GURPS: Ecosystems and Evolution

[roguebfl]

Well if this doesn't find a home as an article/supplement it welcome a home over on the GURPS Wiki

[Diogenes]

Another good idea. Wyh didn't I bookmark this link?

[MagiMaster]

I still need some help converting a temperature gradient over an area to (maximum) watts, if anyone knows which equations I should be looking at.

Anyway, for mana, normal levels probably shouldn't be worth too much biomass, since it'd be in addition to the energy from sunlight in most places. Very high mana should probably be a little less than the maximum for sunlight, so a pitch black cave with very high mana will be about as lush as a rain forest or reef, but not as overgrown as a swamp. This would also mean that a swamp in a very high mana area will be oveflowing with life. Normal mana should probably not even support as much life as cultivated lands without some other energy source or it'd start to (more than) significantly raise the overall abundance of life.

Are there any other interesting energy sources I'm overlooking? Kinetic energy (in wind, water, whatever) sounds too far out there. Electricity, lightning specifically, might deserve a paragraph, even if it's already in watts.

(Note to self: add a paragraph about taking away energy sources.)

[Gizensha]

Originally Posted by MagiMaster

I still need some help converting a temperature gradient over an area to (maximum) watts, if anyone knows which equations I should be looking at.

Anyway, for mana, normal levels probably shouldn't be worth too much biomass, since it'd be in addition to the energy from sunlight in most places. Very high mana should probably be a little less than the maximum for sunlight, so a pitch black cave with very high mana will be about as lush as a rain forest or reef, but not as overgrown as a swamp. This would also mean that a swamp in a very high mana area will be oveflowing with life. Normal mana should probably not even support as much life as cultivated lands without some other energy source or it'd start to (more than) significantly raise the overall abundance of life.

Are there any other interesting energy sources I'm overlooking? Kinetic energy (in wind, water, whatever) sounds too far out there. Electricity, lightning specifically, might deserve a paragraph, even if it's already in watts.

(Note to self: add a paragraph about taking away energy sources.)

In some sci-fi universes, maybe psionic? (Thinking about Planet in Alpha Centauri here)

[MagiMaster]

I don't think that the psionic powers in Alpha Centaur actually fed the life there, just connected it. On the other hand, treating it like mana would be pretty easy.

Another question I need to write down: If you have four animals, A consumes its body weight per day, B is just like A but has trait X and consumes 3/4 its body weight, C is just like A but has the (non-conflicting) trait Y and also consumes 3/4, and D has traits X and Y. How much should D consume?

Let's see:
A has a modifier of 0.8
B has a modifier of 0.6
C has a modifier of 0.6
D probably has a modifier of either 0.4 or 0.45 (additive or multiplicative)

Hmm... I can't currently see any good reason to pick one over the other and I can't think of any RL animals that fit so nicely into the kind of lists I need.

[MagiMaster]

Well, rethinking the problem with converting heat to watts, I think I have a first draft of an answer. The Stefan-Boltzmann law says that a hot surface emits energy at a rate of emissivity * constant * (temperature in Kelvin)^4 in watts per sq. meter. The Carnot efficiency is the maximum theoretical efficiency a heat engine can attain, though the endoreversible efficiency gives slightly more reasonable numbers. Multiplying the two gives an answer that's not completely unreasonable, but may be somewhat too big. For a hot temperature of 200 F and a cold of 50 F, I get about 290,000,000 watts per sq. mile, which converts to about 9,500 lbs of biomass per day, which seems high. Either I've got the wrong equation, or there needs to be a conversion efficiency on top of everything else (1% - 5% probably).

Anyway, can someone else play with the equation a bit and see if there are any cases where it gives really obviously wrong results?

Th equation is: 5.67*10^-8 * e * Th^4 * (1 - sqrt(Tc/Th)) * 86
Where: e is emmisivity of the surface (0.9 is an average for rock), Th is the hot temperature in Kelvin and Tc is the cold temperature in Kelvin. (5.67*10^-8 is the Stefan-Boltzmann constant, and the 86 is converting watts per square meter to lbs of biomass per square mile per day.)

Edit: I can't decide if it'd be Th^4 to Tc^4. On one hand, the hot side is what's supplying the energy. On the other hand, if more energy is being transfered than what the cold side is radiating away, it wouldn't stay cold. Also, if you use Tc^4, lowering the cold temperature while keeping the hot the same would lower the power produced. I'm not sure that makes much sense.

Edit again: Oh yeah. My wife also mentioned adding belief to the list of energy sources. I'm not quite sure where to start with that one.

[Anthony]

Originally Posted by MagiMaster

I still need some help converting a temperature gradient over an area to (maximum) watts, if anyone knows which equations I should be looking at.

That's mostly not a useful value (it depends on the design of your heat engine); for any real source what matters is the rate at which the temperature gradient recreates itself when consumed, as the total energy of a reasonable temperature gradient is not large.

[MagiMaster]

I'm looking for the maximum possible wattage. I know that any real system will be below that. Anyway, how would I estimate how quickly the gradient is being consumed? I'm assuming that the temperatures don't actually change significantly over time, since it's stable enough for life to evolve around it.

(Note to self: Add a comment on energy cycles.)

[Anthony]

Originally Posted by MagiMaster

I'm looking for the maximum possible wattage.

Depends on the efficiency of thermal transport; theoretical max is insanely high.

Originally Posted by MagiMaster

Anyway, how would I estimate how quickly the gradient is being consumed?

You can assume that anything in an equilibrium state is consuming heat as quickly as the heat is generated. Thus, you really just need to figure out how fast the heat is being generated, and assume that the maximum percentage of that heat which can be captured to do useful work is equal to the carnot efficiency.

[MagiMaster]

If it's in equilibrium, then the heat generated and the heat radiated should be the same (though conduction is more efficient than radiation, which is what most hat engines would use). The Stefan-Boltzmann law gives heat radiated, and that's what I've got above. It still seems like I'm doing something wrong, but I can't figure out what.