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As the title says, why divide surface area to volume for strength in living beings ? I mean why all surface area ? Shouldn't it be area touching the ground ? Thanks in advance! :)

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  • $\begingroup$ The question I linked may not seem a duplicate at first sight but it does explain why strength scales as size squared. $\endgroup$ Dec 8, 2015 at 6:14
  • $\begingroup$ This is a badly stated question, but I will give a shot. $\endgroup$ Dec 8, 2015 at 6:21
  • $\begingroup$ @RossMillikan I mean, for strength why do we divide surface are to volume. Is that a derivation ? $\endgroup$
    – ysn_akst
    Dec 8, 2015 at 13:08
  • $\begingroup$ We don't. The strength of a bar is proportional to the cross sectional area. Tensile strength of materials is quoted as pounds/square inch, which you multiply by the cross section to give the force a bar can take. $\endgroup$ Dec 8, 2015 at 15:04
  • $\begingroup$ @RossMillikan No we do. For living beings we say strength is surface area / volume $\endgroup$
    – ysn_akst
    Dec 9, 2015 at 14:54

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For a given style of animal, if you double the linear dimensions, the volume increases by a factor of eight. If we assume the density is constant-people are about the density of water-the mass supported increases by a factor of eight. All that mass is supported by the leg bones. The cross section of the bones only increases by a factor of four, so the stress (which is force divided by area) is doubled.

You can see the effect of this. Large animals have much thicker legs (in proportion to body size) than small animals. This is to give more surface area to the leg bones so they can support the weight. You can't do this forever, which is why large animals tend to walk instead of jump.

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    $\begingroup$ Just missing a simple statement connecting to the question, for example: "regardless of shape, if you double the size of an object you quadruple its surface area. So while we really consider cross sectional area for strength, the two are linearly related." $\endgroup$
    – Floris
    Dec 8, 2015 at 6:41

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