const FGMatrix33& FGBuoyantForces::GetGasMassInertia(void)
{
const unsigned int size = Cells.size();
if (size == 0) return gasCellJ;
gasCellJ = FGMatrix33();
for (unsigned int i=0; i < size; i++) {
gasCellJ += Cells[i]->GetInertia();
}
return gasCellJ;
}
const FGMatrix33& FGBuoyantForces::GetGasMassInertia(void)
{
const unsigned int size = Cells.size();
if (size == 0) return gasCellJ;
gasCellJ = FGMatrix33();
for (unsigned int i=0; i < size; i++) {
FGColumnVector3 v = MassBalance->StructuralToBody( Cells[i]->GetXYZ() );
// Body basis is in FT.
const double mass = Cells[i]->GetMass();
// FIXME: Verify that this is the correct way to change between the
// coordinate frames.
gasCellJ += Cells[i]->GetInertia() +
FGMatrix33( 0, - mass*v(1)*v(2), - mass*v(1)*v(3),
- mass*v(2)*v(1), 0, - mass*v(2)*v(3),
- mass*v(3)*v(1), - mass*v(3)*v(2), 0 );
}
return gasCellJ;
}
const FGMatrix33& FGMassBalance::CalculatePMInertias(void)
{
size_t size = PointMasses.size();
if (size == 0) return pmJ;
pmJ = FGMatrix33();
for (unsigned int i=0; i<size; i++) {
pmJ += GetPointmassInertia( lbtoslug * PointMasses[i]->Weight, PointMasses[i]->Location );
pmJ += PointMasses[i]->GetPointMassInertia();
}
return pmJ;
}
const FGMatrix33& FGPropulsion::CalculateTankInertias(void)
{
size_t size = Tanks.size();
if (size == 0) return tankJ;
tankJ = FGMatrix33();
for (unsigned int i=0; i<size; i++) {
tankJ += FDMExec->GetMassBalance()->GetPointmassInertia( lbtoslug * Tanks[i]->GetContents(),
Tanks[i]->GetXYZ());
tankJ(1,1) += Tanks[i]->GetIxx();
tankJ(2,2) += Tanks[i]->GetIyy();
tankJ(3,3) += Tanks[i]->GetIzz();
}
return tankJ;
}
static FGMatrix33 ReadInertiaMatrix(Element* document)
{
double bixx, biyy, bizz, bixy, bixz, biyz;
bixx = biyy = bizz = bixy = bixz = biyz = 0.0;
if (document->FindElement("ixx"))
bixx = document->FindElementValueAsNumberConvertTo("ixx", "SLUG*FT2");
if (document->FindElement("iyy"))
biyy = document->FindElementValueAsNumberConvertTo("iyy", "SLUG*FT2");
if (document->FindElement("izz"))
bizz = document->FindElementValueAsNumberConvertTo("izz", "SLUG*FT2");
if (document->FindElement("ixy"))
bixy = document->FindElementValueAsNumberConvertTo("ixy", "SLUG*FT2");
if (document->FindElement("ixz"))
bixz = document->FindElementValueAsNumberConvertTo("ixz", "SLUG*FT2");
if (document->FindElement("iyz"))
biyz = document->FindElementValueAsNumberConvertTo("iyz", "SLUG*FT2");
return FGMatrix33( bixx, -bixy, bixz,
-bixy, biyy, -biyz,
bixz, -biyz, bizz );
}
void FGLocation::ComputeDerivedUnconditional(void) const
{
// The radius is just the Euclidean norm of the vector.
mRadius = mECLoc.Magnitude();
// The distance of the location to the Z-axis, which is the axis
// through the poles.
double r02 = mECLoc(eX)*mECLoc(eX) + mECLoc(eY)*mECLoc(eY);
double rxy = sqrt(r02);
// Compute the sin/cos values of the longitude
double sinLon, cosLon;
if (rxy == 0.0) {
sinLon = 0.0;
cosLon = 1.0;
} else {
sinLon = mECLoc(eY)/rxy;
cosLon = mECLoc(eX)/rxy;
}
// Compute the sin/cos values of the latitude
double sinLat, cosLat;
if (mRadius == 0.0) {
sinLat = 0.0;
cosLat = 1.0;
} else {
sinLat = mECLoc(eZ)/mRadius;
cosLat = rxy/mRadius;
}
// Compute the longitude and latitude itself
if ( mECLoc( eX ) == 0.0 && mECLoc( eY ) == 0.0 )
mLon = 0.0;
else
mLon = atan2( mECLoc( eY ), mECLoc( eX ) );
if ( rxy == 0.0 && mECLoc( eZ ) == 0.0 )
mLat = 0.0;
else
mLat = atan2( mECLoc(eZ), rxy );
// Compute the transform matrices from and to the earth centered frame.
// See Stevens and Lewis, "Aircraft Control and Simulation", Second Edition,
// Eqn. 1.4-13, page 40. In Stevens and Lewis notation, this is C_n/e - the
// orientation of the navigation (local) frame relative to the ECEF frame,
// and a transformation from ECEF to nav (local) frame.
mTec2l = FGMatrix33( -cosLon*sinLat, -sinLon*sinLat, cosLat,
-sinLon , cosLon , 0.0 ,
-cosLon*cosLat, -sinLon*cosLat, -sinLat );
// In Stevens and Lewis notation, this is C_e/n - the
// orientation of the ECEF frame relative to the nav (local) frame,
// and a transformation from nav (local) to ECEF frame.
mTl2ec = mTec2l.Transposed();
// Calculate the inertial to ECEF and transpose matrices
double cos_epa = cos(epa);
double sin_epa = sin(epa);
mTi2ec = FGMatrix33( cos_epa, sin_epa, 0.0,
-sin_epa, cos_epa, 0.0,
0.0, 0.0, 1.0 );
mTec2i = mTi2ec.Transposed();
// Now calculate the local (or nav, or ned) frame to inertial transform matrix,
// and the inverse.
mTl2i = mTec2i * mTl2ec;
mTi2l = mTl2i.Transposed();
// Calculate the geodetic latitude based on "Transformation from Cartesian
// to geodetic coordinates accelerated by Halley's method", Fukushima T. (2006)
// Journal of Geodesy, Vol. 79, pp. 689-693
// Unlike I. Sofair's method which uses a closed form solution, Fukushima's
// method is an iterative method whose convergence is so fast that only one
// iteration suffices. In addition, Fukushima's method has a much better
// numerical stability over Sofair's method at the North and South poles and
// it also gives the correct result for a spherical Earth.
double s0 = fabs(mECLoc(eZ));
double zc = ec * s0;
double c0 = ec * rxy;
double c02 = c0 * c0;
double s02 = s0 * s0;
double a02 = c02 + s02;
double a0 = sqrt(a02);
double a03 = a02 * a0;
double s1 = zc*a03 + c*s02*s0;
double c1 = rxy*a03 - c*c02*c0;
double cs0c0 = c*c0*s0;
double b0 = 1.5*cs0c0*((rxy*s0-zc*c0)*a0-cs0c0);
s1 = s1*a03-b0*s0;
double cc = ec*(c1*a03-b0*c0);
mGeodLat = sign(mECLoc(eZ))*atan(s1 / cc);
double s12 = s1 * s1;
double cc2 = cc * cc;
GeodeticAltitude = (rxy*cc + s0*s1 - a*sqrt(ec2*s12 + cc2)) / sqrt(s12 + cc2);
// Mark the cached values as valid
mCacheValid = true;
}
bool FGMassBalance::Load(Element* elem)
{
string element_name = "";
double bixx, biyy, bizz, bixy, bixz, biyz;
string fname="", file="";
string separator = "/";
fname = elem->GetAttributeValue("file");
if (!fname.empty()) {
file = FDMExec->GetFullAircraftPath() + separator + fname;
document = LoadXMLDocument(file);
if (document == 0L) return false;
} else {
document = elem;
}
FGModel::Load(document); // Perform base class Load.
bixx = biyy = bizz = bixy = bixz = biyz = 0.0;
if (document->FindElement("ixx"))
bixx = document->FindElementValueAsNumberConvertTo("ixx", "SLUG*FT2");
if (document->FindElement("iyy"))
biyy = document->FindElementValueAsNumberConvertTo("iyy", "SLUG*FT2");
if (document->FindElement("izz"))
bizz = document->FindElementValueAsNumberConvertTo("izz", "SLUG*FT2");
if (document->FindElement("ixy"))
bixy = document->FindElementValueAsNumberConvertTo("ixy", "SLUG*FT2");
if (document->FindElement("ixz"))
bixz = document->FindElementValueAsNumberConvertTo("ixz", "SLUG*FT2");
if (document->FindElement("iyz"))
biyz = document->FindElementValueAsNumberConvertTo("iyz", "SLUG*FT2");
SetAircraftBaseInertias(FGMatrix33( bixx, -bixy, bixz,
-bixy, biyy, -biyz,
bixz, -biyz, bizz ));
if (document->FindElement("emptywt")) {
EmptyWeight = document->FindElementValueAsNumberConvertTo("emptywt", "LBS");
}
Element *element = document->FindElement("location");
while (element) {
element_name = element->GetAttributeValue("name");
if (element_name == "CG") vbaseXYZcg = element->FindElementTripletConvertTo("IN");
element = document->FindNextElement("location");
}
// Find all POINTMASS elements that descend from this METRICS branch of the
// config file.
element = document->FindElement("pointmass");
while (element) {
AddPointMass(element);
element = document->FindNextElement("pointmass");
}
double ChildFDMWeight = 0.0;
for (int fdm=0; fdm<FDMExec->GetFDMCount(); fdm++) {
if (FDMExec->GetChildFDM(fdm)->mated) ChildFDMWeight += FDMExec->GetChildFDM(fdm)->exec->GetMassBalance()->GetWeight();
}
Weight = EmptyWeight + in.TanksWeight + GetTotalPointMassWeight()
+ in.GasMass*slugtolb + ChildFDMWeight;
Mass = lbtoslug*Weight;
PostLoad(document, PropertyManager);
Debug(2);
return true;
}
void FGBallonet::Calculate(double dt)
{
const double ParentPressure = Parent->GetPressure(); // [lbs/ft^2]
const double AirPressure = in.Pressure; // [lbs/ft^2]
const double OldTemperature = Temperature;
const double OldPressure = Pressure;
unsigned int i;
//-- Gas temperature --
// The model is based on the ideal gas law.
// However, it does look a bit fishy. Please verify.
// dT/dt = dU / (Cv n R)
dU = 0.0;
for (i = 0; i < HeatTransferCoeff.size(); i++) {
dU += HeatTransferCoeff[i]->GetValue();
}
// dt is already accounted for in dVolumeIdeal.
if (Contents > 0) {
Temperature +=
(dU * dt - Pressure * dVolumeIdeal) / (Cv_air * Contents * R);
} else {
Temperature = Parent->GetTemperature();
}
//-- Pressure --
const double IdealPressure = Contents * R * Temperature / MaxVolume;
// The pressure is at least that of the parent gas cell.
Pressure = max(IdealPressure, ParentPressure);
//-- Blower input --
if (BlowerInput) {
const double AddedVolume = BlowerInput->GetValue() * dt;
if (AddedVolume > 0.0) {
Contents += Pressure * AddedVolume / (R * Temperature);
}
}
//-- Pressure relief and manual valving --
// FIXME: Presently the effect of valving is computed using
// an ad hoc formula which might not be a good representation
// of reality.
if ((ValveCoefficient > 0.0) &&
((ValveOpen > 0.0) || (Pressure > AirPressure + MaxOverpressure))) {
const double DeltaPressure = Pressure - AirPressure;
const double VolumeValved =
((Pressure > AirPressure + MaxOverpressure) ? 1.0 : ValveOpen) *
ValveCoefficient * DeltaPressure * dt;
// FIXME: Too small values of Contents sometimes leads to NaN.
// Currently the minimum is restricted to a safe value.
Contents =
max(1.0, Contents - Pressure * VolumeValved / (R * Temperature));
}
//-- Volume --
Volume = Contents * R * Temperature / Pressure;
dVolumeIdeal =
Contents * R * (Temperature / Pressure - OldTemperature / OldPressure);
// Compute the inertia of the ballonet.
// Consider the ballonet as a shape of uniform density.
// FIXME: If the ballonet isn't ellipsoid or cylindrical the inertia will
// be wrong.
ballonetJ = FGMatrix33();
const double mass = Contents * M_air;
double Ixx, Iyy, Izz;
if ((Xradius != 0.0) && (Yradius != 0.0) && (Zradius != 0.0) &&
(Xwidth == 0.0) && (Ywidth == 0.0) && (Zwidth == 0.0)) {
// Ellipsoid volume.
Ixx = (1.0 / 5.0) * mass * (Yradius*Yradius + Zradius*Zradius);
Iyy = (1.0 / 5.0) * mass * (Xradius*Xradius + Zradius*Zradius);
Izz = (1.0 / 5.0) * mass * (Xradius*Xradius + Yradius*Yradius);
} else if ((Xradius == 0.0) && (Yradius != 0.0) && (Zradius != 0.0) &&
(Xwidth != 0.0) && (Ywidth == 0.0) && (Zwidth == 0.0)) {
// Cylindrical volume (might not be valid with an elliptical cross-section).
Ixx = (1.0 / 2.0) * mass * Yradius * Zradius;
Iyy =
(1.0 / 4.0) * mass * Yradius * Zradius +
(1.0 / 12.0) * mass * Xwidth * Xwidth;
Izz =
(1.0 / 4.0) * mass * Yradius * Zradius +
(1.0 / 12.0) * mass * Xwidth * Xwidth;
} else {
// Not supported. Revert to pointmass model.
Ixx = Iyy = Izz = 0.0;
}
// The volume is symmetric, so Ixy = Ixz = Iyz = 0.
ballonetJ(1,1) = Ixx;
ballonetJ(2,2) = Iyy;
ballonetJ(3,3) = Izz;
// Transform the moments of inertia to the body frame.
ballonetJ += MassBalance->GetPointmassInertia(GetMass(), GetXYZ());
}
FGGasCell::FGGasCell(FGFDMExec* exec, Element* el, unsigned int num,
const struct Inputs& input)
: FGForce(exec), in(input)
{
string token;
Element* element;
FGPropertyManager* PropertyManager = exec->GetPropertyManager();
MassBalance = exec->GetMassBalance();
gasCellJ = FGMatrix33();
gasCellM = FGColumnVector3();
Buoyancy = MaxVolume = MaxOverpressure = Temperature = Pressure =
Contents = Volume = dVolumeIdeal = 0.0;
Xradius = Yradius = Zradius = Xwidth = Ywidth = Zwidth = 0.0;
ValveCoefficient = ValveOpen = 0.0;
CellNum = num;
// NOTE: In the local system X points north, Y points east and Z points down.
SetTransformType(FGForce::tLocalBody);
type = el->GetAttributeValue("type");
if (type == "HYDROGEN") Type = ttHYDROGEN;
else if (type == "HELIUM") Type = ttHELIUM;
else if (type == "AIR") Type = ttAIR;
else Type = ttUNKNOWN;
element = el->FindElement("location");
if (element) {
vXYZ = element->FindElementTripletConvertTo("IN");
} else {
std::stringstream error;
error << "Fatal Error: No location found for this gas cell." << endl;
throw std::runtime_error(error.str());
}
if ((el->FindElement("x_radius") || el->FindElement("x_width")) &&
(el->FindElement("y_radius") || el->FindElement("y_width")) &&
(el->FindElement("z_radius") || el->FindElement("z_width"))) {
if (el->FindElement("x_radius")) {
Xradius = el->FindElementValueAsNumberConvertTo("x_radius", "FT");
}
if (el->FindElement("y_radius")) {
Yradius = el->FindElementValueAsNumberConvertTo("y_radius", "FT");
}
if (el->FindElement("z_radius")) {
Zradius = el->FindElementValueAsNumberConvertTo("z_radius", "FT");
}
if (el->FindElement("x_width")) {
Xwidth = el->FindElementValueAsNumberConvertTo("x_width", "FT");
}
if (el->FindElement("y_width")) {
Ywidth = el->FindElementValueAsNumberConvertTo("y_width", "FT");
}
if (el->FindElement("z_width")) {
Zwidth = el->FindElementValueAsNumberConvertTo("z_width", "FT");
}
// The volume is a (potentially) extruded ellipsoid.
// However, currently only a few combinations of radius and width are
// fully supported.
if ((Xradius != 0.0) && (Yradius != 0.0) && (Zradius != 0.0) &&
(Xwidth == 0.0) && (Ywidth == 0.0) && (Zwidth == 0.0)) {
// Ellipsoid volume.
MaxVolume = 4.0 * M_PI * Xradius * Yradius * Zradius / 3.0;
} else if ((Xradius == 0.0) && (Yradius != 0.0) && (Zradius != 0.0) &&
(Xwidth != 0.0) && (Ywidth == 0.0) && (Zwidth == 0.0)) {
// Cylindrical volume.
MaxVolume = M_PI * Yradius * Zradius * Xwidth;
} else {
cerr << "Warning: Unsupported gas cell shape." << endl;
MaxVolume =
(4.0 * M_PI * Xradius * Yradius * Zradius / 3.0 +
M_PI * Yradius * Zradius * Xwidth +
M_PI * Xradius * Zradius * Ywidth +
M_PI * Xradius * Yradius * Zwidth +
2.0 * Xradius * Ywidth * Zwidth +
2.0 * Yradius * Xwidth * Zwidth +
2.0 * Zradius * Xwidth * Ywidth +
Xwidth * Ywidth * Zwidth);
}
} else {
std::stringstream error;
error << "Fatal Error: Gas cell shape must be given." << endl;
throw std::runtime_error(error.str());
}
if (el->FindElement("max_overpressure")) {
MaxOverpressure = el->FindElementValueAsNumberConvertTo("max_overpressure",
"LBS/FT2");
}
if (el->FindElement("fullness")) {
const double Fullness = el->FindElementValueAsNumber("fullness");
if (0 <= Fullness) {
Volume = Fullness * MaxVolume;
} else {
cerr << "Warning: Invalid initial gas cell fullness value." << endl;
}
}
if (el->FindElement("valve_coefficient")) {
ValveCoefficient =
el->FindElementValueAsNumberConvertTo("valve_coefficient",
"FT4*SEC/SLUG");
ValveCoefficient = max(ValveCoefficient, 0.0);
}
// Initialize state
SetLocation(vXYZ);
if (Temperature == 0.0) {
Temperature = in.Temperature;
}
if (Pressure == 0.0) {
Pressure = in.Pressure;
}
if (Volume != 0.0) {
// Calculate initial gas content.
Contents = Pressure * Volume / (R * Temperature);
// Clip to max allowed value.
const double IdealPressure = Contents * R * Temperature / MaxVolume;
if (IdealPressure > Pressure + MaxOverpressure) {
Contents = (Pressure + MaxOverpressure) * MaxVolume / (R * Temperature);
Pressure = Pressure + MaxOverpressure;
} else {
Pressure = max(IdealPressure, Pressure);
}
} else {
// Calculate initial gas content.
Contents = Pressure * MaxVolume / (R * Temperature);
}
Volume = Contents * R * Temperature / Pressure;
Mass = Contents * M_gas();
// Bind relevant properties
string property_name, base_property_name;
base_property_name = CreateIndexedPropertyName("buoyant_forces/gas-cell", CellNum);
property_name = base_property_name + "/max_volume-ft3";
PropertyManager->Tie( property_name.c_str(), &MaxVolume, false );
PropertyManager->GetNode()->SetWritable( property_name, false );
property_name = base_property_name + "/temp-R";
PropertyManager->Tie( property_name.c_str(), &Temperature, false );
property_name = base_property_name + "/pressure-psf";
PropertyManager->Tie( property_name.c_str(), &Pressure, false );
property_name = base_property_name + "/volume-ft3";
PropertyManager->Tie( property_name.c_str(), &Volume, false );
property_name = base_property_name + "/buoyancy-lbs";
PropertyManager->Tie( property_name.c_str(), &Buoyancy, false );
property_name = base_property_name + "/contents-mol";
PropertyManager->Tie( property_name.c_str(), &Contents, false );
property_name = base_property_name + "/valve_open";
PropertyManager->Tie( property_name.c_str(), &ValveOpen, false );
Debug(0);
// Read heat transfer coefficients
if (Element* heat = el->FindElement("heat")) {
Element* function_element = heat->FindElement("function");
while (function_element) {
HeatTransferCoeff.push_back(new FGFunction(PropertyManager,
function_element));
function_element = heat->FindNextElement("function");
}
}
// Load ballonets if there are any
if (Element* ballonet_element = el->FindElement("ballonet")) {
while (ballonet_element) {
Ballonet.push_back(new FGBallonet(exec,
ballonet_element,
Ballonet.size(),
this, in));
ballonet_element = el->FindNextElement("ballonet");
}
}
}
FGBallonet::FGBallonet(FGFDMExec* exec, Element* el, unsigned int num,
FGGasCell* parent, const struct FGGasCell::Inputs& input)
: in(input)
{
string token;
Element* element;
FGPropertyManager* PropertyManager = exec->GetPropertyManager();
MassBalance = exec->GetMassBalance();
ballonetJ = FGMatrix33();
MaxVolume = MaxOverpressure = Temperature = Pressure =
Contents = Volume = dVolumeIdeal = dU = 0.0;
Xradius = Yradius = Zradius = Xwidth = Ywidth = Zwidth = 0.0;
ValveCoefficient = ValveOpen = 0.0;
BlowerInput = NULL;
CellNum = num;
Parent = parent;
// NOTE: In the local system X points north, Y points east and Z points down.
element = el->FindElement("location");
if (element) {
vXYZ = element->FindElementTripletConvertTo("IN");
} else {
std::stringstream error;
error << "Fatal Error: No location found for this ballonet." << endl;
throw std::runtime_error(error.str());
}
if ((el->FindElement("x_radius") || el->FindElement("x_width")) &&
(el->FindElement("y_radius") || el->FindElement("y_width")) &&
(el->FindElement("z_radius") || el->FindElement("z_width"))) {
if (el->FindElement("x_radius")) {
Xradius = el->FindElementValueAsNumberConvertTo("x_radius", "FT");
}
if (el->FindElement("y_radius")) {
Yradius = el->FindElementValueAsNumberConvertTo("y_radius", "FT");
}
if (el->FindElement("z_radius")) {
Zradius = el->FindElementValueAsNumberConvertTo("z_radius", "FT");
}
if (el->FindElement("x_width")) {
Xwidth = el->FindElementValueAsNumberConvertTo("x_width", "FT");
}
if (el->FindElement("y_width")) {
Ywidth = el->FindElementValueAsNumberConvertTo("y_width", "FT");
}
if (el->FindElement("z_width")) {
Zwidth = el->FindElementValueAsNumberConvertTo("z_width", "FT");
}
// The volume is a (potentially) extruded ellipsoid.
// FIXME: However, currently only a few combinations of radius and
// width are fully supported.
if ((Xradius != 0.0) && (Yradius != 0.0) && (Zradius != 0.0) &&
(Xwidth == 0.0) && (Ywidth == 0.0) && (Zwidth == 0.0)) {
// Ellipsoid volume.
MaxVolume = 4.0 * M_PI * Xradius * Yradius * Zradius / 3.0;
} else if ((Xradius == 0.0) && (Yradius != 0.0) && (Zradius != 0.0) &&
(Xwidth != 0.0) && (Ywidth == 0.0) && (Zwidth == 0.0)) {
// Cylindrical volume.
MaxVolume = M_PI * Yradius * Zradius * Xwidth;
} else {
cerr << "Warning: Unsupported ballonet shape." << endl;
MaxVolume =
(4.0 * M_PI * Xradius * Yradius * Zradius / 3.0 +
M_PI * Yradius * Zradius * Xwidth +
M_PI * Xradius * Zradius * Ywidth +
M_PI * Xradius * Yradius * Zwidth +
2.0 * Xradius * Ywidth * Zwidth +
2.0 * Yradius * Xwidth * Zwidth +
2.0 * Zradius * Xwidth * Ywidth +
Xwidth * Ywidth * Zwidth);
}
} else {
std::stringstream error;
error << "Fatal Error: Ballonet shape must be given." << endl;
throw std::runtime_error(error.str());
}
if (el->FindElement("max_overpressure")) {
MaxOverpressure = el->FindElementValueAsNumberConvertTo("max_overpressure",
"LBS/FT2");
}
if (el->FindElement("fullness")) {
const double Fullness = el->FindElementValueAsNumber("fullness");
if (0 <= Fullness) {
Volume = Fullness * MaxVolume;
} else {
cerr << "Warning: Invalid initial ballonet fullness value." << endl;
}
}
if (el->FindElement("valve_coefficient")) {
ValveCoefficient =
el->FindElementValueAsNumberConvertTo("valve_coefficient",
"FT4*SEC/SLUG");
ValveCoefficient = max(ValveCoefficient, 0.0);
}
// Initialize state
if (Temperature == 0.0) {
Temperature = Parent->GetTemperature();
}
if (Pressure == 0.0) {
Pressure = Parent->GetPressure();
}
if (Volume != 0.0) {
// Calculate initial air content.
Contents = Pressure * Volume / (R * Temperature);
// Clip to max allowed value.
const double IdealPressure = Contents * R * Temperature / MaxVolume;
if (IdealPressure > Pressure + MaxOverpressure) {
Contents = (Pressure + MaxOverpressure) * MaxVolume / (R * Temperature);
Pressure = Pressure + MaxOverpressure;
} else {
Pressure = max(IdealPressure, Pressure);
}
} else {
// Calculate initial air content.
Contents = Pressure * MaxVolume / (R * Temperature);
}
Volume = Contents * R * Temperature / Pressure;
// Bind relevant properties
string property_name, base_property_name;
base_property_name = CreateIndexedPropertyName("buoyant_forces/gas-cell", Parent->GetIndex());
base_property_name = CreateIndexedPropertyName(base_property_name + "/ballonet", CellNum);
property_name = base_property_name + "/max_volume-ft3";
PropertyManager->Tie( property_name, &MaxVolume, false );
PropertyManager->GetNode()->SetWritable( property_name, false );
property_name = base_property_name + "/temp-R";
PropertyManager->Tie( property_name, &Temperature, false );
property_name = base_property_name + "/pressure-psf";
PropertyManager->Tie( property_name, &Pressure, false );
property_name = base_property_name + "/volume-ft3";
PropertyManager->Tie( property_name, &Volume, false );
property_name = base_property_name + "/contents-mol";
PropertyManager->Tie( property_name, &Contents, false );
property_name = base_property_name + "/valve_open";
PropertyManager->Tie( property_name, &ValveOpen, false );
Debug(0);
// Read heat transfer coefficients
if (Element* heat = el->FindElement("heat")) {
Element* function_element = heat->FindElement("function");
while (function_element) {
HeatTransferCoeff.push_back(new FGFunction(PropertyManager,
function_element));
function_element = heat->FindNextElement("function");
}
}
// Read blower input function
if (Element* blower = el->FindElement("blower_input")) {
Element* function_element = blower->FindElement("function");
BlowerInput = new FGFunction(PropertyManager,
function_element);
}
}
void FGGasCell::Calculate(double dt)
{
const double AirTemperature = in.Temperature; // [Rankine]
const double AirPressure = in.Pressure; // [lbs/ft^2]
const double AirDensity = in.Density; // [slug/ft^3]
const double g = in.gravity; // [lbs/slug]
const double OldTemperature = Temperature;
const double OldPressure = Pressure;
unsigned int i;
const size_t no_ballonets = Ballonet.size();
//-- Read ballonet state --
// NOTE: This model might need a more proper integration technique.
double BallonetsVolume = 0.0;
double BallonetsHeatFlow = 0.0;
for (i = 0; i < no_ballonets; i++) {
BallonetsVolume += Ballonet[i]->GetVolume();
BallonetsHeatFlow += Ballonet[i]->GetHeatFlow();
}
//-- Gas temperature --
if (HeatTransferCoeff.size() > 0) {
// The model is based on the ideal gas law.
// However, it does look a bit fishy. Please verify.
// dT/dt = dU / (Cv n R)
double dU = 0.0;
for (i = 0; i < HeatTransferCoeff.size(); i++) {
dU += HeatTransferCoeff[i]->GetValue();
}
// Don't include dt when accounting for adiabatic expansion/contraction.
// The rate of adiabatic cooling looks about right: ~5.4 Rankine/1000ft.
if (Contents > 0) {
Temperature +=
(dU * dt - Pressure * dVolumeIdeal - BallonetsHeatFlow) /
(Cv_gas() * Contents * R);
} else {
Temperature = AirTemperature;
}
} else {
// No simulation of complex temperature changes.
// Note: Making the gas cell behave adiabatically might be a better
// option.
Temperature = AirTemperature;
}
//-- Pressure --
const double IdealPressure =
Contents * R * Temperature / (MaxVolume - BallonetsVolume);
if (IdealPressure > AirPressure + MaxOverpressure) {
Pressure = AirPressure + MaxOverpressure;
} else {
Pressure = max(IdealPressure, AirPressure);
}
//-- Manual valving --
// FIXME: Presently the effect of manual valving is computed using
// an ad hoc formula which might not be a good representation
// of reality.
if ((ValveCoefficient > 0.0) && (ValveOpen > 0.0)) {
// First compute the difference in pressure between the gas in the
// cell and the air above it.
// FixMe: CellHeight should depend on current volume.
const double CellHeight = 2 * Zradius + Zwidth; // [ft]
const double GasMass = Contents * M_gas(); // [slug]
const double GasVolume = Contents * R * Temperature / Pressure; // [ft^3]
const double GasDensity = GasMass / GasVolume;
const double DeltaPressure =
Pressure + CellHeight * g * (AirDensity - GasDensity) - AirPressure;
const double VolumeValved =
ValveOpen * ValveCoefficient * DeltaPressure * dt;
Contents =
max(0.0, Contents - Pressure * VolumeValved / (R * Temperature));
}
//-- Update ballonets. --
// Doing that here should give them the opportunity to react to the
// new pressure.
BallonetsVolume = 0.0;
for (i = 0; i < no_ballonets; i++) {
Ballonet[i]->Calculate(dt);
BallonetsVolume += Ballonet[i]->GetVolume();
}
//-- Automatic safety valving. --
if (Contents * R * Temperature / (MaxVolume - BallonetsVolume) >
AirPressure + MaxOverpressure) {
// Gas is automatically valved. Valving capacity is assumed to be infinite.
// FIXME: This could/should be replaced by damage to the gas cell envelope.
Contents =
(AirPressure + MaxOverpressure) *
(MaxVolume - BallonetsVolume) / (R * Temperature);
}
//-- Volume --
Volume = Contents * R * Temperature / Pressure + BallonetsVolume;
dVolumeIdeal =
Contents * R * (Temperature / Pressure - OldTemperature / OldPressure);
//-- Current buoyancy --
// The buoyancy is computed using the atmospheres local density.
Buoyancy = Volume * AirDensity * g;
// Note: This is gross buoyancy. The weight of the gas itself and
// any ballonets is not deducted here as the effects of the gas mass
// is handled by FGMassBalance.
vFn.InitMatrix(0.0, 0.0, - Buoyancy);
// Compute the inertia of the gas cell.
// Consider the gas cell as a shape of uniform density.
// FIXME: If the cell isn't ellipsoid or cylindrical the inertia will
// be wrong.
gasCellJ = FGMatrix33();
const double mass = Contents * M_gas();
double Ixx, Iyy, Izz;
if ((Xradius != 0.0) && (Yradius != 0.0) && (Zradius != 0.0) &&
(Xwidth == 0.0) && (Ywidth == 0.0) && (Zwidth == 0.0)) {
// Ellipsoid volume.
Ixx = (1.0 / 5.0) * mass * (Yradius*Yradius + Zradius*Zradius);
Iyy = (1.0 / 5.0) * mass * (Xradius*Xradius + Zradius*Zradius);
Izz = (1.0 / 5.0) * mass * (Xradius*Xradius + Yradius*Yradius);
} else if ((Xradius == 0.0) && (Yradius != 0.0) && (Zradius != 0.0) &&
(Xwidth != 0.0) && (Ywidth == 0.0) && (Zwidth == 0.0)) {
// Cylindrical volume (might not be valid with an elliptical cross-section).
Ixx = (1.0 / 2.0) * mass * Yradius * Zradius;
Iyy =
(1.0 / 4.0) * mass * Yradius * Zradius +
(1.0 / 12.0) * mass * Xwidth * Xwidth;
Izz =
(1.0 / 4.0) * mass * Yradius * Zradius +
(1.0 / 12.0) * mass * Xwidth * Xwidth;
} else {
// Not supported. Revert to pointmass model.
Ixx = Iyy = Izz = 0.0;
}
// The volume is symmetric, so Ixy = Ixz = Iyz = 0.
gasCellJ(1,1) = Ixx;
gasCellJ(2,2) = Iyy;
gasCellJ(3,3) = Izz;
Mass = mass;
// Transform the moments of inertia to the body frame.
gasCellJ += MassBalance->GetPointmassInertia(Mass, GetXYZ());
gasCellM.InitMatrix();
gasCellM(eX) +=
GetXYZ(eX) * Mass*slugtolb;
gasCellM(eY) +=
GetXYZ(eY) * Mass*slugtolb;
gasCellM(eZ) +=
GetXYZ(eZ) * Mass*slugtolb;
if (no_ballonets > 0) {
// Add the mass, moment and inertia of any ballonets.
for (i = 0; i < no_ballonets; i++) {
Mass += Ballonet[i]->GetMass();
// Add ballonet moments due to mass (in the structural frame).
gasCellM(eX) +=
Ballonet[i]->GetXYZ(eX) * Ballonet[i]->GetMass()*slugtolb;
gasCellM(eY) +=
Ballonet[i]->GetXYZ(eY) * Ballonet[i]->GetMass()*slugtolb;
gasCellM(eZ) +=
Ballonet[i]->GetXYZ(eZ) * Ballonet[i]->GetMass()*slugtolb;
gasCellJ += Ballonet[i]->GetInertia();
}
}
}
