FGColumnVector3 FGPropeller::GetPFactor()
{
double px=0.0, py, pz;
py = Thrust * Sense * (GetActingLocationY() - GetLocationY()) / 12.0;
pz = Thrust * Sense * (GetActingLocationZ() - GetLocationZ()) / 12.0;
return FGColumnVector3(px, py, pz);
}
FGColumnVector3 FGPropeller::GetPFactor() const
{
// These are moments in lbf per ft : the lever arm along Z generates a moment
// along the pitch direction.
double p_pitch = Thrust * Sense * (GetActingLocationZ() - GetLocationZ()) / 12.0;
// The lever arm along Y generates a moment along the yaw direction.
double p_yaw = Thrust * Sense * (GetActingLocationY() - GetLocationY()) / 12.0;
return FGColumnVector3(0.0, p_pitch, p_yaw);
}
double FGPropeller::Calculate(double PowerAvailable)
{
double omega, alpha, beta;
double Vel = fdmex->GetAuxiliary()->GetAeroUVW(eU);
double rho = fdmex->GetAtmosphere()->GetDensity();
double RPS = RPM/60.0;
if (RPS > 0.00) J = Vel / (Diameter * RPS); // Calculate J normally
else J = 1000.0; // Set J to a high number
if (MaxPitch == MinPitch) ThrustCoeff = cThrust->GetValue(J);
else ThrustCoeff = cThrust->GetValue(J, Pitch);
ThrustCoeff *= CtFactor;
if (P_Factor > 0.0001) {
alpha = fdmex->GetAuxiliary()->Getalpha();
beta = fdmex->GetAuxiliary()->Getbeta();
SetActingLocationY( GetLocationY() + P_Factor*alpha*Sense);
SetActingLocationZ( GetLocationZ() + P_Factor*beta*Sense);
}
Thrust = ThrustCoeff*RPS*RPS*D4*rho;
omega = RPS*2.0*M_PI;
vFn(1) = Thrust;
// The Ixx value and rotation speed given below are for rotation about the
// natural axis of the engine. The transform takes place in the base class
// FGForce::GetBodyForces() function.
vH(eX) = Ixx*omega*Sense;
vH(eY) = 0.0;
vH(eZ) = 0.0;
if (omega > 0.0) ExcessTorque = GearRatio * PowerAvailable / omega;
else ExcessTorque = GearRatio * PowerAvailable / 1.0;
RPM = (RPS + ((ExcessTorque / Ixx) / (2.0 * M_PI)) * deltaT) * 60.0;
if (RPM < 1.0) RPM = 0; // Engine friction stops rotation arbitrarily at 1 RPM.
vMn = fdmex->GetPropagate()->GetPQR()*vH + vTorque;
return Thrust; // return thrust in pounds
}
double FGPropeller::Calculate(double EnginePower)
{
FGColumnVector3 localAeroVel = Transform().Transposed() * in.AeroUVW;
double omega, PowerAvailable;
double Vel = localAeroVel(eU);
double rho = in.Density;
double RPS = RPM/60.0;
// Calculate helical tip Mach
double Area = 0.25*Diameter*Diameter*M_PI;
double Vtip = RPS * Diameter * M_PI;
HelicalTipMach = sqrt(Vtip*Vtip + Vel*Vel) / in.Soundspeed;
PowerAvailable = EnginePower - GetPowerRequired();
if (RPS > 0.0) J = Vel / (Diameter * RPS); // Calculate J normally
else J = Vel / Diameter;
if (MaxPitch == MinPitch) { // Fixed pitch prop
ThrustCoeff = cThrust->GetValue(J);
} else { // Variable pitch prop
ThrustCoeff = cThrust->GetValue(J, Pitch);
}
// Apply optional scaling factor to Ct (default value = 1)
ThrustCoeff *= CtFactor;
// Apply optional Mach effects from CT_MACH table
if (CtMach) ThrustCoeff *= CtMach->GetValue(HelicalTipMach);
Thrust = ThrustCoeff*RPS*RPS*D4*rho;
// Induced velocity in the propeller disk area. This formula is obtained
// from momentum theory - see B. W. McCormick, "Aerodynamics, Aeronautics,
// and Flight Mechanics" 1st edition, eqn. 6.15 (propeller analysis chapter).
// Since Thrust and Vel can both be negative we need to adjust this formula
// To handle sign (direction) separately from magnitude.
double Vel2sum = Vel*abs(Vel) + 2.0*Thrust/(rho*Area);
if( Vel2sum > 0.0)
Vinduced = 0.5 * (-Vel + sqrt(Vel2sum));
else
Vinduced = 0.5 * (-Vel - sqrt(-Vel2sum));
// We need to drop the case where the downstream velocity is opposite in
// direction to the aircraft velocity. For example, in such a case, the
// direction of the airflow on the tail would be opposite to the airflow on
// the wing tips. When such complicated airflows occur, the momentum theory
// breaks down and the formulas above are no longer applicable
// (see H. Glauert, "The Elements of Airfoil and Airscrew Theory",
// 2nd edition, §16.3, pp. 219-221)
if ((Vel+2.0*Vinduced)*Vel < 0.0) {
// The momentum theory is no longer applicable so let's assume the induced
// saturates to -0.5*Vel so that the total velocity Vel+2*Vinduced equals 0.
Vinduced = -0.5*Vel;
}
// P-factor is simulated by a shift of the acting location of the thrust.
// The shift is a multiple of the angle between the propeller shaft axis
// and the relative wind that goes through the propeller disk.
if (P_Factor > 0.0001) {
double tangentialVel = localAeroVel.Magnitude(eV, eW);
if (tangentialVel > 0.0001) {
double angle = atan2(tangentialVel, localAeroVel(eU));
double factor = Sense * P_Factor * angle / tangentialVel;
SetActingLocationY( GetLocationY() + factor * localAeroVel(eW));
SetActingLocationZ( GetLocationZ() + factor * localAeroVel(eV));
}
}
omega = RPS*2.0*M_PI;
vFn(eX) = Thrust;
// The Ixx value and rotation speed given below are for rotation about the
// natural axis of the engine. The transform takes place in the base class
// FGForce::GetBodyForces() function.
vH(eX) = Ixx*omega*Sense;
vH(eY) = 0.0;
vH(eZ) = 0.0;
if (omega > 0.0) ExcessTorque = PowerAvailable / omega;
else ExcessTorque = PowerAvailable / 1.0;
RPM = (RPS + ((ExcessTorque / Ixx) / (2.0 * M_PI)) * deltaT) * 60.0;
if (RPM < 0.0) RPM = 0.0; // Engine won't turn backwards
// Transform Torque and momentum first, as PQR is used in this
// equation and cannot be transformed itself.
vMn = in.PQR*(Transform()*vH) + Transform()*vTorque;
return Thrust; // return thrust in pounds
}
double FGPropeller::Calculate(double EnginePower)
{
FGColumnVector3 localAeroVel = Transform().Transposed() * in.AeroUVW;
double omega, PowerAvailable;
double Vel = localAeroVel(eU);
double rho = in.Density;
double RPS = RPM/60.0;
// Calculate helical tip Mach
double Area = 0.25*Diameter*Diameter*M_PI;
double Vtip = RPS * Diameter * M_PI;
HelicalTipMach = sqrt(Vtip*Vtip + Vel*Vel) / in.Soundspeed;
if (RPS > 0.0) J = Vel / (Diameter * RPS); // Calculate J normally
else J = Vel / Diameter;
PowerAvailable = EnginePower - GetPowerRequired();
if (MaxPitch == MinPitch) { // Fixed pitch prop
ThrustCoeff = cThrust->GetValue(J);
} else { // Variable pitch prop
ThrustCoeff = cThrust->GetValue(J, Pitch);
}
// Apply optional scaling factor to Ct (default value = 1)
ThrustCoeff *= CtFactor;
// Apply optional Mach effects from CT_MACH table
if (CtMach) ThrustCoeff *= CtMach->GetValue(HelicalTipMach);
Thrust = ThrustCoeff*RPS*RPS*D4*rho;
// Induced velocity in the propeller disk area. This formula is obtained
// from momentum theory - see B. W. McCormick, "Aerodynamics, Aeronautics,
// and Flight Mechanics" 1st edition, eqn. 6.15 (propeller analysis chapter).
// Since Thrust and Vel can both be negative we need to adjust this formula
// To handle sign (direction) separately from magnitude.
double Vel2sum = Vel*abs(Vel) + 2.0*Thrust/(rho*Area);
if( Vel2sum > 0.0)
Vinduced = 0.5 * (-Vel + sqrt(Vel2sum));
else
Vinduced = 0.5 * (-Vel - sqrt(-Vel2sum));
// P-factor is simulated by a shift of the acting location of the thrust.
// The shift is a multiple of the angle between the propeller shaft axis
// and the relative wind that goes through the propeller disk.
if (P_Factor > 0.0001) {
double tangentialVel = localAeroVel.Magnitude(eV, eW);
if (tangentialVel > 0.0001) {
// The angle made locally by the air flow with respect to the propeller
// axis is influenced by the induced velocity. This attenuates the
// influence of a string cross wind and gives a more realistic behavior.
double angle = atan2(tangentialVel, Vel+Vinduced);
double factor = Sense * P_Factor * angle / tangentialVel;
SetActingLocationY( GetLocationY() + factor * localAeroVel(eW));
SetActingLocationZ( GetLocationZ() + factor * localAeroVel(eV));
}
}
omega = RPS*2.0*M_PI;
vFn(eX) = Thrust;
// The Ixx value and rotation speed given below are for rotation about the
// natural axis of the engine. The transform takes place in the base class
// FGForce::GetBodyForces() function.
FGColumnVector3 vH(Ixx*omega*Sense*Sense_multiplier, 0.0, 0.0);
if (omega > 0.0) ExcessTorque = PowerAvailable / omega;
else ExcessTorque = PowerAvailable / 1.0;
RPM = (RPS + ((ExcessTorque / Ixx) / (2.0 * M_PI)) * in.TotalDeltaT) * 60.0;
if (RPM < 0.0) RPM = 0.0; // Engine won't turn backwards
// Transform Torque and momentum first, as PQR is used in this
// equation and cannot be transformed itself.
vMn = in.PQRi*(Transform()*vH) + Transform()*vTorque;
return Thrust; // return thrust in pounds
}