Trans RINA, Vol 156, Part B2, Intl J Small Craft Tech, Jul-Dec 2014


Both methods generally give similar values for most vessels, but


three ship types stand out as having


significant differences. For a Survey Motor Boat, a small hard-chine aluminium craft, the classic method underestimated KG by 21 mm. The RAN Landing Ship Heavy, though generally wall-sided, has a significant chine aft with pronounced bottom flare below, and KG was underestimated by 56 mm. The ACPB, as noted earlier, has a deadrise of less than 45o at the waterplane throughout most of its length, and KG was underestimated by 122 mm — an order of magnitude greater than the expected experimental error.


7. VALIDATION BY EXAMPLE


To validate the method for an extreme case with asymmetry and a large heel angle, a simulated inclining experiment on a proa (Figure 4) is presented. The data has been arranged so that,


outrigger comes out of the water and the craft is close to the point of capsize. The proa is symmetric fore and aft.


Hydrostatics were run for the as-inclined condition and KM0 found to be 6.427 m.


The classic pendulum plot, from the data in Table 2, is shown in Figure 5. A linear trendline through all points, shown dotted, clearly does not fairly represent the full set of results.


7.1 EVALUATION BY THE CLASSIC METHOD


at one mass move, the


Figure 5: Proa Pendulum Plot In practice, the outlying point


at Move 5 would be


discarded and, to achieve a reasonable fit, so too might the point from Move 2. The linear trendline through the remaining points is shown as a solid line.


This gives a GM0 of 5.904 m. With a KM0 of 6.427 m, the KG is calculated from Equation 5 to be:


KGI = 6.427 – 5.904 = 0.523 m Figure 4: Mesh Model of a Proa


The craft is very stiff when heeling towards the outrigger, but quite tender when heeling away. This gives rise to significantly different values of GM0, depending on the direction of heel.


A 3-D mesh model was built with Rhinoceros software and used to generate the inclining experiment data shown in Table 2. Calculated pendulum deflections have been rounded to the nearest 0.5 mm. At Move 5, when the outrigger comes clear of the water, a heel of over 5o is developed. This is clearly illustrated in Table 2 by the large pendulum deflection.


Table 2: Proa Inclining Experiment Data


An R2 value of 0.9961 suggests that a reasonable result could be expected, but it is clear that the calculated KG does not compare well with the actual KG of 0.375 m.


With differing values of GMs to port and starboard, a single trendline almost inevitably leads to this result.


7.2 EVALUATION BY THE NEW METHOD


The proposed new method copes easily with this data. An analysis performed in Excel is shown in Table 3 with the results plotted in Figure 6. At each move, HZ is calculated as shown in Equation 8 and KG sin as shown in Equation 13.


KNo is calculated to be –0.079 m and, using a third-order polynomial trendline, the HZ intercept in Figure 5a (HZo) is found to be 0.071 m. Equation 12 then gives:


TCGI = –0.079 – 0.071 = –0.150 m


The coefficient of determination R2 of the linear trendline of KG sinvs sinin Figure 5b is 1.000 and the slope gives:


KGL = KGI = 0.375 m With the proa having no trim, KGI and KGL are the same.


Even in this extreme case, the results are correct to the nearest millimetre.


B-104


©2014: The Royal Institution of Naval Architects


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