## 6D buoys: Results |

For general information on selecting and producing results, see the producing results topic.

The position, relative to global axes, of a user-specified point $\vec{p}$ on the buoy. The point $\vec{p}$ is given in buoy local coordinates; if $\vec{p}=(0,0,0)$ then the position and orientation reported are those of the buoy origin.

The position of the user-specified point $\vec{p}$ on the buoy, relative to the static position of $\vec{p}$, and with respect to the static orientation of the buoy. By static position and static orientation we mean the position and orientation in the model's static state. So, if $\vec{p}_\textrm{inst}$ is the instantaneous position, and $\vec{p}_\textrm{static}$ is the static position, then these results report $\vec{p}_\textrm{inst} - \vec{p}_\textrm{static}$ with respect to the buoy's static axis directions.

Define the orientation of the buoy relative to global axes.

Rotation 2 is in the range -90° to +90°. Range jump suppression is applied to rotation 1 and rotation 3, so values outside the range -360° to +360° might be reported.

The orientation of the buoy relative to its static orientation. Considered as a vector, $\vec{R} = (Rx, Ry, Rz)$ defines the rotation from the static orientation to the instantaneous orientation. The rotation is about the direction of the vector $\vec{R}$, and has magnitude $\lvert\vec{R}\rvert$.

The azimuth and declination of the local $z$-axis.

Acceleration, GX acceleration, GY acceleration, GZ acceleration

The magnitude and components of the velocity and acceleration of the buoy, relative to earth and with respect to global axes, at the user-specified point $\vec{p}$ on the buoy.

x acceleration, y acceleration, z acceleration

The components of the velocity and acceleration of the buoy, relative to earth and with respect to buoy axes, at the user-specified point $\vec{p}$ on the buoy.

Angular acceleration, x angular acceleration, y angular acceleration, z angular acceleration

The magnitude and components of the angular velocity and acceleration of the buoy, relative to earth and with respect to buoy axes.

The magnitude and components, in buoy axes directions, of the acceleration of the user-specified point $\vec{p}$ on the buoy, relative to the vertically downwards acceleration due to gravity.

This relative acceleration can be thought of as the acceleration of the point $\vec{p}$ relative to the free-falling state, and corresponds to the acceleration which would be reported by an accelerometer attached to the buoy at $\vec{p}$ (since an accelerometer reading of zero corresponds to free-falling), with its measurement directions aligned with the buoy local axes directions.

If the buoy experiences sea state disturbance, this will be accounted for in the sea state results.

The length of buoy above the water surface, calculated as follows:

- For a lumped buoy, this is $(1 - \PW)h$ where $\PW$ is the proportion wet and $h$ the buoy height.
- For a spar buoy it is the sum of the dry lengths of each of its cylinders, where the dry length of an individual cylinder is calculated as (cylinder length) $\times$ (cylinder volume above surface) / (cylinder total volume).

The remaining sea state results are reported at the user-specified point $\vec{p}$ on the buoy.

The global $Z$ coordinate of the instantaneous sea surface directly above or below $\vec{p}$.

The vertical clearance from $\vec{p}$ to the instantaneous sea surface. Negative values indicate submergence.

Sea acceleration, sea X acceleration, sea Y acceleration, sea Z acceleration

The magnitude and global $X$, $Y$ and $Z$ components of the water particle velocity (due to current and waves) and acceleration (due to waves) at $\vec{p}$. If $\vec{p}$ is above the water surface then the value at the water surface is reported.

Connection x force, connection y force, connection z force,

Connection x moment, connection y moment, connection z moment

These connection load results are only available for buoys that are connected to other objects. They report the total force and moment applied to the buoy by the object to which it is connected, *including* structural inertia loads and added inertia loads.

**Connection force** and **connection moment** report the magnitudes of the connection loads. The $x$, $y$ and $z$ results report the components of the connection force and moment in the local buoy axes directions. The moments given are moments about the buoy origin.

Note that these connection force and moment results include the structural and added inertial load on the buoy due to any acceleration of the parent object to which it is connected. This means that these results can be used for sea fastening calculations, by using a 6D buoy to represent the object to be fastened and connecting it to a vessel. The connection force and moment include the weight of the buoy and the inertial loads due to the vessel acceleration. Note that if the vessel motion is given by a time history then the time history interpolation method used is important since it affects the calculation of vessel acceleration and hence the inertial load.

Applied Lx force, applied Ly force, applied Lz force,

Applied Lx moment, applied Ly moment, applied Lz moment

The sum of all the local and global applied loads, reported in the local buoy axes directions.

Lx force, Ly force, Lz force, Lx moment, Ly moment, Lz moment,

GX force, GY force, GZ force, GX moment, GY moment, GZ moment

These results are not available for buoys that are connected to other objects – you can instead use the **connection force** and **connection moment** results for these.

These results are the total force and moment applied to the buoy, *excluding* structural inertia loads and added inertia loads due to acceleration of the buoy. They include the loads from any objects connected to the buoy, but again *exclude* structural inertia and added inertia loads on the connected object. The reported loads therefore correspond to the left-hand side of the equation of motion, $\text{total load} = \text{virtual inertia} \times \text{acceleration}$, where virtual inertia is the total structural and added inertia of the buoy and any connected objects.

**Force** and **moment** report the magnitudes of the loads. The $Lx$, $Ly$ and $Lz$ results report the components of the force and moment in the local buoy axes directions. The $GX$, $GY$ and $GZ$ results report the components of the force and moment in the global axes directions. The moments given are about the buoy origin.

Solid contact Lx force, solid contact Ly force, solid contact Lz force

The magnitude and components, in local buoy axes directions, of the force due to contact with elastic solids.

Morison element results are available for the buoy if it has one or more Morison elements. The results (other than the summed results) are specific to an individual element, chosen by its number. Segment results are reported at a user-specified arc length.

The magnitude and components (in buoy axes directions and at the buoy origin) of the sum of the loads on the buoy due to all of its Morison elements.

The magnitude and components (in buoy axes directions) of the total drag force on an individual Morison element.

The magnitude and components (in buoy axes directions) of the total fluid inertia force on an individual Morison element.

The proportion of a Morison element segment that is submerged in the sea. The value is in the range 0 to 1, a value of 0 meaning no submersion and 1 meaning completely submerged.

The magnitude and components (in element axes directions) of the relative fluid velocity for a Morison element segment.

The components (in element axes directions) of the drag coefficient for a Morison element segment.

The magnitude and components (in element axes directions) of the drag force, per unit length, applied to a Morison element segment.

The magnitude and components (in element axes directions) of the fluid inertia force, per unit length, applied to a Morison element segment.

Support results are available for the buoy if it has one or more supports. The results (other than the summed results) are specific to an individual support, chosen by its number. The **support contact clearance**, **support contact arc length**, **support lift out** and **support off end contact distance** results also allow a supported line to be selected, in which case the result is specific to that supported line; alternatively for those results, *(all supported lines)* may be selected to report the result across all lines supported by the buoy.

The magnitude and components (in support axes directions) of the reaction load on the support due to contact between the support and the supported line(s).

The minimum distance between the contact surfaces of the support cylinders and the supported line spline. If *(all supported lines)* is chosen, then the minimum contact clearance across all supported lines is reported. If the result is negative it means one or more of the supported lines has penetrated one or more of the support cylinders and the result represents the greatest penetration. If the point of closest approach on the supported line spline(s) falls more than one support cylinder radius beyond either end of the supported line(s), this result is not available: see the **support off end contact distance** result.

The arc length along the selected supported line at which contact with the support occurs. For a support that has more than one support cylinder, it is the arc length of the point of contact with the smallest **support contact clearance**. A negative value indicates that the support cylinder is beyond the end of the supported line, but by less than the support cylinder radius. If the point(s) of closest approach on the supported line spline are beyond the end of the supported line by more than one support cylinder radius, then there is no contact and this result is not available.

A supported line must be specified to obtain values for this result – contact arc length for *(all supported lines)* is not available.

The maximum distance, in the support z direction, from the support position to the point of closest approach on the supported line(s) spline axis. If *(all supported lines)* is selected, the maximum lift out over all supported lines is reported. If the point of closest approach on the supported line spline falls beyond the end of the supported line by more than one support cylinder radius, this result is not available.

Essentially this result gives the distance, in the support $z$ axis direction, by which the supported line axis has lifted away from the support position.

The maximum **support lift out** across all of the buoy's supports.

If the supported line is in contact with a support cylinder at a point beyond the support cylinder's ends this result reports the distance from the end of the support cylinder to the point of closest approach on the axis of the support cylinder. If the support has multiple support cylinders, and more than one of them is in contact with the supported line, then the maximum off-end contact distance across all these cylinders is reported. If *(all supported lines)* is specified, then the maximum off-end contact distance over all supported lines is reported. If none of the support cylinders and specified supported line(s) are in contact, or all the points of contact on the support cylinders are within the length of the support cylinders, this result is zero.

This enables you to check for the potential escape of support lines from their supports; the support cylinders are drawn with finite length but for the purpose of contact they are assumed to have infinite axial extent, so it is possible that the supported line is being contained by a non-physical part of the support.

The maximum **support off end contact distance** across all of the buoy's supports.

The magnitude and components (in buoy axes directions and at the buoy origin) of the sum of *all* the reaction loads and resulting moments on the buoy's supports. These results are the only support results which are *not* specific to an individual support, but are summed over all supports.

These results are only available for 6D lumped buoys that have non-zero slam area and slam coefficient and for spar buoys and towed fish that have a non-zero slam coefficient.

Slam force reports the total instantaneous slamming load experienced as the body enters or exits the water. Slam force acts in the direction normal to the water surface. The $GX$, $GY$ and $GZ$ results give components of the total slam load in the global axes directions.

The components in global axes directions of the moment of the slam force about the body reference origin.

If the 6D buoy has wings attached then for each wing the following results are available.

The position of the wing origin, relative to global axes.

The orientation angles of the wing, relative to the buoy.

The lift force, drag force and drag moment applied to the wing.

The lift force is applied at 90° to the relative flow direction. Positive values mean a force trying to push the wing towards its positive side, negative values towards its negative side.

The drag force is applied in the relative flow direction and is always positive.

The drag moment is applied about the line that is in the wing plane and at 90° to the relative flow direction. Positive values are moments trying to turn the wing to bring the wing y-axis $W\urm{y}$ to point along the relative flow direction; negative values are moments trying to turn the wing the opposite way.

For the purposes of reporting these results we use the concept of the *principal fluid* affecting the wing and report only the load on the wing due to the principal fluid, defined as follows:

- If the proportion dry $1{-}\PW\gt 0.5$ and wind loads on wings are included, then the principal fluid is the air.
- Otherwise the principal fluid is the sea

The angle, $\alpha$, that the relative flow vector makes with the plane of the wing, in the range -90° to +90°. Positive values mean that the flow is towards the positive side of the wing (i.e. hitting the negative side) and negative values mean that the flow is towards the negative side of the wing (i.e. hitting the positive side).

The value reported is with respect to the *principal fluid* affecting the wing.

The angle $\beta$ of the relative flow direction, measured in the wing plane. More specifically, it is the angle between wing x-axis $W\urm{x}$ and the projection of the relative flow vector onto the wing plane, measured positive towards $W\urm{z}$. Angle $\beta{=}0$ means that this projection is in the $W\urm{x}$ direction, 90° means it is along $W\urm{z}$ and -90° means it is in the negative $W\urm{z}$ direction.

The value reported is with respect to the *principal fluid* affecting the wing.

Range jump suppression is applied to the beta angle, so values outside the range -360° to +360° might be reported.