Engineers and "exact" calculations
20 Jan 2011Here is an interesting fraction from our good friend Richard Feynman. I use this as an illustration whenever I talk to engineering students about significant digits and uncertainty. 1 / 243 = 0.00411522633744855967…
Nothing in the engineered world can touch the precision of this fraction. And yet, I remember as an undergrad engineering student wanting to be very exact and as a result would compute the design moment or capacity of a beam as something like:
452.83726583243 kipft
Nevermind that:

I guessed the design load.

I have no idea how the owner will use it (a la the sinking libraries myth).

I applied a statistically determined factor of safety to the design load I guessed.

I probably used a simplified elastic analysis (i.e. FEA).

My analysis used material properties that will differ from those constructed.

I probably didn’t account for construction tolerances.

Any precision beyond 34 sig figs are likely numerical artifacts with no meaning.
So, all things considered, I think it’s okay to report the beam’s capacity as a cool 450 kipft. This is after all why we learned about significant digits in high school chemistry.