Simple fluid dynamics

Quote:

6d. Given the curPos velocity and curNormal, you can now compute fluid interaction: e.g. flat plate force => 1/2*rho*V^2*angle applied in the direction of curNormal, surface/parasitic drag (in the direction of velocity projected to the plane defined by curPos and curNormal). This step will introduce drag/damping so that more complicated methods (such as dealing with rotational fluid effects and associated energy loss) aren't necessary for realistic looking behavior. Forces are added for each FluidSample (point of application: curPos):

Fluid resistance is usually taken against the cross sectional area of an object. The cross section is taken on the plane perpendicular to the velocity. In this case, it looks like he is dividing the hull into several equal chunks of area, in other words the polygons of the mesh.

Assuming that each polygon has an area of 1, you can find it's cross sectional area by taking the dot product of the polygon's normal and the velocity's normal.

In general, fluid resistance can be defined as the force:
F = -c₁V -c₂V² ...
The force is applied in the direction of V.

There is a point in most fluids where the fluid becomes turbulent due to the velocity of the object, at which point V² strongly dominates the force. Below that point (Reynolds Number,) the V term dominates. In the case of a boat in water, it's very likely to be the square term.

In this case the constant is represented by:
c₂ = ½ρV²A

But because he's assuming that the polygons are all of equal area, he let's that term become:
A = N⋅V/|V|
Where N is the polygon's normal, and V/|V| is the velocity's normal.

ρ is the density of the fluid, in this case water.

"angle" was probably a little misleading as a variable name.

Example code here.

angle is a dot product between the fluid velocity at the sample point and the surface normal. The force direction in the simple case is applied in the direction of the surface normal. The example code includes an efficiency term to allow elimination of induced drag. Skin or surface drag can also be added: the force is applied opposite fluid velocity in the plane of the surface normal at the sample point. In the case of a simple boat, applying skin drag regardless of angle will also work OK: force direction is opposite sample point velocity.