Page 3 model

Have you ‘herd’? The world’s largest cow is over six feet tall and weighs more than 1.3 tonnes. Is a bigger cow possi-bull? Will the future contain infinitely large cows? The steaks have never been higher! To answer this question, let’s take a look at the cow’s legs. If the main (meaty) bit of the cow has a volume �� and density �� then its weight is ������. So each leg supports a load of about

In pursuit of glory, let’s now make the length, height and width of the cow bigger by a factor ��. The cow’s new volume is ������ and so the load on each leg is ������: it grows cubically as �� increases. Can the legs cope? If we model the legs as cylinders (since they already ‘lactose’...), we can use a 1757 result from the famous cow enthusiast Euler: if a cylinder has height �� and radius ��, the maximum load it can support standing upright is

��max =

���� ������ ��

�� here is just a property of the material: its stiffness, or Young’s moo-dulus. With our scaling, �� and �� are now �� times bigger. Our new maximum load is

�������� ���������� ��

=������max.

Uh oh... this only scales as ����: quadratically. So even though ��max starts above �� (it has to, given that these cows exist!), there will come a maximum possible ��, after which there will beef-ar too much cow and its legs will give way... an udder disaster.

This analysis tells us something really important about biology—that there is a natural maximum size for land mammals. But have we reached it for cows? Brody & Lardy’s 1000-page tome Bioenergetics and Growth from 1946 has all the de-tail you need. We’ll leave you to ruminate on the cow-culations.