function [CD,CL,CY,Cl,Cm,Cn,Thrust] = AeroModelMach(x,u,Mach,alphar,betar,V) % Aerodynamic Coefficients of the Aircraft, Thrust Model, % and Geometric and Inertial Properties % September 1, 2006 % =============================================================== % Copyright 2006 by ROBERT F. STENGEL. All rights reserved. % Business Jet -- Low-Angle-of-Attack, Mach-Dependent Model % Landing Gear: Up or Down (GEAR = 1 or 0) % Flap Setting, u(6): 0 deg or 38 deg (0 or 0.66 rad) % Symmetric Spoiler: Deployed or Closed (SPOIL = 1 or 0) global m Ixx Iyy Izz Ixz S b c GEAR CONHIS SPOIL SMI % Typical Mass and Inertial Properties m = 4536; % Mass, kg Ixx = 35926.5; % Roll Moment of Inertia, kg-m^2 Iyy = 33940.7; % Pitch Moment of Inertia, kg-m^2 Izz = 67085.5; % Yaw Moment of Inertia, kg-m^2 Ixz = 3418.17; % Nose-high(low) Product of Inertia, kg-m^2 % Geometric Properties c = 2.14; % Mean Aerodynamic Chord, m b = 10.4; % Wing Span, m S = 21.5; % Reference Area, m^2 ARw = 5.02; % Wing Aspect Ratio taperw = 0.507; % Wing Taper Ratio sweepw = 13 * .01745329; % Wing 1/4-chord sweep angle, rad ARh = 4; % Horizontal Tail Aspect Ratio sweeph = 25 * .01745329; % Horiz Tail 1/4-chord sweep angle, rad ARv = 0.64; % Vertical Tail Aspect Ratio sweepv = 40 * .01745329; % Vert Tail 1/4-chord sweep angle, rad lvt = 4.72; % Vert Tail Length, m % Thrust Properties StaticThrust = 26243.2; % Static Thrust @ Sea Level, N % Current Thrust [airDens,airPres,temp,soundSpeed] = Atmos(-x(6)); Thrust = u(4) * StaticThrust * (airDens / 1.225)^0.7 ... * (1 - exp((-x(6) - 17000) / 2000)); % Thrust at Altitude, N % Current Mach Effects, normalized to Test Condition B (Mach = 0.1734) PrFac = 1 / (sqrt(1 - Mach^2) * 1.015); % Prandtl Factor WingMach = 1 / ((1 + sqrt(1 + ((ARw/(2 * cos(sweepw)))^2) ... * (1 - Mach^2 * cos(sweepw)))) * 0.268249); % Modified Helmbold equation HorizTailMach = 1 / ((1 + sqrt(1 + ((ARh/(2 * cos(sweeph)))^2) ... * (1 - Mach^2 * cos(sweeph)))) * 0.294539); % Modified Helmbold equation VertTailMach = 1 / ((1 + sqrt(1 + ((ARv/(2 * cos(sweepv)))^2) ... * (1 - Mach^2 * cos(sweepv)))) * 0.480338); % Modified Helmbold equation % Current Longitudinal Characteristics % ==================================== % Lift Coefficient CLo = 0.1095; % Zero-AoA Lift Coefficient (B) if GEAR >= 1 CLo = CLo - 0.0192; % Gear-down correction end if u(6) >= 0.65 CLo = CLo + 0.5182; % 38 deg-flap correction end if SPOIL >= 1 CLo = CLo - 0.1897; % 42 deg-Symmetric Spoiler correction end CLar = 5.6575; % Lift Slope (B), per rad if u(6) >= 0.65 CLar = CLar - 0.0947; end CLqr = 4.231 * c / (2 * V); % Pitch-Rate Effect, per rad/s CLdSr = 1.08; % Stabilator Effect, per rad if u(6) >= 0.65 CLdSr = CLdSr - 0.4802; % 38ç-flap correction end CLdEr = 0.5774; % Elevator Effect, per rad if u(6) >= 0.65 CLdEr = CLdEr - 0.2665; % 38 deg-flap correction end CL = CLo + (CLar*alphar + CLqr*x(8) + CLdSr*u(7) + CLdEr*u(1)) ... * WingMach; % Total Lift Coefficient, w/Mach Correction % Drag Coefficient CDo = 0.0255; % Parasite Drag Coefficient (B) if GEAR >= 1 CDo = CDo + 0.0191; % Gear-down correction end if u(6) >= 0.65 CDo = CDo + 0.0836; % 38 deg-flap correction end if SPOIL >= 1 CDo = CDo + 0.0258; % 42 deg-Symmetric Spoiler correction end epsilon = 0.0718; % Induced Drag Factor if u(6) >= 0.65 epsilon = 0.079; % 38 deg-flap correction end CD = CDo * PrFac + epsilon * CL^2; % Total Drag Coefficient, w/Mach Correction % Pitching Moment Coefficient Cmo = 0; % Zero-AoA Moment Coefficient (B) if GEAR >= 1 Cmo = Cmo + 0.0255; % Gear-down correction end if u(6) >= 0.65 Cmo = Cmo - 0.058; % 38 deg-flap correction end if SPOIL >= 1 Cmo = Cmo - 0.0154; % 42 deg-Symmetric Spoiler correction end Cmar = -1.231; % Static Stability (B), per rad if u(6) >= 0.65 Cmar = Cmar + 0.0138; end Cmqr = -18.8 * c / (2 * V); % Pitch-Rate + Alpha-Rate Effect, per rad/s CmdSr = -2.291; % Stabilator Effect, per rad if u(6) >= 0.65 CmdSr = CmdSr + 0.121; % 38 deg-flap correction end CmdEr = -1.398; % Elevator Effect, per rad if u(6) >= 0.65 CmdEr = CmdEr + 0.149; % 38 deg-flap correction end Cm = Cmo + (Cmar*alphar + Cmqr*x(8) + CmdSr*u(7) + CmdEr*u(1)) ... * HorizTailMach; % Total Pitching Moment Coefficient, w/Mach Correction % Current Lateral-Directional Characteristics % =========================================== % Side-Force Coefficient CYBr = -0.7162; % Side-Force Slope (B), per rad if u(6) >= 0.65 CYBr = CYBr + 0.0826; end CYdAr = -0.00699; % Aileron Effect, per rad CYdRr = 0.1574; % Rudder Effect, per rad if u(6) >= 0.65 CYdRr = CYdRr - 0.0093; % 38 deg-flap correction end CYdASr = 0.0264; % Asymmetric Spoiler Effect, per rad if u(6) >= 0.65 CYdASr = CYdASr + 0.0766; % 38 deg-flap correction end CY = (CYBr*betar + CYdRr*u(3)) * VertTailMach ... + (CYdAr*u(2) + CYdASr*u(5)) * WingMach; % Total Side-Force Coefficient, w/Mach Correction % Yawing Moment Coefficient CnBr = 0.1194; % Directional Stability (B), per rad if u(6) >= 0.65 CnBr = CnBr - 0.0092; end Cnpr = CL * (1 + 3 * taperw)/(12 * (1 + taperw)) * (b / (2 * V)); % Roll-Rate Effect, per rad/s Cnrr = (-2 * (lvt / b) * CnBr * VertTailMach - 0.1 * CL^2) ... * (b / (2 * V)); % Yaw-Rate Effect, per rad/s CndAr = 0; % Aileron Effect, per rad if u(6) >= 0.65 CndAr = CndAr + 0.0028; end CndRr = -0.0713; % Rudder Effect, per rad if u(6) >= 0.65 CndRr = CndRr - 0.0185; % 38 deg-flap correction end CndASr = -0.0088; % Asymmetric Spoiler Effect, per rad if u(6) >= 0.65 CndASr = CndASr - 0.0106; % 38 deg-flap correction end Cn = (CnBr*betar + CndRr*u(3)) * VertTailMach ... + Cnrr * x(9) + Cnpr * x(7) ... + (CndAr*u(2) + CndASr*u(5)) * WingMach; % Total Yawing-Moment Coefficient, w/Mach Correction % Rolling Moment Coefficient ClBr = -0.0918; % Dihedral Effect (B), per rad if u(6) >= 0.65 ClBr = ClBr - 0.0092; end Clpr = -CLar * (1 + 3 * taperw)/(12 * (1 + taperw)) ... * (b / (2 * V)); % Roll-Rate Effect, per rad/s Clrr = (CL * (1 + 3 * taperw)/(12 * (1 + taperw)) ... * ((Mach * cos(sweepw))^2 - 2) / ((Mach * cos(sweepw))^2 - 1)) ... * (b / (2 * V)); % Yaw-Rate Effect, per rad/s CldAr = 0.1537; % Aileron Effect, per rad if u(6) >= 0.65 CldAr = CldAr + 0.01178; end CldRr = 0.01208; % Rudder Effect, per rad if u(6) >= 0.65 CldRr = CldRr + 0.01115; % 38 deg-flap correction end CldASr = -0.01496; % Asymmetric Spoiler Effect, per rad if u(6) >= 0.65 CldASr = CldASr - 0.02376; % 38 deg-flap correction end Cl = (ClBr*betar + CldRr*u(3)) * VertTailMach ... + Clrr * x(9) + Clpr * x(7) ... + (CldAr*u(2) + CldASr*u(5)) * WingMach; % Total Rolling-Moment Coefficient, w/Mach Correction