I don't understand square law of thermal dissipation

[UnluckyKate]

Square law is a square factor for size increase and cube factor for volume increase.

For an animal, its size influence its heat dissipation.

Take a one cm long animal. Now scale it up to one meter long. That's a 100 times increase in lenght, but a 100 square in surface and 100 cube in volume.


But i dont get it. A larger animal would have much more surface to dissipate heat. Yet, smaller animal eat up to their weight in food in a day when giant mammal eat only 2 to 7% of their weight per day.

Why smaller animal loose heat so much faster and need so much more energy to keep up when their surface dissipation should be so much lower than larger animals.

 

[John Dunbar]

ask questions like this and they'll kick you out of the matrix

 

[neon/drifter]

I think it's less about size/mass and more about circulatory systems?

 

[SteveWinwood]

they have more surface area yes but that's not what matters

it's about the ratio between that and the volume which goes down as the size increases

cubing gets bigger faster than squaring. by a lot

 

[Anoregon]

the chonker holds in the hot juice

 

[ajszenk]

Me either dude.

 

[Deleted member 4367]

Surface area ratios tend to get worse the larger something gets.

 

[BLEEN]

Gravity, mostly.

 

[RiOrius]

Why smaller animal loose heat so much faster and need so much more energy to keep up when their surface dissipation should be so much lower than larger animals.

Click to shrink...

Their absolute surface dissipation is lower, but their surface dissipation relative to volume is much higher. So their absolute food intake is lower, but their food intake relative to volume is higher.

 

[Doukou]

Because the smaller you are the higher the ratio from surface area to mass is. So a bigger animal that weighs a ton only could have like a 1 to 1 ratio and require less than 5% of weight to cover that heat. While a smaller animal with 50 to 1 ratio when needed 250% of their weight to cover their surface area.

Also this isn't true for cold blooded animals. A snake can live off a rat for awhile

 

[Dolobill]

I understand why people with struggle with this, but the reason is because in your mental reasoning of scaling up an object to a larger size, you are also erroneously scaling up the units of measurement. Allow me to explain:

Compare a 1mm diameter sphere to a 1m sphere.

1mm Dia. Sphere
Surface Area = 3.14 mm2
Volume = 0.52 mm3
Ratio of Surface to Volume = 157:26

1m Dia. Sphere
Surface Area = 3.14 m2
Volume = 0.52m3
Ratio of Surface to Volume = 157:26

The reason the above is the same, is because we scaled the unit of measurement by the same amount as the diameter. We know that for a correct comparison, we need to compare millimeters to millimeters, not millimeters to meters.

Let's try again:

1mm Dia. Sphere
Surface Area = 3.14 mm2
Volume = 0.52 mm3
Ratio of Surface to Volume = 157:26

1m Dia. Sphere
Surface Area = 3140 mm2
Volume = 524,000,000 mm3
Ratio of Surface to Volume = 157:2,600,000

Clearly, when you use the right units, the ratio of surface changes accordingly. The reason is because the surface is scaled by a squared factor while the volume is scaled by a cubed factor.

Now when talking about living things, our "unit" is a cell. For the sake of argument, assume the cells of all mammals are roughly the same size. The square law of thermal dissipation should make more sense if you think of it like our millimeter to millimeter sphere example.

A larger animal would have much more surface to dissipate heat. Yet, smaller animal eat up to their weight in food in a day when giant mammal eat only 2 to 7% of their weight per day.

Click to shrink...

You have it in reverse. The larger animal has a much smaller surface to volume ratio.

 

[Lishi]

It's always help to put some number example when you find something hard to grasp

an square animal (for simplicity)
of size 1x1x1
will have 1 unit of volume and 6 unit of surface.
something of 10x10x10
will have 1000 unit of volume and 600 unit of surface.

so let's suppose that 1 unit of volume produce 1 unit of energy

This mean that the 1x1x1 have 6 unit of surface to dissipate 1 unit of energy a ratio of 6/1

the 10x10x10 instead will have 600 unit of surface to dissipate 1000 of energy a ratio of 6/10.

 

[Hecht]

Your problem is that you're using uniform measu---

I understand why people with struggle with this, but the reason is because in your mental reasoning of scaling up an object to a larger size, you are also erroneously scaling up the units of measurement. Allow me to explain:

Compare a 1mm diameter sphere to a 1m sphere.

1mm Dia. Sphere
Surface Area = 3.14 mm2
Volume = 0.52 mm3
Ratio of Surface to Volume = 157:26

1m Dia. Sphere
Surface Area = 3.14 m2
Volume = 0.52m3
Ratio of Surface to Volume = 157:26

The reason the above is the same, is because we scaled the unit of measurement by the same amount as the diameter. We know that for a correct comparison, we need to compare millimeters to millimeters, not millimeters to meters.

Let's try again:

1mm Dia. Sphere
Surface Area = 3.14 mm2
Volume = 0.52 mm3
Ratio of Surface to Volume = 157:26

1m Dia. Sphere
Surface Area = 3140 mm2
Volume = 524,000,000 mm3
Ratio of Surface to Volume = 157:2,600,000

Clearly, when you use the right units, the ratio of surface changes accordingly. The reason is because the surface is scaled by a squared factor while the volume is scaled by a cubed factor.

Now when talking about living things, our "unit" is a cell. For the sake of argument, assume the cells of all mammals are roughly the same size. The square law of thermal dissipation should make more sense if you think of it like our millimeter to millimeter sphere example.



You have it in reverse. The larger animal has a much smaller surface to volume ratio.

Click to shrink...

yeah this guy gets it

 

[UnluckyKate]

I understand why people with struggle with this, but the reason is because in your mental reasoning of scaling up an object to a larger size, you are also erroneously scaling up the units of measurement. Allow me to explain:

Compare a 1mm diameter sphere to a 1m sphere.

1mm Dia. Sphere
Surface Area = 3.14 mm2
Volume = 0.52 mm3
Ratio of Surface to Volume = 157:26

1m Dia. Sphere
Surface Area = 3.14 m2
Volume = 0.52m3
Ratio of Surface to Volume = 157:26

The reason the above is the same, is because we scaled the unit of measurement by the same amount as the diameter. We know that for a correct comparison, we need to compare millimeters to millimeters, not millimeters to meters.

Let's try again:

1mm Dia. Sphere
Surface Area = 3.14 mm2
Volume = 0.52 mm3
Ratio of Surface to Volume = 157:26

1m Dia. Sphere
Surface Area = 3140 mm2
Volume = 524,000,000 mm3
Ratio of Surface to Volume = 157:2,600,000

Clearly, when you use the right units, the ratio of surface changes accordingly. The reason is because the surface is scaled by a squared factor while the volume is scaled by a cubed factor.

Now when talking about living things, our "unit" is a cell. For the sake of argument, assume the cells of all mammals are roughly the same size. The square law of thermal dissipation should make more sense if you think of it like our millimeter to millimeter sphere example.



You have it in reverse. The larger animal has a much smaller surface to volume ratio.

Click to shrink...

the thing is, I dont get what the volume does to the heat dissipation ?

 

[kami_sama]

the thing is, I dont get what the volume does to the heat dissipation ?

Click to shrink...

Because the thing that generates heat is the cells inside the body, more volume, more cells, more heat, and the volume increases with the cube, while the surface, what dissipates heat only increases with the square.

 

[Psittacus]

Because the thing that generates heat is the cells inside the body, more volume, more cells, more heat, and the volume increases with the cube, while the surface, what dissipates heat only increases with the square.

Click to shrink...

Heat capacity is proportional to volume too, so a larger animal's temperature is more stable

 

[UnluckyKate]

Heat capacity is proportional to volume too, so a larger animal's temperature is more stable

Click to shrink...

ah, this makes sens thanks all

 

[kami_sama]

Heat capacity is proportional to volume too, so a larger animal's temperature is more stable

Click to shrink...

Heat capacity is just the amount of energy a kg of some material needs to increase in temperature by one degree celsius.
Increasing the volume doesn't increase the heat capacity, it increases the energy required to increase the temperature for the whole animal's body.
The only thing you're changing is the ratio between area and volume.

 

[Psittacus]

Heat capacity is just the amount of energy a kg of some material needs to increase in temperature by one degree celsius.
Increasing the volume doesn't increase the heat capacity, it increases the energy required to increase the temperature for the whole animal's body.
The only thing you're changing is the ratio between area and volume.

Click to shrink...

You're thinking of specific heat capacity. Total heat capacity is what I was talking about and you mentioned in your response.

 

[seki]

they have more surface area yes but that's not what matters

it's about the ratio between that and the volume which goes down as the size increases

cubing gets bigger faster than squaring. by a lot

Click to shrink...

Incidentally, this is also more or less the prevailing theory in the modern NBA.

 

[cakely]

Larger animals have a much larger ratio of internal volume / external skin surface.

 

[Dennis8K]

Larger animals have a much larger ratio of internal volume / external skin surface.

Click to shrink...

This. Simple, no?

 

[julia crawford]

Now that the OP was answered someone explain magnets please

 

[Meauxse]

We see this in ships going from tow tank scale to real life. While surface area and volume can parametrically scale, other parameters, such as your thermal changes, cannot be scaled as such and have specific equations.

Heat dissipation is not solely a surface area issue. Scaled animal does not have the same thermal coefficient as its technically the same makeup but the arrangement differs. In addition, greater depth of material to heat source.

 

[Aureon]

Now that the OP was answered someone explain magnets please

Click to shrink...

They're magic.

 

[Hrothgar]

Now that the OP was answered someone explain magnets please

Click to shrink...

Tide goes in, tide goes out. You can't explain that!

 

[cakely]

Now that the OP was answered someone explain magnets please

Click to shrink...

Fucking magnets, how do they work?

 

[Cow Mengde]

OP, are you looking into gigantothermy?

Gigantothermy - Wikipedia

en.wikipedia.org

Basically, you're looking at the outside surface of the animal, but forgetting about the inside. Imagine it in layers. If the animal is big on the outside, it also has many many layers of fat, muscle and tissue underneath its skin.