/* wave drag in terms of froude number
2
/ sin(Pi - F^-2) \
Drag = | ----------------------- |
\ (Pi - F^-2) (1 + Pi F^2) /
___
V = F * \/g l
F = sqrt(g * l) / V;
g = 9.8 (gravity constant)
l is length of vessel in meters
V is meters per second
Reaches a peak at F=Pi^-.5 which is about .56
The huge increase starts at F = .4 (normal hull speed setting)
Also interesting to note that at 80% of normal hull speed, the wave
drag is zero as well, but the first hump occurs from .32 to .4
This works for the full range from displacement to planing mode.
*/
double Boat::WakeDrag(double VB)
{
#if 0 // this may be theoretically correct in flat water, but is complex and not practical
if(VB == 0) return 0;
const double G = 9.8;
double L = ft2m(lwl_ft);
double F = knots2m_s(VB) / sqrt(G * L);
double F2 = square(F), invF2 = 1/F2;
double D = square(sin(M_PI - invF2) / (M_PI - invF2) / (1 + M_PI * F2));
return wake_drag * wake_drag * D * VB * VB; /* D is max of .25 (at F=.56) so normalize to 1 */
#else
// classic hull speed exponential without planing possible
// double hull_speed = 1.34*sqrt(lwl_ft);
// double our_wave_drag = 2 * wake_drag * (pow(8, VB / sqrt(lwl_ft)) - 1);
double coeff = VB / 1.34 / sqrt(lwl_ft);
if(coeff < 1)
return 0;
double drag = (pow(32, coeff - 1) - 1) * wake_drag * 10;
if(drag > VB)
drag = VB;
return drag;
#endif
}
/* wave drag in terms of froude number
2
/ sin(Pi - F^-2) \
Drag = | ----------------------- |
\ (Pi - F^-2) (1 + Pi F^2) /
___
V = F * \/g l
F = sqrt(g * l) / V;
g = 9.8 (gravity constant)
l is length of vessel in meters
V is meters per second
Reaches a peak at F=Pi^-.5 which is about .56
The huge increase starts at F = .4 (normal hull speed setting)
Also interesting to note that at 80% of normal hull speed, the wave
drag is zero as well, but the first hump occurs from .32 to .4
This works for the full range from displacement to planing mode.
*/
double Boat::WakeDrag(double VB)
{
if(VB == 0) return 0;
const double G = 9.8;
double L = ft2m(lwl_ft);
double F = knots2m_s(VB) / sqrt(G * L);
double F2 = square(F), invF2 = 1/F2;
double D = square(sin(M_PI - invF2) / (M_PI - invF2) / (1 + M_PI * F2));
return wake_drag * wake_drag * D * VB * VB * 4; /* D is max of .25 (at F=.56) so normalize to 1 */
}
