Replies

Swordmaker: "No, that is UNTRUE. The muscular structure required to support and MOVE those wings is also a requirement you repeatedly ignore."

"Required" by who, your cockamamie scientific "laws" or by creatures who actually flew?

Swordmaker: "That is what the cube/square law is about.
Yes, you can increase the size of the wing, but then it WON'T BE THE SAME STRUCTURE AS A MODERN EAGLE!
The shape of the bird would be different.
As one increases the sail area, the muscle size must increase by the cube of the square area of the wing."

First of all, your "cube/square law" must be considered as baloney-to-the-max, since your presentation of it consists 100% of assertion-insult followed by more assertion-insults.
There's no "proof" in anything you've said.

Second, there's no scientific "law" which says the avian wing-load of 5 lbs. per square foot stops functioning beyond 30 pounds, or 50 pounds.
Since it's basically the same limit as hang-gliders and ultra-light aircraft, there's no upper weight limit.

Yes, of course, I "get" your idea that a bird's (or pterosaur's) body size might grow faster than its wing area.
To make your argument for you, you claim that:

if a 25 pound bird needs 5 square-feet of wing-lift area, and accomplishes this with wings 10 feet long and half a foot wide, and
if it needed to grow wings 15 feet long by one foot wide, to lift a higher body-weight of 75 lbs -- you claim that
by the time its wings grew from 10 to 15 feet, its body-weight must absolutely necessarily, according to some mythological "cube/square law" you fanaticize, the bird's weight must be more than 75 lbs.

Sure I "get" that, but its rubbish for at least the following reasons:

You have not proof that your alleged "cube/square law" effectively limits sizes of any animals, and fossil evidence shows it does not.
Your "cube/square law" cannot predict what the weight (in the example above) of a 15 foot wing-span bird must be.
All actual scientific estimates of prehistoric flying-creature weights fall within the 5 lbs. per square-foot of wing-load limit.
You cannot "prove" any of those estimates wrong.

I therefore conclude that you folks are simply advocates of an anti-science agenda, motivated more by theology than any serious interest in finding natural explanations for natural processes.

Swordmaker: "The teratorn fossil structure was essentially a scaled up eagle without oversized wings.
You can theorize oversized wings all you want but they weren't there and neither were the muscles"

In fact, your claim here notwithstanding: large teratorns like Argentavis are the very definition of "scaled up" and "oversized wings".
And in all cases, the scientific estimates of wing-size versus body-weight obey the 5 lbs. per spare-foot of wing rule.
So, why and how you fanaticize that your alleged "cube/square rule" overrules the simple wing-load is beyond rational comprehension.

Swordmaker: "Nor were the muscles in the dinosaurs capable of swinging or lifting a cantilevered neck using bone and sinew as the structural materials. . . the engineering math simply doesn't work."

Sure, I "get" that this was a problem from the beginning, over 100 years ago.
That's why, many years ago, sauropods were often pictured mostly under water.
And I'm still not convinced there's anything particularly wrong with that -- consider nostrils on top.
Today they are always portrayed out-of-water, with head and tail counterbalanced parallel to the ground, not reaching (much less rearing) up for high branches.

Bottom line: there's no evidence, certainly none presented on this thread, which "proves" that your alleged "cube/square law" magically limits the sizes of prehistoric beasts to that of modern elephants.

Since your math doesn't work, obviously your math is wrong.
Time for you to reexamine your ridiculous assumptions.

Out of time, must run...

You know, BroJoeK? The only one here that is throwing insults around is YOU.

I just inquired with two men here in my office. . . Both with doctorates. They both defined the square-cube law exactly as I have to you. When I told them that you described it as "cockamamie" and "baloney-to-the-max" they both started laughing uproariously and said you were ignorant of basic math AND science. I agree. You are ignorant. . . and apparently willfully so. Good thing ignorance, unlike stupidity, is curable.

Let's find out exactly how "unscientific" and "cockamamie" the square-cube law is, shall we? By the way, although it was more that forty years ago, I tutored in Physics and Math in college as an honors student in those subjects before I changed my major to Economics. The undergraduate Biology courses I took also covered how the Square-cube applied in that field. But let's look. . .

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First, let's define exactly what is a "scientific law?" It is a precise meaning, separate from a hypothesis or a theory.

"A scientific law is a statement based on repeated experimental observations that describes some aspect of the world. A scientific law always applies under the same conditions, and implies that there is a causal relationship involving its elements. Factual and well-confirmed statements like "Mercury is liquid at standard temperature and pressure" are considered too specific to qualify as scientific laws. A central problem in the philosophy of science, going back to David Hume, is that of distinguishing causal relationships (such as those implied by laws) from principles that arise due to constant conjunction.[1]
Laws differ from scientific theories in that they do not posit a mechanism or explanation of phenomena: they are merely distillations of the results of repeated observation. As such, a law is limited in applicability to circumstances resembling those already observed, and may be found false when extrapolated. Ohm's law only applies to linear networks, Newton's law of universal gravitation only applies in weak gravitational fields, the early laws of aerodynamics such as Bernoulli's principle do not apply in case of compressible flow such as occurs in transonic and supersonic flight, Hooke's law only applies to strain below the elastic limit, etc. These laws remain useful, but only under the conditions where they apply.
Many laws take mathematical forms, and thus can be stated as an equation; for example, the Law of Conservation of Energy can be written as (Equations omitted because my iPad doesn't have the font. You can find them at the link. — Swordmaker).
The term "scientific law" is traditionally associated with the natural sciences, though the social sciences also contain laws.[2] An example of a scientific law in social sciences is Zipf's law.
Like theories and hypotheses, laws make predictions (specifically, they predict that new observations will conform to the law), and can be falsified if they are found in contradiction with new data."

Second, what about is the square-cube law? Per Wikipedia:

"The square-cube law (or cube-square law) is a mathematical principle, applied in a variety of scientific fields, which describes the relationship between the volume and the area as a shape's size increases or decreases. It was first described in 1638 by Galileo Galilei in his Two New Sciences.
This principle states that, as a shape grows in size, its volume grows faster than its area. When applied to the real world this principle has many implications which are important in fields ranging from mechanical engineering to biomechanics. It helps explain phenomena including why large mammals like elephants have a harder time cooling themselves than small ones like mice, and why building taller and taller skyscrapers is increasingly difficult."
(Mathematical formulation of Square-Cube Law omitted — Swordmaker)
"When an object undergoes a proportional increase in size, its new surface area is proportional to the square of the multiplier and its new volume (and consequently its mass—Swordmaker) is proportional to the cube of the multiplier."
Engineering
"When a physical object maintains the same density and is scaled up, its mass is increased by the cube of the multiplier while its surface area only increases by the square of said multiplier. This would mean that when the larger version of the object is accelerated at the same rate as the original, more pressure would be exerted on the surface of the larger object.
Let us consider a simple example of a body of mass, M, having an acceleration, a, and surface area, A, . . . (Math omitted — Swordmaker)
Thus, just scaling up the size of an object, keeping the same material of construction (density), and same acceleration, would increase the thrust by the same scaling factor. This would indicate that the object would have less ability to resist stress and would be more prone to collapse while accelerating.
This is why large vehicles perform poorly in crash tests and why there are limits to how high buildings can be built. Similarly, the larger an object is, the less other objects would resist its motion, causing its deceleration.
Engineering examples

Steam engine: James Watt, working as an instrument maker for the University of Glasgow, was given a scale model Newcomen steam engine to put in working order. Watt recognized the problem as being related to the square-cube law, in that the surface area of the model's cylinder surface to volume ratio was greater than the much larger commercial engines, leading to excessive heat loss.[1] Experiments with this model led to Watt's famous improvements to the steam engine.
Airbus A380: the lift and control surfaces (wings, rudders and elevators) are relatively big compared to the fuselage of the airplane. In, for example, a Boeing 737 these relationships seem much more 'proportional', but designing an A380 sized aircraft by merely magnifying the design dimensions of a 737 would result in wings that are too small for the aircraft weight, because of the square-cube rule.
A clipper needs relatively more sail surface than a sloop to reach the same speed, meaning there is a higher sail-surface-to-sail-surface ratio between these crafts than there is a weight-to-weight ratio.
Biomechanics
If an animal were isometrically scaled up by a considerable amount, its relative muscular strength would be severely reduced, since the cross section of its muscles would increase by the square of the scaling factor while its mass would increase by the cube of the scaling factor. As a result of this, cardiovascular and respiratory functions would be severely burdened.
In the case of flying animals, the wing loading would be increased if they were isometrically scaled up, and they would therefore have to fly faster to gain the same amount of lift. Air resistance per unit mass is also higher for smaller animals, which is why a small animal like an ant cannot be seriously injured from impact with the ground after being dropped from any height.
As was elucidated by J. B. S. Haldane, large animals do not look like small animals: an elephant cannot be mistaken for a mouse scaled up in size. This is due to allometric scaling: the bones of an elephant are necessarily proportionately much larger than the bones of a mouse, because they must carry proportionately higher weight. To quote from Haldane's seminal essay On Being the Right Size, "...consider a man 60 feet high...Giant Pope and Giant Pagan in the illustrated Pilgrim's Progress.... These monsters...weighed 1000 times as much as Christian. Every square inch of a giant bone had to support 10 times the weight borne by a square inch of human bone. As the human thigh-bone breaks under about 10 times the human weight, Pope and Pagan would have broken their thighs every time they took a step." Consequently, most animals show allometric scaling with increased size, both among species and within a species.
The giant monsters seen in horror movies (e.g., Godzilla or King Kong) are also unrealistic, as their sheer size would force them to collapse. However, the buoyancy of water negates to some extent the effects of gravity. Therefore, sea creatures can grow to very large sizes without the same musculoskeletal structures that would be required of similarly sized land creatures, and it is no coincidence that the largest animals to ever exist on earth are aquatic animals."

The above citations are from Wikipedia, but since you've been using that, I decided it should suffice. . . however, there are literally thousands of others on the scientific basis of the square-cube LAW, which is neither, how did you put it? Oh, yes, "unscientific" and "cockamamie." It is YOU, BroJoeK, that is ignorant of science that seems to not understand science.

We have the almost complete skeletons of Argentine Teratorns that, while essentially identical in structure to modern Eagles and Condors, are three times their size... and 27 times their mass... with wings and wing musceles that are no larger proportionately to their size than those of their smaller, modern cousins. We know the size of the muscles by the stress points and anchorages on the bones.

A 7 foot tall Teratorn skeleton found in Argentina, Its flight feathers would have been 5 feet long. California Teratornis Meriami, found in the La Brea Tarpit. It's 1/3rd larger than the largest California Condor. 1.333=2.35 X 23 lbs Condor weight = Merriam's Teratorn weight of ~54 Lbs. (But this weight calculation ignored the Square-Cube Law and was incorrectly made just by proportion increase.— Swordmaker)

Calculations have been done by Ornithologists working with Aeronautical Engineers on the power the Argentavis magnificens had available to it under modern conditions (the only one's the team of scientists who did the calculations even considered — Swordmaker) to maintain level flight under 1G. They found that the Teratorn would require 600 Watts of continuous aerobic power just to maintain level flight... but they calculated the theoretical maximum power the bird could generate with its muscles (using extremely conservative estimates for its mass, and extremely liberal estimates for its wing area and flight muscle mass) was only 170 Watts. (Oops. It couldn't sustain level flight under 1G conditions! — Swordmaker)

In addition, it was calculated that their ideal Argentavis magnificens' stall speed for landing was 39 Mph... far too fast for a safe landing... and its take off speed with no headwind required the bird, whom ornithologists say was not well designed for running, to run at 39 mph... for ~100 feet down a 10º slope to gain air speed and lift and then hope it finds an 300 foot diameter continuous updraft of at least 3 feet per second to use to climb before it crashes back to the ground. Of course if our hypothetical bird were lucky, and if found an obliging headwind, it could run a bit slower or for a lesser distance. An alternative method to get into the air required the bird to climb up a >65 foot tree or cliff and jump off into a 5 mph head wind and hope to level off before hitting the ground... and THEN, again, find an large updraft. . . All the while avoiding hungry, ground based predators.

Strangely, while some Argentavis magnificens skeletons have been found in the Andes, the majority have been found on the Pampas... flat, level, treeless plains. (Again, oops... how does it get airborne? Sounds to me like an awful lot of luck and ideal conditions was needed to get this over sized, over weight bird into the air.— Swordmaker)

Other scientists were able to get the Merriam's Teratorn, a much smaller bird, into simulated flight... but to do it they assumed that the bird, 1/3rd larger then the California Condor, also weighed only 1/3rd more than the Condor! That is totally ignoring the Square Cube Law—which they are apparently familiar with—because they DID multiply the wing area of the Teratorn by the square of the size multiplier but didn't multiply the mass by the CUBE of the size multiplier... Why not? Did they think that the Teratorn's muscles and bones were 2.35 times lighter or more efficient than a Condor's? Most likely they fudged because that's what it would take to keep the mass only 1/3rd more. In other words, they cheated.