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Primitive Shapes and Mesh Densities |
  
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Primitive Shapes and Mesh Densities |
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The following presents the results for the primitive shapes at mesh densities between 0.5 and 1.0. The shapes were also compared to analytic results for sinkage levels of +/- 1.0 meter at a mesh density of 0.7.
2.1 Cube Results
The cube is 10 meters in length with its vertical center on the horizontal construction plane.
Table 2.1.1 Cube Mesh Density 0.5-0.7 Results
Table 2.1.2 Cube Mesh Density 0.8-1.0 Results
Model Sinkage = -1.0m |
Water Density 1025.9 kg/m^3 |
Mesh Density 0.7 |
% Error |
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Analytic |
|
Orca3D |
|
|
Displaced Volume |
400.000 |
m^3 |
400 |
m^3 |
0.000 |
VCB |
-3.000 |
m |
-3.000 |
m |
0.000 |
Area Moment of Inertia |
833.333 |
m^4 |
833.3 |
m^4 |
0.004 |
Waterplane Area |
100.000 |
m^2 |
100.00 |
m^2 |
0.000 |
Immersed Area |
40.000 |
m^2 |
40.0 |
m^2 |
0.000 |
Wetted Surface |
260.000 |
m^2 |
260.00 |
m^2 |
0.000 |
Wetted Girth |
18.000 |
m |
18.00 |
m |
0.000 |
BM |
2.083 |
m |
2.083 |
m |
0.016 |
Table 2.1.3 Cube Negative Sinkage Results
Model Sinkage = 1.0m |
Water Density 1025.9 kg/m^3 |
Mesh Density 0.7 |
% Error |
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Analytic |
|
Orca3D |
|
|
Displaced Volume |
600.000 |
m^3 |
600 |
m^3 |
0.000 |
VCB |
-2.000 |
m |
-2.000 |
m |
0.000 |
Area Moment of Inertia |
833.333 |
m^4 |
833.3 |
m^4 |
0.004 |
Waterplane Area |
100.000 |
m^2 |
100.00 |
m^2 |
0.000 |
Immersed Area |
60.000 |
m^2 |
60.0 |
m^2 |
0.000 |
Wetted Surface |
340.000 |
m^2 |
340.00 |
m^2 |
0.000 |
Wetted Girth |
22.000 |
m |
22.00 |
m |
0.000 |
BM |
1.389 |
m |
1.389 |
m |
0.008 |
Table 2.1.4 Cube Positive Sinkage Results
2.2 Sphere Results
The sphere is 10 meters in diameter with its center on the horizontal construction plane.
Table 2.2.1 Sphere Mesh Density 0.5-0.7 Results
Table 2.2.2 Sphere Mesh Density 0.8-1.0 Results
Model Sinkage = -1.0m |
Water Density 1025.9 kg/m^3 |
Mesh Density 0.7 |
% Error |
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Analytic |
|
Orca3D |
|
|
Displaced Volume |
184.307 |
m^3 |
181.4 |
m^3 |
1.577 |
VCB |
-2.455 |
m |
-2.454 |
m |
0.022 |
Area Moment of Inertia |
452.389 |
m^4 |
451.6 |
m^4 |
0.174 |
Waterplane Area |
75.398 |
m^2 |
75.33 |
m^2 |
0.090 |
Immersed Area |
29.337 |
m^2 |
29.3 |
m^2 |
0.126 |
Wetted Surface |
125.664 |
m^2 |
125.59 |
m^2 |
0.059 |
Wetted Girth |
13.694 |
m |
13.69 |
m |
0.032 |
BM |
2.455 |
m |
2.453 |
m |
0.063 |
Table 2.2.3 Sphere Negative Sinkage Results
Model Sinkage = 1.0m |
Water Density 1025.9 kg/m^3 |
Mesh Density 0.7 |
% Error |
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Analytic |
|
Orca3D |
|
|
Displaced Volume |
339.292 |
m^3 |
339 |
m^3 |
0.086 |
VCB |
-1.333 |
m |
-1.333 |
m |
0.025 |
Area Moment of Inertia |
452.389 |
m^4 |
451.7 |
m^4 |
0.152 |
Waterplane Area |
75.398 |
m^2 |
75.34 |
m^2 |
0.077 |
Immersed Area |
49.203 |
m^2 |
49.2 |
m^2 |
0.006 |
Wetted Surface |
188.496 |
m^2 |
188.41 |
m^2 |
0.045 |
Wetted Girth |
17.722 |
m |
17.72 |
m |
0.009 |
BM |
1.333 |
m |
1.333 |
m |
0.025 |
Table 2.2.4 Sphere Positive Sinkage Results
| 2.3 | Vertical Cylinder Results |
The vertical cylinder is 8 meters in diameter and 12 meters in length. The horizontal construction plane intersects the cylinder so that is has a 4 meter draft at 0 sinkage.
Table 2.3.1 Vertical Cylinder Mesh Density 0.5-0.7 Results
Table 2.3.2 Vertical Cylinder Mesh Density 0.8-1.0 Results
Model Sinkage = -1.0m |
Water Density 1025.9 kg/m^3 |
Mesh Density 0.7 |
% Error |
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Analytic |
|
Orca3D |
|
|
Displaced Volume |
150.796 |
m^3 |
150.6 |
m^3 |
0.130 |
VCB |
-2.500 |
m |
-2.500 |
m |
0.000 |
Area Moment of Inertia |
201.062 |
m^4 |
200.4 |
m^4 |
0.329 |
Waterplane Area |
50.265 |
m^2 |
50.18 |
m^2 |
0.170 |
Immersed Area |
24.000 |
m^2 |
24.0 |
m^2 |
0.000 |
Wetted Surface |
125.664 |
m^2 |
125.55 |
m^2 |
0.090 |
Wetted Girth |
14.000 |
m |
14.00 |
m |
0.000 |
BM |
1.333 |
m |
1.331 |
m |
0.175 |
Table 2.3.3 Vertical Cylinder Negative Sinkage Results
Model Sinkage = 1.0m |
Water Density 1025.9 kg/m^3 |
Mesh Density 0.7 |
% Error |
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Analytic |
|
Orca3D |
|
|
Displaced Volume |
251.327 |
m^3 |
250.9 |
m^3 |
0.170 |
VCB |
-1.500 |
m |
-1.500 |
m |
0.000 |
Area Moment of Inertia |
201.062 |
m^4 |
200.4 |
m^4 |
0.329 |
Waterplane Area |
50.265 |
m^2 |
50.18 |
m^2 |
0.170 |
Immersed Area |
40.000 |
m^2 |
40.0 |
m^2 |
0.000 |
Wetted Surface |
175.929 |
m^2 |
175.80 |
m^2 |
0.073 |
Wetted Girth |
18.000 |
m |
18.00 |
m |
0.000 |
BM |
0.800 |
m |
0.799 |
m |
0.125 |
Table 2.3.4 Vertical Cylinder Positive Sinkage Results
| 2.4 | Cone Results |
The cone has a base diameter of 7 meters and a height of 7 meters. The cone is orientated tip down and the horizontal construction plane intersects giving it a draft of 5 meters with 0 sinkage.
Table 2.4.1 Cone Mesh Density 0.5-0.7 Results
Table 2.4.2 Cone Mesh Density 0.8-1.0 Results
Model Sinkage = -1.0m |
Water Density 1025.9 kg/m^3 |
Mesh Density 0.7 |
% Error |
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Analytic |
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Orca3D |
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|
Displaced Volume |
16.755 |
m^3 |
16.7 |
m^3 |
0.329 |
VCB |
-2.000 |
m |
-2.000 |
m |
0.000 |
Area Moment of Inertia |
12.566 |
m^4 |
12.5 |
m^4 |
0.528 |
Waterplane Area |
12.566 |
m^2 |
12.55 |
m^2 |
0.130 |
Immersed Area |
8.000 |
m^2 |
8.0 |
m^2 |
0.000 |
Wetted Surface |
28.099 |
m^2 |
28.08 |
m^2 |
0.069 |
Wetted Girth |
8.944 |
m |
8.94 |
m |
0.048 |
BM |
0.750 |
m |
0.749 |
m |
0.133 |
Table 2.4.3 Cone Negative Sinkage Results
Model Sinkage = 1.0m |
Water Density 1025.9 kg/m^3 |
Mesh Density 0.7 |
% Error |
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Analytic |
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Orca3D |
|
|
Displaced Volume |
56.549 |
m^3 |
56.5 |
m^3 |
0.086 |
VCB |
-0.500 |
m |
-0.500 |
m |
0.000 |
Area Moment of Inertia |
63.617 |
m^4 |
63.4 |
m^4 |
0.341 |
Waterplane Area |
28.274 |
m^2 |
28.23 |
m^2 |
0.157 |
Immersed Area |
18.000 |
m^2 |
18.0 |
m^2 |
0.000 |
Wetted Surface |
63.223 |
m^2 |
63.18 |
m^2 |
0.069 |
Wetted Girth |
13.416 |
m |
13.42 |
m |
0.027 |
BM |
1.125 |
m |
1.123 |
m |
0.178 |
Table 2.4.4 Cone Positive Sinkage Results
| 2.5 | Horizontal Cylinder Results |
The horizontal cylinder has a 6 meter diameter and a 10 meter length. It is orientated on its side with the horizontal construction plane intersecting it giving a 3 meter draft with 0 sinkage.
Table 2.5.1 Horizontal Cylinder Mesh Density 0.5-0.7 Results
Table 2.5.2 Horizontal Cylinder Mesh Density 0.8-1.0 Results
Model Sinkage = -1.0m |
Water Density 1025.9 kg/m^3 |
Mesh Density 0.7 |
% Error |
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|
Analytic |
|
Orca3D |
|
|
Displaced Volume |
82.502 |
m^3 |
82.3 |
m^3 |
0.245 |
VCB |
-1.828 |
m |
-1.827 |
m |
0.078 |
Transverse Area Moment of Inertia |
150.849 |
m^4 |
150.3 |
m^4 |
0.364 |
Longitudinal Area Moment of Inertia |
471.405 |
m^4 |
470.9 |
m^4 |
0.107 |
Waterplane Area |
56.569 |
m^2 |
56.50 |
m^2 |
0.121 |
Immersed Area |
8.250 |
m^2 |
8.2 |
m^2 |
0.609 |
Wetted Surface |
90.358 |
m^2 |
90.27 |
m^2 |
0.097 |
Wetted Girth |
7.386 |
m |
7.39 |
m |
0.057 |
BMT |
1.8284 |
m |
1.826 |
m |
0.133 |
BML |
5.7139 |
m |
5.719 |
m |
0.090 |
Table 2.5.3 Horizontal Cylinder Negative Sinkage Results
Model Sinkage = 1.0m |
Water Density 1025.9 kg/m^3 |
Mesh Density 0.7 |
% Error |
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|
Analytic |
|
Orca3D |
|
|
Displaced Volume |
200.241 |
m^3 |
200 |
m^3 |
0.120 |
VCB |
-0.753 |
m |
-0.752 |
m |
0.178 |
Transverse Area Moment of Inertia |
150.849 |
m^4 |
150.3 |
m^4 |
0.364 |
Longitudinal Area Moment of Inertia |
471.405 |
m^4 |
470.9 |
m^4 |
0.107 |
Waterplane Area |
56.569 |
m^2 |
56.50 |
m^2 |
0.121 |
Immersed Area |
20.024 |
m^2 |
20.0 |
m^2 |
0.120 |
Wetted Surface |
154.686 |
m^2 |
154.61 |
m^2 |
0.049 |
Wetted Girth |
11.464 |
m |
11.46 |
m |
0.033 |
BMT |
0.7533 |
m |
0.752 |
m |
0.178 |
BML |
2.3542 |
m |
2.355 |
m |
0.035 |
Table 2.5.4 Horizontal Cylinder Positive Sinkage Results