It’s Power, Stupid, Not Static Force.

[leong]

Disregarding stroke form, your maximum power (maximum work per unit time that you can perform) is the key measure of how fast you can paddle. That is, it isn’t how strong you are that decides how fast you can paddle; it’s how much power you can put out. And, like an automobile engine, your potential power maximizes at a particular cadence. On a bicycle you can control your cadence using the variable gear ratios. Although you don’t have variable gears on a kayak you have some control of your cadence by using different length paddles.

Here’s a good experiment: Think of riding a bicycle up a steep hill as fast as you can. It’s obvious that muscles can shorten faster against light loads than they can against heavy loads. So try riding up the hill in your highest gear. If the gear ratio is high enough, your muscles will be working against a load that is so high that they can’t shorten. Of course, the static force produced by your muscles will be as high as they can possibly be. But, since there is no muscle movement (i.e. you pedal cadence is 0), the power that your muscles are producing is 0, since power is the product of force and speed of contraction. Now shift into lower and lower gear ratios. When the gear ration is low enough, your pedals will be spinning so fast that the force against them will go to 0; i.e. you can’t push against something that is moving faster than the maximum speed that your muscles can shorten. At this very low gear ratio your power will also be 0.

So here we have 0 power at 0 cadence (a high gear ration) and 0 power again at very high cadence (a low gear ratio). That means, that some where in-between (along the power vs. cadence curve) there must be some cadence where power is maximized. It cannot be any other way. For those of you with some math background, Rolle’s Theorem proves that this is true.

As an aside, if we divide each value of power by its corresponding force along the power vs. cadence curve the result is the famous Hill’s equation that relates force to speed of muscle contraction. So, in one sense, Hill’s Equation is obvious from simple Newtonian physics; i.e. it doesn’t require delving into biophysics.

Now look at this video of the team of Greg Barton and Oscar Chalupsky having a tug-of-war against a guy using a kayak with the Mirage Pedal drive. You can see that because Greg and Oscar are going so slow their cadence is extremely low. As argued above, although these two world class paddlers are producing a very large static force, the power they’re generating is very low because their cadence is low. On the other hand, the Mirage drive has a low effective gear ratio. The result is a high cadence (watch the video to see the very fast leg movement).

And that’s the end of the story. We demonstrated how Hill’s Equation of muscle contraction is almost obvious and why Greg Barton (a Mechanical Engineer) and Oscar should never have agreed to this unfair contest.

-Leon

PS

My two neighbors (both fairly powerful) have this Hobie tandem kayak with Mirage Drive. Except for the first yard or two of sprint races against the two of them I can paddle my sea kayak at about a 50% faster speed than their Hobie.

Edited January 18, 2016 by leong