Scales And Dimensions

Question 1

Consequences of surface/volume ratio

Answer 1

• mass scales with volume (M~kL^3)
• energy production scales with volume ~L^3)
• heat loss from environment scales with surface area ~L^2 (heat loss is problem for small animals)
• transport of gases across membrane scales with surface area ~L^2 - problem evaded by having highly convolutes surface

Question 2

Transport within bodies

Answer 2

• materials can be transported by processes dependant on velocity (eg circulation systems) where x~t (distance travelled proportional to time)
• other main mean of transport is diffusion where x~t^1/2
• as lengthscale increases diffusion becomes less efficient

Question 3

Speeds of molecules

Answer 3

• thermal energy due to translation : 3/2kT = 1/2mv^2
• flicks law : flux of material is directly proportional to concentration gradient

Question 4

Isometric and allometric scaling

Answer 4

• Isometry occurs when different-sized animals retain the same shape
• allometric scaling occurs when aspects of the shape change disproportionately with overall size
• see allometric scaling laws !

Question 5

Why animals must be different shapes

Answer 5

• for constant density, L~M^1/3, forces on skeleton F~M, but cross sectional area A~M^1/3
• therefore stresses increase in skeleton as M^1/3

Question 6

Jumping

Answer 6

• GPE = Mgh
• mass of muscles and therefore energy ~ M
• height an animal can jump is therefore independent of its size
• relative to their lengthscale smaller animals can jump higher