globals->get_controls()->set_mixture(i, FCS->GetMixtureCmd(i));
}
}
+
+ if ( startup_trim->getBoolValue() ) {
+ FGLocation cart(fgic->GetLongitudeRadIC(), fgic->GetLatitudeRadIC(),
+ fgic->GetSeaLevelRadiusFtIC() + fgic->GetAltitudeASLFtIC());
+ double cart_pos[3], contact[3], d[3], vel[3], agl;
+ update_ground_cache(cart, cart_pos, 0.01);
+
+ get_agl_ft(fdmex->GetSimTime(), cart_pos, SG_METER_TO_FEET*2, contact,
+ d, vel, d, &agl);
+ double terrain_alt = sqrt(contact[0]*contact[0] + contact[1]*contact[1]
+ + contact[2]*contact[2]) - fgic->GetSeaLevelRadiusFtIC();
+
+ SG_LOG(SG_FLIGHT, SG_INFO, "Ready to trim, terrain elevation is: "
+ << terrain_alt * SG_METER_TO_FEET );
+
+ if (fgGetBool("/sim/presets/onground")) {
+ FGColumnVector3 gndVelNED = cart.GetTec2l()
+ * FGColumnVector3(vel[0], vel[1], vel[2]);
+ fgic->SetVNorthFpsIC(gndVelNED(1));
+ fgic->SetVEastFpsIC(gndVelNED(2));
+ fgic->SetVDownFpsIC(gndVelNED(3));
+ }
+ fgic->SetTerrainElevationFtIC( terrain_alt );
+ do_trim();
+ needTrim = false;
+ }
+
copy_from_JSBsim(); //update the bus
SG_LOG( SG_FLIGHT, SG_INFO, " Initialized JSBSim with:" );
return;
int multiloop = _calc_multiloop(dt);
-
- int i;
-
- // Compute the radius of the aircraft. That is the radius of a ball
- // where all gear units are in. At the moment it is at least 10ft ...
- double acrad = 10.0;
- int n_gears = GroundReactions->GetNumGearUnits();
- for (i=0; i<n_gears; ++i) {
- FGColumnVector3 bl = GroundReactions->GetGearUnit(i)->GetBodyLocation();
- double r = bl.Magnitude();
- if (acrad < r)
- acrad = r;
- }
-
- // Compute the potential movement of this aircraft and query for the
- // ground in this area.
- double groundCacheRadius = acrad + 2*dt*Propagate->GetUVW().Magnitude();
- double alt, slr, lat, lon;
FGLocation cart = Auxiliary->GetLocationVRP();
- if ( needTrim && startup_trim->getBoolValue() ) {
- alt = fgic->GetAltitudeASLFtIC();
- slr = fgic->GetSeaLevelRadiusFtIC();
- lat = fgic->GetLatitudeDegIC() * SGD_DEGREES_TO_RADIANS;
- lon = fgic->GetLongitudeDegIC() * SGD_DEGREES_TO_RADIANS;
- cart = FGLocation(lon, lat, alt+slr);
- }
- double cart_pos[3] = { cart(1), cart(2), cart(3) };
- double t0 = fdmex->GetSimTime();
- bool cache_ok = prepare_ground_cache_ft( t0, t0 + dt, cart_pos,
- groundCacheRadius );
- if (!cache_ok) {
- SG_LOG(SG_FLIGHT, SG_WARN,
- "FGInterface is being called without scenery below the aircraft!");
-
- alt = fgic->GetAltitudeASLFtIC();
- SG_LOG(SG_FLIGHT, SG_WARN, "altitude = " << alt);
-
- slr = fgic->GetSeaLevelRadiusFtIC();
- SG_LOG(SG_FLIGHT, SG_WARN, "sea level radius = " << slr);
-
- lat = fgic->GetLatitudeDegIC() * SGD_DEGREES_TO_RADIANS;
- SG_LOG(SG_FLIGHT, SG_WARN, "latitude = " << lat);
-
- lon = fgic->GetLongitudeDegIC() * SGD_DEGREES_TO_RADIANS;
- SG_LOG(SG_FLIGHT, SG_WARN, "longitude = " << lon);
- //return;
- }
+ double cart_pos[3];
+
+ update_ground_cache(cart, cart_pos, dt);
copy_to_JSBsim();
trimmed->setBoolValue(false);
- if ( needTrim ) {
- if ( startup_trim->getBoolValue() ) {
- double contact[3], d[3], vel[3], agl;
- get_agl_ft(fdmex->GetSimTime(), cart_pos, SG_METER_TO_FEET*2, contact,
- d, vel, d, &agl);
- double terrain_alt = sqrt(contact[0]*contact[0] + contact[1]*contact[1]
- + contact[2]*contact[2]) - fgic->GetSeaLevelRadiusFtIC();
-
- SG_LOG(SG_FLIGHT, SG_INFO,
- "Ready to trim, terrain elevation is: "
- << terrain_alt * SG_METER_TO_FEET );
-
- if (fgGetBool("/sim/presets/onground")) {
- FGColumnVector3 gndVelNED = cart.GetTec2l()
- * FGColumnVector3(vel[0], vel[1], vel[2]);
- fgic->SetVNorthFpsIC(gndVelNED(1));
- fgic->SetVEastFpsIC(gndVelNED(2));
- fgic->SetVDownFpsIC(gndVelNED(3));
- }
- fgic->SetTerrainElevationFtIC( terrain_alt );
- do_trim();
- } else {
- fdmex->RunIC(); //apply any changes made through the set_ functions
- }
- needTrim = false;
- }
-
- for ( i=0; i < multiloop; i++ ) {
+ for ( int i=0; i < multiloop; i++ ) {
fdmex->Run();
- update_external_forces(fdmex->GetSimTime() + i * fdmex->GetDeltaT());
+ update_external_forces(fdmex->GetSimTime() + i * fdmex->GetDeltaT());
}
FGJSBBase::Message* msg;
//Positions
void FGJSBsim::set_Latitude(double lat)
{
- static SGConstPropertyNode_ptr altitude = fgGetNode("/position/altitude-ft");
- double alt;
- double sea_level_radius_meters, lat_geoc;
+ static SGConstPropertyNode_ptr altitude = fgGetNode("/position/altitude-ft");
+ double alt;
+ double sea_level_radius_meters, lat_geoc;
- // In case we're not trimming
- FGInterface::set_Latitude(lat);
+ if ( altitude->getDoubleValue() > -9990 )
+ alt = altitude->getDoubleValue();
+ else
+ alt = 0.0;
- if ( altitude->getDoubleValue() > -9990 ) {
- alt = altitude->getDoubleValue();
- } else {
- alt = 0.0;
- }
+ SG_LOG(SG_FLIGHT,SG_INFO,"FGJSBsim::set_Latitude: " << lat );
+ SG_LOG(SG_FLIGHT,SG_INFO," cur alt (ft) = " << alt );
- update_ic();
- SG_LOG(SG_FLIGHT,SG_INFO,"FGJSBsim::set_Latitude: " << lat );
- SG_LOG(SG_FLIGHT,SG_INFO," cur alt (ft) = " << alt );
+ sgGeodToGeoc( lat, alt * SG_FEET_TO_METER,
+ &sea_level_radius_meters, &lat_geoc );
+ _set_Sea_level_radius( sea_level_radius_meters * SG_METER_TO_FEET );
- sgGeodToGeoc( lat, alt * SG_FEET_TO_METER,
- &sea_level_radius_meters, &lat_geoc );
- _set_Sea_level_radius( sea_level_radius_meters * SG_METER_TO_FEET );
+ if (needTrim) {
fgic->SetSeaLevelRadiusFtIC( sea_level_radius_meters * SG_METER_TO_FEET );
fgic->SetLatitudeRadIC( lat_geoc );
-
- if (!fdmex->Holding())
- needTrim=true;
+ }
+ else {
+ Propagate->SetLatitude(lat_geoc);
+ FGInterface::set_Latitude(lat);
+ }
}
void FGJSBsim::set_Longitude(double lon)
{
- SG_LOG(SG_FLIGHT,SG_INFO,"FGJSBsim::set_Longitude: " << lon );
+ SG_LOG(SG_FLIGHT,SG_INFO,"FGJSBsim::set_Longitude: " << lon );
- // In case we're not trimming
+ if (needTrim)
+ fgic->SetLongitudeRadIC(lon);
+ else {
+ Propagate->SetLongitude(lon);
FGInterface::set_Longitude(lon);
-
- update_ic();
- fgic->SetLongitudeRadIC( lon );
-
- if (!fdmex->Holding())
- needTrim=true;
+ }
}
// Sets the altitude above sea level.
void FGJSBsim::set_Altitude(double alt)
{
- static SGConstPropertyNode_ptr latitude = fgGetNode("/position/latitude-deg");
-
- double sea_level_radius_meters,lat_geoc;
+ SG_LOG(SG_FLIGHT,SG_INFO, "FGJSBsim::set_Altitude: " << alt );
- SG_LOG(SG_FLIGHT,SG_INFO, "FGJSBsim::set_Altitude: " << alt );
- SG_LOG(SG_FLIGHT,SG_INFO, " lat (deg) = " << latitude->getDoubleValue() );
-
- // In case we're not trimming
- FGInterface::set_Altitude(alt);
-
- update_ic();
- sgGeodToGeoc( latitude->getDoubleValue() * SGD_DEGREES_TO_RADIANS, alt,
- &sea_level_radius_meters, &lat_geoc);
- _set_Sea_level_radius( sea_level_radius_meters * SG_METER_TO_FEET );
- fgic->SetSeaLevelRadiusFtIC( sea_level_radius_meters * SG_METER_TO_FEET );
- SG_LOG(SG_FLIGHT, SG_INFO,
- "Terrain elevation: " << FGInterface::get_Runway_altitude() * SG_METER_TO_FEET );
- fgic->SetLatitudeRadIC( lat_geoc );
+ if (needTrim)
fgic->SetAltitudeASLFtIC(alt);
-
- if (!fdmex->Holding())
- needTrim=true;
+ else {
+ Propagate->SetAltitudeASL(alt);
+ FGInterface::set_Altitude(alt);
+ }
}
void FGJSBsim::set_V_calibrated_kts(double vc)
{
SG_LOG(SG_FLIGHT,SG_INFO, "FGJSBsim::set_V_calibrated_kts: " << vc );
- // In case we're not trimming
- FGInterface::set_V_calibrated_kts(vc);
-
- update_ic();
+ if (needTrim)
fgic->SetVcalibratedKtsIC(vc);
+ else {
+ double mach = getMachFromVcas(vc);
+ double temp = 1.8*(temperature->getDoubleValue()+273.15);
+ double soundSpeed = sqrt(1.4*1716.0*temp);
+ FGColumnVector3 vUVW = Propagate->GetUVW();
+ vUVW.Normalize();
+ vUVW *= mach * soundSpeed;
+ Propagate->SetUVW(1, vUVW(1));
+ Propagate->SetUVW(2, vUVW(2));
+ Propagate->SetUVW(3, vUVW(3));
- if (!fdmex->Holding())
- needTrim=true;
+ FGInterface::set_V_calibrated_kts(vc);
+ }
}
void FGJSBsim::set_Mach_number(double mach)
{
- SG_LOG(SG_FLIGHT,SG_INFO, "FGJSBsim::set_Mach_number: " << mach );
+ SG_LOG(SG_FLIGHT,SG_INFO, "FGJSBsim::set_Mach_number: " << mach );
- // In case we're not trimming
- FGInterface::set_Mach_number(mach);
-
- update_ic();
+ if (needTrim)
fgic->SetMachIC(mach);
+ else {
+ double temp = 1.8*(temperature->getDoubleValue()+273.15);
+ double soundSpeed = sqrt(1.4*1716.0*temp);
+ FGColumnVector3 vUVW = Propagate->GetUVW();
+ vUVW.Normalize();
+ vUVW *= mach * soundSpeed;
+ Propagate->SetUVW(1, vUVW(1));
+ Propagate->SetUVW(2, vUVW(2));
+ Propagate->SetUVW(3, vUVW(3));
- if (!fdmex->Holding())
- needTrim=true;
+ FGInterface::set_Mach_number(mach);
+ }
}
void FGJSBsim::set_Velocities_Local( double north, double east, double down )
{
- SG_LOG(SG_FLIGHT,SG_INFO, "FGJSBsim::set_Velocities_Local: "
- << north << ", " << east << ", " << down );
-
- // In case we're not trimming
- FGInterface::set_Velocities_Local(north, east, down);
+ SG_LOG(SG_FLIGHT,SG_INFO, "FGJSBsim::set_Velocities_Local: "
+ << north << ", " << east << ", " << down );
- update_ic();
+ if (needTrim) {
fgic->SetVNorthFpsIC(north);
fgic->SetVEastFpsIC(east);
fgic->SetVDownFpsIC(down);
+ }
+ else {
+ FGColumnVector3 vNED(north, east, down);
+ FGColumnVector3 vUVW = Propagate->GetTl2b() * vNED;
+ Propagate->SetUVW(1, vUVW(1));
+ Propagate->SetUVW(2, vUVW(2));
+ Propagate->SetUVW(3, vUVW(3));
- if (!fdmex->Holding())
- needTrim=true;
+ FGInterface::set_Velocities_Local(north, east, down);
+ }
}
void FGJSBsim::set_Velocities_Wind_Body( double u, double v, double w)
{
- SG_LOG(SG_FLIGHT,SG_INFO, "FGJSBsim::set_Velocities_Wind_Body: "
- << u << ", " << v << ", " << w );
-
- // In case we're not trimming
- FGInterface::set_Velocities_Wind_Body(u, v, w);
+ SG_LOG(SG_FLIGHT,SG_INFO, "FGJSBsim::set_Velocities_Wind_Body: "
+ << u << ", " << v << ", " << w );
- update_ic();
+ if (needTrim) {
fgic->SetUBodyFpsIC(u);
fgic->SetVBodyFpsIC(v);
fgic->SetWBodyFpsIC(w);
+ }
+ else {
+ Propagate->SetUVW(1, u);
+ Propagate->SetUVW(2, v);
+ Propagate->SetUVW(3, w);
- if (!fdmex->Holding())
- needTrim=true;
+ FGInterface::set_Velocities_Wind_Body(u, v, w);
+ }
}
//Euler angles
void FGJSBsim::set_Euler_Angles( double phi, double theta, double psi )
{
- SG_LOG(SG_FLIGHT,SG_INFO, "FGJSBsim::set_Euler_Angles: "
- << phi << ", " << theta << ", " << psi );
-
- // In case we're not trimming
- FGInterface::set_Euler_Angles(phi, theta, psi);
+ SG_LOG(SG_FLIGHT,SG_INFO, "FGJSBsim::set_Euler_Angles: "
+ << phi << ", " << theta << ", " << psi );
- update_ic();
+ if (needTrim) {
fgic->SetThetaRadIC(theta);
fgic->SetPhiRadIC(phi);
fgic->SetPsiRadIC(psi);
+ }
+ else {
+ FGQuaternion quat(phi, theta, psi);
+ FGMatrix33 Tl2b = quat.GetT();
+ FGMatrix33 Ti2b = Tl2b*Propagate->GetTi2l();
+ FGQuaternion Qi = Ti2b.GetQuaternion();
+ Propagate->SetInertialOrientation(Qi);
- if (!fdmex->Holding())
- needTrim=true;
+ FGInterface::set_Euler_Angles(phi, theta, psi);
+ }
}
//Flight Path
void FGJSBsim::set_Climb_Rate( double roc)
{
- SG_LOG(SG_FLIGHT,SG_INFO, "FGJSBsim::set_Climb_Rate: " << roc );
-
- // In case we're not trimming
- FGInterface::set_Climb_Rate(roc);
+ SG_LOG(SG_FLIGHT,SG_INFO, "FGJSBsim::set_Climb_Rate: " << roc );
- update_ic();
- //since both climb rate and flight path angle are set in the FG
- //startup sequence, something is needed to keep one from cancelling
- //out the other.
- if( !(fabs(roc) > 1 && fabs(fgic->GetFlightPathAngleRadIC()) < 0.01) ) {
+ //since both climb rate and flight path angle are set in the FG
+ //startup sequence, something is needed to keep one from cancelling
+ //out the other.
+ if( !(fabs(roc) > 1 && fabs(fgic->GetFlightPathAngleRadIC()) < 0.01) ) {
+ if (needTrim)
fgic->SetClimbRateFpsIC(roc);
+ else {
+ FGColumnVector3 vNED = Propagate->GetVel();
+ vNED(FGJSBBase::eDown) = -roc;
+ FGColumnVector3 vUVW = Propagate->GetTl2b() * vNED;
+ Propagate->SetUVW(1, vUVW(1));
+ Propagate->SetUVW(2, vUVW(2));
+ Propagate->SetUVW(3, vUVW(3));
+
+ FGInterface::set_Climb_Rate(roc);
}
-
- if (!fdmex->Holding())
- needTrim=true;
+ }
}
void FGJSBsim::set_Gamma_vert_rad( double gamma)
{
- SG_LOG(SG_FLIGHT,SG_INFO, "FGJSBsim::set_Gamma_vert_rad: " << gamma );
+ SG_LOG(SG_FLIGHT,SG_INFO, "FGJSBsim::set_Gamma_vert_rad: " << gamma );
- update_ic();
- if( !(fabs(gamma) < 0.01 && fabs(fgic->GetClimbRateFpsIC()) > 1) ) {
+ if( !(fabs(gamma) < 0.01 && fabs(fgic->GetClimbRateFpsIC()) > 1) ) {
+ if (needTrim)
fgic->SetFlightPathAngleRadIC(gamma);
+ else {
+ FGColumnVector3 vNED = Propagate->GetVel();
+ double vt = vNED.Magnitude();
+ vNED(FGJSBBase::eDown) = -vt * sin(gamma);
+ FGColumnVector3 vUVW = Propagate->GetTl2b() * vNED;
+ Propagate->SetUVW(1, vUVW(1));
+ Propagate->SetUVW(2, vUVW(2));
+ Propagate->SetUVW(3, vUVW(3));
+
+ FGInterface::set_Gamma_vert_rad(gamma);
+ }
+ }
+}
+// Reverse the VCAS formula to obtain the corresponding Mach number. For subsonic
+// speeds, the reversed formula has a closed form. For supersonic speeds, the
+// formula is reversed by the Newton-Raphson algorithm.
+
+double FGJSBsim::getMachFromVcas(double vcas)
+{
+ double p=pressure->getDoubleValue();
+ double psl=fdmex->GetAtmosphere()->GetPressureSL();
+ double rhosl=fdmex->GetAtmosphere()->GetDensitySL();
+
+ double pt = p + psl*(pow(1+vcas*vcas*rhosl/(7.0*psl),3.5)-1);
+
+ if (pt/p < 1.89293)
+ return sqrt(5.0*(pow(pt/p, 0.2857143) -1)); // Mach < 1
+ else {
+ // Mach >= 1
+ double mach = sqrt(0.77666*pt/p); // Initial guess is based on a quadratic approximation of the Rayleigh formula
+ double delta = 1.;
+ double target = pt/(166.92158*p);
+ int iter = 0;
+
+ // Find the root with Newton-Raphson. Since the differential is never zero,
+ // the function is monotonic and has only one root with a multiplicity of one.
+ // Convergence is certain.
+ while (delta > 1E-5 && iter < 10) {
+ double m2 = mach*mach; // Mach^2
+ double m6 = m2*m2*m2; // Mach^6
+ delta = mach*m6/pow(7.0*m2-1.0,2.5) - target;
+ double diff = 7.0*m6*(2.0*m2-1)/pow(7.0*m2-1.0,3.5); // Never zero when Mach >= 1
+ mach -= delta/diff;
+ iter++;
}
- if (!fdmex->Holding())
- needTrim=true;
+ return mach;
+ }
}
void FGJSBsim::init_gear(void )
SG_LOG( SG_FLIGHT, SG_INFO, " Trim complete" );
}
-void FGJSBsim::update_ic(void)
+bool FGJSBsim::update_ground_cache(FGLocation cart, double* cart_pos, double dt)
{
- if ( !needTrim ) {
- fgic->SetLatitudeRadIC(get_Lat_geocentric() );
- fgic->SetLongitudeRadIC( get_Longitude() );
- fgic->SetAltitudeASLFtIC( get_Altitude() );
- fgic->SetVcalibratedKtsIC( get_V_calibrated_kts() );
- fgic->SetThetaRadIC( get_Theta() );
- fgic->SetPhiRadIC( get_Phi() );
- fgic->SetPsiRadIC( get_Psi() );
- fgic->SetClimbRateFpsIC( get_Climb_Rate() );
- }
+ // Compute the radius of the aircraft. That is the radius of a ball
+ // where all gear units are in. At the moment it is at least 10ft ...
+ double acrad = 10.0;
+ int n_gears = GroundReactions->GetNumGearUnits();
+ for (int i=0; i<n_gears; ++i) {
+ FGColumnVector3 bl = GroundReactions->GetGearUnit(i)->GetBodyLocation();
+ double r = bl.Magnitude();
+ if (acrad < r)
+ acrad = r;
+ }
+
+ // Compute the potential movement of this aircraft and query for the
+ // ground in this area.
+ double groundCacheRadius = acrad + 2*dt*Propagate->GetUVW().Magnitude();
+ cart_pos[0] = cart(1);
+ cart_pos[1] = cart(2);
+ cart_pos[2] = cart(3);
+ double t0 = fdmex->GetSimTime();
+ bool cache_ok = prepare_ground_cache_ft( t0, t0 + dt, cart_pos,
+ groundCacheRadius );
+ if (!cache_ok) {
+ SG_LOG(SG_FLIGHT, SG_WARN,
+ "FGInterface is being called without scenery below the aircraft!");
+
+ SG_LOG(SG_FLIGHT, SG_WARN, "altitude = "
+ << fgic->GetAltitudeASLFtIC());
+
+ SG_LOG(SG_FLIGHT, SG_WARN, "sea level radius = "
+ << fgic->GetSeaLevelRadiusFtIC());
+
+ SG_LOG(SG_FLIGHT, SG_WARN, "latitude = "
+ << fgic->GetLatitudeRadIC());
+
+ SG_LOG(SG_FLIGHT, SG_WARN, "longitude = "
+ << fgic->GetLongitudeRadIC());
+ }
+
+ return cache_ok;
}
bool
return true;
}
-inline static double dot3(const FGColumnVector3& a, const FGColumnVector3& b)
-{
- return a(1) * b(1) + a(2) * b(2) + a(3) * b(3);
-}
-
inline static double sqr(double x)
{
return x * x;
static void check_hook_solution(const FGColumnVector3& ground_normal_body, double E, double hook_length, double sin_fi_guess, double cos_fi_guess, double* sin_fis, double* cos_fis, double* fis, int* points)
{
FGColumnVector3 tip(-hook_length * cos_fi_guess, 0, hook_length * sin_fi_guess);
- double dist = dot3(tip, ground_normal_body);
+ double dist = DotProduct(tip, ground_normal_body);
if (fabs(dist + E) < 0.0001) {
sin_fis[*points] = sin_fi_guess;
cos_fis[*points] = cos_fi_guess;
if (got && root_agl_ft > 0 && root_agl_ft < hook_length) {
FGColumnVector3 ground_normal_body = Tl2b * (Tec2l * FGColumnVector3(ground_normal[0], ground_normal[1], ground_normal[2]));
FGColumnVector3 contact_body = Tl2b * Location.LocationToLocal(FGColumnVector3(contact[0], contact[1], contact[2]));
- double D = -dot3(contact_body, ground_normal_body);
+ double D = -DotProduct(contact_body, ground_normal_body);
// check hook tip agl against same ground plane
- double hook_tip_agl_ft = dot3(hook_tip_body, ground_normal_body) + D;
+ double hook_tip_agl_ft = DotProduct(hook_tip_body, ground_normal_body) + D;
if (hook_tip_agl_ft < 0) {
// hook tip: hx - l cos, hy, hz + l sin
// on ground: - n0 l cos + n2 l sin + E = 0
- double E = D + dot3(hook_root_body, ground_normal_body);
+ double E = D + DotProduct(hook_root_body, ground_normal_body);
// substitue x = sin fi, cos fi = sqrt(1 - x * x)
// and rearrange to get a quadratic with coeffs:
FGColumnVector3 wire_end2_body = Tl2b * Location.LocationToLocal(FGColumnVector3(wire_ends_ec[1][0], wire_ends_ec[1][1], wire_ends_ec[1][2])) - hook_root_body;
FGColumnVector3 force_plane_normal = wire_end1_body * wire_end2_body;
force_plane_normal.Normalize();
- cos_fi = dot3(force_plane_normal, FGColumnVector3(0, 0, 1));
+ cos_fi = DotProduct(force_plane_normal, FGColumnVector3(0, 0, 1));
if (cos_fi < 0) cos_fi = -cos_fi;
sin_fi = sqrt(1 - sqr(cos_fi));
fi = atan2(sin_fi, cos_fi) * SG_RADIANS_TO_DEGREES;