/// <summary>
/// Compute the Aerodynamic Influence Coefficienf matrix element w_ij, representing the influence a wing tile j is exerting on the location i.
/// </summary>
/// <param name="ri">The position vector of the point being influenced by tile j.</param>
/// <param name="j">The tile whose horse-shoe vortex is influencing point i.</param>
/// <returns>The vector indicating in which direction a given horse-shoe vortex is contributing velocity.</returns>
public static Vector Wij(Vector ri, WingTile j)
{
Vector xHat = new Vector(new double[] { 1, 0, 0 });
Vector a = ri - j.RA;
Vector b = ri - j.RB;
return((Vector.Cross(a, b) * (1 / a.Mag + 1 / b.Mag) / (a.Mag * b.Mag + a * b) + Vector.Cross(a, xHat) / ((a.Mag - a * xHat) * a.Mag) - Vector.Cross(b, xHat) / ((b.Mag - b * xHat) * b.Mag)) / (4 * Math.PI));
}
/// <summary>
/// Generates an array of wingtiles.
/// </summary>
/// <param name="camberLine">The camber line represented by a 2-dimensional array of points.</param>
/// <param name="chord">The wing chord length.</param>
/// <param name="wingSpan">The wingspan.</param>
/// <param name="numOfTilesSpanwise">Number of tiles spanwise.</param>
/// <returns>The generated array of wingtiles.</returns>
public static WingTile[] GetWingTiles(double[,] camberLine, double chord, double wingSpan, int numOfTilesSpanwise)
{
double tileWidth = wingSpan / numOfTilesSpanwise;
WingTile[] wingTiles = new WingTile[numOfTilesSpanwise * (camberLine.GetLength(0) - 1)];
int index = 0;
for (int i = 0; i < numOfTilesSpanwise; i++)
{
// camberLine already has the desired amount of points
for (int j = 0; j < camberLine.GetLength(0) - 1; j++)
{
// x - chordwise (backwards)
// y - spanwise (to the right)
// z - normal (upwards)
wingTiles[index++] = new WingTile(new Vector(new double[] {
chord *camberLine[j, 0],
i *tileWidth,
chord *camberLine[j, 1]
}),
new Vector(new double[] {
chord *camberLine[j, 0],
(i + 1) * tileWidth,
chord * camberLine[j, 1]
}),
new Vector(new double[] {
chord *camberLine[j + 1, 0],
i *tileWidth,
chord *camberLine[j + 1, 1]
})
);
}
}
return(wingTiles);
}