Navigation:  Hydrostatics & Stability > Output

Before the hydrostatic and stability calculations are performed, the model will be first be heeled about the world longitudinal axis (if necessary), then trimmed about the world transverse axis (if necessary), and finally sunk along the vertical world coordinate with positive sinkage defined in the negative vertical direction (if necessary) depending on the flotation condition(s) defined.  For more detailed information on defining the flotation condition(s) see the Defining the Flotation Condition(s) section. The results are reported in the coordinates of the boat in its orientation prior to the calculations. If you have chosen to transform the model to equilibrium flotation plane, the output results (such as VCB) are reported in the coordinate system of the original model orientation.

 

 

Equilibrium Condition

A vessel with a given shape and weight may have multiple orientations where it is in equilibrium. These equilibria may be stable or unstable, but they are all equilibrium conditions. For example, consider a cube, with half the density of water (so that it floats with half of its volume out of the water), and its center of gravity in the center of the cube. With an initial flotation plane at the midpoint, this equilibrium flotation plane will be found:

 

 

But of course, the cube is equally happy to float with any of the six sides up, each representing a valid equilibrium.

 

 

But none of these flotation conditions are actually stable. The center of buoyancy and center of gravity are aligned, but if the cube was disturbed, it would rotate to the following condition, which maximizes the waterplane inertia (and this orientation could be repeated with any of the 8 corners of the cube pointing up).

 

 

Orca3D will usually find the equilibrium condition that you expect, but sometimes, particularly when the equilibrium is far away from the initial condition (for example, a large off-center weight is applied that causes a large list angle), an unexpected condition will be found. The report will highlight values of Heel and Trim that are beyond the user-defined threshold values (set in OrcaProperties), to make you aware of the situation. In the figures below, the threshold value for trim has been set to 10 degrees, and the resultant condition had a trim slightly over 10 degrees. Also, the GMt and GMl were less than zero, so all three values are highlighted in the output.

 

 

 

Another way to visualize the equilibrium condition is to insert a plane that represents the waterplane.

 

If you are having difficulty with Orca3D finding the "wrong" equilibrium condition, try the following:

 

Output

The following are the calculated values provided in the hydrostatics and stability report and are provided for each flotation condition defined.

 

Load Condition Parameters

 

The following inputs define the flotation condition(s) by either weight or model sinkage, model trim or LCG, model heel or TCG, and VCG.

 

Weight: the overall weight of the model in the specified fluid density, in the units shown

 

Model Sinkage: the depth of the world origin below the resultant flotation plane, perpendicular to the resultant flotation plane. Positive sinkage is defined as the origin being below the flotation plane. This is sometimes referred to as "origin depth."

 

Figure 1.4 Model Positive Sinkage of 0.5 Meters

 

 

Model Trim: the trim angle of the vessel, in degrees from the horizontal plane in the world coordinates. A right-hand coordinate system is used, so that if positive X is aft, positive Y to starboard, and positive Z is up, a positive trim angle is bow up.

 

 

Figure 1.3 Model Trimmed Positive 3.5 Degrees

 

LCG: the longitudinal center of gravity of the vessel, in the units shown, measured from the world origin

 

Model Heel: the heel angle of the vessel, in degrees from the horizontal plane in the world coordinates. A right-hand coordinate system is used, so that if positive X is aft, positive Y to starboard, and positive Z is up, a positive heel angle is to port.

 

 

Figure 1.2 Model Heeled Positive 30 Degrees

 

 

TCG: the transverse center of gravity of the vessel, in the units shown measured in the transverse axis from the world origin

 

VCG: the vertical center of gravity of the vessel, in the units shown measured in the vertical axis from the Rhino origin

 

 

Resulting Model Attitude and Hydrostatic Properties

 

The resulting model orientation and calculated hydrostatic properties for each defined flotation condition(s). All values include only those surfaces that were selected for the computation. Note that even if you have not chosen the option to "Transform the model to the resultant flotation plane," results are reported as if the model moved in the Rhino coordinate system, such that the plane of the Rhino origin (e.g. Z=0) is the flotation plane. Coordinates are reported in the "vessel's coordinate system." The vessel's coordinates are created by transforming the original coordinate system along with the model (heel, trim, and sinkage). In the figure below, The center of buoyancy (CB) and center of flotation (CB) are shown, with their location in the vessel's coordinates.

 

 

 

A summary of the values used to define the condition are shown (for example, the values of Sinkage, Trim, and Heel that were entered).

 

 

These are the values of the mesh settings for the model.  For a description of how they affect the results, see the Mesh Parameters section of Properties & Units.

 

 

The load condition parameters and resultant model attitude are shown again for the load condition.  Also, the fluid type and fluid density are displayed in the units shown, together with an indicator to show if the geometry was mirrored for the computations.

 

 

Heel Angle: the resultant heel angle, in degrees, of the vessel from the horizontal plane in the world coordinates resulting from the defined flotation condition.

 

Trim Angle: the resultant trim angle, in degrees, of the vessel from the horizontal plane in the world coordinates resulting from the defined flotation condition.

 

Sinkage: the depth of the world origin below the resultant flotation plane, perpendicular to the resultant flotation plane. Positive sinkage is defined as the origin being below the flotation plane. This is sometimes referred to as "origin depth."

 

 

Length Overall, LOA: The length of the vessel, including portions that are not submerged

 

Beam Overall, BOA: The maximum beam of the vessel, including portions that are not submerged. (If the model is a multihull, this dimension is the maximum from the outermost point on one side of the vessel to the outermost point on the opposite side. It does not refer to a single hull.)

 

Depth Overall, D: The maximum depth of the vessel, from the deepest point in the water to the highest point above the water.

 

Loa/Boa: The ratio of the Length Overall to the Beam Overall

 

Boa/D: The ratio of the Beam Overall to the Depth Overall

 

 

Waterline length, Lwl: The  waterline length of the vessel

 

Waterline Beam, Bwl: The waterline beam of the vessel. (If the model is a multihull, this dimension is the maximum from the outermost point on the waterline on one side of the vessel the outermost point on the waterline on the opposite side. It does not refer to the waterline beam of a single hull.)

 

Navigational Draft, T: The distance, perpendicular to the flotation plane, from the flotation plane down to the deepest point on the model. If the model has appendages (such as a sailboat keel), they will be included.

 

Lwl/Bwl: The ratio of the Waterline Length to the Waterline Beam.

 

Bwl/T: The ratio of the Waterline Beam to the Navigational Draft.

 

D/T: The ratio of the Depth Overall to the Navigational Draft

 

 

Displacement: the overall weight of the vessel, in the units shown, as defined in the input or calculated from the defined flotation condition.

 

Volume: The integrated underwater volume of the vessel in the units show.

 

LCB: the longitudinal center of buoyancy of the resultant model orientation in the units shown, reported in the vessel's coordinates.

 

TCB: the transverse center of buoyancy of the resultant model orientation in the units shown, reported in the vessel's coordinates.

 

VCB: the vertical center of buoyancy of the resultant model orientation in the units shown, reported in the vessel's coordinates.

 

Wet Area: the area, in the units shown, of the underwater surfaces selected for the hydrostatic & stability analysis.

 

Moment to Trim: the longitudinal moment required to trim the vessel, in the units shown. For example, a trim of 1 cm means that the vessel has trimmed enough to create a change in draft of 1 cm between the fore and aft ends of the waterline.

 

Displ-Length Ratio: The displacement length ratio, which is always expressed in imperial units of long tons/ft^3. It is defined as (Displacement in long tons / (Length in feet/100)^3)

 

FB/Lwl: The ratio of LCB to LWL, measured from the forward end of LWL; a value less than 0.5 means that the LCB is forward of the midpoint of LWL.

 

TCB/Bwl: The ratio of the transverse center of buoyancy to the waterline beam.

 

 

 

Awp: the area, in the units shown, of the waterplane of the resultant model orientation.

 

LCF: the longitudinal center of flotation of the resultant model orientation in the units shown, reported in the vessel's coordinates.

 

TCF: the transverse center of flotation of the resultant model orientation in the units shown, reported in the vessel's coordinates.

 

Weight to Immerse: the weight required to sink the vessel one unit in the direction perpendicular to the equilibrium flotation plane.

 

FF/Lwl: The ratio of LCF to LWL, measured from the forward end of LWL; a value less than 0.5 means that the LCF is forward of the midpoint of LWL.

 

TCF/Bwl: The ratio of the transverse center of flotation to the waterline beam.

 

 

Ax: the maximum underwater sectional area calculated using Orca sections, in the units shown.  The maximum value is interpolated from the Orca sections, by fitting a parabola to the Orca station of maximum sectional area and the two stations on either side of it. If no Orca sections are specified, this value will be 0.

 

Ax Location: The longitudinal location, in Rhino coordinates, of the station of maximum area (see note on interpolation above)

 

Ax Location / Lwl: The ratio of Ax Location to LWL, measured from the forward end of LWL; a value less than 0.5 means that the Ax is forward of the midpoint of LWL.

 

 

Cb: the block coefficient of the resultant model orientation due to the defined flotation condition, defined as (displaced volume / (LWL x T)), where T is the maximum navigational draft (i.e. the lowest point on the model in the resultant model orientation, which could include objects such as a keel).

 

Cp: the prismatic coefficient of the resultant model orientation, defined as (Ax / (LWL x T)), where T is the maximum navigational draft (i.e. the lowest point on the model in the resultant model orientation, which could include objects such as a keel).  If no Orca sections are defined, this will be 0.

 

Cvp: the vertical prismatic coefficient of the resultant model orientation, defined as (displaced volume / (AWP x T)), where T is the maximum navigational draft (i.e. the lowest point on the model in the resultant model orientation, which could include objects such as a keel).

 

Cx: the maximum section coefficient of the resultant model orientation, defined as (Ax / (BWL x T)), where T is the maximum navigational draft (i.e. the lowest point on the model in the resultant model orientation, which could include objects such as a keel).  If no Orca sections are defined, this will be 0.

 

Cwp: the waterplane coefficient of the resultant model orientation, defined as (AWP / (LWL x BWL)).

 

Cws: the wetted surface coefficient of the resultant model orientation, defined as (wetted surface / SQRT(displaced volume * LWL)).

 

 

Note that the 0 degree condition is taken as the original model orientation, not the equilibrium flotation plane. If a non-zero TCG or a non-zero Model Heel are entered, there will be a non-zero righting arm at 0 degrees of heel. Zero righting arm will correspond to the heel angle at the equilibrium flotation plane.

The calculation of the righting arm allows the model to trim as it heels to maintain a true hydrostatic balance (this is true even if a Model Trim was entered to define the equilibrium flotation plane; the Model Trim is used to determine the center of gravity, which is then used as the model is heeled).

I (transverse): The transverse moment of inertia of the waterplane

 

I (longitudinal): The longitudinal moment of inertia of the waterplane

 

BMt: the transverse metacentric radius (distance from the vertical center of buoyancy to the transverse metacenter) of the resultant flotation condition

 

BMl: the longitudinal metacentric radius (distance from the vertical center of buoyancy to the longitudinal metacenter) of the resultant flotation condition

 

GMt: the transverse metacentric height (distance from the vertical center of gravity to the transverse metacenter) of the resultant flotation condition

 

GMl: the longitudinal metacentric height (distance from the vertical center of gravity to the longitudinal metacenter) of the resultant flotation condition

 

Mt: the height of the transverse metacenter in the resultant flotation condition, measured from the equilibrium flotation plane

 

Ml: the height of the longitudinal metacenter in the resultant flotation condition, measured from the equilibrium flotation plane

 

 

If Orca stations are defined, a plot of the immersed area and wetted girth versus station location is displayed.  A table of station location, measured from the Rhino origin, immersed area and wetted girth is shown.

 

 

If the “Compute Righting Arm at these Heel Angles” box is checked in the Hydrostatics & Stability Analysis dialog, a stability curve will be plotted for righting arm versus heel angle.  A table of trim angle, righting arm and righting moment, in the units shown, is displayed for each defined heel angle. Note that the 0 degree condition is taken as the original model orientation, not the equilibrium flotation plane. If a non-zero TCG or a non-zero Model Heel are entered, there will be a non-zero righting arm at 0 degrees of heel. Zero righting arm will correspond to the heel angle at the equilibrium flotation plane.

 

 

If any Points of Interest have been defined, a table defining their locations will be shown, followed by a table showing their heights above (+) or below (-) the flotation plane at each heel angle.