Mimsey Borogrove
Crusader
So Bill, I went to this interesting site - and the author goes into a lot of science that, frankly is beyond me. You, if you read it, will find it very interesting if you like all manner of algebraic formulas. He goes through all the basic problems of large animals, the square cube law, scaling etc. and even discusses the possibility of the constant of gravity changing. I will cut and paste a few relevant sections and I apologize for the length of the post.
http://www.dinosaurtheory.com/index.html
"DinosaurTheory gives the solution to the paradox of how the dinosaurs and pterosaurs grew so large. Solving the large dinosaur paradox is an important scientific achievement and yet DinosaurTheory is much more than just a discussion about dinosaurs. This is because the large dinosaur paradox has existed for centuries so that now it is entangled with numerous other science incongruities and misconceptions and this has caused considerable confusion. All of this confusion needs to be sorted out so that science can move forward.
In explaining the solution to how the dinosaurs and pterosaurs grew so large, DinosaurTheory is actually a series of incredibly wonderful and scientifically correct solutions to numerous scientific paradoxes. Consider the fact that most people are unsure if size matters and so they are confused on whether the evidence of the exceptionally large terrestrial animals of the Mesozoic era is indeed a scientific paradox. Can objects be any arbitrary size? Understanding how size matters is actually one of the most fundamental concepts in all of science, but science teachers rarely teach this concept correctly and in turn scientists and engineers make countless mistakes as a consequence of the confusion brought on by the large dinosaur paradox. To give another example, what are the requirements for flight that show why it is illogical to believe that the large pterosaurs could have flown in an atmosphere similar to our present atmosphere? DinosaurTheory brings clarity to the flying pterosaur paradox by exploring the general requirements for all types of flight that includes both flying animals and airplanes. For a third example, when we consider that many millions of years ago the Earth's atmosphere may have been different, we should also wonder why Earth's present atmosphere - mostly nitrogen and oxygen - is so different from the atmospheres of all the other planets? Yet once we have the correct understanding of how planets evolve, the differences among the planets are no longer baffling but rather they make perfect sense. Each one of the solutions to these science paradoxes is an extremely significant scientific breakthrough, and yet within DinosaurTheory there is still much more."
He says this after several chapters discussing the problems of the size of dinosaurs:
"This gives us three possible variables that if one or more of these variables were to change then it could change the acceleration due to gravity. However, it is difficult to imagine how either the universal gravitational constant G, the mass of the Earth ME, or the radius of the Earth RE could have changed significantly between the Mesozoic era and the present. Both the physical evidence and simple calculations of what is physically possible confirm that none of these values could have significantly changed during the last hundred and fifty million years. But still, in the spirit of keeping an open mind, let us take a moment to investigate why none of these values could have changed by a significant amount over the last 150 million years.
There has actually been a suggestion that the universal gravity constant G could have changed. But as stated earlier, our preference would be to avoid hypothesizing a change in a fundamental property of science as a means of resolving a science paradox"
snip
"Nevertheless the author is going to rule that the changing gravitational constant hypothesis is not a realistic explanation for how the dinosaurs grew so large. Changes in the gravitational constant G that may, or may not, be possible over vast distances of billions of light years will not work to account for the huge change in the size of terrestrial animals that occurred on the Earth a mere hundred million years ago. Occam's razor directs us to toss out the changing gravitational constant hypothesis; for if we try to use the changing gravitational constant hypothesis to account for the large size of the dinosaurs this in itself creates so many unsolvable problems that it completely muddles our understanding of the laws of reality."
So - how does he solve the paradox of the size of dinosaurs?
"For terrestrial vertebrates, it is the net force produced by their weight that often limits their size. But this is not true for species that exist in the water. For the latter species it is not their weight but rather other factors, such as the availability of food that might limit the size of these species. Without the weight limitation some of these aquatic species grow to display gigantism. It is the buoyancy of water that allows the whales, the largest animals of today, to grow so large. Without this buoyancy to counteract gravity, the poor whale that finds itself stuck on a beach is soon having its bones broken from its own weight.
To produce an effective buoyancy force on dinosaurs the Earth's atmosphere would have to be thick enough to have a density comparable to the density of water. By summing the forces acting on a typical dinosaur such as a Brachiosaurus the density of the necessary atmosphere is calculated as:
ρF = ρS (1 - 1/S.F.)
Derivation of Fluid Density Equation
Fb + FN = Fg
V ρF g + m gef = m g
V ρF g + V ρS gef = V ρS g
ρF g + ρS gef = ρS g
(ρF - ρS)g = - ρS gef
ρF = ρS - ρS (gef/g)
ρF = ρS (1 - 1/S.F.)
where ρF is the density of the fluid, ρs is the density of the substance submerged in the fluid such as the dinosaur, and S.F is the scaling factor. Inserting into this equation a scaling factor of 3.2 and an overall vertebrate density of 970 kg/m3, the Earth's atmospheric density during the late Jurassic period can be calculated to be 670 kg/m3. This says that to produce the necessary buoyancy so that the dinosaurs could grow to their exceptional size, the density of the Earth’s air near the Earth’s surface would need to be 2/3’s of the density of water"
And what planet in our system has that sort of air density and is of a similar size to earth?
"To find the answer we look at Venus, the only planet today that comes close to modeling the Earth’s extremely thick Mesozoic atmosphere. Venus’ atmosphere and the Earth’s Mesozoic atmosphere are comparable in thickness since Venus’s is 91 times thicker and the Earth’s Mesozoic atmosphere was a few hundred times thicker than the Earth’s relatively thin present-day atmosphere. Another shared characteristic is the uniformity of the surface temperature regardless of latitude. Like the Mesozoic Earth, on Venus the surface temperature near its equator is only slightly higher than the surface temperature at either pole.
A primary reason there is almost no variation in temperature over the entire surface of Venus is because Venus has an extremely efficient atmospheric convection current system that uniformly distributes the radiation / thermal energy coming from the Sun. With such a thick atmosphere, there is only one convection cell in each hemisphere carrying the heat from the equator to the one or the other pole. This one cell system is much more effective than the Earth’s present-day three cell system in distributing heat from the lower latitudes to the higher latitudes.
Likewise it is reasonable that the Earth’s much thicker Mesozoic atmosphere would also form a one cell convection system that would be much more effective in transporting heat from the equator to the poles. Today’s atmosphere, being hundreds of times thinner, is compacted too close to the surface to maintain a thin one cell per hemisphere convection system stretching from the equator to each pole. So the thin present atmosphere forms a three cell convection system."
So, Bill, thanks for sending me on a quest that lead to a really much sounder conclusion than a change in the constant of gravity.
Mimsey
http://www.dinosaurtheory.com/index.html
"DinosaurTheory gives the solution to the paradox of how the dinosaurs and pterosaurs grew so large. Solving the large dinosaur paradox is an important scientific achievement and yet DinosaurTheory is much more than just a discussion about dinosaurs. This is because the large dinosaur paradox has existed for centuries so that now it is entangled with numerous other science incongruities and misconceptions and this has caused considerable confusion. All of this confusion needs to be sorted out so that science can move forward.
In explaining the solution to how the dinosaurs and pterosaurs grew so large, DinosaurTheory is actually a series of incredibly wonderful and scientifically correct solutions to numerous scientific paradoxes. Consider the fact that most people are unsure if size matters and so they are confused on whether the evidence of the exceptionally large terrestrial animals of the Mesozoic era is indeed a scientific paradox. Can objects be any arbitrary size? Understanding how size matters is actually one of the most fundamental concepts in all of science, but science teachers rarely teach this concept correctly and in turn scientists and engineers make countless mistakes as a consequence of the confusion brought on by the large dinosaur paradox. To give another example, what are the requirements for flight that show why it is illogical to believe that the large pterosaurs could have flown in an atmosphere similar to our present atmosphere? DinosaurTheory brings clarity to the flying pterosaur paradox by exploring the general requirements for all types of flight that includes both flying animals and airplanes. For a third example, when we consider that many millions of years ago the Earth's atmosphere may have been different, we should also wonder why Earth's present atmosphere - mostly nitrogen and oxygen - is so different from the atmospheres of all the other planets? Yet once we have the correct understanding of how planets evolve, the differences among the planets are no longer baffling but rather they make perfect sense. Each one of the solutions to these science paradoxes is an extremely significant scientific breakthrough, and yet within DinosaurTheory there is still much more."
He says this after several chapters discussing the problems of the size of dinosaurs:
"This gives us three possible variables that if one or more of these variables were to change then it could change the acceleration due to gravity. However, it is difficult to imagine how either the universal gravitational constant G, the mass of the Earth ME, or the radius of the Earth RE could have changed significantly between the Mesozoic era and the present. Both the physical evidence and simple calculations of what is physically possible confirm that none of these values could have significantly changed during the last hundred and fifty million years. But still, in the spirit of keeping an open mind, let us take a moment to investigate why none of these values could have changed by a significant amount over the last 150 million years.
There has actually been a suggestion that the universal gravity constant G could have changed. But as stated earlier, our preference would be to avoid hypothesizing a change in a fundamental property of science as a means of resolving a science paradox"
snip
"Nevertheless the author is going to rule that the changing gravitational constant hypothesis is not a realistic explanation for how the dinosaurs grew so large. Changes in the gravitational constant G that may, or may not, be possible over vast distances of billions of light years will not work to account for the huge change in the size of terrestrial animals that occurred on the Earth a mere hundred million years ago. Occam's razor directs us to toss out the changing gravitational constant hypothesis; for if we try to use the changing gravitational constant hypothesis to account for the large size of the dinosaurs this in itself creates so many unsolvable problems that it completely muddles our understanding of the laws of reality."
So - how does he solve the paradox of the size of dinosaurs?
"For terrestrial vertebrates, it is the net force produced by their weight that often limits their size. But this is not true for species that exist in the water. For the latter species it is not their weight but rather other factors, such as the availability of food that might limit the size of these species. Without the weight limitation some of these aquatic species grow to display gigantism. It is the buoyancy of water that allows the whales, the largest animals of today, to grow so large. Without this buoyancy to counteract gravity, the poor whale that finds itself stuck on a beach is soon having its bones broken from its own weight.
To produce an effective buoyancy force on dinosaurs the Earth's atmosphere would have to be thick enough to have a density comparable to the density of water. By summing the forces acting on a typical dinosaur such as a Brachiosaurus the density of the necessary atmosphere is calculated as:
ρF = ρS (1 - 1/S.F.)
Derivation of Fluid Density Equation
Fb + FN = Fg
V ρF g + m gef = m g
V ρF g + V ρS gef = V ρS g
ρF g + ρS gef = ρS g
(ρF - ρS)g = - ρS gef
ρF = ρS - ρS (gef/g)
ρF = ρS (1 - 1/S.F.)
where ρF is the density of the fluid, ρs is the density of the substance submerged in the fluid such as the dinosaur, and S.F is the scaling factor. Inserting into this equation a scaling factor of 3.2 and an overall vertebrate density of 970 kg/m3, the Earth's atmospheric density during the late Jurassic period can be calculated to be 670 kg/m3. This says that to produce the necessary buoyancy so that the dinosaurs could grow to their exceptional size, the density of the Earth’s air near the Earth’s surface would need to be 2/3’s of the density of water"
And what planet in our system has that sort of air density and is of a similar size to earth?
"To find the answer we look at Venus, the only planet today that comes close to modeling the Earth’s extremely thick Mesozoic atmosphere. Venus’ atmosphere and the Earth’s Mesozoic atmosphere are comparable in thickness since Venus’s is 91 times thicker and the Earth’s Mesozoic atmosphere was a few hundred times thicker than the Earth’s relatively thin present-day atmosphere. Another shared characteristic is the uniformity of the surface temperature regardless of latitude. Like the Mesozoic Earth, on Venus the surface temperature near its equator is only slightly higher than the surface temperature at either pole.
A primary reason there is almost no variation in temperature over the entire surface of Venus is because Venus has an extremely efficient atmospheric convection current system that uniformly distributes the radiation / thermal energy coming from the Sun. With such a thick atmosphere, there is only one convection cell in each hemisphere carrying the heat from the equator to the one or the other pole. This one cell system is much more effective than the Earth’s present-day three cell system in distributing heat from the lower latitudes to the higher latitudes.
Likewise it is reasonable that the Earth’s much thicker Mesozoic atmosphere would also form a one cell convection system that would be much more effective in transporting heat from the equator to the poles. Today’s atmosphere, being hundreds of times thinner, is compacted too close to the surface to maintain a thin one cell per hemisphere convection system stretching from the equator to each pole. So the thin present atmosphere forms a three cell convection system."
So, Bill, thanks for sending me on a quest that lead to a really much sounder conclusion than a change in the constant of gravity.
Mimsey
