Altex Parameters: 3.000000 : (vel) Foward speed, knots. 52.000000 : (Tp) Thrust, Newtons. 795.000000 : (mass) Mass, kg. 4.190000 : (len) Length, Meters. 0.533400 : (dia) Diameter, Meters. 21.000000 : (dia) Diameter, Inches. 0.000000 : (xG) x CG offset, Meters. -0.076200 : (xPcp) Dist from pivot to ring CP, Meters. -3.000000 : (xPcp) Dist from pivot to ring CP, In. 0.063500 : (aR) Dist from c.l. to rudder actuator base, m 0.063500 : (rR2) Dist from c.l. to rudder actuator pivot, m 0.025400 : (rR1) Body x Dist from Tailcone Pivot to Rudder Actuator Pivot, m 0.100000 : (Ts) Control System Sampling Interval, Sec. 15.000000 : (maxDeltaR) Max. Rudder Deflection, Deg. 2400.000000 : (maxActDisp) Max Act. Displacement, counts. 1200.000000 : (maxActRate) Max Actuator Displacement Rate, Counts/Sec 120.000000 : (maxActDispTs) Max Act. Displacment in one Ts, Counts/sample 1.150000 : (ampsAct) Actuator current, full on, amps. 0.010161 : (ControlArea) Control surface Area, Meters^2. 15.750000 : (ControlArea) Control surface Area, Inches^2. 0.233302 : (TotalArea) Area of ring and struts, M^2. 3.111111 : (Ar) Ring/strut aspect ratio. 0.810000 : (Cdc) Crossflow drag coefficient 0.012000 : (Cd0) Constant component of drag coeff. 0.900000 : (Ef) Oswald efficiency factor. 6.280000 : (dCl) Coeff. of lift slope. -1.885500 : (xR) Distance from CG to CP of ring, Meters. -1.809300 : (xP) Distance from CG to pivot point, Meters. 709.164469 : (Izz) Inertia about (principal) z axis, kg-m^2. 22.618987 : (Ixx) Inertia about (principal) x axis, kg-m^2. -59.853025 : (Xudot) Deriv of X wrto u-dot, kg. 126.965545 : (Xrv) Deriv of x wrto rv, kg. -28.674628 : (Xrr) Deriv of x wrto rr, N-sec^2. -20.392506 : (Xuu) Deriv of x wrto uu, kg/m. 88.433587 : (Xvv) Deriv of x wrto vv, kg/m. -149.897250 : (Nr) Deriv of N wrto r, kg-m. -632.025000 : (Nv) Deriv of N wrto v (Munk Moment), kg. 50.880000 : (Yr) Deriv of Y wrto r, kg. -94.868735 : (Yv) Deriv of Y wrto v, kg/m. -636.000000 : (Yvdot) Deriv of Y wrto v-dot (Added Mass),kg. 0.000000 : (Nrdot) Deriv of N wrto r-dot (Added Inr),kg-m^2. 0.000000 : (Yrdot) Deriv of Y wrto r-dot. 0.000000 : (Nvdot) Deriv of N wrto v-dot. 0.000000 : (Yvabsr) Deriv of Y wrto r|v|. -557.828162 : (Yvabsv) Deriv of Y wrto v|v|. 273.480000 : (Nvabsv) Deriv of N wrto v|v|. -983.975515 : (Nrabsr) Deriv of N wrto r|r|. =================== OPEN LOOP ================= Steady-State Values of the OPEN LOOP Sway/Yaw Linear Model: The rudder angle is 10 Deg. The CG drift angle is 13.7468 Deg. The turn rate is -11.0618 Deg/Sec The turn diameter is 15.9877 Meters or 3.8157 vehicle lengths. The control-torque component about the CG is -208.7275 N-m The control-torque component about the pivot point is -7.7718 N-m The total steady-state torque about the CG is 316.5232 N-m The total steady-state torque about the pivot point is 13.4555 N-m The OPEN-LOOP eigenvalues are: evals = -0.3096 -2.2859 The natural frequency, damping ratio, and time constant are: f_n , damping ratio, time constant ans = 0.0493 1.0000 3.2305 0.3638 1.0000 0.4375 The full order (w/ kinematics) open-loop sway system e-values are: evals = 0 0 -0.3096 -2.2859 The eigenvalues of the discretized system are: ---Z Root Information Algorithm--------------------------------- there is (are) 4 real evals, 0 complex pairs and 0 s=0 evals. magnitude and phase (deg): ans = 1.0000 0 1.0000 0 0.9695 0 0.7957 0 time constant, 3 time constants (seconds): ans = 0 0 0 0 3.2305 9.6914 0.4375 1.3124 ---end z root information algorithm------------------------------ =================== Entire System Open Loop ================= The Entire System OPEN-LOOP eigenvalues are: evals = 0 0 0 0 + 5.2510i 0 - 5.2510i -2.2859 -0.3096 -1.8216 -0.3869 + 0.1663i -0.3869 - 0.1663i 0 -0.0736 The natural frequency, damping ratio, and time constant are: f_n , damping ratio ans = 0.8357 0 0.8357 0 0.3638 1.0000 0.0493 1.0000 0.2899 1.0000 0.0670 0.9187 0.0670 0.9187 0.0117 1.0000 There are 4 evalues at zero. jj = 7 Time constants are: ans = 0.4375 3.2305 0.5490 2.5845 2.5845 13.5810 =================== SWAY/YAW CLOSED LOOP ================= ---Z Root Information Algorithm--------------------------------- there is (are) 3 real evals, 1 complex pairs and 0 s=0 evals. magnitude and phase (deg): ans = 0.5136 0 0.9635 0 0.9903 0.4200 0.9903 -0.4200 0.9930 0 damping ratio, natural frequency (hz), time constant, 3*t.c.: ans = 0.7983 0.0194 10.2900 30.8700 0.7983 0.0194 10.2900 30.8700 time constant, 3 time constants (seconds): ans = 0.1501 0.4502 2.6873 8.0618 14.2301 42.6902 ---end z root information algorithm------------------------------ Generating closed loop linear step response. -------------Simulation of Nonlinear EOM:------------- Simulation Initialization: GenMassInv [0][0] = 1.169792e-03 GenMassInv [0][1] = 0.000000e+00 GenMassInv [0][2] = -0.000000e+00 GenMassInv [0][3] = 0.000000e+00 GenMassInv [0][4] = -0.000000e+00 GenMassInv [0][5] = -0.000000e+00 GenMassInv [1][0] = 0.000000e+00 GenMassInv [1][1] = 6.988120e-04 GenMassInv [1][2] = -0.000000e+00 GenMassInv [1][3] = 0.000000e+00 GenMassInv [1][4] = -0.000000e+00 GenMassInv [1][5] = -0.000000e+00 GenMassInv [2][0] = 0.000000e+00 GenMassInv [2][1] = 0.000000e+00 GenMassInv [2][2] = 6.988120e-04 GenMassInv [2][3] = 0.000000e+00 GenMassInv [2][4] = -0.000000e+00 GenMassInv [2][5] = -0.000000e+00 GenMassInv [3][0] = 0.000000e+00 GenMassInv [3][1] = 0.000000e+00 GenMassInv [3][2] = 0.000000e+00 GenMassInv [3][3] = 4.421064e-02 GenMassInv [3][4] = -0.000000e+00 GenMassInv [3][5] = -0.000000e+00 GenMassInv [4][0] = 0.000000e+00 GenMassInv [4][1] = 0.000000e+00 GenMassInv [4][2] = 0.000000e+00 GenMassInv [4][3] = 0.000000e+00 GenMassInv [4][4] = 1.410110e-03 GenMassInv [4][5] = -0.000000e+00 GenMassInv [5][0] = 0.000000e+00 GenMassInv [5][1] = 0.000000e+00 GenMassInv [5][2] = 0.000000e+00 GenMassInv [5][3] = 0.000000e+00 GenMassInv [5][4] = 0.000000e+00 GenMassInv [5][5] = 1.410110e-03 P[MassIx] = 7.950000e+02; P[IxxIx] = 2.261899e+01; P[IyyIx] = 7.091645e+02; P[IzzIx] = 7.091645e+02; P[IxyIx] = 0.000000e+00; P[IyzIx] = 0.000000e+00; P[IzxIx] = 0.000000e+00; P[WIx] = 7.795770e+03; P[xGIx] = 0.000000e+00; P[yGIx] = 0.000000e+00; P[zGIx] = 0.000000e+00; P[BIx] = 7.795770e+03; P[xBIx] = 0.000000e+00; P[yBIx] = 0.000000e+00; P[zBIx] = -8.000000e-02; P[MSurgeIx] = 8.548530e+02; P[velIx] = 1.543333e+00; P[XrvIx] = 1.269655e+02; P[XrrIx] = -2.867463e+01; P[XuuIx] = -2.039251e+01; P[XvvIx] = 8.843359e+01; P[XqqIx] = -2.867463e+01; P[XwqIx] = -1.269655e+02; P[XwwIx] = 8.843359e+01; P[YvIx] = -9.486874e+01; P[YrIx] = 5.088000e+01; P[YwpIx] = 3.136000e+02; P[YrabsrIx] = 3.150000e+01; P[YvabsrIx] = 0.000000e+00; P[YvabsvIx] = -5.578282e+02; P[ZqIx] = -5.088000e+01; P[ZwIx] = -9.486874e+01; P[ZvpIx] = -3.136000e+02; P[ZqabsqIx] = -3.150000e+01; P[ZwabswIx] = -5.578282e+02; P[KpabspIx] = -3.000000e+02; P[MqIx] = -1.498973e+02; P[MwIx] = 6.320250e+02; P[MprIx] = 5.070000e+01; P[MqabsqIx] = -9.839755e+02; P[MwabswIx] = -2.734800e+02; P[NvIx] = -6.320250e+02; P[NrIx] = -1.498973e+02; P[NpqIx] = -5.070000e+01; P[NrabsvIx] = 0.000000e+00; P[NvabsvIx] = 2.734800e+02; P[NrabsrIx] = -9.839755e+02; P[DecoupleIx] = 0.000000e+00; P[xRIx] = -1.885500e+00; P[xPIx] = -1.809300e+00; P[xPRIx] = -2.540000e-02; P[r_Ro_S1_R0Ix] = -7.620000e-02; P[r_Ro_S1_R1Ix] = 0.000000e+00; P[r_Ro_S1_R2Ix] = -1.524000e-01; P[r_Ro_S2_R0Ix] = -7.620000e-02; P[r_Ro_S2_R1Ix] = -1.077631e-01; P[r_Ro_S2_R2Ix] = -1.077631e-01; P[r_Ro_S3_R0Ix] = -7.620000e-02; P[r_Ro_S3_R1Ix] = -1.524000e-01; P[r_Ro_S3_R2Ix] = 0.000000e+00; P[r_Ro_S4_R0Ix] = -7.620000e-02; P[r_Ro_S4_R1Ix] = -1.077631e-01; P[r_Ro_S4_R2Ix] = 1.077631e-01; P[r_Ro_S5_R0Ix] = -7.620000e-02; P[r_Ro_S5_R1Ix] = 0.000000e+00; P[r_Ro_S5_R2Ix] = 1.524000e-01; P[r_Ro_S6_R0Ix] = -7.620000e-02; P[r_Ro_S6_R1Ix] = 1.077631e-01; P[r_Ro_S6_R2Ix] = 1.077631e-01; P[r_Ro_S7_R0Ix] = -7.620000e-02; P[r_Ro_S7_R1Ix] = 1.524000e-01; P[r_Ro_S7_R2Ix] = 0.000000e+00; P[r_Ro_S8_R0Ix] = -7.620000e-02; P[r_Ro_S8_R1Ix] = 1.077631e-01; P[r_Ro_S8_R2Ix] = -1.077631e-01; P[aRIx] = 6.350000e-02; P[rR1Ix] = 2.540000e-02; P[rR2Ix] = 6.350000e-02; P[xRRIx] = 2.921000e-01; P[dClIx] = 6.280000e+00; P[Cl2Ix] = 2.603571e-01; P[Cd0Ix] = 1.200000e-02; P[Cd2Ix] = 1.136821e-01; P[halfRhoSIx] = 5.222893e+00; P[dClRIx] = 1.530000e+00; P[Cl2RIx] = 1.901408e-01; P[Cd0RIx] = 1.000000e-02; P[Cd2RIx] = 8.302292e-02; P[halfRhoSRIx] = 7.813429e+01; P[StallIx] = 5.235988e-01; P[u0] = 1.543333e+00; P[v0] = 0.000000e+00; P[w0] = 0.000000e+00; P[p0] = 0.000000e+00; P[q0] = 0.000000e+00; P[r0] = 0.000000e+00; P[x0] = 0.000000e+00; P[y0] = 0.000000e+00; P[z0] = 0.000000e+00; P[phi0] = 0.000000e+00; P[theta0] = 0.000000e+00; P[psi0] = 0.000000e+00; ------- Nonlinear Steady-State Analysis: ---------- -0.000003 : Computed vSS, Meters/Sec -0.000005 : Simulated vSS, Meters/Sec 52.000000 : Tp. MUST BE ZERO, or else this analysis does not apply. 0.000086 : Yaw rate, Deg/Sec. 0.000000 : Turn Diameter, Meters. -0.000107 : Beta, Deg/Sec. -0.000212 : BetaR, Deg/Sec. 0.001305 : Rudder force resolved to body y axis, Newtons. 0.000673 : Simulated Rudder force, Newtons. 1.548919 1.596579 : uSS [Sim Comp], m/sec.