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Cylinder in a Box Validation |
  
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Cylinder in a Box Validation |
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Cylinder in Box Hydrostatics Validation Test
The first model tested is a 10 meter cube with a vertical cylinder inside. The cylinder has a 2 meter radius and a height of 5 meters starting from the bottom of the cube. The bottom of the cylinder is open and its submerged volume is a loss of buoyancy. The blue plane represents the waterplane location for the validation test.
2.5 meter draft |
Analytic |
Orca3D |
% Diff |
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Displaced Volume |
218.584 |
218.600 |
0.00729 |
VCB |
1.250 |
1.250 |
0.00000 |
Area Moment of Inertia |
820.767 |
820.800 |
0.00403 |
Waterplane Area |
87.434 |
87.450 |
0.01872 |
Immersed Station Area |
15.000 |
15.003 |
0.02000 |
Wetted Surface |
218.850 |
218.860 |
0.00477 |
Wetted Station Girth |
16.000 |
16.000 |
0.00000 |
BM |
3.755 |
3.754 |
0.02465 |
The next two tests involve a model that is a 10 meter cube with a horizontal cylinder inside extending the full length of the cube. The cylinder has a radius of 1 meter and its centroid is located 2 meters from the bottom edge of the cube. The first test assumed the waterplane to intersect the cylinder as can be seen from the image below.
2.0 meter draft |
Analytic |
Orca3D |
% Diff |
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Displaced Volume |
184.292 |
184.300 |
0.00432 |
VCB |
0.951 |
0.951 |
0.00627 |
Transverse Area Moment of Inertia |
826.667 |
826.700 |
0.00403 |
Longitudinal Area Moment of Inertia |
666.667 |
666.800 |
0.02000 |
Waterplane Area |
80.000 |
80.020 |
0.02500 |
Immersed Station Area |
18.429 |
18.430 |
0.00432 |
Wetted Surface |
208.274 |
208.280 |
0.00272 |
Wetted Station Girth |
17.142 |
17.142 |
0.00238 |
BMt |
4.486 |
4.485 |
0.01414 |
BMl |
3.617 |
3.618 |
0.01529 |
The second test assumed the cylinder to be fully submerged.
3.5 meter draft |
Analytic |
Orca3D |
% Diff |
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Displaced Volume |
318.584 |
318.600 |
0.00500 |
VCB |
1.725 |
1.725 |
0.02012 |
Area Moment of Inertia |
833.333 |
833.300 |
0.00400 |
Waterplane Area |
100.000 |
100.000 |
0.00000 |
Immersed Station Area |
31.858 |
31.858 |
0.00128 |
Wetted Surface |
296.549 |
296.560 |
0.00382 |
Wetted Station Girth |
23.283 |
23.283 |
0.00080 |
BM |
2.616 |
2.615 |
0.02832 |
The last test involved a horizontal cylinder with a radius of √2 meters inserted halfway into a 10 meter box. The waterline intersects the cylinder at its centroid.
5.0 meter draft |
Analytic |
Orca3D |
% Diff |
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Displaced Volume |
484.292 |
484.300 |
0.00164 |
VCB |
2.438 |
2.438 |
0.01561 |
Transverse Area Moment of Inertia |
823.905 |
823.900 |
0.00064 |
Longitudinal Area Moment of Inertia |
700.923 |
700.900 |
0.00332 |
Waterplane Area |
85.858 |
85.860 |
0.00249 |
Immersed Station Area |
46.858 |
46.857 |
0.00300 |
Wetted Surface |
322.214 |
322.210 |
0.00137 |
Wetted Station Girth |
24.443 |
24.443 |
0.00048 |
BMt |
1.701 |
1.701 |
0.01511 |
BMl |
1.447 |
1.447 |
0.02178 |