Why does kayak's pivot point move forward as you slow down

Monkeyhead, I’ll try to answer your last point by putting the above excellent explanations of the physics into a commonplace example. Let us consider a motor car driven in an off-road stage of a time trial. The car is approaching, at high speed, a right hand curve of constant radius of curvature (a steady even curve, an arc of a circle) in the dirt track. The highly skilled driver initiates a rear wheel slide by turning the steering wheel of the motor car to her right (clockwise), and then controls the slide by steering on opposite lock (anti-clockwise) and adjusting throttle pressure to control the angle of slide throughout the bend. To the driver, the front of her vehicle will appear to turn to her right, and the rear of the vehicle will appear to turn to her left. The video captured by the drone directly above the bend will show that the motor car actually travels smoothly around the curved track, with the “pivot point” of that smooth and even curve some way off in the woods to the right. If you attached a taut rope to the “pivot point”, and the other end to the center of the car, the rope would stay in the same tension throughout the curve.
The driver will experience the sensation of a “pivot point” within her car, but relative to the outside world, the “pivot point” is out in the woods. In a kayak, the “pivot point” is out across the water. (IMHO)
Nick.
On edit: Another example is the fun fair rides (theme park rides?) where “cars” spin round on the end of long arms which rotate and radiate our from a central axle.

@nickcrowhurst said:
The driver will experience the sensation of a “pivot point” within her car, but relative to the outside world, the “pivot point” is out in the woods. In a kayak, the “pivot point” is out across the water. (IMHO)

Both you and carldelo are looking at the pivot point of a turn. But you both forget that the kayak is not turning.

That is the whole point of moving the paddle during a hanging draw - to avoid that the kayak turns.

So the pivot point in this case is simply the point where a pure lateral force needs to attack if it should neither turn the kayak away from the force or into the force. In other posts referred to as the centre of lateral resistance. And that is very much a point in the kayak, not a point out in the woods.

So I was thinking about this today as I was practicing some strokes and evaluating the effect of different variations. It seemed that one practical effect of moving the blade forward as boat speed decreased was simply to restore some of the lost velocity of water movement past the blade. As I pushed the blade forward, there was a very noticeable, even if short-lasting, increase in the boat’s sideways movement.

Allan, I was describing a turn, not a hanging draw.
Nick.

@Monkeyhead said:
So I was thinking about this today as I was practicing some strokes and evaluating the effect of different variations. It seemed that one practical effect of moving the blade forward as boat speed decreased was simply to restore some of the lost velocity of water movement past the blade. As I pushed the blade forward, there was a very noticeable, even if short-lasting, increase in the boat’s sideways movement.

In doing side-slips with a canoe (something I rely on very heavily for maneuvering on some kinds of rivers), I end up doing that very thing. In fact, a strong reverse stroke combined with pitch will not just shove the boat rapidly sideways by several feet, it will also reduce the speed of the boat or even reverse it relative to the water (which of course allows that it might still be going forward on account of the current, but much slower), which buys a lot of extra time for lining up with that slot between two rocks, etc.

Allan Oleson, your explanation makes sense. Certainly the drag on the static draw paddle’s open face, necessarily offset from the keel line of the boat, must create a yaw couple tending to turn the boat to the on-side that diminishes with speed through the water. And that does explain the need to move the paddle forward without invoking a change in the center of lateral resistance.

Yes, actively pushing the open-face paddle blade forward does get another foot or so of lateral movement at the end of a side-slip.

As already pointed out, we’re starting to mix maneuvers in this thread (i.e., turns and hanging draws) but that’s OK. I’m about 77% sure I understand what you’re saying about turns. But for the sake of argument, and to test the proposition that I do understand it, let me drill into that a bit. I think I would still be inclined to say that the car on the track is pivoting. I’m a little more confident about the kayak though. Let’s say you’re stationary in your kayak and you take a sweep stroke on the left. When I do that my bow moves to the right of where it formerly was and my stern moves to the left of where it formerly was. Would we all agree that there is a pivot point somewhere between the bow and the stern? I’m hoping the answer is yes because that sets up my next question. OK, so now you do the same thing while moving forward. Since you are essentially doing the same thing (to be 1005 accurate, I guess it would need to be mixed with some forward strokes, or be a hybrid forward stroke/sweep to maintain forward movement) it seems as if there would still be a pivot point in your boat even if you and your boat, as a whole, are paddling around the center of a big circle. Here’s another example. The moon rotates on it’s axis. It completes one rotation with each revolution around the earth (so that we always see the same side). We still say that the moon rotates though (i.e., pivots about it’s longitudinal axis). So either this has devolved into a semantic argument in which we both understand what we’re talking about but not using terminology the same way, or I am not fully understanding your point. In any case, and as I said before, I am just happy that I now understand why you generally need to move the paddle forward as your boat slows when executing a hanging draw.

@nickcrowhurst said:
Monkeyhead, I’ll try to answer your last point by putting the above excellent explanations of the physics into a commonplace example. Let us consider a motor car driven in an off-road stage of a time trial. The car is approaching, at high speed, a right hand curve of constant radius of curvature (a steady even curve, an arc of a circle) in the dirt track. The highly skilled driver initiates a rear wheel slide by turning the steering wheel of the motor car to her right (clockwise), and then controls the slide by steering on opposite lock (anti-clockwise) and adjusting throttle pressure to control the angle of slide throughout the bend. To the driver, the front of her vehicle will appear to turn to her right, and the rear of the vehicle will appear to turn to her left. The video captured by the drone directly above the bend will show that the motor car actually travels smoothly around the curved track, with the “pivot point” of that smooth and even curve some way off in the woods to the right. If you attached a taut rope to the “pivot point”, and the other end to the center of the car, the rope would stay in the same tension throughout the curve.
The driver will experience the sensation of a “pivot point” within her car, but relative to the outside world, the “pivot point” is out in the woods. In a kayak, the “pivot point” is out across the water. (IMHO)
Nick.
On edit: Another example is the fun fair rides (theme park rides?) where “cars” spin round on the end of long arms which rotate and radiate our from a central axle.

Monkeyhead, I agree with you that, as is often the case in discussions, it’s a matter of what one understands by particular terms. The fundamental issue for me is that all motion, including rotation, is relative to a chosen frame of reference. Your example of the moon is perfect. Your later addition, on edit, to your post of October 27th, shows that we are indeed on the same page:
Quote: (edit: although thinking about it some more I can see that the bow and stern moving to opposite sides of the original line of travel would not be inconsistent with a pivot point off to the side of the boat “in the water somewhere”)

Nick.

I agree completely with Allan Olesen’s remarks re the center of lateral resistance during the hanging draw. I think this is the correct way to think about it, with no need to invoke a pivot point. It’s true that my response about kayak turning was not relevant to the hanging draw, as I was focused on the concept of a pivot point during a turn - I was definitely off-topic. I also agree with Nick that this is mostly about frame of reference.

Re Monkeyhead’s example about the moon, it is directly on point. It’s a special case of general plane motion that is closely equivalent to a kayak turn, i.e. both bodies present the same side to an overall center of revolution. I wish I had a blackboard, as I’d like to propose a thought experiment to show that mathematically and physically, the motion of the moon can be described in multiple ways, all valid. Consider these models of the motion:

  1. Rotation of the CG of the moon about the CG of Earth, combined with rotation of the moon about its own CG. The period (28 days) of both rotations is the same. This model probably best represents the point of view of someone on the moon and is intuitively satisfying.

  2. Solid body rotation of the moon about the CG of the Earth, i.e. from the point of view of an observer external to both the Earth and moon (e.g. viewed from above the north pole of the system). This is analogous to watching from above while a record album rotates with a quarter placed near its edge. This model of the motion gives all the dynamics of 1 above, and is equivalent. The period of rotation is also 28 days.

  3. Rotation of the nearest point on the surface of the moon about the Earth’s CG (a slightly smaller radius than in 1 above). If this motion is combined with rotation of the moon about the near point, again both with the same 28 day period, the full motion is reproduced. This (perhaps) represents the motion of the moon with respect to what an observer on earth sees.

It’s an easy jump from 3 references frames to many, and the conclusion that no one pivot point is unique in the analysis. That’s why I mentioned that the idea of a pivot point moving around may help someone visualize what’s going on with their boat, but there is no need to invoke any wacky physics to explain the ‘moving around’ because it isn’t actually happening. I have no problem if someone’s mental model of kayak motion includes a moving pivot point, but it’s not correct to say that there is a unique pivot point somewhere on the kayak. It’s doubly incorrect to say that various pressure or ‘inertia’ forces are causing the motion of that fictitious point - this is the part that bothers me.

Having said all that, model 2 above is the simplest representation of the motion, as there is no translation of a secondary point, only rotation about a single fixed point. It does not mean it’s the best model, just the simplest mathematically, and all remain valid. The center of rotation in model 2 is the only unique point in the analysis, and is included in all the models.

Back to boats, there is often some slewing of the kayak during a turn, i.e. the bow may tend to point inwards and the stern to slew outwards. Physically this is a result of the fluid medium around the kayak, couples created by the applied paddle force and the reaction of the hull, and the time delay between application of paddle forces and the acceleration response of the system. The slewing can be accounted for mathematically by a slight mismatch in the two rotation periods in examples 1 and 3 above, or by an offset of the center of rotation (from the CG of Earth) in example 2. Note that the moon does not have a paddle to exert forces on its medium (the vacuum of space) during its motion, so is not fully equivalent. I also note that it’s completely feasible to execute a turn in a kayak without any slewing - I know, because I see good paddlers do so often.

Wow!

Hello all, found this thread closely related to research I have made on large ships a few years back. Let me suggest a simple explanation:

As a force, in this case your hanging draw, causes side movement of the canoe, it drags laterally an amount of water with it. Since the craft is moving forward, this water side drag (or current) acts more on the stern than the bow, as the bow constantly enters fresh undisturbed water. Watch the water movement in the video experiment below. See how it acts on the model when it moves in the fore and aft direction.

You can see a more dynamic experience similar to your canoe behavior at 9:40 of this other video:

Watch the shadows of the lateral current eddies in the bottom of the pool. See how it acts more on the stern than the bow. To counter act this turning force, you have to move your hanging draw more and more away from the center of gravity of the canoe (forward in this case).

Hugues Cauvier

Hugues, that is excellent work, thank you. I have also experienced the contrary directional motion when my sailing yacht is under power. It can be frustrating.
Nick.