Chain: Outer, inner and contact diameters

The line type wizard sets up diameters for a chain as follows:

Outer diameter

The effective outer diameter of the line type representing the chain is obtained using a similar argument to that deployed in obtaining the overall length of bar per link, and with the same notation: see derived data. Firstly, note that the volume per metre $V$ can be expressed both as \begin{equation} \label{V_mass} V = \frac{m}{\rho_\mathrm{s}} \end{equation} and as \begin{equation} \label{V_geom} V = \pi\, O\!D^2 / 4 \end{equation} where $O\!D$ is the equivalent diameter of a line with constant cross section along its length. Equating expressions (\ref{V_mass}) and (\ref{V_geom}) gives us \begin{equation} \label{v_mass} O\!D = \sqrt{\frac{4m}{\pi\rho_{\mathrm{s}}}} = \begin{cases} 1.80 d \text{ m} & \text{(studless)} \\ 1.89 d \text{ m} & \text{(studlink)} \end{cases} \end{equation}

Inner diameter

The inner diameter is set to zero.

Outer contact diameter

The outer contact diameter is set to the chain link envelope diameter\begin{equation} \text{contact diameter} = \begin{cases} 3.35 d \text{ m} & \text{(studless)} \\ 3.60 d \text{ m} & \text{(studlink)} \end{cases} \end{equation}

Inner contact diameter

The inner contact diameter is set to '~'.