This study explores various uses of engineering as a tool for solving problems and improving the quality of life. The experiments in the article show that competitive athletes swim with their fingers spread slightly, because this configuration generates greater speed, the research being based on a principle known as constructional law. The constructional law has been applied to predict all the key features of the design of animal locomotion, which includes human running and swimming. In engineering, the discovery expands a domain of constructal-design results that has been growing fast. Bodies that generate heat volumetrically are endowed with maximum heat transfer density when the spacing between the solid surfaces internal to the volume have certain sizes that are smaller in forced convection than in natural convection. The volumetric cooling of future electronics, avionics, and self-cooling materials rests on this class of constructal designs. The swimming with spread fingers is the corresponding design of a body for maximum momentum transfer density.
Engineering is both an art and a science.
It gives humanity the tools for solving problems and improving the quality of life. The discipline also gives those who follow it a powerful lens through which they can analyze the world around them.
Consider, for instance, something as common as a living body moving through water.
Flippers and webbed feet have evolved to give aquatic animals an advantage in taking prey and avoiding predators. The advantage is speed.
This feature of animal design is considered understood in biology based on the argument that a larger paddle makes swimming more efficient. Upon closer inspection, however, this explanation is questionable from a mechanical engineering perspective, because a larger foot means a larger surface pushing against the body of water, not a higher efficiency.
The figure shows fingers modeled as four parallel cylinders of diameter D, moving downward into water (i.e., moving from right to left in the figure) with the speed V∞.
Configurations A and C have the same frontal area (4D), the force FA must be greater than FC because the stack A has a greater drag coefficient (it is less hydrodynamic) than each of the single cylinders of configuration C.
Though B is a “stack” like A, the frontal area of B = 4D + 3S, and so is broader than the 4D frontal area of A. This happens when the spacing S is approximately the same as the thickness of the laminar boundary layer that surrounds each finger, namely S ~ D Re–1/2, where Re = V∞D/v, when v is the kinematic viscosity.
The fluid friction on the finger surfaces (spaced S apart) sustains the pressure difference between the front and back of the S gap. The four fingers are wearing a glove of water boundary layers.
The fundamental question for biology is why a swimming body should be advantaged by a larger foot or hand. We answered this question by focusing on the shape of the human hand during speed swimming. We showed that competitive athletes swim with their fingers spread slightly because this configuration generates greater speed (note: speed, not efficiency, because the direction of the evolutionary design in this population of swimmers is toward speed).
We arrived at this discovery through research based on a principle we call the constructal law, which reads: “For a finite-size flow system to persist in time, it must evolve in such a way that it provides easier and easier access to the currents that flow through it”
We have applied it to predict all the main features of the design of animal locomotion, which includes human running and swimming. For example, the constructal-law prediction is that taller bodies should travel faster in all media, with speeds that are proportional to the body mass to the power ⅙, or to the body length scale to the power ½.
In particular, for the sport of speed swimming the prediction is that: swimming is the motion of surfing (i.e. falling forward) on the water wave generated by the swimmer; bigger waves travel horizontally faster (with speeds proportional to the wave length to the power of ½, just like the swimmer’s speed); bigger (i.e. longer) swimmers can raise their torsos higher above the water line, and generate bigger waves and greater speeds.
In order to raise the body higher above the water line (i.e., in order to lift a larger weight), the swimmer must be able to push the water downward with a greater force. Speed in sports comes from running “tall” and swimming “tall,” which means falling forward faster because the fall is from a greater height. This holds for all running and swimming animals as well.
In swimming, the greater downward force is achieved with a bigger foot and a bigger hand. In the evolution of the swimming animal (body configuration and motion), the tendency to spread the fingers and the toes came first, and later gave direction to the evolution of webbed hands and feet.
It is counterintuitive to think that the spread hand “steps on water” and pushes the water down, and that it is not the paddle of a boat, which pushes the water backward horizontally. Of course, the swimmer’s spread hand does both, pushing down and back, as both are required by the design of falling-forward locomotion in running, swimming, or flying.
It is counterintuitive to swim with the fingers separated. The “boat paddle” idea is why all of us learn to swim with cupped hands. Swimming animals are not boats. We found first by pure theory, and later with full numerical simulations of fluid dynamics, that there exists an optimal spacing between fingers such that the total force exerted by all the fingers is up to 50 percent greater than when the fingers are held tight.
It’s counterintuitive to swim with the fingers separated . The “boat paddle” idea is why all of us learn to swim with cupped hands.
swimming animals are not boats.
Consider the fingers as four parallel cylinders moving downward into the water. Imagine three configurations of the fingers: A, with no spacing; B, with small spacing; and C, with large spacing. The force generated by configuration B, with small spacing, turns out to be the greatest of the three.
All three configurations consist of four fingers and a palm, but the wide spacing of the cylinders induces the least drag and therefore exerts less force on the water than either of the others. Configuration A has a greater drag coefficient than the four widely spread cylinders of configuration C.
The frontal area of B, consisting of the four fingers and the small spaces between them, is greater than the frontal area of A. The secret is in the spacing. Configuration B pushes like a hand that is significantly wider than four fingers stuck together because the spacing is approximately the same as the thickness of the laminar boundary layer that surrounds each finger. In this configuration, the fluid friction on the finger surfaces sustains the pressure difference between the front and back of the spacing. To the body of water, configuration B behaves as a wider hand and it is in fact wider: the four fingers are wearing a glove of water boundary layers.
Computational fluid dynamics simulations of the flow through and around four cylinders showed that as the spacing increases, the total force increases from configuration A to B, and then it decreases as spacing approaches C. The force is maximum when the space is roughly half the diameter of a finger. The optimal spacing decreases slowly as the Reynolds number increases, because the boundary layer thickness decreases. Similarly, the optimal spacing decreases as velocity increases, and this is why the duck toes are spread more than the fingers of the seal, all the way to zero spacing in the flippers of the whale.
Interesting (and healthy) to us as engineers are the broader implications of this theoretical discovery. First, engineering makes a contribution to biology because this discovery unveils the principle behind the evolutionary design phenomenon evident as webbed hands and feet. It is the same principle (the constructal law) that governs the evolution of animal locomotion and speed sports (100-meter dash, 100-meter freestyle).
In engineering, this discovery expands a domain of constructaldesign results that has been growing fast. Bodies that generate heat volumetrically are endowed with maximum heat transfer density when the spacing between the solid surfaces internal to the volume have certain (unambiguous) sizes that are smaller in forced convection than in natural convection. The volumetric cooling of future electronics, avionics, and self-cooling materials rests on this class of constructal designs. The swimming with spread fingers is the corresponding design of a body for maximum momentum transfer density.