Fix equation superscript squishing

Question

Because isentropic fluid flow is beautiful, I have these wonderful equations to deal with:

Notice how the superscripts have been squished vertically to fit. Is is possible to prevent this from happening? Or at least make the squishing effect square up instead of distorting the characters? I understand that they really need to be shorter, but I would love to have some control over how much smaller and at what aspect ratio it changes the sizing at.

Here's the code for the example:

    \begin{equation}
        M=\sqrt{\frac{2}{\gamma-1}
        {\Bigg[\Bigg(\frac{p_0}{p}\Bigg)^{\frac{\gamma-1}{\gamma}}-1\Bigg]}}
    \end{equation}

    \begin{equation}
        \frac{\dot{m}}{A}=
        \frac{p_0}{\sqrt{T_0}}
        \sqrt{\frac{\gamma}{R}}M
        \Bigg(1+\frac{\gamma-1}{2}M^2\Bigg)^{-\frac{\gamma+1}{2(\gamma-1)}}
    \end{equation}

    \begin{equation}
        \frac{\dot{m}}{A}=
        \frac{p_0}{\sqrt{T_0}}
        \sqrt{\frac{\gamma}{R}}\sqrt{\frac{2}{\gamma-1}{\Bigg[\Bigg(\frac{p_0}{p}\Bigg)^{\frac{\gamma-1}{\gamma}}-1\Bigg]}}
        \Bigg(1+\frac{\gamma-1}{2}\Bigg(\frac{2}{\gamma-1}{\Bigg[\Bigg(\frac{p_0}{p}\Bigg)^{\frac{\gamma-1}{\gamma}}-1\Bigg]}\Bigg)^2\Bigg)^{-\frac{\gamma+1}{2(\gamma-1)}}
    \end{equation}

Answer 1

If you feel that the fractional terms in the superscript positions are too small (they're rendered in scriptscript-style, in case you're curious), I suggest you switch from \frac to inline-fraction notation. That way, the elements in the superscript positions will be rendered in script-style, which is about 42% larger than script-script style.

A separate suggestion: Employing \Bigg to size the round parentheses and square brackets makes these "fences" unnecessarily large. Use \Big instead. Don't worry: your readers will still notice the "fences". However, they will now find it much easier to notice and process the material that's inside the fences.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
M    &= \sqrt{\frac{2}{\gamma-1}
        \Bigl[\Bigl(\frac{p_0}{p}\Bigr)%
          ^{\!(\gamma-1)/\gamma}\!-1
        \Bigr]}  \\
\frac{\dot{m}}{A}
     &= \frac{p_0}{\sqrt{T_0}} 
        \sqrt{\frac{\gamma}{R}}\,M
        \Bigl(1+\frac{\gamma-1}{2}M^2\Bigr)%
          ^{\!-(\gamma+1)/(2(\gamma-1))} \\
\frac{\dot{m}}{A}
     &= \frac{p_0}{\sqrt{T_0}}
        \sqrt{\frac{\gamma}{R}}\sqrt{\frac{2}{\gamma-1}\,
        \Bigl[\Bigl(\frac{p_0}{p}\Bigr)%
          ^{\!(\gamma-1)/\gamma}\!-1 \Bigr]} \notag\\
     &\quad\times\Bigl(1+\frac{\gamma-1}{2}
        \Bigl(\frac{2}{\gamma-1}
        \Bigl[\Bigl(\frac{p_0}{p}\Bigr)%
          ^{\!(\gamma-1)/\gamma}\!-1 \Bigr]
        \Bigr)^{\!2}\,\Bigr)^{\!-(\gamma+1)/(2(\gamma-1))}
\end{align}
\end{document}

Answer 2

Note that scripts aren’t squished to save space; they’re squished to be more legible at small sizes. Still, you can turn them off.

With unicode-math, script-style and script-script-style are OpenType font features that are active for superscripts and subscripts by default. You can turn them off by setting script-features and sscript-features to empty when you load the math font.

I’ve taken the liberty of rewriting the sample to use \left, \right, align and split.

\documentclass[preview,varwidth]{standalone}

\usepackage[leqno]{amsmath}
\usepackage{unicode-math}

\setmainfont{TeX Gyre Pagella}
\setmathfont[script-font={Latin Modern Math},
             script-features={},
             sscript-font={Latin Modern Math},
             sscript-features={}
            ]{Latin Modern Math}

\begin{document}

\begin{align}
   M &= \sqrt{\frac{2}{\gamma-1}
     {\left[\left(\frac{p_0}{p}\right)^{\frac{\gamma-1}{\gamma}}-1\right]}} \\
   \frac{\dot{m}}{A} &=
     \frac{p_0}{\sqrt{T_0}}
     \sqrt{\frac{\gamma}{R}}M
     \left(1+\frac{\gamma-1}{2}M^2\right)^{-\frac{\gamma+1}{2(\gamma-1)}} \\
  \begin{split}
    \frac{\dot{m}}{A} &=
      \frac{p_0}{\sqrt{T_0}}
      \sqrt{\frac{\gamma}{R}}\sqrt{\frac{2}{\gamma-1}{\left[\left(\frac{p_0}{p}\right)^{\frac{\gamma-1}{\gamma}}-1\right]}} \cdot\\
      &\quad \left(1+\frac{\gamma-1}{2}\left(\frac{2}{\gamma-1}{\left[\left(\frac{p_0}{p}\right)^{\frac{\gamma-1}{\gamma}}-1\right]}\right)^2\right)^{-\frac{\gamma+1}{2(\gamma-1)}}
  \end{split}
\end{align}

\end{document}

You probably do not need to do this with Latin Modern Math, however. Here is the same code with the default settings:

Those are not especially good rasterizations, but the PDFs look better.

You can set other options on the scripts as well, including optical sizes, or even substitute another font for them entirely.

Answer 3

Here are some options. There are four math styles: \displaystyle, \textstyle, \scriptstyle and \scriptscriptstyle. To change text font sizes, you have to get out of math mode first.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

{A\small A\footnotesize A\scriptsize A}

    \begin{equation}
        M=\sqrt{\frac{2}{\gamma-1}
        {\Bigg[\Bigg(\frac{p_0}{p}\Bigg)^{\frac{\gamma-1}{\gamma}}-1\Bigg]}}
    \end{equation}

    \begin{equation}
        M=\sqrt{\frac{2}{\gamma-1}
        {\Bigg[\Bigg(\frac{p_0}{p}\Bigg)^{\mbox{\footnotesize$\frac{\gamma-1}{\gamma}$}}-1\Bigg]}}
    \end{equation}

    \begin{equation}
        M=\sqrt{\frac{2}{\gamma-1}
        {\Bigg[\Bigg(\frac{p_0}{p}\Bigg)^{\mbox{\small$\frac{\gamma-1}{\gamma}$}}-1\Bigg]}}
    \end{equation}

    \begin{equation}
        M=\sqrt{\frac{2}{\gamma-1}
        {\Bigg[\Bigg(\frac{p_0}{p}\Bigg)^{\textstyle \frac{\gamma-1}{\gamma}}-1\Bigg]}}
    \end{equation}
\end{document}