modelled boats sail upwind slowly and downwind fast, the same % difference in speed upwind will cause for a greater advantage in elapsed time. Because the negative phenomenon has more time to impact on the endresult on the slower (upwind) leg. Correcting this negative impact requires a bigger speed difference, maybe even an unrealistic speeds difference, on the faster dowwind course. Think of it. |