On the size of Beasty

Wendy, you missed some quality biophysics today!

The argument basically followed from Josh's earlier post, entitled `Tyranids'. I had commented on this that it might be favourable for a large creature to have a sub-divided circulatory system.

As it turns out, for a creature composed of many sub-entities with space-filling fractal transport networks (as in BIPH2000) you get no decrease in metabolic rate with sub-entity number. The total metabolic rate of such a creature scales as the number of sub-entities to the power of one quarter, so B actually increases!

Our second major question is how large can an organism (affectionately known as Beasty) be if it is a) spherical b) completely powered by photosynthesis (assumed to be perfectly efficient)? Furthermore, we assume that the energy flux is equal to that observed on Earth (1.4kW.m^-2) and that Beasty has the same density (\rho) as water (at least on average).

We recall that B = kM^0.75, where k is a constant of proportionality which we assume is the same for all creatures. From the resting metabolic rate of a human (around 100W) we find that (assuming a mass of 70kg) k takes a value of approximately 5W.kg^-0.75 (not far off what we assumed for Beasty by other methods... around k=10).

Thus if we set the total metabolic rate B equal to the cross-sectional area of Beasty multiplied by the energy flux (\phi) we can rearrange for the radius of the sphere.
r =(\pi\phi/k)^{4}(3/(4\pi\rho))^{3} ~ 8m
From this we find the mass to be M~2*10^6kg, or around 2000 tonnes. This is about ten times heavier than a blue whale!

It is interesting that we get such a result based on only a few assumptions, and that it doesn't seem too(oooo) ridiculous. I encourage you to check my working!

If Seth seems to recall me telling him something different, then he recalls correctly: I had made a mistake with exponents and estimated Beasty's maximum mass to be a meagre twenty tens (one tenth of a blue whale).