6D buoys: Wings

6D buoys can have a number of wings attached which may be used to represent lift surfaces, diverters etc. Each wing has its own data and results available.

A wing is a rectangular surface, attached to the buoy at a specified position and orientation, which experiences lift force, drag force and drag moment, due to the relative flow of fluid past the wing. These loads are calculated from user-defined coefficients which are functions of the incidence angle of the relative fluid flow.

The fluid referred to here can be the sea, the air, or both, as follows.

Whenever the wing is completely below the instantaneous water surface, then the lift and drag loads are calculated using the sea density, velocity and incidence angle.
Whenever the wing is completely above the water surface, and if you have elected to include wind loads on wings, then air lift and drag loads are calculated and applied, using the same coefficients and formulae but with air density, velocity and incidence angle.
When the wing is partially submerged, OrcaFlex calculates what proportion of the wing area is below the instantaneous water surface, by assuming a planar sea surface defined by the instantaneous surface height and normal direction at the wing origin. This is the wing's proportion wet, $\PW$. The water lift and drag loads are calculated as if the wing was fully submerged, but then scaled by $\PW$ before they are applied. If you include wind loads on wings, then OrcaFlex also calculates the air lift and drag loads (as if the wing was not submerged at all) and scales them by $1{-}\PW$, i.e. the proportion dry.

Notes:	The true effects of a wing breaking surface, for instance planing and slamming, are much more complex than this and are not accounted for here (though slam loads on the 6D buoy itself can be included).
	The wing results relating to fluid flow are reported for the principal fluid affecting the wing.

Wings do not have any mass, added mass or buoyancy associated with them: any of these quantities due to wings should be added into the properties of the buoy itself.

The drag force on a wing is applied in the direction of relative flow. The lift force is the force at 90° to that direction. The moment represents that which arises if the centre of pressure is not at the wing centre. The details of the calculation of these loads are given below.

Figure:

Wing model

Each wing has its own set of local wing axes, with origin $W$ at the wing centre and axes $W\urm{x}$, $W\urm{y}$ and $W\urm{z}$.

$W\urm{y}$ is normal to the wing surface and points towards the positive side of the wing, i.e. the side towards which positive lift forces act.
$W\urm{x}$ and $W\urm{z}$ are in the plane of the wing. The wing is therefore a rectangle in the $W\urm{xz}$ plane, centred on $W$.
$W\urm{z}$ is the principal axis of the wing, about which the wing can easily be pitched by adjusting the wing gamma angle.
$W\urm{x}$ is normal to $W\urm{z}$, so that $(W\urm{x},W\urm{y},W\urm{z})$ form a right-hand triad.
We normally choose $W\urm{z}$ and $W\urm{x}$ so that $W\urm{x}$ is towards the leading edge of the wing. With this arrangement, increasing the wing gamma angle moves the leading edge in the direction of positive lift.

We refer to the wing's length in the $W\urm{z}$ direction as its span and its width in the $W\urm{x}$ direction as its chord.

Incidence angle

The incidence angle $\alpha$ is that which the relative flow vector makes to the wing surface, and is calculated as 90° minus the angle between $W\urm{y}$ and the relative flow vector.

This angle is always in the range $-90\degree \le\alpha\le +90\degree$; an error will be reported if the first and last angles in the table are not -90° and +90° respectively. A positive value for $\alpha$ means that the flow is towards the positive side of the wing (i.e. hitting the negative side) and a negative value means that the flow is towards the negative side of the wing (i.e. hitting the positive side).

Linear interpolation is used to obtain coefficients for angles between the values given.

Note:

The wing lift, drag and moment are assumed to depend only on the incidence angle, not on the angle of attack in the wing plane. OrcaFlex will therefore use the same lift, drag and moment coefficients for flow (with the same incidence angle) onto the front, the side or the back of the wing, even though your data may only apply over a limited range of in-plane attack angles. You can check that the angle of attack in the wing plane stays within the range of your data by examining the beta angle result.

Forces and moment on wings

The hydrodynamic and aerodynamic loads applied to the wing are calculated as follows. Aerodynamic loads are only applied if include wind loads on 6D buoy wings is enabled in the environment data.

The lift coefficient $\C{l}(\alpha)$ governs the lift force applied to the wing. The lift coefficients may be positive or negative; the magnitude of the lift force is given by \begin{equation} f\urm{L} = \frac12 p\, \C{l}(\alpha) \rho\, a |\vec{v}|^2 \end{equation} where

$p=$ proportion wet or proportion dry as appropriate

$\rho=$ density of the fluid (water or air as appropriate)

$a=$ area of wing

$\vec{v}=$ relative flow velocity at the wing centre.

The lift force is applied at the wing centre, along the line that is at 90° to the relative flow vector and in the plane of that vector and $W\urm{y}$. For $\alpha=\pm 90\degree$, this direction is ill-defined and the lift coefficient must be zero: this is enforced by OrcaFlex. Positive lift coefficients mean lift pushing the wing towards its positive side (see the wing model diagram).

The drag force is defined by the drag coefficient $\C{d}(\alpha)$ using the formula \begin{equation} \vec{f}\urm{D} = \frac12 p\, \C{d}(\alpha) \rho\, a \vec{v}|\vec{v}| \end{equation} The drag coefficient $\C{d}$ cannot be negative (again this is enforced by OrcaFlex), so the drag force is always in the relative flow direction.

The moment coefficient $C\urm{M}(\alpha)$ defines a moment that is applied to the wing to represent the fact that the position of the centre of pressure may depend on the incidence angle $\alpha$. The moment coefficients can be positive or negative; the moment has magnitude given by \begin{equation} m = \frac12 p\, \C{m}(\alpha) \rho\, a |\vec{v}|^2 c \end{equation} where

$c=$ the chord of the wing.

This moment is applied about the line that is in the wing plane and is at 90° to the relative flow vector. For $\alpha=\pm 90\degree$ this direction is ill-defined, so OrcaFlex requires that the moment coefficient is zero here. Positive moment coefficients mean that the moment is trying to turn the wing to bring $W\urm{y}$ to point along the relative flow direction.