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# The center of lateral resistance

-- Last Updated: Oct-20-11 3:20 AM EST --

Where should you place the paddle to most effectively execute a drawing sideslip? Why? Do you place the paddle in this same spot to most effectively execute a prying sideslip? Why or why not?

The simple but non-obvious answers to these questions require an understanding of a hull's center of lateral resistance (CLR). I am indebted to some old writings of Pat Moore for clarifying this whole subject for me.

The CLR, which should be basic knowledge to all sailors, is the place along the longitudinal waterline where a force will move the boat sideways without turning the bow or stern. For example, if you stood in the water next to your boat and pushed it with your finger at the CLR, the boat would sideslip with no turning (yaw) of bow or stern.

If you push forward or aft of the CLR the boat will still sideslip some but, in addition, the bow will respectively turn away or towards you. Hence, a force applied forward or aft of the CLR will produce a less effective sideslip because some of that force is vectored into producing bow yaw.

Now let's hop in a solo boat and do some actual and thought experiments with the CLR.

If you do a draw stroke adjacent to the CLR, the canoe will sideslip to the on-side with no yaw. If you do a pry (or pushaway) adjacent to the CLR, the canoe will sideslip perfectly to the off-side. However, the further draws and pries are positioned forward or aft of the CLR, the less they will function as sideslips and the more they will function as bow or stern turning strokes.

This leads to the design question of where the CLR should be. I think it should be adjacent to the center of the solo paddler's forward stroke. This will give the paddler the control flexibility to use the first half of his stroke for bow adjustments and the second half of his stroke for stern adjustments. If we assume a kneeling paddler at a center solo station with a straight shaft paddle, the center of the forward stroke would be about at the knee. So, let's assume the design CLR is a point between the ends of the paddler's knees.

Now, lets put the boat in motion so we can start trying some static paddle sideslips -- that is, no pulling-to-the-boat with the static "draws" and no pushing-away-from-the-boat with the static "pries". First, put the paddle adjacent to the CLR (knees) statically with the leading edge slicing perfectly forward parallel to the keel line. What happens? Nothing. The boat doesn't sideslip and the bow doesn't yaw.

(For pedagogical purposes, I'm ignoring the friction of the slicing paddle, which will in fact eventually draw and yaw the boat on-side.)

Why no sideslip? Because, to sideslip a moving hull with a static paddle, there must be water force load on a blade face. Therefore, the leading edge of the static paddle must be opened (to, say, 2 o'clock) to produce a drawing force of water on the power face, or closed (to 10 o'clock) to produce a prying force of water on the back face.

If I angle the static blade closed or open when it is directly adjacent to the CLR (knees) in a moving boat, will I get a maximally efficent, yawless sideslip? NO!!! My static (hanging) draw sideslip turns the bow on-side, and my static pry sideslip does the same thing. Statically planting an angled paddle adjacent to the CLR in a moving boat is obviously the WRONG PLACE for either sideslip. Rats!

So is this whole CLR thing irrelevant to static paddle sideslips when the boat is in motion? No. It is still key.

On my own and with some freestyle instruction, I eventually figured out empirically where to position the paddle to avoid sideslip yaw in practice, but never understood the underlying theory until I read Pat's non-obvious but simple explanation.

Pat employs an ingenious illustrative concept he calls the "fulcrum ray", which is an imaginary ray that projects outward from the center of the paddle's powerface. Think of sticking one of those kiddie suction cup arrows right in the middle of the power face. The shaft of the arrow represents the fulcrum ray.

Now, here's THE SIDESLIP RULE: The most effective and yawless sideslip is done by positioning a force-loaded paddle such that the fulcrum ray is aimed at the CLR.

In our perfectly designed canoe, the CLR is the point between our kneecaps. Since our static draw sideslip is done with the leading edge of the paddle blade opened to 2 o'clock, the paddle must be positioned AFT of the CLR (knees) in order for the open-angled fulcrum ray to intersect it. Conversely, since the static pry sideslip is done with the leading edge closed to 10 o'clock, the paddle must be positioned FORWARD of the CLR (knees) so that the closed-angle fulcrum ray aims at it.

Therefore, in order to angle the fulcrum ray in the proper direction -- at the CLR -- a static pry sideslip must always be positioned forward of a static draw sideslip. Simple, but not obvious.

Drawing sideslips may give the paddler postural trouble if the boat is designed poorly -- or the paddler sits in the wrong place -- such that the CLR is too far aft. This will require the paddler to engage in tortuous torso torture as he tries to get the paddle back far enough to angle the fulcrum ray through the CLR. You will see paddlers leaning backwards with their arms arched over the back of their necks trying to get the proper angle. Some of these contortions may be style driven by interpretive freestylers, but in some cases there may also an element of improper CLR design in their boats.

For those of you who have stayed awake through this post, I think the good news is that you will never forget the illustrative Moore rule for perfect sideslipping.

Please add any comments or corrections you may have. For example, I haven't discussed how to figure out where the CLR is in your actual boat, what the optimal static draw/pry angle is (it may not be 2 and 10 o'clock), or how to "juice" the static draw and pry when they start to peter out.

Now, for some homework. Where do you aim the fulcrum ray when doing high brace turns heeled to the on-side (axle turns) and high brace turns heeled to the off-side (post turns)? Why?

Tagged:

• MAN you canoe guys get into it : )
• The Method Works with OC1 and V1
Yes onnopaddle, it is easy to apply the same method in side slipping an OC1 and V1 too. Remind me the next time I'm in Hilo to demonstrate. Perhaps you can design a pedestal to fit in a V1?
• Be kind of easier to....
jump in the water behind the stern. Grab the stern with your two hands and kick your feet like the dog paddle.
just leave the paddle in the boat

Jack L
when going forward and about a foot in back going in reverse.

Fulcrum ray is a PM term but in other terms a styrofoam vector arrow that suction cups onto the paddle is often used. The optimim angle of opening seems to be 15 degrees.

Too far forward on a drawing sideslip and you have a turn...to the paddle side. Call it a hanging bow draw (axles and posts are heeled and pitched)

The curious thing is that when you do a prying sideslip and the momentum dies the boat hence going straight happily wants to turn toward the paddling side. I think its because the CLR has returned to between the knees.
• Too many words. Not enough paddling
Don't worry about it unless you are designing a hull.
Just...
Paddle forward to gain some monentum.
Slice the paddle in beside you with the powerface towards you parallel to your keel line.
Turn the leading edge out away from you just a bit.
Move the paddle forward and back to get a feel for where you side slip and where you do a bow or stern draw.
Do it again but turn the leading edge in towards you just a bit.
Do both again but start off going backwards.
Do all of those a hundred more times but play with the blade angle and fore and aft placement.
The more you play with it the easier it will be to control your boat.

• isnt CLR
That calcium, lime, and rust cleaner. Used to be on tv but now its at Walmart.

Seriously though...snore.

Ryan L.
• Interesting explanation
-- Last Updated: Oct-20-11 11:26 AM EST --

Here is my take on it, also quite wordy

Some notes:
-CLR is a function of speed, location of CLR will change as the boat changes speed.
-Paddle is placed off centerline, there is torque
-Paddle is angled, there will be two force components, one tangental (perpendicular) to the boat, ft, one parallel to the boat, fp. ft moves you sideways, fp yaws the boat.

For a given speed,
if paddle is placed at the CLR, ft is going to draw sideways perfectly, fp is going to yaw bow towards the paddle.

if paddle is placed towards the stern from CLR, ft is going to draw sideways and yaw bow away from the paddle, fp is going to yaw the bow towards the paddle. The yaw movements can be canceled out, leaving only sideways movement.

I sure hope this introduced even more confusion!

• For practical purposes in a canoe
-- Last Updated: Oct-20-11 11:37 AM EST --

the point does not move with speed. Its either ahead of you in one general area or under your knees at a standstill or a foot in back in reverse.

Otherwise sideslips would have to be planted at different locations on the hull with different speeds.

An extreme example would be the aforementioned static bow draw. If you were rocketing along and the CLR moved wway forward it seems you would have to get that plant right up in front of the front thwart. Conversely if you were going slow it could just be in front of your knees. In practice both maneuvers work whippiest in the same place, just in front of your knees.

Naval architects debate this endlessly and there are programs that do calculate the CLR .But the scale is so different in large vessels than a canoe.

I have to find a picture of the USS Enterprise doing a post.

In between vacuum passes I dug up something by John Winters who states the CLR does move forward.

Now that poses the question of why if you get your canoe going very straight and very fast and you do a really hard steering stroke...the canoe keeps going straight..if the CLR is way up there it seems any steering even minor would cause the boat to yaw...

except for that bow wave that pins you.

• .
I don't like when people generalize too much
Your canoe may be different from some other canoe. For the full disclosure, my only time in C1 was rolling it, I can't comment on canoe design.

Explanation that I attempted to provide does not discuss where the placement of CLR is, or how it moves depending on speed.
• Different locations
-- Last Updated: Oct-20-11 3:57 PM EST --

"Otherwise sideslips would have to be planted at different locations on the hull with different speeds."

I'm pretty sure that we do change the location with speed. But since we do it by feel and muscle memory rather than by calclus and dial setting we are not as aware of that.

I know that I have to tweak my sideslip position as my boat slows down.

• I have to admit, Glen...
...you've got my attention with these technical posts. They are making sense to me - although, I'd rather be paddling. ;-)

Thanks!
• agreed
My experience is exactly the same as Tommy's. The paddle placement required for a static draw sideslip without boat yaw changes with boat speed.
• Fine Points
There seems to be some confusion r.e. Clyde Winter, who promotes Hooyer's Peripathetic Pivot Point concept from the his book Behavior and Handling of Ships, Cornell Maritime Press, 83, and as also described by J McPhee in Uncommon Carriers, and John Winters who rejects the idea of a changable pivot in his Shape of the Canoe.

Paffet promotes an interesting concept of lift from heeled hulls in Ships and Water, Nautical Institute, 90, which I haven't quite accepted. More thought, a second reading, etc.

That image of the Enterprise posting up in on page 162 in T Gilmer's Modern Ship Design, Naval Institute Press 75. Cool shot!

Mackenzie blew the math on stall angles at MFS. Parallel sided paddles stall near 38 dg, foiled blades like Pat's early wood and late composites, Quimby's and Crickets stall out closer to 43 dg, so max angle of attack for a side slipping paddle blade is somewhat under 45dg; pretty easy to judge.

For what it's worth, prying sideslips need a closed angle of attack applied roughly at the knee, drawing sideslips an open angle of attack roughly at the seat's back bar, both assuming vertical shafts.

Angling the paddleshaft changes placement. Of note, one can slop the blade in pretty casually with a straight keeled touring hull like the WeNoNah Wilderness, but placements on highly rockered hulls need be pretty precise.

• Where do you place your hand in order
to slap yourself on the forehead while saying "DOH!"?

I have learned where to place my paddle within a few minutes of getting in an unfamiliar boat. I JUST DO IT. Any deviation of the boat from what I intend is sensed through my body and through my arms. My eyes actually have less to do with it.

My slalom c-1 is highly asymmetrical, and my Mad River Guide Solo is symmetrical. I never had to think about what I was doing the first time I paddled either one.

Executing a draw stroke is not like learning to roll. You really have to think about how to roll, especially to roll a c-1. Learning to draw is monkey see, monkey do. You don't need to think more about it, you have to DO it as your motor learning system makes adjustments.

It is the job of the boat designer to offer a craft that cooperates with normal human motor learning. Whether we want to think about it rather than just do it is a matter of taste, but not often useful.
• I love physics and science too and often
think in these terms while paddling. It's fun to think this way and adds validity to what I'm doing. You would love boat building.
• seeing as I've only been
-- Last Updated: Oct-20-11 6:35 PM EST --

hit by 2 other paddlers in my life on water less than cl.3, both times while I was surfing, the latest time by this threads OP, on a river mild and wide, I have to agree with Gary and Tommys take on things.

• Ditto Tommy and Pete
In several of my routines I use prying side slips and try to prolong them as much as possible. I find it necessary to slide the paddle forward as the boat slows. If you look at the beginning of the "You Raise Me Up" routine you'll see me sliding the paddle forward in the second maneuver which is a prying side slip.
• The topic. Some responses.
-- Last Updated: Oct-21-11 2:25 AM EST --

The topic is about explaining the paddle physics and boat architecture that underpin the strokes or moves like the sideslip, which we all may know how to do, practically and empirically.

The theory explains the practical effects, helps predict other effects, and most importantly can instruct less adept paddlers. It is always better to know the "why" as well as the "how". For example, if I were an electrician, I think it would be valuable to understand the basics of electrical theory and physics, in addition to just learning by rote memory where grab a live wire.

If someone isn't interested in exploring the theory underlying paddle and boat physics, why bother entering the thread? Leave it to those who are interested. I happen to enjoy reading technical writers like Moore, Winters, Wilson, Broze and Schade. Their writings enrich the sport and ultimately will translate into better products and skills.

Moreover, someone designed all the boats that the anti-theorists apparently paddle so well and autonomically, so someone did think a lot about the detailed physics and architectural principles while the boats were in the concept, spec and design stages. We should be grateful for that.

Like everything else, these technical discussions become prisoners of terminology and their related acronyms, and there are often multiple definitions for the same term. I think some of you, as Charlie and Kim may be suggesting, are confusing the CLR with the even more confusing and controversial subject of the peripatetic pivot point (PPP).

The CLR is defined by the underwater profile of the hull. That profile shouldn't change very much at the slow velocities of a canoe. (There may be some stern squat, but that should move the CLR aft.) If the fulcrum ray had to be pointed at point that jumps substantially forward a couple feet from the bow when the canoe starts to move, as under the PPP hypothesis, I think it would be pretty hard to do prying sideslips or bow jams/draws near the paddling station.

Marc, you say you move the sidelip pry forward to prolong it as the boat slows. I'm not interested in disputing anyone's practical experience, but rather in explanatory theory. Are you claiming that the CLR moves FORWARD as the boat slows. Why else would you have to move the angled paddle forward? The PPP hypothesis says the opposite: that it moves AFT as the boat slows.

I think Marc's practical experience can be explained by different theories that are more plausible than PPP. One theory would be that Marc has prolonged the sideslip physics because he has changed the stroke he is doing. Marc's forward paddle movement imparts additional sideslip simply because he has changed his paddle stroke from (1) a static pry to (2) a dynamic reverse pitch stroke. A reverse pitch stroke with a closed-angle leading edge will "pry" the boat off-side as it moves forward.

Forthermore, Marc, don't you do the same thing with a static draw as the boat slows -- prolong it by moving it forward? The forward movement of (1) the static open-angled draw now becomes (2) a reverse pitch stroke that draws the boat to the paddle. I suspect that Marc also softens the paddle angle (toward 12 o'clock) as he moves the prying/drawing paddle forward -- which, under Moore's theory, would maintain the fulcrum ray intersection with the (fixed) CLR.

Alternatively, Marc's experience could be explained by an actual forward shift of the physical CLR, because the underwater hull profile changes not only in response to slowed velocity but probably more so in response to Marc increasing bow pitch as he moves his paddle, and weight, forward. (Does that happen?)

In any event, is anyone disputing the analysis of draws, pries, and sideslips in the OP? I mean, even if the physical CLR moved somewhat with velocity -- which I don't yet accept -- doesn't it remain true that a loaded paddle will slip the canoe without yaw if the fulcrum ray is pointed at the CLR. For draws, the paddle can be loaded either because you are doing an actual dynamic draw adjacent to the CLR, or a static draw with an open angled paddle behind the CLR. In all cases, the boat will slip without yaw because the fulcrum ray of the loaded blade intersects the CLR.

Finally, no one has addressed the question of the optimal point, under theory, at which the fulcrum ray should point during an axle and post.

• All of the above are possibilities
I mention the issue in terms of pointing out the practical nature of what happens. This doesn't necessarily dispute the CLR theory but it raises questions.

Moving the paddle forward does constitute a bit of a sculling pry and yes it creates a forward weight shift however if I do not move the static pry forward, eventually the boat does begin to turn toward the paddle side as it slows. If the CLR theory is accurate, there must be additional forces in effect.

Another variable is that I heel the boat slightly toward the paddle, (raising the side of opposition) during the side slip.

I can't speak for others. I don't dispute the theory however it must be noted that in the real world there are numerous, constantly changing other forces that effect the boat's movement and these must be compensated for. It appears from my experience, that hull speed is one of them.
• Paddle angle changes during the duration
of an axle or post as the momentum slows.. So that is not a fixed position of the "fulcrum ray". What is generally agreed on is that an open angle too early stops the boat.

I have often wondered why the prying sideslip involves moving the paddle forward as the boat slows and the drawing one does not.
• ray target
I can not dispute it since it takes quite a while to figure out.

Here is why-
- Force generated by paddle includes lift and drag components, they are both a function of foil shape, angle of attack, speed of movement.
- Since ratios of drag and lift components vary, the location in relationship to CLR will vary as well. I find it a rather entertaining academic exercise, and will, probably, do numerics at some point. Probably will assume the paddle to be flat for simplicity's sake
- CLR definitely moves. Here is how we demonstrate it in a kayak: get on the water, balance your boat so it is stable at beam wind. Get a little forward speed, bow goes into the wind, get a little backward speed, stern goes into the wind. Since the rest of variables doesn't change - explanation of windcocking can be achieved through the movement of fulcrum point.

So yes, it might be true that the imaginary arrow points towards the CLR, but I don't see a way to prove it.
• Theory won't instruct less adept
paddlers any more than theory of bipedal balance would instruct Stephen Maturin how to walk on the rolling deck of the Surprise. Maturin's problem was too much time spent below, reading and playing the cello.

There isn't time, even in tedious ACA instruction, to go through theory. One must quickly demonstrate for the monkeys, and then it's monkey see, monkey do. Understanding of motor/skills learning was developed by psychologists, not physicists.
• Options
COLR & Ship generated sideways current
-- Last Updated: Dec-31-12 7:50 AM EST --

Dear all,

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