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I hesitated to ask this question because it seems so obvious and intuitive. However, I am not able to explain this tendency.

Background

It seems to me that small organisms make faster movements than big organisms. I don't mean that they are able to travel at higher speed (the cheetah is a big animal and is the fastest terrestrial species) but I mean that their movement are fast, quick and their members undergo high acceleration.

Examples

I would guess for example that the legs of a tiger beetle (clade of fast sprinter beetles) (see movie) undergo much higher acceleration than the legs of a cheetah (fastest terrestrial organism on earth) (see movie). To avoid taking the extreme, I would think that the legs of a Drosophila (see movie) undergo higher acceleration than the legs of a dog (see movie). The organism that is able to create the fastest acceleration is the mantis shrimp. Wikipedia says:

Both types (smashers and spearers) strike by rapidly unfolding and swinging their raptorial claws at the prey, and are capable of inflicting serious damage on victims significantly greater in size than themselves. In smashers, these two weapons are employed with blinding quickness, with an acceleration of 10,400 g (102,000 m/s2 or 335,000 ft/s2) and speeds of 23 m/s from a standing start. Because they strike so rapidly, they generate cavitation bubbles between the appendage and the striking surface. The collapse of these cavitation bubbles produces measurable forces on their prey in addition to the instantaneous forces of 1,500 newtons that are caused by the impact of the appendage against the striking surface, which means that the prey is hit twice by a single strike; first by the claw and then by the collapsing cavitation bubbles that immediately follow. Even if the initial strike misses the prey, the resulting shock wave can be enough to stun or kill the prey.

Finally, note that Gabel and Berg (2003) show that the flagella can rotates up to 270 Hz.

Questions

  • Am I right to think that small organisms tend to make faster movements than big organisms?

  • If yes: Why do small creatures make faster movements?

    • Does it has to do with time for chemical diffusion?
    • Does it has to do with mechanics? ($F=ma$... But muscles are smaller as well).
    • Does it has to do with the resistence of biological tissues?
    • ...

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  • $\begingroup$ This might be explainable with physics, force = mass * acceleration, so acceleration = force divided by mass. If the mass is small enough, then it won't take much force to get large accelerations. While smaller muscles won't generate as much force as the larger muscles, their reduced mass may still allow greater acceleration. $\endgroup$ – user137 Oct 8 '14 at 16:12
  • $\begingroup$ Muscles are much smaller as well so that it is not totally intuitive to me why acceleration is higher in small organisms. $\endgroup$ – Remi.b Oct 8 '14 at 16:45
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    $\begingroup$ Right, but I'm not sure how mass and force scale with muscle size. Mass should scale linearly with muscle volume, assuming constant density, but force generation might not scale the same way. If smaller muscles can produce more newtons/gram, they could produce higher accelerations. $\endgroup$ – user137 Oct 8 '14 at 18:27
  • $\begingroup$ Yes, indeed! I'd be curious to get some more info to see if this is a plausible explanation. $\endgroup$ – Remi.b Oct 8 '14 at 18:30
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    $\begingroup$ I think this might have something to do with Kleiber's law which is approximately true. It basically states that larger animals have slower metabolisms than smaller animals. equation-of-the-month.blogspot.co.uk/2012/06/kleiber-law.html If Kleiber's law is true then smaller animals would have more disposable energy per unit mass compared to larger animals which would allow them to have relatively large kinetic energies. $\endgroup$ – Aidan Rocke Oct 8 '14 at 19:14
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It's a general phenomenon that the time scale correlates with the size scale of complex systems. Energy consumption is the main concern dealing with the speed for biological organizations. In the absolute sense, a turtle has a higher speed than a small bug. But based on their sizes, the bug seems much quicker and faster. So we need to normalize the speed with the size scale which we can temporarily call 'fastness".

Here is the relationship between the fastness and the mass:

enter image description here

Where u is speed of the organism, M is mass, alpha is a constant which we assume that the metabolic energy is related to the body mass of the organism with a power law.

The final equation says that if alpha > 1.67 then the larger would be faster. But our observation tells us that the smaller the faster. Therefore, we know alpha < 1.67. In fact Kleiber's law tells us that the alpha is about 0.75.

You can check some numbers related to some animals here

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An increase in linear dimension by $x$ causes an increase of $x^3$ in volume and mass. The force that a muscle can generate roughly scales with the cross-sectional area of the muscle, an increase of $x^2$ for a muscle scaled by a factor of $x$.

This means that larger animals need proportionally larger muscles (by a factor of $\sqrt {x}$) to achieve the force required to generate any given acceleration. This becomes impractical fairly quickly, so we just make do with less acceleration.

If you consider a 1 cm ant scaled to human size with no other modifications (a 200-fold increase), it would be 8,000,000 times more massive but its muscles would only be 40,000 times stronger. It may have started out about 50 times stronger than a human, mass-for-mass, but at human scale, it's only 1/4th as strong; it would barely be able to move at all.

There are other biomechanical factors that can influence speed that favor smaller creatures as well. One example is the ability of mantis shrimp to store amounts of mechanical energy that are quite large on their scale in the curvature of their exoskeleton (like storing energy in a car's leaf spring.) Similar energy storage on a human scale is just not practical.

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