[net.physics] Big things are weaker than small things

flinn@seismo.UUCP (E. A. Flinn) (03/05/84)

Tom Merrick asks:

  >>I'm not sure why this is, but you cannot pick up a full sized
  >>aircraft by one of its appendages either, but you can do so with a model.
  >>Any experts out there who can comment on this one?

Large things are intrinsically weaker than small things.  Since mass
scales as the cube of linear dimension and cross-sectional area as the
square of linear dimension, the stress in members of a structure goes
up as size increases.  A cube of wet sand a centimeter on a side
stands up all right, but a cube of the same sand a kilometer on a side
collapses of its own weight.  Rhinoceri have thick legs to support
their weight, while mice can get by with thin legs.  And so on.
  For good discussion of this, see Galileo's "Dialogs Concerning Two
New Sciences," Darcy Wentworth Thompson's "On Growth and Form," and a
paper by M. King Hubbert in the Bulletin of the Geological Society of
America in the 1950's.

-- Ted Flinn

bobgian@psuvax.UUCP (Bob Giansiracusa) (03/06/84)

And this is also the reason you can drop a fly ten feet without injury,
but the same thing would be fatal to an elephant.

  Bob

Bob Giansiracusa (Dept of Computer Science, Penn State Univ, 814-865-9507)
Arpa:   bobgian%PSUVAX1.BITNET@Berkeley
UUCP:   bobgian@psuvax.UUCP            -or-    allegra!psuvax!bobgian
USnail: 333 Whitmore Lab, Penn State Univ, University Park, PA 16802

ntt@dciem.UUCP (Mark Brader) (03/06/84)

Tom Merrick asked:

  >>I'm not sure why this is, but you cannot pick up a full sized
  >>aircraft by one of its appendages either, but you can do so with a model.
  >>Any experts out there who can comment on this one?

Ted Flinn answered:

  >>Large things are intrinsically weaker than small things.  Since mass
  >>scales as the cube of linear dimension and cross-sectional area as the
  >>square of linear dimension, the stress in members of a structure goes
  >>up as size increases.

And he gave references.  I would just like to add one more: the article
"On Being the Right Size", I believe by J.B.S.Haldane, in the excellent
anthology "The World of Mathematics" edited by James R. Newman.

Mark Brader