Friday, December 28, 2018

The Pitfalls of Using Handbooks and Formulae

A photo of three books: (left) Structures: Or Why Things Don't Fall Down, (center) Intermediate Physics for Medicine and Biology, and (right) The New Science of Strong Materials: Or Why You Don’t Fall Through the Floor.
Structures: Or Why Things Don't Fall Down, by J. E. Gordon.
Last week I discussed James Gordon’s book Structures: Or Why Things Don’t Fall Down. The book contains several appendices. The first appendix is ostensibly about using handbooks and formulas to make structural calculations.
Over the last 150 years the theoretical elasticians have analysed the stresses and deflections of structures of almost every conceivable shape when subjected to all sorts and conditions of loads…Fortunately a great deal of this information has been reduced to a set of standard cases or examples the answers to which can be expressed in the form of quite simple formulae.
Then, to my surprise, Gordon changes tack and warns about pitfalls when using these formulas. His counsel, however, applies to all calculations, not just mechanical ones. In fact, his advice is invaluable for any young scientist or engineer. Below, I quote parts of this appendix. Read carefully, and whenever you encounter a word specific to mechanics substitute a general one, or one related to your own field.
[Formulae] must be used with caution.
A photo of Appendix 1 from Structures: Or Why Things Don't Fall Down, superimposed on the cover of Intermediate Physics for Medicine and Biology.
Appendix 1 of Structures.
  1. Make sure that you really understand what the formula is about.
  2. Make sure that it really does apply to your particular case.
  3. Remember, remember, remember, that these formulae take no account of stress concentrations or other special local conditions.
After this, plug the appropriate loads and dimensions into the formula—making sure that the units are consistent and that the noughts are right. [I’m not sure what “noughts” are, but I think the Englishman Gordon is saying to make sure the decimal point is in the right place.] Then do a little elementary arithmetic and out will drop a figure representing a stress or a deflection.

Now look at this figure with a nasty suspicious eye and think if it looks and feels right. In any case you had better check your arithmetic; are you sure that you haven’t dropped a two?...

If the structure you propose to have made is an important one, the next thing to do, and a very right and proper thing, is to worry about it like blazes. When I was concerned with the introduction of plastic components into aircraft I used to lie awake night after night worrying about them, and I attribute the fact that none of these components ever gave trouble almost entirely to the beneficent effects of worry. It is confidence that causes accidents and worry which prevents them. So go over your sums not once or twice but again and again and again.
Appendix 1 in J. E. Gordon's book Structures: Or Why Things Don't Fall Down has an important lesson for students studying from Intermediate Physics for Medicine and Biology.
Structures: Or Why Things Don't Fall Down.
This is the attitude I try to instill in my students when teaching from Intermediate Physics for Medicine and Biology. I implore them to think before they calculate, and then think again to judge if their answer makes sense. Students sometimes submit an answer to a homework problem (almost always given to five or six significant figures) that is absurd because they didn't look at their answer with a “nasty suspicious eye.” I insist they "remember, remember, remember" the assumptions and limitations of a mathematical model and its resulting formulas. Maybe Gordon goes a little overboard with his “night after night” of lost sleep, but at least he cares enough about his calculation to wonder “again and again and again” if it is correct. A little worry is indeed a “right and proper thing.”

Who would of expected such wisdom tucked away in an appendix about handbooks and formulae?

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