Regarding ferry angles, John Winters wrote: > > >Has anyone done any experiments on the ideal angle? ...SNIP... to which Robert C. Cline responded: > ...SNIP.. > In summary, if you have to paddle at a ferry angle greater than 60 degrees, > the effort and time spent might not be worth it. According to my calculations, this is pretty close. For a current of uniform strength, the break even point is about 57 degrees, which occurs when the ratio of paddling speed to current speed is approximately 1.19 . In other words, if you can paddle more than 19 percent faster than the current, your ferry angle will be less than 57 degrees, and it will take less time to ferry across than to paddle at a straight-across heading (with zero ferry angle, followed by a paddle up current). On the other hand, if your paddling speed is less than 19 percent faster than the current, your ferry angle would have to exceed 57 percent, in which case it will take you less time if you paddle a straight-across heading (zero angle), even though you have to paddle up current once you reach the other side. Now for the math! Using some fairly straightforward trigonometry, it can be shown (if I haven't made an "oops") that the ratio of the straight-angle time (including the upriver paddle) to the ferry-angle time, st/ft, equals (1+c/p)cos(a), where "c" is the speed of the current, "p" is the paddling speed, and "a" is the ferry angle (in degrees) which itself is a function of c/p. The necessary ferry angle "a" equals the inverse sine of c/p. In other words, the time ratio st/ft is a function only of c/p. This ratio equals one when c/p is approximately equal to .83867, which corresponds to a ferry angle of 57 degrees. If the ratio c/p exceeds .83867 (i.e., if p/c is less than 1.1924), then st/ft is less than one and ferrying will actually take more time than paddling at a straight-across heading, even though you have to paddle up current. (I have checked this against a few simulations, and this seems to work, but as always someone should check the math...) So there you have it. Next time you have to cross a current, ask yourself if you can paddle more than 19 percent faster than the current. If so, then you MIGHT save time by ferrying. I say that you might save time, because the above analysis assumes a current of constant strength. But I have never seen such a current. It is typically slower near shore, even in the absence of eddies. And with eddies it is, of course, a whole new ballgame. So actually, it is quite a bit more complicated than in the simple model above (it always is). Add your own fudge factor to the 19 percent rule. But perhaps the "rule" provides a crude staring point... Dan Hagen Belingham, Washington *************************************************************************** PaddleWise Paddling Mailing List Submissions: paddlewise_at_lists.intelenet.net Subscriptions: paddlewise-request_at_lists.intelenet.net Website: http://www.gasp-seakayak.net/paddlewise/ ***************************************************************************Received on Thu Aug 13 1998 - 01:58:50 PDT
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