Galileo Galilei asked himself the question: Why are mammals as large as they are and not much larger? He had a very clever reasoning which I've never seen in print.
But it comes down to the fact that he argued that if the mammal becomes too massive that the bones will break and he thought that that was a limiting factor.
Even though I've never seen his reasoning in print I will try to reconstruct it what could have gone through his head.
Here is a mammal.
And this is one of the four legs of the mammal.
And this mammal has a size S.
And what I mean by that is a mouse is yay big and a cat is yay big.
That's what I mean by size--
very crudely defined.
The mass of the mammal is M and this mammal has a thigh bone which we call the femur, which is here.
And the femur of course carries the body, to a large extent.
And let's assume that the femur has a length l and has a thickness d.
Here is a femur.
This is what a femur approximately looks like.
So this will be the length of the femur...
and this will be the thickness, d and this will be the cross-sectional area A.
I'm now going to take you through what we call in physics a scaling argument.
I would argue that the length of the femur must be proportional to the size of the animal.
That's completely plausible.
If an animal is four times larger than another you would need four times longer legs.
And that's all this is saying.
It's very reasonable.
It is also very reasonable that the mass of an animal is proportional to the third power of the size because that's related to its volume.
And so if it's related to the third power of the size it must also be proportional to the third power of the length of the femur because of this relationship.
Okay, that's one.
Now comes the argument.
Pressure on the femur is proportional to the weight of the animal divided by the cross-section A of the femur.
That's what pressure is.
And that is the mass of the animal that's proportional to the mass of the animal divided by d squared because we want the area here, it's proportional to d squared.
Now follow me closely.
If the pressure is higher than a certain level the bones will break.
Therefore, for an animal not to break its bones when the mass goes up by a certain factor let's say a factor of four in order for the bones not to break d squared must also go up by a factor of four.
That's a key argument in the scaling here.
You really have to think that through carefully.
Therefore, I would argue that the mass must be proportional to d squared.
This is the breaking argument.
Now compare these two.
The mass is proportional to the length of the femur to the power three and to the thickness of the femur to the power two.
Therefore, the thickness of the femur to the power two must be proportional to the length l and therefore the thickness of the femur must be proportional to l to the power three-halfs.
A very interesting result.
What is this result telling you? It tells you that if I have two animals and one is ten times larger than the other then S is ten times larger that the lengths of the legs are ten times larger but that the thickness of the femur is 30 times larger because it is l to the power three halves.
If I were to compare a mouse with an elephant an elephant is about a hundred times larger in size so the length of the femur of the elephant would be a hundred times larger than that of a mouse but the thickness of the femur would have to be 1,000 times larger.
And that may have convinced Galileo Galilei that that's the reason why the largest animals are as large as they are.
Because clearly, if you increase the mass there comes a time that the thickness of the bones is the same as the length of the bones.
You're all made of bones and that is biologically not feasible.
And so there is a limit somewhere set by this scaling law.
Well, I wanted to bring this to a test.
After all I brought my grandmother's statement to a test so why not bring Galileo Galilei's statement to a test? And so I went to Harvard where they have a beautiful collection of femurs and I asked them for the femur of a raccoon and a horse.
A raccoon is this big a horse is about four times bigger so the length of the femur of a horse must be about four times the length of the raccoon.
Close.
So I was not surprised.
Then I measured the thickness, and I said to myself, "Aha!" If the length is four times higher then the thickness has to be eight times higher if this holds.
And what I'm going to plot for you you will see that shortly is d divided by l, versus l and that, of course, must be proportional to l to the power one-half.
I bring one l here.
So, if I compare the horse and I compare the raccoon I would argue that the thickness divided by the length of the femur for the horse must be the square root of four, twice as much as that of the raccoon.
And so I was very anxious to plot that, and I did that and I'll show you the result.
Here is my first result.
So we see there, d over l.
I explained to you why I prefer that.
And here you see the length.
You see here the raccoon and you see the horse.
And if you look carefully, then the d over l for the horse is only about one and a half times larger than the raccoon.
Well, I wasn't too disappointed.
One and a half is not two, but it is in the right direction.
The horse clearly has a larger value for d over l than the raccoon.
I realized I needed more data, so I went back to Harvard.
I said, "Look, I need a smaller animal, an opossum maybe maybe a rat, maybe a mouse," and they said, "okay." They gave me three more bones.
They gave me an antelope which is actually a little larger than a raccoon and they gave me an opossum and they gave me a mouse.
Here is the bone of the antelope.
Here is the one of the raccoon.
Here is the one of the opossum.
And now you won't believe this.
This is so wonderful, so romantic.
There is the mouse.
( students laugh ) Isn't that beautiful? Teeny, weeny little mouse? That's only a teeny, weeny little femur.
And there it is.
And I made the plot.
I was very curious what that plot would look like.
And...
here it is.
Whew! I was shocked.
I was really shocked.
Because look--
the horse is 50 times larger in size than the mouse.
The difference in d over l is only a factor of two.
And I expected something more like a factor of seven.
And so, in d over l, where I expect a factor of seven I only see a factor of two.
So I said to myself, "Oh, my goodness. Why didn't I ask them for an elephant?" The real clincher would be the elephant because if that goes way off scale maybe we can still rescue the statement by Galileo Galilei and so I went back and they said "Okay, we'll give you the femur of an elephant."
They also gave me one of a moose, believe it or not.
I think they wanted to get rid of me by that time to be frank with you.
And here is the femur of an elephant.
And I measured it.
The length and the thickness.
And it is very heavy.
It weighs a ton.
I plotted it, I was full of expectation.
I couldn't sleep all night.
And there's the elephant.
There is no evidence whatsoever that d over l is really larger for the elephant than for the mouse.
These vertical bars indicate my uncertainty in measurements of thickness and the horizontal scale, which is a logarithmic scale...
the uncertainty of the length measurements is in the thickness of the red pen so there's no need for me to indicate that any further.
And here you have your measurements in case you want to check them.
And look again at the mouse and look at the elephant.
The mouse has indeed only one centimeter length of the femur and the elephant is, indeed, hundred times longer.
So the first scaling argument that S is proportional to l that is certainly what you would expect because an elephant is about a hundred times larger in size.
But when you go to d over l, you see it's all over.
The d over l for the mouse is really not all that different from the elephant and you would have expected that number to be with the square root of 100 so you expect it to be ten times larger instead of about the same.
. You must hand wave off the Scaling Argument to make any of your "modeling" appear valid. This is all very basic stuff. And If you truly do hold any degree in engineering. You already know this. But because your motives are agenda driven (the US rejection of your hull concept for example) You must play this game to the truther audience of fools, "children", and others who have an agenda driven axe to grind. You have been outed Anders. 
