[freebeard]

I thought I'd found a solution to the problem of 'rules of thumb' rubbing thin-skinned individuals the wrong way. But the upshot was that the thread in Aerodynamics was locked. I choose to share here instead to spare the feelings of the last poster.

en.wikipedia.org/wiki/Order_of_approximation

Usage in science and engineering
In formal expressions, the ordinal number used before the word order refers to the highest order of derivative in the series expansion used in the approximation. The expressions: a zeroth-order approximation, a first-order approximation, a second-order approximation, and so forth are used as fixed phrases. The expression a zero order approximation is also common. Cardinal numerals are occasionally used in expressions like an order zero approximation, an order one approximation, etc.

The omission of the word order leads to phrases that have less formal meaning. Phrases like first approximation or to a first approximation may refer to a roughly approximate value of a quantity.[1][2] The phrase to a zeroth approximation indicates a wild guess.[3] The expression order of approximation is sometimes informally used to mean the number of significant figures, in increasing order of accuracy, or to the order of magnitude. However, this may be confusing as these formal expressions do not directly refer to the order of derivatives.

So don't say rule of thumb when there is a nerdier expression available.