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Comment by nikic | Hacker News Reader

> Euler was the first person to realize this, afaik. Is there a term to describe these kind of "de-unit-ified" equations? More than once I've found myself needing to reconstruct a proper equation (with correct dimensions and constants) from one of these bastardized non-equations.

Not very surprisingly, it's called nondimensionalization (https://en.wikipedia.org/wiki/Nondimensionalization).

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Damn, got my hopes up. That's close, but not quite the same thing.

The nondimensionalization article is talking about reducing free dimensions in a model by variable substitution (while following all the rules of dimensional analysis), but I'm talking about re-writing a single equation so it can be used by "unit-phobic" people by simply dropping (not substituting!) all units (breaking all the rules of dimensional analysis), and assuming a certain set of units for input and output values.

Compare this (incorrect) formula, which gives no hint as to which units are being used for pressure or height:

  h_alt = ( 1 - ( P_sta / 1013.25 )^0.190284 ) · 145366.45

with this (correct) equation, which always works regardless of what units are chosen (just follow the unit conversion rules):

  h_alt = (1 - (P_sta / (101.325 kPa))^0.190284 · 44307.69396 meter

There are even unit-preserving calculators like Frink, which allow you to specify any units (for instance, giving barometric pressure in light-nanoseconds of mercury[1]).

[1] http://frinklang.org/fsp/frink.fsp?fromVal=%281+-+%282.5+lig...

FWIW, Nondimensionalization for dummies[1] has a nicely-motivated introductory example (from ecology).

[1] http://wp.auburn.edu/radich/wp-content/uploads/2014/08/Nondi...

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