hearts and minds

August 6, 2006

I. The Peripatetic Pivot Point – by clyde winter

Filed under: Paddlesports — Hearts & Minds @ 1:43 pm

A force applied to a free-floating boat tends to change the linear (that means straight line) velocity (that means speed and/or direction) of the boat.  And such a force also usually tends to change the angular momentum of the boat (that means rotation of the boat around a pivot point).  In this article we are focusing on that pivot point.  Knowing where a boat’s pivot point is at any given moment helps to dispel much of the mystery and prevent the disconcerting or unpleasant surprises inherent in self-directed boat travel.  The tricky thing about the pivot point is that the location of the pivot point changes from moment to moment because the location of the pivot point of a boat that is underway depends on how or even whether the boat is already moving relative to the water that it is in contact with at that moment.

It’s wise to be always aware whether you are drifting with the current, or you are moving ahead or astern or sideways through the water that is immediately surrounding you.  Your pivot point is only at the center of gravity (center of mass to be precise) of the (loaded) boat when the boat is motionless with respect to the immediately adjacent water.  When the boat moves ahead through the adjacent water the pivot point also moves ahead (as the speed of the boat increases to hull speed) – to a point in the longitudinal center-line of the boat that is approximately one-third of the waterline distance abaft (behind) the cutwater (bow).  When the boat has sternway (i.e. is moving backwards through the water) the pivot point moves aft, in essentially the same way.  Any force that is applied to the boat, which does not act directly in line with the pivot point, tends to spin or turn the boat around wherever it’s pivot point is located at that moment.

Just a quick note to help you keep your focus where it needs to be:  During this entire essay, and whenever we are thinking about your vessel’s pivot point, remember that we are always and only considering your vessel’s motion relative to the water that is immediately surrounding your boat.  We are NOT talking about your vessel’s motion relative to the dock, the shoreline, the ground, or the rocks or islands in the water, or relative to other floating objects, or even relative to nearby water that is not in direct contact with your boat.  In other words, regardless of whether you are headed (pointed) downriver or upriver (relative to the shore), regardless of whether you are in the main current or a back eddy, regardless of whether you are paddling forward strokes or back strokes (or any other kind of strokes or no strokes), the important thing (as far as your pivot point at that moment is concerned) is which way your boat is moving relative to the water that is right next to your boat.  The simple question is, are you moving ahead through that water, or are you moving astern through that water, or are you dead in that water?

For several reasons – not just for determining your pivot point, by any means – it’s a good habit to maintain situational awareness at all times of the movement of your boat relative to the water that is in direct contact with your hull.  And that requires only a quick glance and/or using your peripheral vision – or maybe just a feel for your boat and the water.  As you learn and acquire more experience, this will become both more automatic and more useful to you – in any kind of water, and in any kind of boat.

The precise location of the pivot point, why it works, and how the boat moves in response to a force, depends on a lot of things with which we don’t have to concern ourselves right now.  Just be aware that when a non-planing displacement hull (like a canoe, a kayak, a fishing boat, a tug, a ferry boat, or a supertanker) moves forward relative to the adjacent water, its pivot point moves forward in the boat.  And when the boat moves ‘backward’ relative to the adjacent water, its pivot point moves aft.

Would you like a little more precise explanation?  Okay.  When you’re moving through the water at “normal” hull speed, your pivot point is located about one-third of the length of the boat’s waterline, measured from where the bow meets the water towards the center of the boat.  If your waterline length is 15 to 18 feet, and you’re moving forward relative to the nearby water at normal speed, your pivot point is five or six feet abaft the bow.  And since the forces of nature don’t care one bit about what you’re thinking, or which way you’re facing, be advised that when your boat gains sternway (relative to the water close to your hull), the pivot point of your boat moves aft towards a point about one-third of the total waterline length forward of the place where your stern meets the waterline. Remember, we’re talking about the relative motion of your boat and the water that is immediately surrounding it.

The basic seat-of-the-pants experience, and operating assumption you need to have is that the pivot point of your canoe or kayak is up towards the bow when your vessel is moving forward through the water, and the pivot point is back towards the stern when you are moving backward through the water, and the pivot point is only at the center of mass of the boat when the boat is “dead in the water” – motionless with respect to the immediately adjacent water. (Disclaimers: [a] This pivot point discussion does not apply to a planing hull, like a speedboat when it is “on step”.  [b]  “Force” has a precise definition, but it basically refers to anything that acts to change your boat’s speed, direction of motion, or rate of turn.  [c] While quick turns and sudden changes in speed and direction are both common and crucial in whitewater boating, the extremely short waterline of modern solo whitewater playboats, combined with the rapidly changing hydraulics impinging on the hull from moment to moment, make conscious awareness of the current precise location of the pivot point both difficult and often irrelevant.  The pivot point of a whitewater play boat is always literally well within your reach.)

Knowing how the pivot point moves helps us to understand and anticipate many otherwise mysterious attributes of boats underway.  “Weathercocking” is one example.  Wind pushes on all exposed parts of the canoe or kayak, including you, but when the boat is moving forward, most of the sail area is usually aft of the pivot point, so no matter what direction you wish to go, or even what direction the wind is blowing, most displacement boats tend to head into the wind, just like a weather vane. Conversely, if you’re backing through the water, once you have established sternway, a typical boat will tend to back into the wind.  (Exceptions occur if the below-waterline shape and trim and/or the above waterline wind profile – “sail area” – is very asymmetrical.)  If weathercocking causes problems, it can be addressed either by hull design or by improvising.  A tendency to head into the wind while making way ahead can be reduced by increasing the sail area at the bow, or by decreasing the sail area aft.  An open canoe is less affected by wind when it is wearing a spray cover.   When a canoe or kayak drifts in windy conditions it tends to lay broadside to the wind and seas (depending on the geometry of the wetted area and that of the sail area) as the pivot point returns to the center of gravity of  a symmetrical boat on an even keel that is making no way through the water.

In general, knowledge of the peripatetic pivot point helps you control your position and trajectory as well as your momentum, and helps avoid nasty surprises.  The pivot point helps enable you to punch upstream out of an eddy, into a strong current, and to paddle strongly against that current, without getting swept away.  Knowledge of the pivot point helps take the difficulty and guesswork out of forward and back ferry maneuvers in strong currents.  Awareness of the pivot point helps you anticipate that initiating a turn, while you’re moving forward through the water, may cause your bow to move one foot to one side, while your stern simultaneously moves two feet to the other side.  When a paddler moves the bow aside or turns at the last second to avoid a hazard, that action may place the stern in jeopardy.  When you make a sweeping turn while paddling ahead, your pivot point will trace your trajectory, but the part of the boat that is ahead of the pivot point will be inside that arc, while the part of the boat that is behind the pivot point will sweep outside of that arc.

The location of the pivot point on a boat underway will likely change during a hard rate of turn, since the speed of the boat relative to the water will be quickly reduced as a result of the hard turn.  If the boat drastically slows as it falls off of its original heading, the pivot point will return towards the center of mass, and the rate of turn will consequently accelerate – like a spinning figure skater.  By the way, the quickest way to stop a displacement boat that is going full speed ahead is NOT by vigorous back paddling or by full power reversing the propellers.  Instead, if room is available for the maneuver, simply put the boat into a hard 180 degree turn for a quick stop in the shortest distance.  In tandem paddle boats, for example, the bow paddler could vigorously draw on one side, while the stern paddler sweeps forward on the other side, in order to get dead in the water right now.  Alternatively, the bow paddler could continue paddling forward on one side while the stern paddler rudders hard on the other side.  Or the bow paddler could draw hard on one side while the stern paddler rudders hard on the same side.  But if you need to suddenly stop moving over the ground while you are paddling ahead in the same direction as, but faster than the current, you will need to first quickly complete a 180 degree sudden turn, and then immediately paddle forward hard (upstream) to stem the current.  That’s a good maneuver to practice in a safe place.

In a tandem canoe or kayak that is moving forward through the water, the pivot point coincides approximately with the bow paddler’s position. So the bow paddler has little or no leverage, for turning, and that’s why the stern paddler usually seems to “overpower” the bow. It has nothing to do with who is the stronger or more effective paddler. It’s due to laws of physics.

In river descents or ascents, verbal co-ordination can be initiated from either end of the boat, but typically the bow paddler is best positioned to read the river and initiate the positioning or defensive moves.  An alert and aware stern paddler can often, without even any verbal cues, react appropriately based on the bow’s lead.  In open water the bow paddler primarily provides the grunt for forward propulsion and the stern paddler establishes and holds the desired course without slowing the forward motion unnecessarily, while efficiently paddling ahead.  In open water it’s better for the person with greater endurance and the more powerful stroke to paddle bow, provided that person doesn’t mind breasting the wind and waves and provided that the stern paddler enjoys paying attention to selecting trajectories, and to holding an efficient course.

However, the great majority of tandem mixed-sex couples habitually paddle with the male in the stern and the female in the bow. On technical rivers, is this because these couples acknowledge the woman’s superior river reading skills and capability for decisive action? On open water is this due to their concurrence that the woman has the stronger stroke and because she has selflessly volunteered to take the brunt of the blast of wind and wave that is the special privilege of the bow station? Or is it because of a tradition with no useful or rational basis that men always paddle stern? Is it because the guy would rather not be on the “short end of the stick” when it comes to having the leveraged power of the pivot point? Tell me what you think.

You might prefer learning and enjoying paddlesport in a solo boat.  Paddling solo, you won’t have to coordinate and communicate effectively with another person in order to develop an understanding of the subtle and complex interaction of the boat, the water, the environment, and yourself. You will almost certainly enjoy paddling more than you imagine. If, after you’ve achieved this understanding and joy, you wish to challenge the additional complexities and pleasures of communication and coordination with another person in the same boat as you, you may want to do so with someone who has also achieved an enjoyment and comprehension of the basics through solo boating. Be proud and pleased to paddle with a partner who you acknowledge is as good as you are – or even a little better. And switch positions. Paddle on a different side of the pivot point or on the other end of the boat. You just might like it for a change.  And you’ll definitely improve as a team.

Learn how to use the pivot point and turning maneuvers to achieve much better control, trajectories, and paddling performance and enjoyment, in “Energy and Momentum – Use It or Lose It“.  Go HERE to see the table of contents and other articles in this series. I appreciate any comments you care to make. This article and series is published and copyright by Clyde Winter, canoeist, kayaker, and U.S. licensed master and chief engineer of motor vessels to 1600 gross tons on any waters.

I first read about the peripatetic pivot point in “The Behavior and Handling of Ships”, an excellent text by Hooyer, about 20 years ago.
During the summer of 2009, an article and a video came to my attention that more closely examines and seeks to explain the complex, ever-changing forces that affect the lateral movement and the rotation of a displacement vessel. Although this article and video are directed towards large ship handling, they can significantly improve your thinking and increase your understanding of how and why your boat is affected by various forces, and provide important insights into canoe and kayak control.
http://www.cpslc.com/understanding_the_pivot_point.pdf
http://ohlinthermotech.com/pivotpoint/

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10 Comments »

  1. Last time I paddled a canoe it was with Regina M, and she took the stern. All the other canoes were left far in our wake.

    Comment by Howard — March 23, 2007 @ 10:29 am | Reply

  2. Clyde,

    I for one, like your post. You state that the pivot point moves forward as hull speed increases. Do you offer any explanation why this occurs? I have always been quite curious about this phenomena.

    Good stuff!

    Kris

    Comment by Kris D — June 23, 2009 @ 10:25 am | Reply

    • I am not certain, but I suspect the explanation for the peripatetic pivot point lies in differential “pressure” on the hull created by the bow wave. It is my distinct impression that the movement of the pivot point is not directly proportional to speed. In fact, the rule of thumb I use is that when moving forward through the water, the pivot point is a third of the way back from the bow, when moving aft through the water, the pivot point is about a third of the distance along the waterline forward of the stern, and when dead in the water, the pivot point is centered.

      Have you seen bow thrusters in use on ships? I have been informed that the effect of a thruster cannot be explained by “thrust” of the engine. Apparently, the power of a bow thruster is also caused by differential water “pressure”. The thruster actually pumps water from one side of the vessel to the other, resulting in a slightly higher water level on one side. The water pressure is greater on every equivalent submerged portion of the bow, and the resulting cumulative force moves the bow sideways, quite handily. When the vessel is dead in the water, the thruster is most effective. As the vessel moves forward (or aft) with increasing speed, the pumping effect of the thruster is negated and soon overwhelmed by the relative movement of the vessel forward through the water. A thruster has virtually no effect on a ship underway at more than just a very few knots.

      I think the pressure differential caused by the bow (or stern) wave (depending on direction of movement) may be the explanation for the peripatetic pivot point. But fluid dynamics is complex, and I hesitate to say that with certainty without some study.

      Thanks for your comment, Kris. There have been about 2500 visits to my series of paddlesports articles over a couple years, and just yesterday, there were actually 200 reader visits to them on my blog. Don’t miss the “Momentum and Energy – Use it or Lose it” article, if you liked this one about the pivot point. Thinking about, and learning the flanking turn will make your day on the next pushy river.

      Comment by clydewinter — June 23, 2009 @ 10:55 am | Reply

  3. When paddling my sea kayak in heavy wind the bow blows downwind or leecocks and I have a very difficult time trying to get the bow to turn back up wind. If I follow your theory correctly if I slow down my pivot point should move more to the centre of my kayak and make it easier to turn the bow. I don’t find slowing down helps.
    This problem occurs when my boat is unladden. Any suggestions to get better control without adding weight?

    Comment by Steve H. — June 30, 2009 @ 11:33 am | Reply

    • Your problem is serious. I wouldn’t paddle a boat whose heading I am unable to control.

      First, you don’t want to turn the bow, you want to turn the boat. And you are more able to turn the boat (all other things being equal) the farther the pivot point is away from where you apply force. Going slower definitely will not help that. You’re probably hardly moving through the water anyway when trying to head into a “heavy wind”.

      Second, it is far more important that you have control of your vessel than that your vessel be unladen. Getting where you’re going is the most essential component of getting there fast. Especially in stiff breezes, the less sail area of your vessel, the better; and the longer the waterline, and the deeper and more even the keel, the better. Check my article on flotation for a few tips on ballast.

      Third, compare and contrast your kayak with others, and connect with other paddlers. Compare by actual paddling. Connect by listening carefully. Maybe your kayak cannot be rigged to do what you expect. Either change your expectations, or learn what you need to learn, or find a kayak that will do what you need and are able to do.

      Sliding seats are employed in some canoes, in order to shift mass, the center of gravity, and the sail area profile. In a solo paddle boat, where paddling forward in wind has the effect of turning the stern into the wind (rather than the more normal effect of the bow heading into the wind) consider the following factors:
      (1) the further forward the peripatetic pivot point is when paddling forward, the greater the tendency to head into the wind. (The location of the pivot point depends on the geometry of the wetted surface area and the velocity through the water.)
      (2) the greater the distance between the pivot point and the application of a force, the greater is the leverage of that force in effecting a change in heading. (In other words, the farther aft you are of the pivot point while paddling forward, the more control you will have of your heading.)
      (3) While paddling forward through the water, sail area forward of your pivot point tends to make your bow fall off of the wind. Sail area aft of your pivot point tends to make you head into the wind. Since the solo paddler presents substantial sail area in a kayak, the further aft you are seated, the more your body’s sail area tends to encourage weather cocking (heading into the wind). However, moving your weight aft shifts the center of gravity aft, which lightens the bow and sinks the stern, which may more than counteract the beneficial effect of simply moving your body’s sail area aft.

      In summary, moving your position aft while carrying ballast forward may provide you the heading control you need while paddling forward in a stiff breeze which (in your particular case, in your particular boat) would otherwise result in your bow being blown downwind. Another thing to experiment with is adding sail area at the stern of your kayak. Something like a skeg or rudder in the raised position might make the needed difference. And while the rudder or skeg in the water helps you track in a light to moderate breeze, it may not help in strong, especially gusty winds. You are certainly aware that your rate of turning is slower while using a rudder than with it up. The symptoms you described may be partly (and ironically) due to a down rudder or skeg.

      This preceding comment and my reply here was about a paddlesport boat that lee-cocks excessively in certain wind conditions. A similar type analysis ( with somewhat opposite recommendations) would apply to a paddlesport boat that weathercocks excessively.

      A well designed sea kayak is a series of compromises. One compromise of any paddlesports boat (other than a flat out sprint racing competition boat) is that it should perform best while carrying a load besides the paddler(s). Obviously, that is true of an expedition boat. So don’t think you’re always getting the best performance out of your boat by paddling it as light as possible. Should it perform best in the worst conditions you will encounter? Probably not, because marketing understandably urges that other criteria take precedence. It’s up to you to choose the boat you need, and to make it work in the conditions in which you place yourself. Build on a sound base of knowledge.

      Comment by clydewinter — June 30, 2009 @ 11:35 am | Reply

  4. I’m sure you are familiar with the technique of “carving circles” or “paddling the inside circle” as it is sometimes called. For those who are not, this describes a phenomenon in which a boat can be paddled in a circle to the paddler’s onside without using correction strokes. By increasing the radius of the circle, the boat can be paddled in a nearly straight line using short forward power strokes without cross-forwards, J stokes, stern prys, bow draws, or C strokes.

    As one paddles an inside circle, one can feel and actually hear a small wave build up on the boat’s offside bow. An adjacent paddler can see it. The resistance on the offside bow resists the normal tendency of the boat to turn toward the paddler’s offside.

    This seems to work best in rockered hulls, only works after gaining some forward momentum, and often seems to me to be facilitated by weighting the bow with some forward lean.

    Your article explains how forward momentum and weighting the bow would both move the pivot point forward. It also seems logical that increasing rocker serves to increase the amount the pivot point shifts. It seems intuitive that the shifting of the pivot point is fundamental to this technique but I’m still not sure I grasp the mechanics of how it works.

    Comment by pblanc — July 1, 2009 @ 6:10 am | Reply

    • There is a “sweet spot” one finds in employing the hit-and-switch technique of forward paddling that is related to pblanc’s carving circles comment. I find that sweet spot when I can paddle (single-blade, straight ahead) using only forward power strokes, several strokes on one side, switching to several strokes on the other, etc. with the heading never significantly altering. It depends on achieving a good forward speed, a fast, steady stroke cadence, and proper anticipation of the swing and timing of the switch. If I did it more often I’d probably be better qualified to describe it. The key is to switch paddling to the side towards which the boat heading is just barely beginning to veer, and paddling several forward power strokes (3 to 5?) to counter the yaw that would otherwise develop, switching again just as the heading begins to veer in the opposite direction.

      This “sweet spot” in “hit-and-switch” power paddling, or the “carving circles” described by pblanc, is achieved by your power stroke just countering the incipient yaw before it has developed and gone out of control. The balance of forces is perhaps easier for me to experience than to scientifically and rigorously describe. Knowing it is there encourages you, too, to find it.

      A solo single-blade paddler can paddle strong, hard, straight and fast this way, for long satisfying stretches. Tandem paddlers can also hit-and-switch in coordination, and paddle long distances efficiently. Whenever my boat’s heading changes significantly and has to be corrected with rudder or other steering strokes, the energy I have expended in building the boat’s forward momentum is lost. The very quickest way to stop a boat (without hitting something hard) is to allow or cause it to rapidly change heading. If you want to get a good hard workout, without going very far, or seeing very much country, just zig-zag through the water between here and there, rather than hold a steady heading.

      Now, I am going to leave you to your suppositions and the mechanics of how a canoe or kayak turns, because my priority is the health care crisis that our country is in. We can no longer leave the administration of America’s health care system to corporations which have virtually all of us playing Russian roulette with illness and injury; which have driven health care costs so high, with so little return, that we are now paying twice per capita for “health care” what is paid by the three dozen other industrialized countries of the world which have better overall measured health care outcomes than does the United States of America. There is no excuse for that. It’s not the doctors and nurses, or the people at fault. It’s the administration of the system by insurance corporations that is at fault.

      We don’t need health insurance, we need health care.
      It costs less to administer comprehensive health care as though it is a basic human right than to ration and distribute it according to who individually “deserves” what standard of care for what particular condition.
      Insurance corporations have failed to efficiently and effectively administer America’ health care system in terms of the needs of people and families, and they cannot rationally be expected to do otherwise.
      Businesses that employ American workers are at a competitive disadvantage with businesses that employ workers in other industrialized countries that have lower health care costs while providing comprehensive health care for everyone, regardless of employment.
      We need government that is of, by, and for the people – not government that is by and for the corporations and the lobbyists – in order to get the health care America needs.

      Support HR 676 and S 703 now – as if your life and your future depends on it.

      Comment by clydewinter — July 1, 2009 @ 10:34 am | Reply

  5. Good day Mr. Winter,

    I am not really sending this msg for publication, just for your curiosity. I am the mariner who produced the article and video about the pivot point you mention in your article. Thanks for your comments.

    I am not a kayakist but here are a few comments that I suspect may apply to the type of boat and could help your readers understand the involved physics:

    Basic principle: “apparent” pivot point is directly function of the location of applied lateral force. Let’s take a symetrical boat evenly loaded fore and aft stopped in the water.
    1)Push water sideways with your paddle at midship level: no pivot point because no rotation. Only sideways motion.
    2)Same experiment, this time paddle acting a bit more aft: again important sideways motion but this time with rotation, combination of both motions have result of non moving point(apparent pivot point) very far at the other end (forward)near the bow, maybe even ahead of the boat.
    3)If you can bend forward and reach very far to push water sideways, you can, even if you have some headway, have an initial pivot point aft (about 1/3 ship lenght): the lateral force (paddle) creates a lot of rotation, but little side motion. Again the combination of both motions results in a pivot point at the end opposed to where the lateral force is applied.

    For the gentleman with the bow going downwind, here is a possibility: if there is more underwater surface aft, i.e. trim by the stern, large stern fin stabilizer, this underwater area will resist more to sideways movement while the rest of the vessel (forward) will be more prone to downwind drift. creating the tendency to turn down wind. The distribution of the windage area is also important of course.

    I have a few powerpoints that could also help your readers, maybe, but I would need your e-mail to forward them.

    Best regards,

    H Cauvier

    Comment by Hugues Cauvier — August 10, 2009 @ 6:15 pm | Reply

  6. Why does a woman paddle in the bow? Because of an intuitive tendency of balancing a vessel by having the stern lower in the water than the bow, simple as that. Women are generally lighter than men, and therefore they generally get to sit in the bow. For the same reason, I sit my son there.

    I wonder whether the intuitive tendency is correct though.

    Comment by Petr — July 25, 2011 @ 1:39 pm | Reply

    • Although trimming by the stern is preferable to trimming by the bow, the best trim of a canoe or kayak is generally achieved with an even keel. And the best trim is achieved on any well designed boat by loading it properly.

      The best performance of a tandem canoe, paddled by two relatively equally competent paddlers, is generally achieved by placing the paddler with the strongest, most effective power stroke in the bow.

      If you have a well designed tandem boat, paddled by two competent paddlers, place them and any load in the boat in positions that will achieve an even keel and a neutral trim. Encourage tandem paddlers to occupy, and become familiar with, and enjoy both stern and bow positions.

      Are you going to suddenly and permanently yield the stern to your son when he becomes bigger than you? Wouldn’t it be better to find a way (by moving your relative paddling positions and shifting your load, for example) to maintain proper trim, that allows for more flexibility, variety, empathy, and learning by experience?

      Paddling stern and paddling bow provide two very different experiences, and those experiences can and should be available to be enjoyed by all. It shouldn’t be necessary for the “little lady” and the growing child to get away from the family in order to learn and enjoy the stern.

      Comment by clydewinter — July 26, 2011 @ 11:44 am | Reply


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