Quite a lengthy one for you this time.
The ‘well-known fact’ that “If a flea were the size of a human, it could jump over the Eiffel Tower” is an interesting misconception – one that disregards laws of scaling and structural engineering. A brief analysis of the claim can reveal some of its substantial flaws. But before we go any further, let’s use our imaginations, if only as a preliminary thought-experiment.
Picture a human-sized flea (let’s say about 170cm in length), henceforth named ‘enormo-flea’. It has the exact same proportions as an ordinary flea, but happens to be 170cm long.
The enormo-flea is waiting near the Eiffel Tower in Paris, camera-crews at the ready, special news correspondents completing their introductions of the main event, watchers barricaded out by those little metal fences they use. Perhaps there’d be a small stage. When given the signal, somehow comprehending French, the enormo-flea’s hind legs are brought closer to its body by extrinsic muscles of the metathorax, ready to release and propel it skywards. To outward observers the enormo-flea is about to jump, but alas, it must prime itself in mind and spirit. After what seems an age to the enormo-flea, it is now at one. All is silent except for the odd shouty member of public. The enormo-flea, in the literal and metaphorical spotlight, commences its jump and soars upward. However, screams fill the air, for it does not soar skyward in one piece. At this size, the structural qualities of the enormo-flea’s chitinous integument (exoskeleton) simply are not enough to withstand the enormous forces it generates with the jump, (one of the many problems of the claim) and the enormo-flea explodes volcanically in an eruption of haemolymph and chitin. The spray of various parts of the enormo-flea rain down upon special news correspondents, the public, and filming equipment in equal measure, sparking a new wave of morbid viral videos, thereby ending the thought experiment.
Okay, perhaps my own personal thought experiment went off-kilter, but it does highlight the flaws in the claim. Can you imagine a flightless, human sized animal accelerating itself sufficiently quickly to jump over the Eiffel Tower, without damaging itself? There certainly seems to be a suspicious absence of other animals that can perform this feat. Whilst being unable to imagine something is not strong evidence against a phenomenon existing, perhaps it should induce further research into the idea. Let’s delve into the numbers and concepts behind the claim.
There are real physical constraints that restrict ‘enormo-fleas’ from existing. It’s easiest to understand these after going through the process of how a flea normally jumps. As already stated, the flea contracts several extrinsic muscles of the metathorax that bring the hind legs closer to the body. This compresses a pad of special protein, called resilin, which acts like rubber in that it can store and release energy when prompted (i.e. it is highly elastic). At a specific moment of this contraction of the legs, pegs of cuticle slip into notches on the sternum, “cocking the system” as it were (Gillott, 2005). The actual jump is initiated not when muscles innervating the legs are contracted, but when laterally inserted muscles contract, pulling the pegs of cuticle out of their notches, allowing the massive stored energy in the resilin to be released all at once, extending the legs (Rothschild et al., 1972). What happens here is that work (force x distance) can be done slowly, which is then stored by the elastic qualities of resilin. The energy is then expended more rapidly than it could otherwise be when it is triggered, amplifying power (work/time) (Vogel, 2013), launching the flea into the air. This is the same principle behind how a bow can fire an arrow much faster than it could be thrown.
So why wouldn’t this work for the enormo-flea? Our problem is that if a flea were the size of a human, and was somehow able to jump over the Eiffel Tower, it would not look like a flea, nor be made of the same materials as a flea. In short, it would cease to be a flea. The insect cuticle is an excellent structural component when considering animals of insect size and somewhat larger (think Meganeura, the extinct, giant relative of dragonflies with a wingspan of about 75cm), but at significantly larger sizes it falls short as a method of supporting weight. Arthropod bodies can be considered, in the engineering sense, as tubular shells (cylinders) that are thin in relation to their total size. Compared to rods of the same cross-section (i.e. no cavity in the centre but has the same amount of material), tubular shells are about 3 times as strong (Locke, 1974)! The force required to deform the chitinous shell is proportional to its thickness, and inversely proportional to the cross-section of the insect body. Ergo, in smaller organisms, where the relative thickness of the shell is great compared to the cross-sectional area of the insect body, the use of a chitinous exoskeleton is extremely effective (just look at the diversity and success of arthropods!). In the enormo-flea, the benefit of extra rigidity provided by a shell type skeleton is outweighed by the huge increase in shell thickness that would be required to support the bodyweight, as well as the cost of producing the material (Gillott, 2005). Thus, there are no terrestrial insects approaching anywhere near the weight of the average human because* chitin just is not up to the job of supporting such weight as a material and dreams of an enormo-flea are shot down in flames. In a magical land, where an enormo-flea actually existed and it attempted to jump, the work exerted and energy stored in resilin pads would simply cause the exoskeleton to crumple in on itself before any release of energy can be made.
On the other hand, if we want to disregard all principles of biology and physics, the idea can be easily explored. Take an average cat flea (Ctenocehpalides felis) 1.5mm in length. They can vertically jump 180mm, i.e. 120 times their body length. Let’s enlarge this hypothetical flea to the size of our ‘average human’ about 170cm tall (a more or less arbitrary figure), i.e. back to our friend the enormo-flea. Now, if our 170cm long enormo-flea jumps 120 times its own body length vertically, it will be able to jump 204m. For comparison, the Eiffel Tower is roughly 300m tall and the Empire State building is roughly 440m tall (including the mast). So, even disregarding all principles of biology and physics, our enormo-flea is still unable to jump over the Eiffel Tower! This implies that if we were to produce a very small scale replica/model of the Eiffel Tower so that a flea has the same proportion to it as a human does to the real Eiffel Tower, it would fail to clear it. And someone has indeed tested this (instead, using the Empire State building and several marginally different measurements – link here for the video).
Evolutionary pressures have led structures like the resilin pads to be present and used for jumping, whilst the impressive qualities of the insect exoskeleton provide fleas with enough structural support to withstand distortion of the resilin at that scale and provide rapid acceleration. If a flea really were the size of a human, it wouldn’t be able to jump much higher than a normal sized flea, because animals with a similar body plan tend to have the same maximum jump height regardless of size (Borelli, 1680; Hill, 1950), though there are several addenda to this rule (perhaps the topic of a later article).
Thankfully, next time someone makes the claim that “If a flea were the size of a human, it could jump over the Eiffel Tower”, you can go on a long and pedantic – but ultimately correct – explanation as to why they are wrong.
Or, you could simply direct them to this blog.
Until next time.
*There are numerous other reasons that insects do not reach the same size as other animals, as well as the constraints presented by their chitinous integument (e.g. oxygen absorption rates, being out-competed by other animals at larger sizes etc.).
Article written by Max Tercel (Twitter: @MaximumInsect; Email: email@example.com)
Featured image – An illustration by Robert Hooke, from his 1665 publication Micrographia – wikipedia – link
Eiffel Tower – wikipedia – link
Flea gif – fleascience.com – link
Borelli, G. A., 1680. On the Movement of Animals. P. Maquet, trans., 1989. Berlin: Springer-Verlag (10, 485).
Dryden, M. W. and Rust, M. K., 1994. The cat flea: biology, ecology and control. Veterinary Parasitology, 52, pp. 1–19.
Gillott, C., 2005. Entomology. Springer Science & Business Media.
Hill, A. V., 1950. The dimensions of animals and their muscular dynamics. Science Progress, 38, pp. 209-30.
Locke, M., 1974. The structure and formation of the integument in insects, in: The Physiology of Insecta, 2nd ed., Vol. VI (M. Rockstein, ed.), Academic Press, New York.
Rothschild, M., Schlein, Y., Parker, K., and Sternberg, S., 1972. Jump of the oriental rat flea Xenopsylla cheopis (Roths.). Nature, 239, 45-48.
Vogel, S., 2013. Comparative Biomechanics: life’s physical world. Princeton University Press.