# A flea that jumps vertically 200 times its length - possible?

I was reading an article today about a disease called tungiasis which is caused by the flea known as Tunga penetrans. One statement in the article grabbed my attention and struck me as possibly being an exaggeration.

Specifically, one reads in the article:

Can that be possible? A 1 mm organism jumping up 200 mm? My knowledge of basic mechanics is far too limited to prove or disprove the assertion. However, my intuition (ha!) makes me seriously doubt that there’s a mechanism that would permit an organism to jump vertically into the air to a height which is 200 times its length. It would be as if we could jump 1200 feet in the air!

I mean, using mechanical energy/forces alone, how could such a jump be accomplished? Even if a flea’s hind legs were as twice as long as its body (and scanning EMs indicate that they are less than that, approximately the same length as its body), it would be a case of a 2 mm lever or (spring?) propelling the entire body upward 100 times that length.

Bottom line - using basic principles of mechanics per se can one prove/disprove that a 1 mm organism can jump vertically to 200 mm?

Actually, a quick search online for Tunga penetrans shows several references that it’s a poor jumper, only reaching 20cm, but I think that’s more of an indication of its danger to humans.

[bolding mine]

Is this a whoosh or a typo?

Doesn’t seem unreasonable to me. To the first order of approximation, similarly constructed creatures of different sizes would have approximately the same absolute jumping ability, due to the well-known square-cube law.

Consider a being with 1 meter range of motion in its legs and a 1 meter vertical leap. It attains this leap via the work performed by those legs exerting an average force F over that one-meter distance; the kinetic energy F *1 m created is enough to overcome 1 meter of gravitational potential, roughly 10 M m^2/s^2 for a creature of mass M.

Now, an otherwise identical being 1000 times smaller (we’ll call him ‘Spud’), will have a 1 mm range of motion in its legs, and will be able to exert a force of approximately F/1,000,000 (structural strength scales at approximately the square of the linear dimension), so the kinetic energy supplied by those legs will be 1/1,000,000,000 of that provided by the larger creature. But Spud has a mass of about M/1,000,000,000 (mass scales with the cube of the linear dimension); so that kinetic energy should be able to overcome that same 1 meter of gravitational potential energy for that smaller mass! Spud has roughly the same leaping ability as the full-sized creature.

This is a very rough approximation, of course. There are a lot more differences between large and small creatures than just the sizes. But it should make it clear that it’s not absurd to imagine a 1 mm flea jumping 200 mm.

One doesn’t need to. It has been observed that fleas can jump 100 times their own body length. I’m not sure about 200 ties, but it doesn’t sound completely impossible.

The first point to note is that you are only 3 feet long if we measure you the same way as we measure the flea: eyeball to arsehole. So it’s only equivaent to 600 feet.

And you can do exactly that. Simply build a winch and connect it to length of hardwood. Wind the winch until the wood is sufficiently flexed to catapault you 600 feet into the air. Not too hard.

Fleas use the same principle. A flea doesn;t jump as such. It uses a modification of the flight mechanism of its fly ancestors. In flies the exoskeleton deforms when the muscles are contracted and then allowed to snap back into place to provide the speed needed to move the wings. Fleas have coupled that to the legs rather than the wings, but the reuslt is the same. The muscles contract numeorus times over a short distance to wind the spring plates of the body into position and they are then locked. Whent he flea needs to jump it unlocks the plates and the body is catapulted into the air. If you ever catch a flea you will notice that can only jump really high once and then needs to rest for a few seconds before it can take another large jump so it can recock the spring.

I don’t see why this is so hard to believe. A 2 foot bow will easly launch an arrow 200 feet or more, and a 3 foot bow will launch an arrow 300 yards or more, and wood isn’t a particularly good spring material. Granted we are only talking about the size of the spring here, but with small animals scaling issues mean that the spring is a sizable proportion of the whole animal’s weight.

Further discussion of fleas, catapults, bows & energy storage here.

A 1967 paper on the matter.

J. Exp. Biol. 47 59 (1967) – PDF

Wow! Thanks to all of you.

Boy, was I mistaken.

Much obliged.