# 4.6.1.2: Metacentric Height, $$\overline{GM}$$, Measurement

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The metacentric height can be measured by finding the change in the angle when a weight is moved on the floating body. Moving the weight, $$T$$ a distance, $$d$$ then the moment created is $M_{weight} = Td$ This moment is balanced by $M_{righting} = W_{total}\overline{GM_{new}}\theta$ Where, $$W_{total}$$, is the total weight of the floating body including measuring weight. The angle, $$\theta$$, is measured as the difference in the orientation of the floating body. The metacentric height is $\overline{GM_{new}} = \frac{Td}{W_{total}\theta}$ If the change int he $$\overline{GM}$$ can be neglected, equation 58 provides the solution. The calculation of $$overline{GM}$$ can be improved by taking into account the effect of the measuring weight. The change in height of $$G$$ is $\not{g} m_{total} G_{new} = \not{g} m_{ship} G_{actual} + \not{g} T h$ Combinging equation 59 with equation 58 results in $\overline{GM_{actual}} = \overline{GM_{new}} \frac{m_{total}}{m_{ship}} - h\frac{T}{m_{ship}}$ The weight of the ship is obtained from looking at the ship depth.

This page titled 4.6.1.2: Metacentric Height, $$\overline{GM}$$, Measurement is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.
This page titled 4.6.1.2: Metacentric Height, $$\overline{GM}$$, Measurement is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by Genick Bar-Meir via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.