Line with floats: Properties of the floats

When modelling lines with floats, the floats are assumed to be short cylinders fitted co-axially on the line at constant spacing. The following notation is used for the float properties.

\begin{align*} l_f &= \text{length} \\ d_f &= \text{diameter} \\ \rho_f &= \text{density} \\ s_f &= \href{LinewithFloats.htm}{\text{float pitch}} \\ m_h &= \text{float hardware mass (e.g. fixing clamps, bolts, etc.)} \\ C_{\mathrm{Dn}f} &= \text{normal drag coefficient} \\ C_{\mathrm{Da}f1} &= \text{axial drag coefficient due to form} \\ C_{\mathrm{Da}f2} &= \text{axial drag coefficient due to skin friction} \\ C_{\mathrm{an}f} &= \text{normal added mass coefficient} \\ C_{\mathrm{aa}f} &= \text{axial added mass coefficient} \\ \end{align*}

With this notation, and that for the base line type, the volume occupied by an individual float is \begin{equation} v_f = \frac{\pi}{4} \left(d_f^2 - O\!D_l^2\right) l_f \end{equation}

\begin{equation} m_f = v_f \rho_f + m_h \end{equation}