Today, can you jump as high as a flea? The
University of Houston's College of Engineering
presents this series about the machines that make
our civilization run, and the people whose
ingenuity created them.
Here's one for you: How high
can a horse jump? Or a flea? How high can you jump?
Variations among individual fleas, horses or people
are large, but healthy members of any jumping
species raise their centers of gravity about one
meter when they leap.
The center of gravity of a high-jumper who clears a
two-meter bar was already a meter or so high as he
approached the bar. His body flattens out
horizontally as it passes over the bar. So he jumps
his center of gravity only an additional meter or
so.
A horse's center of gravity is even higher than a
human's. The horse also stretches its legs out
horizontally to get over the bar, and he likewise
rises only three or four feet. My dog gets her
front paws higher than my head when she tries to
chase a squirrel up a tree. And her center of
gravity likewise rises a meter or so.
So what about that flea? It jumps hundreds of times
its own height, but that also gets it about a yard
off the ground. It seems spooky -- all God's
jumping creatures reaching the same height. How can
that be? Franklin Felber explains it in a letter to
the magazine Physics Today. It comes down to
modeling laws.
Here's how it works: Our jumping capability should
increase with the length of our leg, and
with its strength. Length is proportional to
linear size, and strength is proportional to the
leg's cross-sectional area. But area increases as
the square of size. That means jumping
ability should go up as the cube of linear
size.
If that were the whole story, we'd be able to jump
far higher than any flea. But we also need to
consider the weight opposing the height of a
jump. It too increases with the size cubed. (Go to
the bookshelf and pick up a large book and one half
its size. The large book will weigh eight times as
much as the small one.)
Since both the opposition to jumping and jumping
ability vary with the cube of size, that means size
cancels out. The height any creature can jump is
independent of its size. What a flea can do,
so can a grasshopper, a monkey, or a lion.
There'll always be champions among cats, dogs and
humans. There'll also be individuals who can come
nowhere near a meter. The one-meter figure may be
approximate, but it signals our kinship with other
species. For we're all bound by the same rules of
mathematics and of nature. Those rules keep us
balanced in odd ways.
That message is pervasive and humbling. On the
larger canvas it reminds us that size, strength,
even brains, fail to erase a primary equity that
exists among creatures. We try to make leaping into
a metaphor that denies equity. Shakespeare cries,
... here upon this bank and shoal of time,
We'd jump the life to come.
We want our leaps to take us so much further than
they really do. I think it helps keep things in
proportion to remember that you and I can really
leap no higher than a lowly flea.
I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds
work.
(Theme music)
