Regarding the subject whether the really large dinosaurs, Sauropods, were warm-blooded or cold-blooded, there seems to be a consideration which needs to be considered that may not previously been discussed. The Rate of Metabolism and the relative size of the mouth must be proportionate. Any warm-blooded animal MUST eat (ingest) sufficient food to provide both functional energies of the various organs, muscles and other components, and also provide enough energy to replace the thermal heat losses from the (warm) skin to a cooler environment.
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Consider an African Elephant. They weigh around 8 tons, 16,000 pounds, and each day they must find and eat around 500 pounds (230 kg) of food. They are relatively slow-moving animals that would have difficulty in catching any animals for food, and both actual observational evidence and the shape of their teeth confirm that they are exclusively plant-eaters. The need to find and eat 500 pounds of plants every day means that eating is nearly a full-time activity.
Now consider a Diplodocus, a large sauropod dinosaur that weighed around 11 tons or so, more than a dozen times the weight of a horse or cow. However, their skull and mouth are of a size that are comparable to that of a horse or cow. It was a very large animal, with around twice the surface skin area of an African Elephant. That means that as a warm-blooded animal, roughly twice the heat radiation and convection would have occurred from the skin. That implies that possibly twice as much food might have had to have been eaten every day for survival, on the order of 1000 of plants every day.
The question should occur: Could a warm-blooded Diplodocus have been able to eat enough food to provide all the necessary energy? It seems somewhat unlikely! Fairly simple math calculations suggest that even if it ate continuously during all waking hours, and the availability of plants was unlimited, there are just not enough hours in a day for such a small mouth to have eaten and chewed sufficient food. Each of the cells in that much more massive Diplodocus body also would have needed to use energy for normal bodily processes, such as using the Krebs' Cycle within each cell. In addition, the rather large surface area of the Diplodocus (around 30 times or more of that of a horse) means that the lost radiative and convective heat energy from the skin would also be 30 or more times as high as for a horse of the same body temperature.
When estimates for the numbers are used, it seems unlikely that a Diplodocus, with its smallish head and mouth, could possibly ingest enough plant material to provide all the required energies. Examination of the teeth have convinced all experts that the sauropods (including Diplodocus) were all plant-eaters. Therefore, there seems to be a potential problem in thinking that they were warm-blooded.
There is actually an alternate possibility which resolves this issue. IF the Diplodocus existed nearly continuously within WARM shallow water or swamp, then the thermal analysis becomes compatible with the size of its mouth and the surface area of its skin. In fact, an estimate for the temperature of the water or swamp can be made from this analysis based on the size of its mouth and thermodynamic energy flow analysis.
This all seems to eliminate those large sauropods from being warm-blooded, UNLESS the environment was EXTREMELY warm! IF the air around a Diplodocus was consistently within a few degrees of its internal body temperature, the amount of radiative heat losses might have been small enough to permit a warm-blooded energy balance. If that were not the case, it seems that this might be a strong argument that they had to be cold-blooded!
However, like the Diplodocus comments above, if an Apatosaurus lived nearly continuously within warm water or a warm swamp, metabolism of being warm-blooded becomes compatible with the small size of its mouth.
It seems surprising that no researcher seems to have ever examined this subject area. The simplest of energy audits of an Apatosaurus shows that the size of mouth is not remotely large enough to ingest sufficient food energy to maintain skin temperatures of warm-blooded animals as land-dwelling creatures. Extremely thick blubber can represent some thermal insulation, as in walruses, but there still seems to be a serious logical problem in claiming both land-dwelling and warm-blooded for a creature such as an Apatosaurus on land, given the very small mouth size.
In contrast, much smaller dinosaurs like T. Rex had very large mouths. Part of that was to enable chewing and swallowing large prey animals, due to being a carnivore or omnivore, but the difference in mouth sizes between most sauropods and other dinosaurs is striking.
Cold-blooded metabolism seems to have had a significant survival advantage for some such animals. Similarly, if they spent much of their existence in WARM swamps or ponds (for partial flotation) then the heat losses from that very large area of skin may have been less because of the warmth of the water and the consistency of the water temperature in any large ocean or sea, possibly requiring less consumption of plants. This reasoning might fit in with a swamp environment, as that WOULD have had the essentially unlimited supply of plants to eat.
However a FRESHWATER pond or swamp may have been small such that its temperature could have varied significantly, representing a severe danger of survival for such warm-blooded animals. This might all suggest that IF really large sauropods such as Apatosaurus were warm-blooded animals, they may have had to live in very large water supplies regarding a more consistent water temperature, which might then imply that it was a saltwater sea or ocean or swamp.
Sauropod Dinosaur Physics Subjects. A logical discussion of several poor assumptions regarding dinosaurs
Sauropod Dinosaur Mouth Analysis Regarding Cold-/Warm-Blooded The size of dinosaurs' mouths and the capability to be warm-blooded
Sauropod Dinosaur Neck Physics Analysis The strength of neck bones, muscles and tendons in dinosaurs
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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago