I'm going to use two dinosaurs that we have somewhat complete skeletons and already established estimated weights from the paleontology community. Our comparable dinosaur is the Brachiosaurus for which we have a 100% complete skeleton.
I posted these both as part of the list in Reply #146. They are:
I selected them because they increase in size by exactly 5 meters and 10 meters in length over the Brachiosaurus which we will use as our comparable. They are also essentially proportional in build in every dimension to the Brachiosaurus, i.e. they are scaled up Brachiosaurs, which makes it easier to do.
For our purposes we will assume that all internal organs and spaces, such as gastro-instestinal tract, stomachs, bladders, and cysts, are also proportional in size to the brachiosaurus and that the density of bone, organs, and other body parts are essentially identical to the brachiosaurus' bones, organs, and body parts. This is a logical assumption as we find that modern animals who have variable sizing in a single species, such as birds, dogs, cats, horses, etc., have identical densities of those various organs, bones and body parts. Spaces within their bodies are also proportional to their sizes.
The Square Cube Law states that when you increase the size of 3 dimensional object, retaining its proportions in all dimensions, the surface area increases by the square (second power) of the multiplier and the volume enclosed by the increases by the cube (third power) of the multiplier. Since we are assuming no change in the density of the subjects' flesh, bone and spaces, the mass of the object is proportional to its volume and also increases by the cube (third power) of the multiplier.
Since our three dinosaurs are proportional, we can use any dimension we find to scale them. In this instance, we will use length. Our Brachiosaurus is 25 meters in length... and the next largest is the Argyrosaurus at 30 meters. The multiplier is therefore 30m/25m= 1.2. The Argyrosaurus is 1.2 times larger than the Brachiosaurus in every dimension because the two animals are proportionate.
Since we have a complete Brachiosaurus skeleton, scientists have been able to accurately calculate the mass of the bone, tissue, organs, and assumed internal spaces and have come up with an estimated weight for the Brachiosaurus of ~70,000 to ~90,000 lbs. (~31,750 to ~40,825Kg).
Using the Cube Square Law, the skin area of the Argyrosaurus is 1.22 times the skin area of the Brachiosaurus. 1.22 = a multiplier of 1.44 times for the skin area... or 44% more skin to radiate body heat.
What we are interested in, however, is the body mass... which would be 1.23 = 1.728 times the volume or the mass of the Brachiosaurus.
To find the lower weight estimate of the Argyrosaurus, we multiply the mass of the Brachiosaurus by 1.23 = ~70,000 Lbs X 1.728 = ~120,960 Lbs.To find the upper weight estimate of the Argyrosaurus, we multiply the mass of the Brachiosaurus by 1.23 = ~90,000 Lbs X 1.728 = ~155,520 Lbs.
Argyrosaurus Estimated weight = ~121,000 to ~156,000 Lbs. (~55,000 to 71,000 Kg.)
Moving to the Argentinasaurus.
We determine the size multiplier again using length: 35m/25m = 1.4. The Argentinasaurus is 1.4 times larger than the Brachiosaurus in every dimension because the two animals are proportionate.
Our skin area multiplier is 1.42 = 1.96 times the skin area of the Brachiosaurus... twice the skin area to radiate heat.
Again, to find the mass multiplier, we calculate 1.43 = 2.744 times the volume or the mass of the Brachiosaurus.
To find the lower weight estimate of the Argentinasaurus, we multiply the mass of the Brachiosaurus by 1.43 = ~70,000 Lbs. X 2.744 = ~192,080 Lbs.To find the upper weight estimate for Agentinasaurus, we multiply the mass of the Brachiosaurus by 1.43 = ~90,000 Lbs. X 2.744 = ~246,960 Lbs.
Argentinasaurus Estimated Weight - ~192,000 to 247,000 Lbs. (~87,000 to 112,000 Kg.)
As I mentioned in an earlier reply, paleontologists were so shocked at the figures they were getting using the Square Cube Law, they started fudging the figures downward to make them more acceptable to themselves and their colleagues... not very scientific, but what were they to do? Start asking uncomfortable questions about the viability of their subject animals??? In these instances they fudged their figures to around 25% to 40% less than the actual figures the math says they should be.
I am therefore 2.91 times taller than she is. Let's pretend I am 6 feet so we can avoid decimals. Now I am triple her height. Forgive me if I have misread your statements, but it appears that I would then be 27 times her body weight, or 486 pounds. This cannot be right, so I assume there is an error somewhere in here. Where have I made the error?
It worked for sparrows, didn't it? It works for humans, doesn't it?
Why not try it for critters whose length is largely determined by necks and tails?
A sane person, noting that assumptions about proportions and scaling lead to questionable answers, first thinks about adjusting assumptions.
But you, who are clever enough to equate the proportions of your seven foot fossil with that of a teratorn, are a world class expert on assumptions.