djlewis

Did you follow the "Here" link to the mathematical account? It's an area I'm not particularly experienced in, so I'd appreciate your opinion about the math. These mathematicians do claim it's a classical pursuit curve, and while that's not as celebrated a curve as: Parabola, Circle, Witch of Agnesi (sic!), Catenary(alysoid, funicular), Brachistochrone, Cycloid, Epicycloid, Rose (rhodonea) and the like, I think it's a legit family of curves and a meaningful, widely-recognized name. --David (wondering why, if he has time to look all this up, he's not out paddling)

What curve does a kayak make when crossing in a crosswind or crosscurrent, keeping the bow aimed at the target feature? It's common knowledge that the kayak does not go in a straight line, but as it drifts downwind, it has to aim farther and farther upwind to keep the target off the bow. So the course ends up kind of "hooking" back toward the target near the end. The solution usually recommended is to start with a ferry angle, calculated from the drift rate and distance to travel, and then keep reducing the angle as you approach the target. Done properly, that will give you a straight line course. Whether that course is actually the most efficient one is a different question to be dealt with later. Anyway, it's often asked what is the shape of the hooking-back track if you do it "wrong", that is, don't use a ferry angle. The answer is, it's a pursuit curve, which is a family of mathematical curves that arise when a predator chases a moving prey. Obviously the kayak in this case is not chasing a moving prey. But the effect is the same, since the crosscurrent is constantly changing the frame of reference for the fixed target, so the target is, in effect, moving with respect to the frame. Here is a mathematical analysis of this exact curve for the kayaking problem. This has not, to my knowledge, been published anywhere to date, but I haven't done a thorough search. Any questions?! Yes -- what about the relative efficiency of the pursuit curve and the straight line? I've seen it suggested that the pursuit curve may actually be more efficient even though it is longer, because you are going with the drift as much as possible; when you use a ferry angle, you are constantly working against the current. On general thermodynamic grounds (a steady, smooth expenditure of energy is generally more efficient than a varying one), I suspect the ferry-angle-straight-line course is still the best. But I will ask the mathematicians after the buzz from this question has died down. --David (substituting thinking about paddling for actual paddling on this picture-perfect day)

I'm posting a (pointer to) complete mathematical answer on the main board. Nope, I did not do it... I called on an active community of mathematicians who love solving these sorts of problems for points, badges and bragging rights. BTW, it's called a "pursuit curve", which comes up when a pursuer is chasing a moving prey.

Aquanaut -- Avocet's "big sister". It's curved for sure, but I doubt parabolic -- any mathematicians wanna name that curve? (I don't know it). Sometimes it takes $100 to get someone's attention. I only bet that much on sure things, and that doesn't include horses.

Not skinning you, I hope, but do you think the best way can be with a GPS -- what did folks do before GPS's? My response uses a more "traditional", but not utterly "traditional" gadget, and works the same as the GPS method. That's the pending $100 bet -- you wanna side bet? But you are correct (IMHO) that either the GPS or my method is best combined with calculating a good initial correction -- the celebrated ferry angle -- and there is a rough-and-ready mathematical way to do it, based on drift either observed or estimated. As for ranges on two objects, it's pretty rare to keep finding two appropriately situated objects, especially on an open crossing, so that's only good for calculating initial drift, IMHO. We came up with #3 and #5. I like your others too!

Five intrepid paddlers (paddlers are always intrepid, aren't they?)(Leon, Bryan, Phil & Lori (different than Phil & Lorrie), and moi) put Bs in Bs at 11:30 AM on Friday in Lane's Cove and paddled off in search of adventure. What they found was: the North Shore of Cape Ann, with its homes of the 1.0%, 0.1% and 0.01%; a lovely lunch at a nearby undisclosed location near an undisclosed lighthouse, complete with a friendly Puerto Rican mutt cadging scraps; the north mouth of the Annisquam; a deserted Wingaersheek Beach; the delightful sandy peninsula on the north side of the Essex Bay mouth, where they assiduously observed the postings to protect nesting birds; and some 1' riffles in the Essex mouth that passed for excitement on this basically flat, sunny day. Not found prior to 3:30 return was the predicted rainstorm which did hit further east. On the straight crossing back, Leon and David continued their many stimulating online "discussions" in person, with topics such as: "what shape track will you take if you keep your bow pointed at a distant feature, with a crosswind going", "what's a good way to insure that track is a straight line when you actually try to paddle it", "why are traditional kayak bows upswept", "who on this trip is the oldest", "who on this trip is the fastest", and so on. There were two $100 bets proffered, one rejected after some clarification and one still pending -- hint: they were not about age, speed, kayak bows or feathered paddles. Approximate track, reconstructed from memory -- http://www.gmap-pedometer.com/?r=5504374 Leon's photographs -- http://djlewis.smugmug.com/Kayaking/Trips/Lanes-Essex-2012-06-08/23453834_cSZR7N Respectfully submitted -- moi.

I like my Canon D10 -- good quality images and decent LCD. Yes, a bit thick, but it still goes in my stretchy-top PFD pocket. But to tell the truth, I haven't yet submerged it much, so it may still show leakage later.

Good advice! CRCK has excellent rolling instructors and classes. But sign up early, as slots go fast. --David (no relationship with CRCK other than a long-time satisfied customer; got my first roll there with Kevin)

Agree -- postpone. The 4-6-footers might make a fun L4 day (rare for stuff that big to get so deep into Salem Sound -- wave direction has to be just right), but the wind will not be so much fun for anyone.

Looks like waves will be 1-2 in that area (using the more accurate graphical forecast), which is close for L2. But the wind will definitely not be L2, nor even L3 for that matter, more like L3.5-4. And though it may be moot, we could check t-storms to some extent with the radar maps in the morning.

Oh, dear, Pru -- please let me know if you won't make it. I was hoping you'd lend your experience and training to help out.

Great, Gene -- hope to see you. Hoping for a few more experienced paddlers so we can break into two groups of different lengths and levels. Do you feel up to that role, Gene? --David.

Moi aussi

Different strokes...

Point well taken. But in fact, a "correct" forward stroke greatly increases your "stamina" in the sense of how far you can paddle (and how fast, when the limitation is tiring out). All too often have I watched very strong (muscularly speaking), well-conditioned paddlers flag way before they had to because of arm paddling, sometimes embarrassingly so. When I (finally) figured out more-or-less correct form, my range took an immediate upward leap of well over 30%.

Interesting idea -- use the forward sweep as an initial model for the forward stroke. Morph the sweep into a forward stroke by changing paddle angle and blade placement, but still using the same hip/torso dynamics. Sounds like it might work. I have done something similar in teaching forward stroke for a few years, but statically, not via the forward sweep. This seems worth trying. Except... many (most?) students might say fairly soon -- you mean I've got to go to those extremes of hip twisting with every stroke. One way or another, I find it often comes down to that -- too "unnatural", too much work, too much concentration -- not worth it -- I'll stick with my old, relaxed style, even if it's less efficient, gives me less power, less range.

Yes, Jen Kleck -- a wonderful coach and person. She set Deborah and me up with some great paddling and equipment for two days in San Diego... and personally ferried us to La Jolla so we could make a one-way trip back to San Diego. At some symposia long ago, she has more than once helped me boost my paddling to higher levels. What she says about feathering -- and rolling -- is interesting, and reflects my own experience, though certainly at a lower level of performance. When I change feather angle, my stroke too almost automatically and unconsciously corrects itself within a few cycles. As for rolling, in the days when I paddled much more and practiced rolling more as well, I had a lovely, reliable, thought-free roll in most any boat. Now that I paddle less and have become one of those kayakers who "avoid conditions in which they might have to brace or roll", my roll and brace have gone to heck, which, of course, leads to more avoidance and more deterioration.

Excellent point! I'd go even further -- stick your head and hand inside the cockpit with a hose and thoroughly rinse the footbar sliders AND work them back and forth at the same time and again afterwards. I didn't use to do this, of course, with the result being all-but-frozen sliders on occasion. (Another reason to have a short bulkhead and measured pads against it rather than footpegs -- but I don't have that luxury in my second boat). As for removing the sand from the cockpit altogether -- and it can be annoying when it builds up -- I'd love to hear how people do that. I have found it frustratingly difficult. A cockpit makes a very nice bowl -- with all the ridges and bumps -- that retains sand with astonishing persistence and cannot be flushed like washing a dish in a sink! On occasion, after taking in a lot of sand (from a bad surfy beach landing), I have gone in with first a scoop, and then a sponge, to remove sand one tiny load at a time. I couldn't make any other method work, and this one took me the better part of 20-30 minutes of gritty work.

Side issue -- but important. Be sure to really hose down the car thoroughly, especially if you use that method. Admittedly my 2002 Subie Wagon has been doing kayak duty for awhile (sorry, Ern), but the last year or two I am seeing a lot of rust on the edges of the roof. In fact, the hinges on the rear hatch door were approaching danger level -- looked like the whole door would work its way off at some point soon. I had that fixed, but have postponed the areas of rust around the front posts and the edges of the side. The rest of the car has very little if any rust. I think this happened from the kayak(s) up on top dripping salt water on the way home. I did not hose it thoroughly from the roof down after each trip -- but I do now! I'd worry that Leon's method would make things even worse, and make hosing down more vital. BTW, I use Doug's method for gear -- lay everything out in the driveway -- hose with high-speed jet -- turn stuff over -- hose again -- pick up the pfd and skirt and hose while hanging from my hand to make really sure -- hose out the boots especially well -- hose out the big storage bucket -- load it all into the bucket -- schlepp to basement -- hang everything on the dedicated kayak gear rack. One danger of the high-speed water jet -- destroying electronics. I once killed a camera that way when I inadvertently left it in an open pfd pocket and then hit it almost directly with a jet of water. -------------------- One question -- may generate controversy -- I've never understood why people consider it so important to wash the kayak inside and outside so thoroughly. Seems to me that all the materials in a kayak are extremely corrosion-resistant, and it would do fine even if it never got hosed with fresh water. Is that true?

Yes, Peace!

I agree -- too many mistakes and questionable reasonings in your last post to make any more discussion worthwhile. ;-))) See ya on the water-- we'll do some more experiments. --David

Good summary of my position. I think evidence of the size of the air resistance effect is how much propulsion you can get by waving a paddle around in the air! Have you tried it? Who won? Sound high to me. But even if it's that high or higher, bear in mind that the maximum resistance only occurs for a small part of a stroke cycle. Even integrating (averaging, for non-geeks) over a whole cycle seems likely to be under 10-20% of that, so we are talking tenths of a %. Any biomechanical effects are worth far far more than that, so they wash out air issues, which still feel like a non-factor for racers and general efficiency. As for recreational paddlers in high wind, I'll say again -- carrying a storm paddle will do far more to eliminate wind-on-paddle issues -- that's what it's for and why it's named that. 'Course you gotta learn how to use a storm paddle, with a sliding stroke etc, but it's kinda neat, IMHO (not that I am an expert).

And when paddling with a tail wind, it's a propeller, right?! Actually, neither, on average. The push forward of the dry blade generates, on average, only as much backward propulsion as it would in still air. (See prior mathematical model, of which this is a non-technical summary.) So while the dry blade sail effect may seem uncomfortable in a high head wind, it's actually not any worse for drag, on balance. Of course, that discomfort is a potential problem of a different sort. But if you're worried about a dry blade being buffeted by wind apart from blade motion, then feathering is again irrelevant, on average, because the wind can come equally likely from any direction. Unless, of course, Peter, you are one of those lucky paddlers who always have a head wind. But then you have bigger problems than just your paddle in the air, dontcha. You need to get a storm paddle! And remind me to do circuits the opposite direction from you, when possible.

Hah! Another reason to feather not. (Just kidding ;-))). --David