Clothing costs for different sizes

[Anthony]

Originally Posted by Varyon

I think metabolic rate scales roughly as the square of height* (given equal proportions), so given surface area scales the same, it looks like you'd want constant thickness for clothing - that is, clothing weight would also scale with the square of height. That follows from what ravenfish said about fur thickness being roughly the same between a fox and a moose, and is sort of what I initially expected.

Yeah, most estimates of metabolic rate vs mass hover close enough to the 2/3 power to make insulation thickness being scale-independent sound plausible. Note that cinematic giant scaling actually produces metabolic rate that varies with the 7/6 power of mass.

[whswhs]

Originally Posted by Anthony

[Y]ou're making the assumption that metabolic rate is linear in mass (the amount of insulation required is proportional to surface area / metabolic rate), which isn't a particularly good model for either realistic animals or cinematic giants.

I believe we are talking about two different things. Your concern is with metabolic rate, or the rate at which heat is generated inside an animal (at least a homeothermic animal); that is indeed proportional to the surface area, and thus approximately to the square of body length. But my concern was with cooling rate, or the rate at which an existing amount of thermal energy is lost to the surroundings. Since the quantity of thermal energy is proportional to the body mass, and the rate of energy loss is proportional to the body surface, the time required for cooling works out to be approximately proportional to the first power of body length

These seem to be two different questions.

[ravenfish]

Originally Posted by whswhs

I believe we are talking about two different things. Your concern is with metabolic rate, or the rate at which heat is generated inside an animal (at least a homeothermic animal); that is indeed proportional to the surface area, and thus approximately to the square of body length. But my concern was with cooling rate, or the rate at which an existing amount of thermal energy is lost to the surroundings. Since the quantity of thermal energy is proportional to the body mass, and the rate of energy loss is proportional to the body surface, the time required for cooling works out to be approximately proportional to the first power of body length

These seem to be two different questions.

The actual question is "does the animal maintain a healthy temperature", for which one must consider both heat gained and heat lost. You can't make a financial budget if you don't know how much income you have, and you can't make an energy budget if you don't consider how much energy is coming in.

EDIT: The conclusion seems to be that metabolism, and therefore heat generated, increases at roughly the same rate as surface area, so (assuming heat lost also increases with surface area) larger animals don't need to further decrease heat loss to maintain their temperature- which conclusion appears to be empirically supported by the source I quoted upthread.


EDITEDIT: Ectotherms, who gain a substantial portion of their body heat from the environment, operate under a different regime, but they also don't seem to be relevant to this (scaling-humanoid-inspired) discussion, unless we are trying to work out how to dress a komodo dragon.

EDITEDITEDIT: The answer to what a komodo dragon wears is, of course, "anything it wants".

[Anthony]

Originally Posted by whswhs

I believe we are talking about two different things. Your concern is with metabolic rate, or the rate at which heat is generated inside an animal (at least a homeothermic animal); that is indeed proportional to the surface area, and thus approximately to the square of body length. But my concern was with cooling rate, or the rate at which an existing amount of thermal energy is lost to the surroundings. Since the quantity of thermal energy is proportional to the body mass, and the rate of energy loss is proportional to the body surface, the time required for cooling works out to be approximately proportional to the first power of body length

These seem to be two different questions.

The quantity of thermal energy doesn't matter, what matters is the rate of generation of thermal energy. Larger creatures that fall out of thermal equilibrium will change temperature slower than smaller creatures, but that doesn't particularly relate to maintaining thermal equilibrium.

[Varyon]

Originally Posted by whswhs

Since the quantity of thermal energy is proportional to the body mass...

Is it? It seems to me that the quantity of heat output over a given unit of time should scale linearly with the amount of energy in the food that must be consumed during that same time, unless larger animals turn more of their food calories into heat than smaller animals (and as I understand it, the opposite is more likely to be true). As the amount of fuel consumed scales as the square of height (and thus generally as the 2/3 power of weight), so too should the heat output.