Question about the square cube law

[ghostshade]

Hi i post this here becasue i hope you can help me with a little question i have not yet been able to figure out myself.

 

i know what the square cube law say: When an object undergoes a proportional increase in size, its new volume is proportional to the cube of the multiplier and its new surface area is proportional to the square of the multiplier.

 

However all examples that i have found has been examples of very large examples like for example humans at 60 feet in height.

 

That is not really helping me since i try to find out what the square cube law would say about something far smaller then that.

 

But enough of a backstory

 

I am writing a scfi/fantasy story for myself and the largest bipedal races are 6 meter or 19.685 foot or for simplicity 20 foot when they stand erect on two legs.

 

Is this possible without breaking the square cube law?

 

i estimate their weight under standard gravity at around 2000 - 2500 kilogram or 4409.25-5511.56 pounds

 

Looking forward to your answers

Edited July 28, 2013 by ghostshade

[timo]

Hi Ghostofshade,

 

the relations of surfaces going with the 2nd power of a scaling parameter and 3D-volumes going with the 3rd power (and N-dimensional volumes going with the N'th power) are purely mathematical in nature and scale-free. That means:

- It holds for 20-feet humanoids as well as for 60-feet humanoids, as well as for 6000-feet humanoids.

- It even holds the other way round: If the linear size of an object is reduced by half (in every direction), the volume is reduced to 1/8.

- Being the mathematically correct scaling does not imply that the result makes sense biologically: Scaling up a seagull by a linear factor of four will result in a giant seagull that is probably unable to fly (weight goes up by a factor 4³ = 64 while wing area only goes up by a factor of 4²=16 - and that's without considering the factor of physical strength). Similarly, applying the mathematically correct scaling to a humanoid still does not guarantee the result makes sense biologically.

 

Btw.: I didn't check your numbers.