Fit the height of the chapter number to n-times the height of the chapter name

Question

I would to get the chapter number tall n-times the chapter name in order to have a better proportion between the two elements. Why I get errors and how can I fix that behaviour?

I thought something like this to include it:

\setbox4\hbox{\resizebox*{!}{\myheight}{\hspace{10pt}}}
\edef\hchapterspace{\the\wd4}

And use \hchapterspace

but I get: Package graphics Error: Division by 0 }

So the simplest way is:

...\hspace{10pt}\vline\hspace{10pt}}\ }{0pt}

but is the same thing to use {10pt} as \titleformat argument?

---

\documentclass[headinclude,footinclude]{scrbook}
\usepackage[eulerchapternumbers,pdfspacing]{classicthesis}
\usepackage{arsclassica}
\usepackage{lipsum}

\setbox10\hbox{\normalfont\Large\sffamily\spacedallcaps{\chaptername}}

\setbox20\hbox{\resizebox*{!}{\dimexpr\ht10*3\relax}{\chapterNumber\thechapter}}

\titleformat{\chapter}[block]%
        {\normalfont\Large\sffamily}%
        {{\color{halfgray}\box20%
        \hspace{10pt}\vline}  }{10pt}%
        {\spacedallcaps}

\begin{document}

\chapter{graphic test}
\lipsum[1-3]

\end{document}

Answer 1

\documentclass[headinclude,footinclude]{scrbook}
\usepackage[eulerchapternumbers,pdfspacing]{classicthesis}
\usepackage{arsclassica,graphicx}
\usepackage{lipsum}

\setbox0\hbox{\normalfont\Large\sffamily\spacedallcaps{\chaptername}}
\edef\myheight{\the\dimexpr 3\ht0\relax}


\titleformat{\chapter}[block]%
        {\normalfont\Large\sffamily}%
        {\color{halfgray}\resizebox*{!}{\myheight}{\chapterNumber\thechapter
        \hspace{10pt}\vline}}{10pt}%
        {\spacedallcaps}

\begin{document}
\refstepcounter{chapter}

\chapter{graphic test}
\lipsum[1-3]

\end{document}

It is only safe to use boxes 0 2 4 6 8 as local scratch registers and you need to use them locally you can not assume that if you set it at one place the box has a usable value later in the document. Also you did not want a box at all for the chapter number that boxed the text when the counter was at 0 and so using the box in the chapter heading would not give the chapter number even if box20 had been safe to use.

---

Comment on the updated question about horizontal spacing. If you add the space after the resizebox or (I suspect, equivalently) in the following argument of \titleformat then the space added will be the space specified. If on the other hand you add the space before the closing } of the \resizebox then the space will be scaled in proportion to the scaling of the number, so if the \resizebox ends up scaling by (say) 3.1 times then \hspace{10pt} will produce 31pt of white space in the output. The choice is entirely up to you which you feel a more natural specification.