- }
- case ttMilspec:
- case ttTustin: {
- // an index of zero means turbulence is disabled
- if (probability_of_exceedence_index == 0) {
- vTurbulenceNED(1) = vTurbulenceNED(2) = vTurbulenceNED(3) = 0.0;
- vTurbPQR(1) = vTurbPQR(2) = vTurbPQR(3) = 0.0;
- return;
- }
-
- // Turbulence model according to MIL-F-8785C (Flying Qualities of Piloted Aircraft)
- double
- h = FDMExec->GetPropagate()->GetDistanceAGL(),
- V = FDMExec->GetAuxiliary()->GetVt(), // true airspeed in ft/s
- b_w = wingspan,
- L_u, L_w, sig_u, sig_w;
-
- // clip height functions at 10 ft
- if (h <= 10.) h = 10;
-
- // Scale lengths L and amplitudes sigma as function of height
- if (h <= 1000) {
- L_u = h/pow(0.177 + 0.000823*h, 1.2); // MIL-F-8785c, Fig. 10, p. 55
- L_w = h;
- sig_w = 0.1*windspeed_at_20ft;
- sig_u = sig_w/pow(0.177 + 0.000823*h, 0.4); // MIL-F-8785c, Fig. 11, p. 56
- } else if (h <= 2000) {
- // linear interpolation between low altitude and high altitude models
- L_u = L_w = 1000 + (h-1000.)/1000.*750.;
- sig_u = sig_w = 0.1*windspeed_at_20ft
- + (h-1000.)/1000.*(POE_Table->GetValue(probability_of_exceedence_index, h) - 0.1*windspeed_at_20ft);
- } else {
- L_u = L_w = 1750.; // MIL-F-8785c, Sec. 3.7.2.1, p. 48
- sig_u = sig_w = POE_Table->GetValue(probability_of_exceedence_index, h);
- }
-
- // keep values from last timesteps
- // TODO maybe use deque?
- static double
- xi_u_km1 = 0, nu_u_km1 = 0,
- xi_v_km1 = 0, xi_v_km2 = 0, nu_v_km1 = 0, nu_v_km2 = 0,
- xi_w_km1 = 0, xi_w_km2 = 0, nu_w_km1 = 0, nu_w_km2 = 0,
- xi_p_km1 = 0, nu_p_km1 = 0,
- xi_q_km1 = 0, xi_r_km1 = 0;
-
-
- double
- T_V = DeltaT, // for compatibility of nomenclature
- sig_p = 1.9/sqrt(L_w*b_w)*sig_w, // Yeager1998, eq. (8)
- sig_q = sqrt(M_PI/2/L_w/b_w), // eq. (14)
- sig_r = sqrt(2*M_PI/3/L_w/b_w), // eq. (17)
- L_p = sqrt(L_w*b_w)/2.6, // eq. (10)
- tau_u = L_u/V, // eq. (6)
- tau_w = L_w/V, // eq. (3)
- tau_p = L_p/V, // eq. (9)
- tau_q = 4*b_w/M_PI/V, // eq. (13)
- tau_r =3*b_w/M_PI/V, // eq. (17)
- nu_u = GaussianRandomNumber(),
- nu_v = GaussianRandomNumber(),
- nu_w = GaussianRandomNumber(),
- nu_p = GaussianRandomNumber(),
- xi_u=0, xi_v=0, xi_w=0, xi_p=0, xi_q=0, xi_r=0;
-
- // values of turbulence NED velocities
-
- if (turbType == ttTustin) {
- // the following is the Tustin formulation of Yeager's report
- double
- omega_w = V/L_w, // hidden in nomenclature p. 3
- omega_v = V/L_u, // this is defined nowhere
- C_BL = 1/tau_u/tan(T_V/2/tau_u), // eq. (19)
- C_BLp = 1/tau_p/tan(T_V/2/tau_p), // eq. (22)
- C_BLq = 1/tau_q/tan(T_V/2/tau_q), // eq. (24)
- C_BLr = 1/tau_r/tan(T_V/2/tau_r); // eq. (26)
-
- xi_u = -(1 - C_BL*tau_u)/(1 + C_BL*tau_u)*xi_u_km1
- + sig_u*sqrt(2*tau_u/T_V)/(1 + C_BL*tau_u)*(nu_u + nu_u_km1); // eq. (18)
- xi_v = -2*(sqr(omega_v) - sqr(C_BL))/sqr(omega_v + C_BL)*xi_v_km1
- - sqr(omega_v - C_BL)/sqr(omega_v + C_BL) * xi_v_km2
- + sig_u*sqrt(3*omega_v/T_V)/sqr(omega_v + C_BL)*(
- (C_BL + omega_v/sqrt(3.))*nu_v
- + 2/sqrt(3.)*omega_v*nu_v_km1
- + (omega_v/sqrt(3.) - C_BL)*nu_v_km2); // eq. (20) for v
- xi_w = -2*(sqr(omega_w) - sqr(C_BL))/sqr(omega_w + C_BL)*xi_w_km1
- - sqr(omega_w - C_BL)/sqr(omega_w + C_BL) * xi_w_km2
- + sig_w*sqrt(3*omega_w/T_V)/sqr(omega_w + C_BL)*(
- (C_BL + omega_w/sqrt(3.))*nu_w
- + 2/sqrt(3.)*omega_w*nu_w_km1
- + (omega_w/sqrt(3.) - C_BL)*nu_w_km2); // eq. (20) for w
- xi_p = -(1 - C_BLp*tau_p)/(1 + C_BLp*tau_p)*xi_p_km1
- + sig_p*sqrt(2*tau_p/T_V)/(1 + C_BLp*tau_p) * (nu_p + nu_p_km1); // eq. (21)
- xi_q = -(1 - 4*b_w*C_BLq/M_PI/V)/(1 + 4*b_w*C_BLq/M_PI/V) * xi_q_km1
- + C_BLq/V/(1 + 4*b_w*C_BLq/M_PI/V) * (xi_w - xi_w_km1); // eq. (23)
- xi_r = - (1 - 3*b_w*C_BLr/M_PI/V)/(1 + 3*b_w*C_BLr/M_PI/V) * xi_r_km1
- + C_BLr/V/(1 + 3*b_w*C_BLr/M_PI/V) * (xi_v - xi_v_km1); // eq. (25)
-
- } else if (turbType == ttMilspec) {
- // the following is the MIL-STD-1797A formulation
- // as cited in Yeager's report
- xi_u = (1 - T_V/tau_u) *xi_u_km1 + sig_u*sqrt(2*T_V/tau_u)*nu_u; // eq. (30)
- xi_v = (1 - 2*T_V/tau_u)*xi_v_km1 + sig_u*sqrt(4*T_V/tau_u)*nu_v; // eq. (31)
- xi_w = (1 - 2*T_V/tau_w)*xi_w_km1 + sig_w*sqrt(4*T_V/tau_w)*nu_w; // eq. (32)
- xi_p = (1 - T_V/tau_p) *xi_p_km1 + sig_p*sqrt(2*T_V/tau_p)*nu_p; // eq. (33)
- xi_q = (1 - T_V/tau_q) *xi_q_km1 + M_PI/4/b_w*(xi_w - xi_w_km1); // eq. (34)
- xi_r = (1 - T_V/tau_r) *xi_r_km1 + M_PI/3/b_w*(xi_v - xi_v_km1); // eq. (35)
- }
-
- // rotate by wind azimuth and assign the velocities
- double cospsi = cos(psiw), sinpsi = sin(psiw);
- vTurbulenceNED(1) = cospsi*xi_u + sinpsi*xi_v;
- vTurbulenceNED(2) = -sinpsi*xi_u + cospsi*xi_v;
- vTurbulenceNED(3) = xi_w;
-
- vTurbPQR(1) = cospsi*xi_p + sinpsi*xi_q;
- vTurbPQR(2) = -sinpsi*xi_p + cospsi*xi_q;
- vTurbPQR(3) = xi_r;
-
- // vTurbPQR is in the body fixed frame, not NED
- vTurbPQR = Tl2b*vTurbPQR;
-
- // hand on the values for the next timestep
- xi_u_km1 = xi_u; nu_u_km1 = nu_u;
- xi_v_km2 = xi_v_km1; xi_v_km1 = xi_v; nu_v_km2 = nu_v_km1; nu_v_km1 = nu_v;
- xi_w_km2 = xi_w_km1; xi_w_km1 = xi_w; nu_w_km2 = nu_w_km1; nu_w_km1 = nu_w;
- xi_p_km1 = xi_p; nu_p_km1 = nu_p;
- xi_q_km1 = xi_q;
- xi_r_km1 = xi_r;
-
- }