Math typesetting conventions: two-letter subscripts in an equation

Question

Are there any conventions for using two-letter subscripts in equations?

I need to use fr for friction, and the normal math italic in TeX ($\omega_{fr}$) doesn't look very good, it appears like f and r are two unrelated concepts hanging out together rather than a unified thing.

\documentclass[border=1mm]{standalone}
\begin{document}
$\omega_{fr}$ vs.
$\omega_{\mathrm{fr}}$ vs.
$\omega_{f\!r}$ vs.
$\omega_{\!f\!r}$
\end{document}

Note: this question is not how to accomplish typesetting in TeX (which I can ask on tex.stackexchange.com) but how it should be typeset, and where I might find this kind of information from a reputable source.

I found the AMS Style Guide online and it states "Stet italic superscript and subscript functions if used consistently." --- that is using $x_{max}$ ($x_{max}$) is OK if done consistently rather than $x_{\max}$ ($x_{\max}$) --- as well as in Appendix A, "These functions and operators are set in roman type in both roman and italic text; however, you may stet superscript and subscript italic functions and operators." (Which I would interpret as, "Authors should put well-known functions and operators in roman type, but if you really want to leave them in regular italics, we won't complain.") But there's no guidance about other multicharacter subscripts.

Answer 1

Looks like there are a couple of style guidelines in other related fields (physics, electrical engineering) that do make clear recommendations:

• NIST SI unit rules

  Superscripts and subscripts are in italic type if they represent variables, quantities, or running numbers. They are in roman type if they are descriptive.

  (although IMHO the example given is really lousy, $c_p$ for specific heat capacity at constant pressure, "p" = pressure, but $m_{\mathrm{p}}$ for mass of a proton, "p" = proton)

• Physical Review Style and Notation Guide

  Abbreviations in subscripts and superscripts fall into two categories: (1) single-letter and (2) multiletter abbreviations. Most single-letter abbreviations are conventionally printed in the italic font, i.e., $E_C$ where $C$ stands for Coulomb. Multiletter abbreviations are conventionally printed in the roman font whether they represent one or more words, i.e., $E_{\mathrm{lab}}$, where lab stands for laboratory (truncated word—lowercase) and $E_{\mathrm{HF}}$, where HF stands for Hartree and Fock (acronym), two proper names. Please note that you should always capitalize abbreviations that represent proper names.

• IEEE Editorial Style Manual

  Displayed Equations
  Certain types of material in displayed equations are automatically italic. Some simple general rules apply. All variables are italic. (e.g., $x$, $y$, $n$). Function names and abbreviations are Roman (sin, cos, sinc, sinh), as are units or unit abbreviations (e.g., deg, Hz,) complete words (e.g., in, out), and abbreviations of words (e.g., max, min), or acronyms (e.g., SNR). Single letter superscripts and subscripts may be italic even if they are abbreviations, unless this leads to inconsistency between italic and roman characters for similar types of subscripts.

Answer 2

As you point it out, the main problem is the ambiguity of the index $\mathrm{fr}$, that may appear like two unrelated symbols $f$ and $r$. Looking at the Wikipedia entry for Energy of friction, I found a formula using $\mathbf{F}_{\mathrm{fric}}$ for the friction force. All of a sudden, the ambiguity of $\mathrm{fr}$ disappears when you use $\mathrm{fric}$ instead of $\mathrm{fr}$, and whether to use italics, slanted or roman becomes a lesser issue. I would follow @littleO and use $\mathrm{fric}$, but in order to ensure a consistent use, I would define a macro (that you could reuse in other articles)

\newcommand{\fric}{\mathrm{fric}}

and then use

$\omega_\fric$

Note that the other example you mention is already unambiguous. Everybody will understand if you write, for instance

The temperature $T$ ranges between $T_{\mathrm{min}}$ and $T_{\mathrm{max}}$.

In my opinion, avoiding ambiguities should be your first priority (and not only in mathematical texts...), even at the cost of a slightly longer formula.