THE surface area TO volume ratio OR WHY ELEPHANTS have big EARS

There are very few things that are so far reaching across numerous different disciplines, ranging from biology to engineering, as is the relation of the surface area to the volume of tělo. This is not a law, as Newton’s second one, or a theory as Darwin’s evolution theory. but it has consequences in a diverse set of situations. It discusses why cells are the size they are, why some animals have a unusual morphology, why flour explodes while wheat grains don’t and numerous other phenomena that we will explore in this article.

What Is SA:V?

All bodies have a volume, and a surface area. It is as easy as dividing the area of the body in question by its volume to obtain the ratio we are interested in. consider for example a cube of 1 m in side. It has a volume of 1 m³  (1 cubic meter). At the same time each of its 6 faces has an area of 1 m² (1 square meter), and a total surface area of 6 square meters, for that reason the surface area to volume ratio (or SA:V for short) is 6/1 = 6 m-1. This ratio varies with the body size, if you do the same calculation for a cube of 2 m to a side, you get a SA:V ratio of 3 m-1, and for a 10 m cube the value goes down to 0.6 m-1. It will tend to zero as the cube gets larger.  The SA:V ratio also depends on the morphology of the body,  for a given volume, the sphere is the object that has the smallest SA:V ratio.

Why the surface area to volume ratio Is Important

The surface of a body is essential in numerous ways, because numerous reaction and transfer processes are directly proportional to surface area. Some examples are:

Heat transfer: heat is transferred to and from a body mainly through its surface, but a large body has less surface available per unit volume (and mass if the body is homogeneous). In the figure below, the larger cube has  54 units of surface and 27 of volume, with a SA:V ratio of 2. The smaller one, has 6 units of surface and one unit of volume, with a SA:V ratio of 6. That implies that the smaller cube can be heated or cooled 3 times as fast as the larger one.

Change in the SA:V ratio as a body is scaled. image from OBEN science 7E.
Animals need to get rid of excess heat, but this becomes increasingly challenging for big species that have a small surface area compared to their body mass. So, special adaptations are needed in purchase to amazing off a large animal. Such is the case with the elephant in the feature image. The big ears and the skin wrinkles offer the additional surface that is needed for cooling. small animals have the opposite problem, they lose heat at a very fast rate, so they should eat large quantities of food in purchase to replace the energy that has been lost as heat.

Steel wool catches fire when heated by the electric current from a battery. image from creating wonder blog
Objects that are very small have a very large SA:V ratio and for that reason they heat very quickly. This is the reason why even metals can “burn”, like the steel wool shown in the image or the powder metals used as fuel.

Another dramatic example is grain dust, that can be explosive. The terrific Mill disaster is a sad example of that. In 1878, the Washburn A Mill exploded along with several adjacent flour mills, killing 18 workers and destroying the largest industrial building in Minneapolis.

Biology: The cells in every living thing need a set of substances to get into it in purchase to fuel the cell reactions. At the same time waste products need to be taken out. Cells rely on diffusion through its membrane in purchase to relocation substances in and out. As the cells grow, their SA:V ratio becomes smaller, and the membrane area is no longer sufficient to relocation substances at the required rate. because of this, the SA:V ratio does impose an upper limit on the size of a cell. On a larger scale, several body structures have developed to maximize the SA:V ratio, such as the lungs and the intestines. Your intestines have no less than 300 m2 of surface area available for digestion.

The SA:V ratio dictates in some way the form and shape of animals. image from Tall.Life
Engineering: In engineering, the SA:V ratio is also known as the square-cube law. When an object is scaled up by some multiplier, its mass increases as the cube of the multiplier, but its surface and cross sectional area are enhanced only as the square of the multiplier.

Consider a very large airplane such as the Airbus 380. Its wings are proportionately larger that those of a smaller airplane such as the Boeing 747. just scaling up the 747 to the size of the 380 will result in wings with not enough surface area to give enough lift for the weight of the airplane. A skycraper that is double the size of another in its dimensions has eight times the weight, but only four times the base area, for that reason you may need different construction techniques, such as using steel rather than only wood and brick.

You may have dispokryté, jak jsou různé velmi malá zvířata porovnána s většími. Mravenci mají nohy, které jsou velmi hubené ve srovnání se svými těly, a mohou zvednout mnohokrát jeho vlastní váhu. Sloni na druhé straně mají husté nohy a nemohou zvednout úžasné váhy ve srovnání s jejich vlastní hmotností. Důvodem je stejný, když rozměry rostou, hmotnost se zvyšuje rychleji než oblast nohou a tlak vyvíjený je podstatně větší.

Dali jsme jen několik příkladů mnoha instancí, kde má poměr SA: v vliv. Je těžké myslet na disciplínu lidských znalostí, kde se tato zásada neplatí. Nakonec můžeme říci, že ano, velikost dělá.