Elaine wrote; >Re correcting for weathercocking, anybody ever put a continuous loop from >the cockpit to the bow, and fasten a windcatching gadget (such as a small >balloon) to it so that it could be run out as far forward as necessary to >balance the stern's turning moment? e You might correct for the weathercocking but may do more harm than good. Weathercocking results from a combination of aerodynamic and hydrodynamic forces. As you paddle across the wind the boat gets blown sideways (called leeway) so if you kept your boat always pointing at your destination you will travel a curved course of greater distance than if you made no leeway. How much leeway you make will depend upon the windage and the lateral resistance of the boat. If you do nothing to increase the lateral resistance, adding anything above the water will increase the wind resistance and cause greater leeway. So, even though you will not turn into the wind you will have to paddle further due to the greater leeway. Even if you head above the direct course the added leeway will cause more resistance since the boat is traveling kind of crab like rather than straight through the water. Somewhere I have a report of a study of an International sailing canoe that showed a considerable increase in resistance at relatively small leeway angles of about 5 degrees. If I recall correctly it was something in the order of 40% for a boat with a centerboard down. I will dig around and see if I can find more somewhere in my stack of papers. Rudders and skegs with good airfoil shapes can help reduce leeway and weathercocking by providing some lift. Narrow deep draft hulls have greater lateral resistance and that helps too. Keels can help although the long full length keels have less effect than a short deeper keel. I have had good results with centerboards although they do take up a bit of room. The hydrodynamic aspect of weathercocking (and turning) are explained in my completely non-commercial web page at http://home.ican.net/~735769/control.htm with no advertising. Cheers, John Winters Redwing Designs Web site address, http://home.ican.net/~735769 *************************************************************************** PaddleWise Paddling Mailing List Submissions: paddlewise_at_lists.intelenet.net Subscriptions: paddlewise-request_at_lists.intelenet.net Website: http://www.paddlewise.net/ ***************************************************************************
John Winters wrote: > >...<snip>... How much > leeway you make will depend upon the windage and the lateral resistance of > the boat. ...<snip>... > > ... the added leeway will cause more > resistance since the boat is traveling kind of crab like rather than > straight through the water. ...<snip>... > Narrow deep draft hulls have greater > lateral resistance and that helps too. ... All of this certainly makes sense (at least to my feeble mind). Doesn't this also imply that hulls with a single hard chine may have an advantage in such circumstances, since they tend to be more resistant to "side-slipping", thereby reducing leeway? Has anyone tested the resistance of different hull designs to slide-slipping? It would seem as though this may an important factor in "real-world" performance. As someone who paddles frequently in the wind, I do not spend much time traveling in the direction my boat is pointed. And yet the standard resistance formulas measure (or seek to measure) the resistance of a boat that is traveling straight ahead. It would be useful to know more about these other factors. Dan Hagen *************************************************************************** PaddleWise Paddling Mailing List Submissions: paddlewise_at_lists.intelenet.net Subscriptions: paddlewise-request_at_lists.intelenet.net Website: http://www.paddlewise.net/ ***************************************************************************
Hi guys, here's another one: with all these complicating factors of wind, current, boat design... can we always say that the most energy-efficient route from one point to another (assuming homogeneous conditions, of course) is in a straight over-the-ground course between the 2 points? It seems intuitively that it should be so, but on further thought not obvious. How about it, you physicists out there? e Elaine Harmon - eilidh_at_dc.seflin.org - eharmon_at_cs.miami.edu *************************************************************************** PaddleWise Paddling Mailing List Submissions: paddlewise_at_lists.intelenet.net Subscriptions: paddlewise-request_at_lists.intelenet.net Website: http://www.paddlewise.net/ ***************************************************************************
Elaine Harmon wrote: > > Hi guys, here's another one: with all these complicating factors of wind, > current, boat design... can we always say that the most energy-efficient > route from one point to another (assuming homogeneous conditions, of > course) is in a straight over-the-ground course between the 2 points? ... I have worked this out for a current (using some simplifying assumptions), but not for a side wind. The latter is more complicated, due to the slide slipping. (The current moves you sideways with the water, but not sideways relative to the water. The wind blows you sideways relative to the water, in addition to the former.) In the simpler case of a current, there are some circumstances where you are better off if you do not ferry across, but instead paddle with your boat pointed straight across and then paddle forward along the bank into the current to recover from your sideways drift. When would this be true? The following draws from my earlier posting on this subject: For the case of a current with uniform strength, my very rough model suggests that the break-even point is for a ferry angle of 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 error) that the ratio of the straight-angle time (including the up-current 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...) 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 above "rule" provides a crude staring point. I would certainly welcome a more complex model, if someone knows of one or has the desire to develop one. Again, the case of a side wind would be more complicated. But given that ferrying is not always faster for a side current, the same may be true in the case of a side wind--but the parameters would certainly change. Dan Hagen *************************************************************************** PaddleWise Paddling Mailing List Submissions: paddlewise_at_lists.intelenet.net Subscriptions: paddlewise-request_at_lists.intelenet.net Website: http://www.paddlewise.net/ ***************************************************************************
Elaine Harmon wrote: > Hi guys, here's another one: with all these complicating factors of wind, > current, boat design... can we always say that the most energy-efficient > route from one point to another (assuming homogeneous conditions, of > course) is in a straight over-the-ground course between the 2 points? It > seems intuitively that it should be so, but on further thought not > obvious. How about it, you physicists out there? e Oh-oh!! Sounds like another brachistochrone problem! Can this result in the invention of a form of mathematics more intimidating than the calculus of variations? Where are the Newtons, Liebnitzs, Bernoullis? Gak, where is Inverbon? Mike Actually, David Burch's book on kayak navigation covers wind and current effects on the paddler and how to "best" handle them. However, I don't think it's worked out on the basis of a minimum energy path. Note that minimum energy path isn't necessarily the same as minimum time or minimum paddle force, so it may not always be appropriate for all paddlers. For example, minimum energy requiring a really high stroke force for a short period (i.e. a _hard_ sprint) may be outside the abilities of all but an Olympic class paddler. Energy is always harder to work with than force or momentum. Too many sources of energy loss to mess up the calculations. My years of engineering etc tells me not to touch this one and just enjoy the paddling. *************************************************************************** PaddleWise Paddling Mailing List Submissions: paddlewise_at_lists.intelenet.net Subscriptions: paddlewise-request_at_lists.intelenet.net Website: http://www.paddlewise.net/ ***************************************************************************
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