Boats and the Bees

If you give an object to Heather and to me, we will largely agree on it: “That’s a nice object” we might say in unison. 

But what we do with it is very different – Heather will fit that object into a larger context; expanding it, making it beautiful and artistic and a building block of an expanded universe. I will probably take the object apart; see what it’s made of, and how it works. She finds macroscopic beauty, I find microscopic. (Read her post that started it all here)

Given the object of that meme about how bumblebees can’t fly, I need to know why, and how that fits-in with the physics of the rest of my world, probably bringing it around to boats.

The bumblebee secret is speed. Fast wings. They flap those silly little wings about 200 times per second. Blink your eyes as fast as you can – that took about 400 milliseconds.  In the amount of time it took you to blink, a bumblebee flapped his wings about 80 times. You know hummingbirds flap their wings fast – every time a hummingbird flaps her wings, the bumblebee flapped his four times. 

Bumblebees, previously known as Humblebees or Dumbledors, actually flap their wings faster than they can – which sounds like the paradox of the original meme; but they actually do flap faster than their nervous system can fire a motor response. So they don’t “flap” their wings like a hummingbird, they “vibrate” them like a guitar string. They tension their little wing muscles, then twang them, so their wings vibrate at their resonant frequency. 

That, it turns out, is unbelievably efficient for a couple reasons. First, imagine if you could sweep the floor without moving your arms: you tension your arms and then twang them – and the broom sweeps 200 times per second while you stand still!  But it also gets into the very nature of work – and this is where we get back to boats, and life in general:

Imagine, if you will, that you are paddling a canoe alone in still water. Now say you want to go faster – and you can either use a paddle that’s twice as big moved through the water at the same speed – or use the same paddle and move it through the water twice as fast. It seems like both would double the force you’re exerting with the paddle – but there’s actually an exponential difference…

A simplified formula for the force exerted by a paddle is “F=A•(V•V)”, where F is the force exerted, A is the surface area of the paddle, and V is the velocity of the paddle through the water. In that simplified formula, the velocity, or speed of the paddle-strokes (or wing-flaps) is squared, making that velocity much more important than the area, or how much work is done per stroke (or flap). 

So, to leave out units for simplicity, say the surface area of your paddle is 1, and the speed you’re propelling it though the water is 1; then F=1•(1•1)=1

Double the size of the paddle:

OR, double the speed of the paddle:

Simply, working faster but easier gets more work done than working harder but slower – how’s that for a metaphor?   It’s the same as a bicycle: being in a high gear and standing on the pedals with all your force is much less efficient than using a lower gear and peddling faster with less force. 

In paddling a canoe or peddling a bike or just about anything else you have to do, there is an ideal rate for your body to move – start with that: find your own cadence first, even if you don’t feel like you’re doing much work. In the long run, you’ll go further, go faster, and get much more work done than if you overload yourself. 

Unlike bicycles, paddles and insect wings don’t have gears – the “gear” of a paddle or wing is it’s size. And most kayak paddles in particular are sized for an Olympic-level athlete in a sprint race; using a paddle like that recreationally is like riding around town on a Tour-de-France bike stuck in 22nd gear!  

The bumblebees and the Inuit figured this out without mathematical formulas. Bumblebees use tiny little wings at incredible velocity – Eskimos use tiny little kayak paddles that they swing fast. Both of them go further, faster, and with less exertion than others who look like they’re working harder. 

We don’t have a Greenland Inuit Kayak Paddle class yet (we should, shouldn’t we?), but the Driftboat class will be a good Bumblebee experience: Not a thing we do will be difficult. We’re not using blueprints or any materials that we can’t get from a hardware store in Keene. But we will have to flap our wings pretty fast to build a boat in two days!