Some Thoughts on the Centre of Lateral Resistance (CLR) and Canoeing
The Center of Lateral Resistance (CLR) is the point along the boat where adding a perpendicular force will move the boat directly sideways. The CLR can be equated to the pivot point (or perceived pivot point) of the canoe. Adding a force in front, or back, of this point will cause the canoe to turn. Having an idea of the CLR is helpful in many paddling situations such as moving directly sideways, pivots, running side slips, and turns. Since a movement is relative to the water it will also help in moving water for ferrying, or generally dealing with current. It is an other illustration of why trim is important.
It is relatively easy to empirically identify the CLR by pushing (or pulling) the canoe directly sideways from a single point. Depending on how the canoe is weighted, and if the canoe is in motion, the CLR may be in various locations.
Things get a little more complicated when a canoe is in motion - in practise the CLR moves forward a little for a boat that is in motion. Using an arm-waving explanation: The bow of a canoe in motion cuts into the bow wave. The bow is, in effect, deeper in the water (as if forward weighted) and held in place. This means the CLR will be closer to the bow. Think about the adjustment of trim in the stationary canoe in the first experiment below. This is not a strong effect so the change in the CLR for normal paddling speeds may only be 10-25cm (although I have found it can be as much as a meter for some combinations of boat and paddler).
For a canoe in motion the new CLR location is sometimes called the perceived pivot point (PP). There is a nuanced difference when the boat is actually turning but I will leave that for another day...
I generally recommend intermediate and advanced paddlers determine the CLR of their own canoe from their normal paddling position, for both a stationary canoe and when in motion. This page relates to a solo paddler but understanding the CLR is also helpful for tandem paddlers.
Determination of CLR - with a stationary boat:
With the help of a friend, a door clip (for a car roof rack) that fits over the gunwale, and a light 4m piece of string or parachute cord tied to the clip.
Position the canoe perpendicular to a dock, about 3m out, with the a paddler sitting or kneeling in their 'usual' location.
Hook the clip over the gunwale beside the paddler.
Have the friend, standing on the dock, pull the canoe with the string directly into the dock.
Do this several times moving the clip forward, and backward until you find a point the canoe does not pivot when being pulled. Mark this point (I use coloured tape).
Repeat this procedure with the paddler sitting in other locations (trim), changes in heel, and position of equipment. Have fun, play around a bit...
Video will start at CLR determination with stationary canoe
You will find the CLR will be behind the paddler when the trim is toward the stern - typical of a Canadian Style paddler position. When the paddler is near the middle of the canoe (e.g. when paddling a more dedicated solo boat with central seating) the CLR may be right beside the paddling station. In the case of AFS when doing a high kneel or using other forward weighting techniques, the CLR will be in front of the paddlers location. Adding equipment to the canoe and changing the trim will move the CLR forward (or back).
Determination of CLR - with a boat in motion:
You will need a somewhat longer dock, string, a door clip, and two friends for this experiment.
Position the canoe perpendicular to the dock, about 3m out, with the a paddler sitting or kneeling in their 'usual' location.
Have your new friend push the canoe forward (from the stern). Do this several times until the canoe runs in a straight line the length of the dock at a moderate to quick walking speed.
Hook the clip over the gunwale beside the paddler, give the other end of the string to the person on the dock.
Have the friend on the dock walk along beside the canoe, perpendicular to the clip location, and at the same speed. Pull the canoe sideways to the dock. When starting out the string should be loose, but not dragging in the water, to ensure no torque is added to the canoe.
Do this several times, moving the clip, until the canoe pulls directly sideways (as in a running side slip). This is the CLR of the canoe in motion. Assuming that the paddler is in the same location as the stationary test this point should be somewhat further forward. Mark this point (I use different coloured tape).
Repeat this procedure with the paddler in different locations (trim), changes in heel, and additional equipment. If you are an AFS practitioner mark these points when in a high kneel, transverse kneel, forward lunge, etc.... I might also suggest marking these points when the canoe is going backward.
Video will start at CLR determination with canoe in motion
Some uses of this new found knowledge:
Understanding the location of the pivot point will allow you to use box strokes, sweeps, or circle strokes to maximum effect. In some cases you will want to pivot around the paddling position, rather than the natural pivot point, and knowing the CLR will allow you to adjust appropriately with each stroke.
Using the CLR as a marker, and ensuring you draw (or pry) directly to that point will mean a nice straight side displacement without any yaw. By using a draw (or pry) ahead or behind the CLR you can complete a side displacement with a constant yaw. Putting pivots and side displacement together you can move the CLR along a line for doing line pivots.
Running Side Slips (note radial line to paddle, note pitch can be pretty slight)
One of the cool things about knowing the CLR is executing nice clean consistent running side slips. The key is to plant the blade so it is along a tangential line from the CLR. The blade is perpendicular to a radial line from the CLR. OK - the face of the blade looks directly at the CLR.
In practise this means a running draw is planted behind the CLR, and a running pry is planted forward of the CLR. My recommendation for running strokes is to plant them with a miniumum of pitch, and a little further forward than required - especially with a running pry don't try to move the paddle forward.
Understanding the CLR will also help with ferrying in moving water for the same reason.
Planting a running draw or pry ahead of the CLR will cause the canoe to turn.
Adjusting trim (on the fly) to control turns
Understanding weather cocking
Some Things to Note:
The empirical method has some limitations but it is useful as a starting point.
The actual pivot point (or perceived PP) will most likely be somewhere in the centre of the canoe, between the gunwales. Use of the gunwale provides a convenient marker (approximation) rather than the actual location.
The sideways motion, or turning point, of a canoe is impacted by many other things such as drag, weighting, wind, paddling practise, hull shape, ..... The CLR location may move under various external conditions. Use this as a starting point and adjust accordingly.
Yes, the CLR will move a little depending on the speed of the canoe (e.g. as the canoe slows during the glide) but the change is usually not that significant.
There is a strong influence on the perceived PP of any existing angular momentum or additions of torque. A common example: When doing an offside running side slip many paddlers find they have to continue to move the paddle forward as the canoe slows (or more distance covered). This seems to be contradictory to the discussion above with regard to the CLR moving in front of the paddler with increased speed. I expect what has happened is the plant (or slice) into the running side slip adds adds a slight torque to the canoe behind the CLR. This causes the canoe to start to rotate slightly toward the paddling side, and over distance this must be adjusted for by sliding the paddle further forward. Adjusting for this also involves moving weight further forward, freeing the stern to swing like a long lever, increasing the turn which needs to be compensated for even more. My suggestion is to try again but plant initially further forward and slide the paddle back into location.
The addition of accidental torque can be compensated for by the paddler. With advanced paddlers this is usually done unconsciously based on experience.
The bow wave has been brought up in many other places - especially in the calculation of the 'maximum' hull speed. Some paddlers use the bow wave to explain carving turns by using the bow wave to hold a turn. The shape of the bow has implications with regard to how well the bow is 'held' and how carving is supported/resisted.
The motion of the canoe is relative to water. When in current a canoe may be stationary compared to shore, but still be in motion relative to the water.
Currents can be messy, rocks, shorelines, etc... change the direction. This is why I do most of my experimentation on a calm morning in a place with no current. That being said if you can find a place with laminar flow - it is also great for experimentation.
Hull shape can cause the canoe to turn - this is particularly noticeable when the canoe is tilted or heeled. You need to adjust for this when experimenting.
Paddlers, especially experienced paddlers, adjust for a lot of conditions. This is why I suggest having a friend push the canoe forward, rather than trying to paddle yourself in a straight line, or experiment with running strokes to find the CLR (although one-haned running strokes seem to be a great equalizer).
The weight in the canoe does not have to be a paddler - although I recommend doing the experimentation with an actual paddler (rather than a barrel or something else for ballast).
An understanding of CLR alone is not good enough.
Next summer I need to experiment with boats with different stem shapes and rocker. If I am correct then narrow, stems on boats with minimal rocker will have the most movement.
There are probably other things I have missed, I will add them when they come up.