[Shryke]

Ok, thanks. I am, however, a complete layman in this matter. Nonetheless, let me ask some questions regarding your various assumptions and math: you appear to rely on this Square Cube Law. I am going to use it in regards to my 8 month old daughter, Reagan, and me. My daughter is 24 inches tall and weighs 18 pounds - well within the norm. She is also normally porportioned. I am 70 inches tall.

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?

[js1138]

Where have I made the error?

Are either of you idealized spheres?

[Swordmaker]

Where have I made the error?

An infant and an adult are not proportional.

[Swordmaker]

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?

OK, I'm home now and not replying on my iPhone. I can give you a little more information.

The error is in the mis-application of the Square Cube Law. It's the same error JS1138 made with his Chestnut Sparrow -> California Condor attempt at scaling. The Chestnut Sparrow does not look like a California Condor except only in the fact they both are birds and have wings, beaks, and feathers.

In your case, infants and adults are not proportional to each other. Your daughter's arms and legs are not the same proportion to her torso as yours arms and legs are to your torso, nor is her head the same ~1/8th her body length that an adult man's head is normally... its more like 1/4. Also babies have baby fat... you no longer have your's (I hope).

Basic Proportions and Height

Adult Man - 8 heads height; 3 heads up to waistline; 4 heads up to the crotch
Adult Woman - 7-3/4 heads height; 3 heads up to waistline; 4 heads up to the crotch
Children - 6 heads height; 2-1/2 heads up to waistline; 3 heads up to the crotch
Infant - 4 heads = total body length

Picture that six feet tall...

Again, like JS's sparrow, if we were to scale your daughter, as she is, up by 3 times... she would look exactly like she does now... with proportionately the same short legs and arms, large head (now about 18" from chin to crown and about 15" from ear to ear), and baby fat... only she's 3 times larger and it's no wonder she would weigh somewhere around 486 pounds. The infant's shoulders are ~9" but the scaled up infant's shoulders are 27". My shoulders are 19" and I am not a small man. Her waist is probably about 16" - 18" now... after scaling her three times it would be 48" to 54" and her ~9" long torso would be a ~36" torso . . .

She would need a diaper 3² or 9 times larger in area than the one she uses now (cloth diaper size for infant up to 20 lbs = 14" x 17" = 238 square inches = 1.65 square feet. Multiply that times 3².

9 x 1.65 Square feet = a 14.85 Square Foot diaper... 42" X 52".

If, however, your daughter looked just like you with exactly the same proportions of legs and arms to torso, with a head ~1/8th her body length and lacked the baby fat, everything exactly 1/3 smaller, when scaled up three times, she would be six feet tall and look just like you and weigh what you do.

This is exactly the problem of the megafauna... we are looking at animals that ARE proportionate to the smaller versions without adaptation to handle the greater weight.