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

I’ve read in Nigel Foster’s new book (The Art of Kayaking), and saw somewhere else in a youtube video, that when executing a hanging draw, you need to move the paddle blade forward as you slow down because the pivot point also moves forward (so if you don’t move the blade forward, your hanging draw becomes a stern rudder). I don’t doubt that that’s true, but it’s a bit counter-intuitive to me. As you move faster, the bow becomes increasingly pinned by the pressure of the water it’s parting (and conversely, the stern is freed up), right? So wouldn’t this mean that at as speed increases (not decreases), the pivot point moves FORWARD, eventually reaching (at least theoretically) the bow? Not sure if my premises or conclusion is wrong but something isn’t adding up.

What’s the difference between a “hanging draw” and a bow rudder?

@magooch said:
What’s the difference between a “hanging draw” and a bow rudder?

Hanging draw/sideslip:

Bow rudder:

Is this a question question, or a Socratic question ? Either way, so far as I can tell, it’s pretty much just the position of the blade with respect to the pivot point (ahead of the pivot point for a bow rudder vs at the pivot point for the hanging draw). So the former pulls preferentially on the bow forcing your kayak to rotate, whereas the latter pulls more-or-less equally on bow and stern and all points in-between such that your kayak maintains it’s original heading (pointed north, for example) but the line of travel is shifted a few feet one way or the other.

Decreasing speed the pivot point moves backward. There is some disagreement whether this is all in one or incrememental sliding back.
However as you lose speed the angle of the blade may need to open as there is less force on it. Moving to a narrower part of the boat seems to maximize what force you have left.

Just try it different ways. Sheesh.

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I agree that with diminishing speed the hull pivot point moves aft. But I also agree that when side-slipping a canoe or kayak hull your static draw paddle blade placement must move forward to keep the hull from turning to the offside.

Apparently, the hulls pivot point and the center of lateral resistance are not the same and move in opposite directions.

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My original post misattributed “The Art of Kayaking” to Nigel Dennis rather than Nigel Foster. I’ve edited that to correctly reflect authorship. He does say though that “as you slow down, the pivot point of your kayak will move forward” (p. 80). Well, maybe he should have said “center of lateral resistance” - a term that I am unfamiliar with but will try to Google.

Man, this got complicated fast. Googled center of lateral resistance. Most of what I saw sees it as synonymous with pivot point. Then I read this thread https://forums.paddling.com/discussion/1452776/the-center-of-lateral-resistance from a few years ago which seemed very relevant and interesting but also technical and theory-laden to a point that it was difficult to follow. I’ll have another crack at it tonight. I agree that ultimately it’s an empirical question, but there’s also such a thing as intellectual curiosity, the fruits of which can be rewarding in their own right and which also may impact what you try on the water.

I don’t pretend to fully understand the dynamics going on here, but intuitively it seems to me that the forces that apply when attempting to yaw or turn a hull are not the same as those that apply when one attempts to move it directly abeam. .

@pblanc said:
I agree that with diminishing speed the hull pivot point moves aft. But I also agree that when side-slipping a canoe or kayak hull your static draw paddle blade placement must move forward to keep the hull from turning to the offside.

Apparently, the hulls pivot point and the center of lateral resistance are not the same and move in opposite directions.

Marc Ornstein led a long discussion about that addresses this and related things, several years ago. It turns out that it’s not simply the where the blade is placed alongside the canoe and the mere fact that some kind of lateral force is being applied, but where along the length of the boat a line perpendicular to the paddle face actually points to. This is the part that really gets into the physics of the situation since it has to do with true direction of force that’s applied, and to me at least, and I bet most people, that’s often very different from what’s intuitive based on where the paddle is located. That’s as much detail as I really care to mess with right now, but by my understanding (thanks, Marc Ornstein) that’s where answer to the dilemma you posted lies.

As I think back I may have done this useful move already to avoid some trees and pilings. I’ll try it this weekend. I think it may be easier to go do it than think about it.

I don’t think of the pivot point as moving - if I am kneeing in the center of my solo canoe, the pivot point is directly under me. It doesn’t move, but other forces may effect the paddle placement that is needed to the move boat in a particular direction. To planc’s example, you do need to slide the paddle forward when doing a hanging draw sideslip to prevent the boat from spinning to the offside, but that is because force of the water on the side of the boat. Raising the side of opposition (the way you are moving) reduces this force, but if you hold the sideslip long enough, eventually you are going to need to slide the paddle forward. I guess you could think of it as the pivot point moving, but to me that doesn’t seen to be what is happening.

You have two force pairs working here, not only one.

One of the two force pairs you have already described: The lateral force from the paddle and the lateral force from the water on the hull. This force pair will try to rotate the kayak if the two forces are not aligned. So if you only consider this force pair, you will need to invent an explaination about the centre of the lateral forces on the hull moving.

However, there is another force pair: The “inertia force” from the weight of the paddler and kayak trying to keep its velocity forward, and the drag force from the paddle in the water trying to slow down the boat. These two forces can never be aligned and they will always try to rotate the boat so it turns to the side where you have planted the paddle.

So to avoid that the kayak turns during the hanging draw, you have to make these two force pairs cancel each other out. You do that by planting the paddle at a distance behind the pivot point. I don’t know a term for this distance, so I will call it the “rear offset”. The more drag you have on the paddle (and the more you have extended the paddle from the side of the kayak), the more rear offset you will need.

Since the drag force decreases with speed (both because of less resistance and because of a more open blade in the last seconds of the hanging draw), you need to decrease the rear offset as the boat slows down.

Apparently this effect is stronger than the effect of the pivot point moving backward at slower speed, so the net result is that you need to move the paddle forward.

@magooch said:
What’s the difference between a “hanging draw” and a bow rudder?

The bow rudder is supposed to turn the kayak. The hanging draw is supposed to pull the kayak sideways without turning it.

It is incredibly useful if you for example paddle next to another kayak and the two of you need to raft up. Just make a hanging draw both of you, and the kayaks will end up right next to each other - without turning the bows into each other.

@Allan Olesen said:
You do that by planting the paddle at a distance behind the pivot point. I don’t know a term for this distance, so I will call it the “rear offset”. The more drag you have on the paddle (and the more you have extended the paddle from the side of the kayak), the more rear offset you will need.

That’s true - you do have to start behind the pivot point and move forward.

@Allan Olesen said:
The hanging draw is supposed to pull the kayak sideways without turning it.

You use sideslips all the time in river paddling to avoid obstacles and move into clear channels.

I love explanations that are easy to follow AND, make intuitive sense. Thanks!

@Allan Olesen said:
You have two force pairs working here, not only one.

One of the two force pairs you have already described: The lateral force from the paddle and the lateral force from the water on the hull. This force pair will try to rotate the kayak if the two forces are not aligned. So if you only consider this force pair, you will need to invent an explaination about the centre of the lateral forces on the hull moving.

However, there is another force pair: The “inertia force” from the weight of the paddler and kayak trying to keep its velocity forward, and the drag force from the paddle in the water trying to slow down the boat. These two forces can never be aligned and they will always try to rotate the boat so it turns to the side where you have planted the paddle.

So to avoid that the kayak turns during the hanging draw, you have to make these two force pairs cancel each other out. You do that by planting the paddle at a distance behind the pivot point. I don’t know a term for this distance, so I will call it the “rear offset”. The more drag you have on the paddle (and the more you have extended the paddle from the side of the kayak), the more rear offset you will need.

Since the drag force decreases with speed (both because of less resistance and because of a more open blade in the last seconds of the hanging draw), you need to decrease the rear offset as the boat slows down.

Apparently this effect is stronger than the effect of the pivot point moving backward at slower speed, so the net result is that you need to move the paddle forward.

The whole pivot point discussion has come up before, and seems to have spurred a lot of misinformation. John Winters has a good description of what’s going on in “The Shape of the Canoe”, page 28. In short, the idea that there is a moving pivot point on the boat is effectively an illusion. To quote from the source:

“During the turn, the hull rotates about its center of gravity that, in obeying Newton’s first law of motion, attempts to continue along its original path. The bow describes a smaller arc than the CG and angles toward the inside the turning circle. Meanwhile, the stern describes a larger arc behind. To paddlers the boat appears to rotate about a point lying approximately twenty percent of the length aft of the bow (the precise point varies with hull configuration, heel, trim, etc.). The flow of water across the hull and the drift angle (sideslip) causes this illusion. Since the boat rotates about its CG, the force moments causing the turn determine the rate and radius of the turn. Increasing the lateral resistance forward by trimming down by the bow or using a control stroke increases the turn rate and decreases the turn radius. Increasing the lateral resistance aft, say by trimming down by the stern, decreases the turn rate and increases the radius.”

The standard physics analysis of the situation involves vector mechanics (general plane motion of a rigid body), which is complicated and I won’t go into it. However, one of the basic tenets of the math involved is that ANY point on the boat can be considered a pivot point for the analysis - the choice is totally arbitrary, and is usually taken to be the CG as John Winters says above. The only truly unambiguous pivot point in the situation is the center of the circular path the boat is following at any time during its turn (termed the instantaneous center of zero velocity). This point is nearly always out in the water somewhere, not on the boat.

There is a cottage industry in explaining why the pivot point changes location on a moving boat, none of which are very convincing. This follows since there is not an actual point that is being moved. If the concept of a moving pivot point helps someone visualize what’s going, there may be a benefit, but invoking physics that doesn’t happen is always problematic. Allan’s description above using the concept of force pairs (couples) seem quite good to me, although invoking the pivot point is not necessary. The truth is a couple of a given strength placed anywhere on a body will have the same effect - this is another manifestation of the fact that the choice of pivot point is arbitrary. Changing the strength of a couple is done by increasing the physical separation of the two forces from each other, and is not affected by where the forces are placed relative to an assumed pivot point.

This was longer than I meant it to be, and I hope it makes some sense to someone somewhere…

I’m just happy I now understand why it’s usually necessary to move the blade forward, during a hanging draw, as your velocity decreases. As for the pivot point, it may not be a useful theoretical construct in describing the forces at play with a turning boat, but I know that with some turning strokes my stern temporarily moves to one side of my original line of travel whereas the bow moves to the other side. Based on common usage of the term pivot point, I don’t see how that can imply anything other than a pivot point somewhere between the bow and stern (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”).

Now just throw a light wind into the mix. Determine for every possible degree of direction of the wind relative to the boat. Spend more time thinking about it than paddling.

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