Here we have a walking device just to remind you of how something walks.
This is an artificial limb.
And we've loaded it a little bit to make it look a little more real.
And now if I walk I make the limb swing, but I don't press hard.
That's what a walking gait is.
I just let the leg fall back into place, so to speak, without any special drive.
That's not at all the same as running and we'll talk about running later.
But I think if you think to yourself when you're walking or running next,
try to see how it is you're moving. It's a complicated action
but the essential feature is that it moves slower and fall back,
move forward and fall back in just that fashion.
Now that... Thank you, Bill.
That gives rise to the
notion that the principal determiner of the speed of walking is not at all the,
as one might think, the complicated mechanics of the muscles and the bones.
In fact it is very simple. The main determiner, perhaps not the only thing,
because we're trying to simplify a rather complicated kind of motion,
the main determiner is the swing as the swing of a pendulum.
A very stratightforward matter.
And that swing, as you know with a pendulum, takes longer,
the bigger the pendulum length.
The greater the pendulum length, the more the swing of the pendulum.
Therefore, we can say that the time for the swing
is proportional to the square root of the length of the pendulum.
In this case the length of a characteristic bone or characteristic typical size of the
animal.
Any size you want to choose, any dimension, let's say his leg length.
I can write that of course that's the same as the fractional exponent L to the one half.
If you prefer this notation, why very good.
Now then notice what that says, that says the time for a pace
is longer the bigger the animal.
Let us try that a little bit, to see if there is any reality in that picture.
I don't think we need those, well, alright.
Alright, we shall look at them then very quickly.
Just to remind you what a pendulum looks like.
Here is a long pendulum.
And here a short one.
Notice many more beats in the same interval of time.
That's quite familiar and if we were to measure it you would find
it would go very tolerably like the square root of L.
Thank you, Bill.
Now let us do that for a few animals to see what they look like.
And their appearance is as follows.
Can we have again some of our boy walking schemes.
Now, the idea is to walk, Martin, and not to hurry.
You're sauntering down past the park in the summer time and not very busy,
and not late for school, and just walking along.
Go ahead and I'll give a start to Bill to start, you just walk along peacefully.
And start. One. 1, 4, 5, 6, 7, 8, 9, 10.
What did we get?
Six seconds. - Six seconds!
Well that seems pretty good.
And six seconds for a boy walk.
Now let us try a smaller animal. I think we have a performer here again.
Tessa, a member of the Coates family as I recall.
This is a complete Coates performance here.
And let's see how Tessa walks. Let's start her off and I'll try to count.
Start. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Three seconds? Very interesting.
And now you see quite well that the smaller animal has taken much less time for a pace.
Let us look now at a larger animal.
Again we have our same problem, hard to bring in the large animal,
but not so difficult with the splendid effect of film.
So let us look in a film a large animal and try again to count with me her paces once
I begin.
Start.1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Splendid.
8.5 seconds.
There's certainly no question about the time increasing from 8.5,
from three seconds to eight and a half seconds for ten paces.
We may... that's a factor of about two something, 2.4 or so.
If I were to square that I would get about six or eight,
and it seems reasonable that dog's leg height is about a foot or a little more than a foot.
And the giraffe's leg height is about six or seven times that, six or seven feet,
and that comes tolerably close to the square root of L.
But notice something. Does that mean that a giraffe walks slower?
Her paces are slower, but does she walk slower than Tessa?
Who would win in a race?
A walking race.
What do you think?
The giraffe, yes.
Why?
Paces are slower but... but what everybody?
Takes longer per pace, that's exactly right.
The speed after all is found this way.
The speed is the distance over the time.
But the distance per step surely is proportional to the size of the animal's leg.
He makes a long step. So proportional to L divided by the time,
which goes like L to the one half.
The overall effect then is like L to the 1/2 and the speed is greater
the walking speed for the bigger animal.
I recommend you to try that on boys of different heights,
on girls, on horses, men, women, dogs, squirrels anything you can find.
See if this rule really works for walking. I think that it does.