ZOO 2090 Lecture Notes - Lecture 21: Vector Calculus, Dimensionless Quantity, Countercurrent Exchange
1 May 2018
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ZOO2090 – Function and Biological Design
Important Factors:
1. Size (length, SA, and volume)
• Square-cube Law: if you double the size of an object, you increase the SA 4x and
increase the volume 8x
• Surface Area:
o Large size means relatively small surface area, leaving less space for
exchange with environment (heat, gas, etc)
o Scaling study of size and its consequences
• Metabolism:
o Metabolism scales with size
o Heat loss is proportional to surface area; heat production is proportional to
volume
• Supporting System:
o Mass is proportional to volume
o Limb strength is proportional to cross-sectional area
o Ex. Comparison of leg bones of mouse, human and elephant
• Examples of increasing SA without significantly increasing volume:
o Lung/gill (due to small compartments)
o Gut wall
o Nasal turbinate
2. Force
• Biomechanism attempts to clarify biological design
o Basic physical concepts are length (distance), time (flow of events) and mass
(inertia)
o For the latter recall that mass is a property of matter, weight is a measure of
force
o Force is the effect of a body on another through mass and acceleration
• Vector
o Measurements that have magnitude and direction (some muscles built upon
this principle)
o Second law of motion: F=a*m
o Vector analysis takes advantage of the fact that force parameters can be
measured (against weight and against friction) *polar bear example
• Lever
o Muscles generate forces and skeleton applies this forces
o Represented by torques and levers
o Ex. Lever arm = fulcrum (pivot point)
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