Lean away from the turn? Or toward the turn?

Yes, you are basically correct about losing more speed with leaning than with edging. Why is this so? I.e., what is causing the boat to slow? The answer is the resistance of the water to the object moving through it.

Your kayak will generate the least resistance when gliding straight forward. Any turning motion will increase resistance by itself, and the sharper the turn, the greater the resistance. Additionally, the altered shape of the submerged part of the heeled kayak (compared to its submerged shape when level) glides less efficiently, & will further increase the resistance of the water to its movement. In general, the more you heel the boat, the more the resistance will increase.

You can heel a kayak more by leaning it than by edging. Most good paddlers that I’ve seen can hold a sea kayak edge of about 30 degrees or so. Someone who is very flexible, with excellent balance & proprioception can do better than that, but I’ve never seen anyone hold an edge of 45 degrees or more–around that point, and certainly past it, it becomes impossible to keep your body mass centered over the kayak, and you will capsize. In contrast, with a decent brace, you can heel your boat over to 90 degrees or even past 90 degrees–very briefly, until you stop moving–at which point you must pop up, or convert to sculling, or capsize.

If you heel the boat more, you’ll bleed speed faster–so leaning–associated with more heeling than edging–will slow you faster. In addition, because you’ve added your paddle to the mix–by bracing–you’ve added water resistance to the paddle blade, even if it’s just “skimming” the surface. So, leaning has a couple of factors that will generally increase the water resistance and slow you faster.

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Outside edge turns are super useful for normal correction in the course of a paddling day. One sweep or a “fling” of water under the stern as you edge and the kayak can turn very dramatically and as long as you hold that edge after the turn starts the kayak continues that turn with every normal stroke.

But at times when you need or want to turn RIGHT NOW and you need a major correction in your direction a leaning turn with bracing is the best.
Here is another vid and this vid taught me to do this turn. I do it all the time, not because I need to, but because I want to maintain my skills. In my Necky Chatham17 or in my Eddyline Fathom I can get my lean over far enough that the water is engulfing my entire lower body and a tight fit with the spray skirt is needed, or I’d swamp instantly. But doing this turn I can go 180 degrees in 2 strokes when conditions favor me, and in 3 strokes in flat water, or if turning into the wind.

I have found that slowing down the paddle stroke a bit so I have thrust in the water for a few seconds longer actually speeds up the turn itself. NOTE you must scull the paddle in the reversing direction to make this turn work. Once the turning is underway it’s important to not let it stop so at the end of the 1st stroke just scull the paddle back to the starting position and lean on it hard to stay in the extreme leaning position. If my kayak is almost edge wise (say 75 degrees of lean) it spins like a snow saucer.
Drive the kayak to the paddle with your leg, and don’t try to pull the paddle to the kayak.

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