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About leong

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    Paddle Upwind

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    Kayak racing, fishing and touring; road bike racing and touring; ski touring; swimming and fitness workouts.

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  1. Correction: I think the center of rotation (pivot point) is close to the center of the paddle. Say half of paddle length is 100 cm. Thus the top of the blade is ~ 80 cm from the center of rotation. Thus the bottom of the blade moves ~25% faster than the top of the blade (100/80).
  2. Correct. Obviously the paddle is moving, but not much. A wing paddle locks better than a flat Euro paddle which locks better that a GP paddle. >> I cant' believe I've gotten sucked into this. Resistance is futile. I think the center of rotation (pivot point) is close to the center of the paddle. Say half of paddle length is 100 cm. Thus the top of the blade is ~ 90 cm from the center of rotation. Thus the bottom of the blade moves ~11% faster than the top of the blade (100/90).
  3. That's called locking the blade. It's theoretically not possible but this how-to video shows how to almost do it.
  4. Exactly. But a larger blade will move a larger mass of water and thus does not move through the water as fast. From a mechanical efficiency standpoint that is a good thing, because the kinetic energy of the water is lost. However, there is a trade-off. It also reduces your cadence and that may be a bad thing. That’s because, according to Hill’s Equation, there is an optimal cadence where human muscles can put out their maximum power. So that’s one reason people use smaller blade paddles and, perhaps, GPs.
  5. Rob, Note that the blade velocity should be with respect to the water, not with respect to the moving boat. If it's with respect to the boat you have to subtract the boat velocity to get the velocity with respect to the water.
  6. I made up some example numbers for this. My point was to show that while you are paddling, each stroke must accelerate the boat. I included the comment because someone (outside of this thread) said that, in steady state, you're not accelerating. I'm not trying to equate the work of startup vs.steady state or even the average acceleration. When I paddle fast it's quite noticeable that I pull very hard at the start of the catch. That results is a short burst of acceleration. But I just (based on my guess of 0.1 mph and 0.5 secs) computed the average acceleration. Nothing more, nothing less.
  7. Rob, Your calculation for M (mass of water) and V (blade velocity) is unnecessary if all you want to do is compute the ratio of velocities for the conservation of momentum approach. To compute the percentage change in velocity for two different boat weights you perform this divide (MV/245)/(MV/240) Because MV cancels out the result is 240/245 ~ .98 (a 2% decrease in speed) But perhaps you’re onto something; i.e. your values of M and V result in a very small kayak velocity (~ 0.67 knots as you calculated). That would mean that the contribution of momentum to accelerate the kayak is trivial compared to water drag. However, I think the problem is that your value for M (which you express as weight = 41 pounds) is wrong. With each stroke your paddle is imparting momentum to some theoretical volume of water. And if you know what this theoretical volume of water is you can calculate M. But how do you what is the theoretical volume of water in the conservation of momentum equation? It’s a complex problem in fluid dynamics. But if your estimate of M is reasonable then you’ve shown that drag is the more significant part of the slowdown with increasing weight. I am aware that the answer I gave is an overestimate of the total percentage of slowdown just due to the momentum argument; that’s because it doesn’t account for the slowdown due to just drag. But the Guillemot Kayaks link I gave does use a conservation of momentum argument, just like I did. -Leon
  8. GPS-watches

    Ha ha, yes. I probably meant the correct current line. My head hurts! PS Note should be: if the velocity is (east = 3 knots, north = 4 knots) you're moving at 36.9 degrees at 5 knots. Note above should have be: if the velocity is (east = 3 knots, north = 4 knots) you're moving at 36.9 degrees east of north at 5 knots.
  9. GPS-watches

    Andy, I'm not sure I understand your contradiction. But, perhaps, the following will straighten it out: Think of it this way. You're a point on the water moving along due to variable paddling, wind, current, waves and whatever. The GPS has the coordinates of your point (say, east and north) and your velocity vector (say, east_rate and north_rate). The GPS knows when your velocity vector is not pointing to the waypoint. With an arrow (or something) it tells you to turn and stop turning when your velocity vector is pointing towards the waypoint. Note: if the velocity is (east = 3 knots, north = 4 knots) you're moving in the northeast direction at 5 knots.
  10. A reader questioned my analysis saying the conservation of momentum argument applies to accelerating a boat from a standstill, not to steady-state boat speed. Did you ever notice while kayaking when you start the catch you have to pull hard to accelerate the kayak (the blade sort of stands still in the water and you lever past it)? Remember, between each paddle stroke a kayak slows down (it must slow down because of the water drag). Assume it slows down by 0.1mph (my guess, but use another value if you want to). Assume a paddle is in the water 0.5 seconds (my guess, but use another value if you want to). So the stroke has to increase the kayak’s velocity by 0.1 mph in 0.5 seconds. So the average acceleration during the stroke is (0.1/0.5)/3600 = 5.6 * 10exp(-5) [mph/sec squared] Now from a standing start say it takes 15 seconds (my guess, but use another value if you want to) to accelerate the kayak to 5 mph. So the average acceleration at startup is (5/15)/3600 = 9.3 * 10exp(-5) [mph/sec squared] So, using my estimated values, the acceleration while the paddle is in the water is comparable to the startup acceleration. Although the momentum argument is not the whole story, it demonstrates its own energy requirement due to mass. Obviously, additionally drag from increasing weight also slows a kayak down for different reasons. -Leon
  11. GPS-watches

    With a true Goto function you don't have to perform a new Goto when you stray off the original line. That's because the line is always a straight line from your current position to the waypoint. The GPS will always try to keep you on the current line whether it's the original line or a newly computed line. It knows the location of your variable position and the fixed waypoint. So if you're to the right of the current line just turn a little left until you're back on the line. Remember, the GPS knows your current velocity vector (speed and direction of motion). It has no idea which direction your bow is pointed at. You're just a point on a map to the GPS, including two velocity components (say, east rate and north rate) On my el-cheapo GPS there is an arrow. My job is to adjust my heading accordingly to keep the arrow pointing to the top of the screen.
  12. GPS-watches

    Yes, indeed.
  13. Stiff boats are faster for pretty much the same reason a well inflated tire is faster. Flex costs energy. But I don't think you'd notice the energy lost on a standard fiberglass boat compared to a stiffer carbon boat. Nevertheless, racers want to save every second.
  14. GPS-watches

    Andy, As you explained it, the Sight'n go function can't function as a true Goto unless you enter the distance to the waypoint. If not, it can't provide a true Goto function. A standard GPS Goto function continuously draws an imaginary line from your latest position to the stored waypoint. Say you stray from the original Goto-line and drift off a significant distance. What sense would if make to go back to the original line? I’m almost sure that the watch GPS doesn’t have software to remember the old line, anyway. The Sight'n go function seems like just a fancy compass to me. Of course, if you don’t drift sideways it doesn’t make any difference. In a standard GPS there’s a continuously changing line from your latest position to the waypoint. That latest line is the shortest great-circle “line” to the waypoint. The original old line is useless from your new position. Bottom line: I was just pointing out the luxury that a standard GPS’s Goto function eliminates the need for estimating ferry angles. If you don’t care then my point is irrelevant. -Leon
  15. GPS-watches

    Andy, Some GPSs have compasses. When the compass is on I think that GPS always tries to point your heading vector to the waypoint. It would be like if you could visually see a tree and always paddled towards the tree your course over ground would be a curved path (a pursuit curve) if you drifted sideways. But, I guess that since the watch GPS doesn't know where on the direction line you want to go to it might just be acting like a compass. Perhaps I'm confused. But I don't think the watch GPS will attempt to keep you on the initial straight line to the target. Here's a long post about the pursuit curve and the use of GPS to keep you on the shortest distance path to the waypoint. PS I'll invite Lisa to join this discussion. She has more practical experience with a GPS than anyone I know. In my case, the following quote applies to me (a guy who knows the math of the topic but has limited practical experience). In theory, there is no difference between theory and practice. But, in practice, there is.