\begin{table} \begin{center} \caption{Summary of Relationships for Scale Model Testing} \makeqnum \begin{tabular}{||l|c||} \hline \multicolumn{1}{|c}{Parameter} &\multicolumn{1}{|c||}{Scaling Relationships}\\ Geometry and & \\ Initial Conditions: &\\ \quad Overall Length & $l_{sm} = l_{fs} \times (Scale)^{1}$\\ \quad Mass & $M_{sm} = M_{fs} \times (Scale)^{3}$\\ \quad Moment of Inertia & $I_{sm} = I_{fs} \times (Scale)^{5}$\\ \quad Spring Constants: &\\ \quad \quad Loading & $Kl_{sm} = Kl_{fs} \times (Scale)^{1}$\\ \quad \quad Unloading & $Ku_{sm} = Ku_{fs} \times (Scale)^{1}$\\ \quad Initial Velocity & $Vi_{sm} = Vi_{fs} \times (Scale)^{0}$\\ \quad Initial Angle & $\theta i_{sm} = \theta i_{fs} \times (Scale)^{0}$\\ \hline Results: & \\ \quad Linear Accelerations & $a_{sm} = a_{fs} \times (Scale)^{-1}$\\ \quad Angular Accelerations & $\alpha _{sm} = \alpha _{fs} \times (Scale)^{-2}$\\ \quad Linear Velocities & $V_{sm} = V_{fs} \times (Scale)^{0}$\\ \quad Angular Velocities & $\omega _{sm} = \omega _{fs} \times (Scale)^{-1}$\\ \quad Linear Displacements & $\Delta _{sm} = \Delta _{fs} \times (Scale)^{1}$\\ \quad Angular Displacements & $\theta _{sm} = \theta _{f} \times (Scale)^{0}$\\ \hline \end{tabular} \end{center} \end{table}