YACD":3akw3zdw said:
Maybe I can save Joe the trouble

The heat content of the coffee is proportional to its volume, and it loses heat at a rate proportional to its surface area. To conserve heat you would like a high ratio of volume to surface area, i.e. for a given volume the smallest possible surface area. The shape which solves this problem is a sphere, but I haven't noticed any spherical thermos jugs in WalMart. They are all cylinders so I guess we'd better look at that case. If the radius is R and the length is L the volume is proportional to L x R x R and the surface area is proportional to L x R. The ratio of volume to surface area is proportional to R so if you have 2 cylinders and the radius of one is half the radius of the other, the smaller radius one will be half as 'good' as the larger radius one. What if you keep the same radius and make the cylinder half the length? Then the two cylinders have the same ratio of volume to surface area and are in that sense equally 'good'. Maybe Joe can straighten me out on this but it seems that it is better to cut the cylinder perpendicular to its length to reduce it rather than reduce its radius. A shorter thermos would seem better than a longer one of the same volume.
All 100% correct! An A+ for your paper!
The ratio of volume to surface area is the absolute ruling factor for a given design.
Your explanation is as good as I can write from a mathematical point of view, and easy to follow for those with some math inclinations.
The same ratio of surface area to internal volume can be seen in animals. We'll use a deer as an example, at first.
A big deer from a northern climate like Maine and a small deer from Florida of the same species look to the casual observer to have the same body plan, proportions, and probable surface area ratio to internal volume, but not so!
The deer's internal dimensions, when multiplied, rise as a product of length times width, times height, or with the cube (third power) of the dimensions.
At the same time, the surface area of the deer rise as length times width, or with the square (second power) of the dimensions.
Thus larger deer have much more internal volume to generate and contain heat in proportion to their surface area. They generate more heat, and have less surface area through which to lose heat.
This accounts for why a deer of a given species may weigh 250 lbs in Maine, but it's same species cousin in Florida may weigh 90 lbs. There the same species, but natural selection on a local basis has selected the larger animal (with it's genes) to survive better in Maine's cold winter climates, whereas the Florida relative doesn't need this otherwise cumbersome size to tolerate the winter cold.
This same phenomena can be seen in most all animals. Think of the common arctic and near arctic animals: polar bears, walruses, whales, moose, caribou, musk oxes, giant brown bear, elephant seals, etc. All are very big to survive the cold arctic conditions, even considering migration habits.
The same thing happens during the ice ages. Animals evolve over the short term to survive the conditions. The wooly mamouths, saber tooth tigers, buffalo, wolves, and a host of other animals evolve over the 10,000 year or so period from smaller species to better survive the cold conditions, then when the Earth goes back through a warming cycle, the process reverses an they get smaller or are replaced by other smaller species.
Of course their are exceptions, but bigger animals survive better in colder climates.
Your 289 lb brother will have a much easier time staying warm in Nome, Alaska than you with your Charles Atlas reject 98 lb bag skin and bones.
Russian men seem to prefer very large, heavily built (warm) wives. With one of them and a healthy supply of vodka, the winter may just not be so hard to bear!
The Russian practice may not too bad a substitute, I guess, when central heating and cheap fuel are not readily available. Do you suppose that's a viable plan for Americans with the rising fuel/energy costs? :cocktail :cocktail :cocktail :crook
Joe. :teeth :thup