My understanding of canoeing is physics-based. I’m writing this post in case there’s anyone who’d benefit from this way of thinking. I know I would’ve when I was learning.
Make sure the canoe isn’t frontheavy. The back needs to be able to act as a rudder. If you have no stuff, just equally-heavy people, you’d be hard-pressed to end up with a frontheavy canoe. If you’re canoeing alone, be in the middle of the canoe, not the back.
The canoe is long but not wide. It will tip by rolling left or right. Maintaining balance on one foot, put your other foot in the canoe in the middle. That is, not on the right or left, but you can get into the exact center of the canoe, or the front, or the back. transfer your weight from one foot to the other. Sit down, maintaining balance on the one foot in the canoe. You can help someone get in by preventing the canoe from translating and rolling. A good way to do this is by holding one end of the canoe between your legs. In this way you’re enhancing what the person trying to get in is trying to do. You can’t help someone get in by preventing the canoe from sinking a bit. An inexperienced canoer might try helping by holding the side of a canoe exactly in place. As the person getting in puts their weight in, the canoe starts to roll, which would never happen if the canoe was not held. In this way you’re complicating the operation for the person trying to get in.
The canoe has linear momentum and angular momentum. Each is changed by a stroke, and decays over time. Sideways momentum decays faster than forward momentum. This is different than a car, which has a gas pedal (mostly) independent of the steering wheel. A car’s angular momentum is proportional to the displacement of the steering wheel. In this way, you can slowly bring the wheel to center as you find the direction you want to go. In a canoe, you have to stroke when you’re at (or nearing) your desired direction.
A stroke has two characteristics: how much it pulls forward or pushes backward, and how much it pushes water away from the canoe or pulls it in. The first characteristic changes both linear and angular momentum, and the effect on angular momentum depends on whether the stroke is made from the front or back of the canoe. The second characteristic changes the angular momentum of the canoe. By manipulating these two characteristics, one can independently change the linear and angular momentum of the canoe.
The person at the front of the canoe has less thinking to do. Be predictable to the person in the back. Pick a side and stick to it for a while. With your strokes, pull forward. Don’t try to correct the momentum of the canoe. Listen to the person in the back — they may need you to stop, go backward, pull water in, or push water out.
The person at the back of the canoe is driving. Most of the time the canoe is supposed to go forward, so this boils down to controlling angular momentum. Most of the time you’ll want to paddle on the opposite side of the person in front.
When you’re going forward, there are two strokes to make. One pulls forward then pulls water into (under, really) the canoe. The other pulls forward then pushes water away from the canoe. We’ll consider strokes on the right side of the canoe. The mirror situation happens on the left.
At the back of the canoe, the first stroke turns the canoe left. In particular, it bestows forward momentum, leftward angular momentum. Because the canoe turned left, some of the forward momentum is not rightward momentum.
Again at the back, the second stroke turns the canoe right. It’s a tougher stroke to do correctly. I’ll explain why in a bit. But if you find it still turns the canoe left, instead try using the paddle as a rudder to turn right. Over time, try to make a fluid motion out of appending ruddering to a normal forward stroke. Anyway, this stroke bestows forward momentum and rightward angular momentum.
The second stroke is harder to do because pulling the canoe forward causes it to turn left, but you’re trying to turn the canoe right. So the second part of the stroke must overcome the first. With the first stroke, both parts of the stroke turn the canoe left.
To help drive these points home, let’s consider what would happen if the person at the front of the canoe did each stroke. At the front, pulling forward still causes the canoe to turn left, but this opposes pulling water into the canoe, which tends to turn the canoe right. So the first stroke is harder to do at the front. The opposite is true of the second stroke.
The canoe tips by rolling left or right. When the right side of the canoe is entirely the crest of a wave and the left is a trough, the canoe is most likely to tip, especially if as the canoe moves over the waves, it hits a resonance frequency. It’s not particularly likely you’ll tip, but it might be noticeably harder to get the canoe to do what you want it to. The solution to this is obvious: turn the boat a bit so you aren’t perfectly aligned with the waves.