Trans RINA, Vol 156, Part B2, Intl J Small Craft Tech, Jul-Dec 2014 Table 3: Proa Workup by the New Method


Figure 6a: Proa. Heeling Arm vs Heel Angle 8. WORKED EXAMPLE


This example shows the workup of an actual inclining experiment on a patrol


boat. The data


experiment is shown in Table 4. Table 4: Patrol Boat Inclining Experiment Data


from the


Figure 6b: Proa. KG sin vs sin


The coefficient of determination R2 in Figure 7b is 1.000, indicating good accuracy, and the slope gives:


KGI = 4.098 m


The patrol boat had significant trim so KGI needs to be rotated into the vessel’s coordinate system to give KGL. LCG is close to 0.1 LBP and, with a trim of 0.589 m, a correction of 0.059 m is required giving:


KGL = 4.098 + 0.059 = 4.157 m


The result shows KG to be 0.122 m higher than by the classic method.


9. There are inherent The classic method gives GM0 = 1.296 m.


KM0 is found from the craft’s hydrostatics at the initial state shown in Table 4. From Equation 5, KGL is calculated to be:


KGL = 5.331 – 1.296 = 4.035 m


An analysis performed in Excel using the proposed new method is shown in Table 5 with the results plotted in Figure 7.


Having a symmetric hull, KNo is 0.000 m. The intercept in Figure 7a gives HZo as –0.014 m, so Equation 12 gives:


TCGI = 0.000 – (–0.014) = 0.014 m


CONCLUSIONS errors


in the classic method of


evaluating inclining experiments using wall-sided theory. In most cases, though not in the example of the proa, calculations of the as-inclined ship condition which rely on GM will underestimate KG.


Further, a high coefficient of determination R2 of the linear trendline through the classic pendulum plot is no guarantee of an accurate result.


The new method described above is simple, robust and accurate. It can be used with confidence for any hull form and can cope with angles of heel outside the range normally prescribed for inclining experiments.


The method will ensure good correlation between actual KG and limiting KG, and avoids the errors associated with the assumptions of a symmetrical, wall-sided ship and fixed metacentre.


©2014: The Royal Institution of Naval Architects


B-105


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