SailingVMG BoatPlan::GetVMGApparentWind(double VA)
{
SailingVMG avmg;
for(int i=0; i<4; i++) {
int iters = 0;
double VW = VA, lp = 1;
for(;;) {
SailingVMG vmg = GetVMGTrueWind(VW);
double W = vmg.values[i];
if(isnan(W) || iters++ > 128) {
avmg.values[i] = NAN;
break;
}
double VB = Speed(W, VW);
double cVA = VelocityApparentWind(VB, deg2rad(W), VW);
if(fabsf(cVA - VA) < 2e-1) {
avmg.values[i] = W;
break;
}
VW -= (cVA - VA) * lp;
lp *= .97;
}
}
return avmg;
}
double BoatPlan::SpeedAtApparentWind(double A, double VA, double *pW)
{
int iters = 0;
double VW = VA, W = A, VB = 0; // initial guess
double lp = 1;
for(;;) {
double cVB = Speed(W, VW);
VB -= (VB - cVB) * lp;
double cVA = VelocityApparentWind(VB, deg2rad(W), VW);
double cA = rad2posdeg(DirectionApparentWind(cVA, VB, deg2rad(W), VW));
if(isnan(cVA) || isnan(cA) || iters++ > 256) {
if(pW) *pW = NAN;
return NAN;
}
if(fabsf(cVA - VA) < 2e-2 && fabsf(cA - A) < 2e-2) {
if(pW) *pW = W;
return cVB;
}
VW -= (cVA - VA) * lp;
W -= (cA - A) * lp;
lp *= .97;
}
}
double Polar::SpeedAtApparentWindDirection(double A, double VW, double *pW)
{
int iters = 0;
double VB = 0, W = A; // initial guess
double lp = 1;
for(;;) {
double cVB = Speed(W, VW);
VB -= (VB - cVB) * lp;
double VA = VelocityApparentWind(VB, W, VW);
double cA = positive_degrees(DirectionApparentWind(VA, VB, W, VW));
if(isnan(cA) || iters++ > 256) {
if(pW) *pW = NAN;
return NAN;
}
if(fabs(cA - A) < 2e-2) {
if(pW) *pW = W;
return cVB;
}
W -= (cA - A) * lp;
lp *= .97;
}
}
/* start out with the boat stopped, and over time, iterate accelerating boat
until it reaches steady state. The speed of the boat is known already
from apparent wind, this function finds it for true wind */
void BoatPlan::BoatSteadyState(double W, double VW, double &B, double &VB, double &A, double &VA,
Boat &boat)
{
/* starting out not moving */
VB = 0, A = W, VA = VW;
double lp = .1;
const int count = 128;
double bucket = 0;
int bcount = 0;
for(;;) {
double v = VelocityBoat(A, VA);
if(v == 0) { // we cannot sail this way
B = 0;
VB = 0;
return;
}
double a = v - VB;
double drag = boat.FrictionDrag(VB) + boat.WakeDrag(VB);
if(isnan(drag)) {
VB = 0;
return;
}
a -= drag;
if(bcount == count) {
VB = bucket / count;
a = 0;
}
if(fabs(a) < 1e-2 || lp < 1e-2) {
if(VB < 0) // not allowing backwards sailing
VB = 0;
B = AngleofAttackBoat(A, VA);
return; /* reached steady state */
}
if(a < 0) {
bucket += VB;
bcount++;
// lp *= .97;
}
VB = (1-lp)*VB + lp*(VB+a); /* lowpass to get a smooth update */
VA = VelocityApparentWind(VB, W, VW);
A = DirectionApparentWind(VA, VB, W, VW);
}
}
double BoatPlan::SpeedAtApparentWindSpeed(double W, double VA)
{
int iters = 0;
double VW = VA, VB = 0; // initial guess
double lp = 1;
for(;;) {
double cVB = Speed(W, VW);
VB -= (VB - cVB) * lp;
double cVA = VelocityApparentWind(VB, deg2rad(W), VW);
if(isnan(cVA) || iters++ > 256)
return NAN;
if(fabsf(cVA - VA) < 2e-2)
return cVB;
VW -= (cVA - VA) * lp;
lp *= .97;
}
}
/* start out with the boat stopped, and over time, iterate accelerating boat
until it reaches steady state. The speed of the boat is known already
from apparent wind, this function finds it for true wind */
void BoatPlan::BoatSteadyState(double W, double VW, double &B, double &VB, double &A, double &VA,
Boat &boat)
{
/* starting out not moving */
VB = 0, A = W, VA = VW;
double lp = .03;
for(;;) {
double v = VelocityBoat(A, VA);
double a = v - VB;
double drag = boat.FrictionDrag(VB) + boat.WakeDrag(VB);
a -= drag;
if(fabs(a) < 1e-2 || a < 0) {
B = AngleofAttackBoat(A, VA);
return; /* reached steady state */
}
VB = (1-lp)*VB + lp*(VB+a); /* lowpass to get a smooth update */
VA = VelocityApparentWind(VB, W, VW);
A = DirectionApparentWind(VA, VB, W, VW);
}
}
double BoatPlan::DirectionApparentWind(double VB, double W, double VW)
{
double VA = VelocityApparentWind(VB, W, VW);
return DirectionApparentWind(VA, VB, W, VW);
}
