WOLFRAM SYSTEM MODELER
DouglasDC8Model of Douglas DC-8 using state-space representation |
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Diagram
Wolfram Language
In[1]:=
SystemModel["Aircraft.StateSpace.FixedWing.DouglasDC8"]
Out[1]:=
Information
This model extends the DefaultAircraft model and contains the parameters of the Douglas DC-8-20.
References for Aircraft Parameter Values
[1] Teper, G.L., Aircraft stability and control data (1969).
Hawthorne, CA.: Systems Technology, Inc and Ames Research Center,
NASA.
Available at: https://ntrs.nasa.gov/api/citations/19690022405/downloads/19690022405.pdf.
[2] Wikipedia. (2021). "Douglas DC-8". [online]
Available at: https://en.wikipedia.org/wiki/Douglas_DC-8#Specifications. [Accessed 24 Oct. 2022].
Parameters (94)
| x0y0 |
Value: {0, 0} Type: Position[2] (m) Description: Initial lateral position of the aircraft (x and y coordinates in world frame) |
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| refVtot |
Value: 100 Type: Velocity (m/s) Description: Total velocity for reference flight condition (Also used as initial velocity) |
| refAlt |
Value: 1000 Type: Height (m) Description: Altitude for reference flight condition (Also used as initial altitude) |
| refGamma |
Value: 0 Type: Angle (rad) Description: Flight path for reference flight condition (Becomes a variable if no propulsion) |
| CDW0 |
Value: 0.03 Type: Real Description: Drag coefficient of wing-body at zero lift |
| CmW0 |
Value: -0.0711 Type: Real Description: Moment coefficient of wing-body at alpha = 0 |
| CLalphaWing3D |
Value: 4 Type: Real (rad⁻¹) Description: Change in the lift coefficient of the wing-body due to alpha |
| mAC |
Value: 86182.5503 Type: Mass (kg) Description: Aircraft mass |
| xCMdry |
Value: -7.0104 * 0.15 Type: Length (m) Description: Aircraft center of mass from wing leading edge at mean chord (positive x-axis towards nose) |
| IxxDry |
Value: 4216593.8245 Type: MomentOfInertia (kg⋅m²) Description: Aircraft moment of inertia about x-axis |
| IyyDry |
Value: 3986104.773 Type: MomentOfInertia (kg⋅m²) Description: Aircraft moment of inertia about y-axis |
| IzzDry |
Value: 7972209.546 Type: MomentOfInertia (kg⋅m²) Description: Aircraft moment of inertia about z-axis |
| ARwing |
Value: bWing ^ 2 / SrefWing Type: Real Description: Main wing aspect ratio |
| TRwing |
Value: cWingTip / cWingRoot Type: Real Description: Main wing taper ratio |
| etaWing |
Value: 1 / (Modelica.Constants.pi * ARwing * kdWing * CDW0 + 1 / (0.99 * sdWing)) Type: Real Description: Oswald efficiency factor for main wing |
| sdWing |
Value: 0.9998 + 0.0421 * (wFus / bWing) - 2.6286 * (wFus / bWing) ^ 2 + 2 * (wFus / bWing) ^ 3 Type: Real Description: Fuselage drag factor for main wing |
| Kw |
Value: 1 / (Modelica.Constants.pi * ARwing * etaWing) Type: Real Description: Induced drag factor for main wing |
| bWing |
Value: 43.37304 Type: Length (m) Description: Main wing span |
| cWingTip |
Value: 1.836 Type: Length (m) Description: Main wing root chord (where wing intersects with fuselage) |
| cWingRoot |
Value: 10.20 Type: Length (m) Description: Main wing root chord (where wing intersects with fuselage) |
| alphaw0 |
Value: -0.0349065850398866 Type: Angle (rad) Description: Zero-lift angle of attack of wing |
| gammaWing |
Value: 0.0872664625997165 Type: Angle (rad) Description: Main wing dihedral angle |
| SrefWing |
Value: 241.547904 Type: Area (m²) Description: Main wing reference area |
| xWingAC |
Value: -7.0104 * 0.25 Type: Length (m) Description: Main wing aerodynamic center from wing leading edge at mean chord (positive x-axis towards nose) |
| iWing |
Value: 0.0523598775598299 Type: Angle (rad) Description: Main wing incidence angle |
| cWingMean |
Value: 7.0104 Type: Length (m) Description: Main wing mean chord length |
| lambdaWing |
Value: 0.541052068118242 Type: Angle (rad) Description: Main wing sweep angle at 1/4 chord |
| epsilon0 |
Value: 0.0349065850398866 Type: Angle (rad) Description: Zero-lift downwash angle |
| CDHT0 |
Value: 0.03 Type: Real Description: Drag coefficient of horizontal tail at zero lift |
| vHT |
Value: SrefHT / SrefWing * (lHTcm / cWingMean) Type: Real Description: Horizontal tail volume coefficient |
| ARht |
Value: bHT ^ 2 / SrefHT Type: Real Description: Aspect ratio of horizontal tail |
| CLalphaHT3D |
Value: 4 Type: Real (rad⁻¹) Description: Change in the lift coefficient of the horizontal tail due to alpha |
| tauElv |
Value: 1.129 * (Selv / SrefHT) ^ 0.4044 - 0.1772 Type: Real Description: Elevator effectiveness parameter |
| SrefHT |
Value: 53.2 Type: Area (m²) Description: Horizontal tail reference area |
| lHTcm |
Value: 23.00 Type: Length (m) Description: Horizontal tail arm length (from aircraft center of mass to 1/4 chord) |
| iHT |
Value: 0 Type: Angle (rad) Description: Horizontal tail incidence angle |
| Selv |
Value: 6.00 Type: Area (m²) Description: Elevator area |
| bHT |
Value: 14.86 Type: Length (m) Description: Horizontal tail span |
| kdHT |
Value: -3.333 * 10 ^ (-4) * lambdaHT ^ 2 + 6.667 * 10 ^ (-5) * lambdaHT + 0.38 Type: Real Description: Empirical constant for Oswald efficiency factor for horizontal tail |
| etaHT |
Value: 1 / (Modelica.Constants.pi * ARht * kdHT * CDHT0 + 1 / (0.99 * sdHT)) Type: Real Description: Oswald efficiency factor for horizontal tail |
| sdHT |
Value: 0.9998 + 0.0421 * (dFusHT / bHT) - 2.6286 * (dFusHT / bHT) ^ 2 + 2 * (dFusHT / bHT) ^ 3 Type: Real Description: Fuselage drag factor for horizontal tail |
| lambdaHT |
Value: 0.575958653158129 Type: Angle (rad) Description: Horizontal tail sweep angle at 1/4 chord |
| lVTcm |
Value: 21.00 Type: Length (m) Description: Vertical tail arm length (from aircraft center of mass to vertical tail 1/4 chord) |
| zVTacCM |
Value: -5.80 Type: Length (m) Description: z-coordinate w.r.t. aircraft center of mass of center of pressure of vertical tail |
| etaVT |
Value: 0.8 Type: Real Description: Vertical tail efficiency factor |
| SrefVT |
Value: 28.00 Type: Area (m²) Description: Vertical tail reference area |
| vVT |
Value: SrefVT / SrefWing * (lVTcm / bWing) Type: Real Description: Vertical tail volume coefficient |
| tauRdr |
Value: 1.129 * (Srdr / SrefVT) ^ 0.4044 - 0.1772 Type: Real Description: Rudder effectiveness parameter |
| Srdr |
Value: 8.00 Type: Area (m²) Description: Rudder area |
| dFusHT |
Value: 2.32 Type: Length (m) Description: Fuselage diameter at horizontal tail 1/4 chord |
| wFus |
Value: 3.92 Type: Length (m) Description: Fuselage maximum width |
| nEng |
Value: 4 Type: Integer Description: Number of engines |
| zTau |
Value: 1.5 Type: Length (m) Description: z-coordinate w.r.t. aircraft center of mass of thrust line for side (#2-5) engines and single engine |
| zTauMid |
Value: 0 Type: Length (m) Description: z-coordinate w.r.t. aircraft center of mass of thrust line for middle (#1) engine |
| zTauTotal |
Value: if nEng == 3 then (zTau * 2 + zTauMid) / 3 else zTau Type: Length (m) Description: z-coordinate of thrust line |
| Tstatic |
Value: 76000 Type: Force (N) Description: Static thrust of one engine at sea level |
| negThrust |
Value: 0 Type: Real Description: Maximum negative thrust (0 to 1 of thrust available) |
| kappa |
Value: 0 Type: Angle (rad) Description: Engine thrust line angle for side (#2-5) engines and single engine |
| deltaElvMax |
Value: 0.392699081698724 Type: Angle (rad) Description: Maximum elevator deflection |
| deltaAilMax |
Value: 0.392699081698724 Type: Angle (rad) Description: Maximum aileron deflection |
| deltaRdrMax |
Value: 0.785398163397449 Type: Angle (rad) Description: Maximum rudder deflection |
| kCnDeltaAil |
Value: -0.13 Type: Real Description: Empirical factor for the yaw moment derivative due to ailerons. Based on Figure 3.12 in Flight Stability and Automatic Control 2nd Edition |
| tauAil |
Value: 1.129 * (Sail / SrefWing) ^ 0.4044 - 0.1772 Type: Real Description: Aileron effectiveness parameter |
| Sail |
Value: cAil * (yAilTip - yAilRoot) * 2 Type: Area (m²) Description: Aileron area (of both wings) |
| cAil |
Value: 1.10 Type: Length (m) Description: Aileron average chord |
| yAilRoot |
Value: 11.84 Type: Length (m) Description: Aileron root y-coordinate w.r.t. fuselage centerline |
| yAilTip |
Value: 18.85 Type: Length (m) Description: Aileron tip y-coordinate w.r.t. fuselage centerline |
| cAilWingRoot |
Value: 5.68 Type: Length (m) Description: Local main wing chord at aileron root |
| cAilWingTip |
Value: 3.00 Type: Length (m) Description: Local main wing chord at aileron tip |
| kdWing |
Value: -3.333 * 10 ^ (-4) * lambdaWing ^ 2 + 6.667 * 10 ^ (-5) * lambdaWing + 0.38 Type: Real Description: Empirical constant for Oswald efficiency factor for main wing |
| epsilonAlpha |
Value: 2 * CLalphaWing3D / (Modelica.Constants.pi * ARwing) Type: Real Description: Change in downwash due to alpha |
| sigmaBeta |
Value: 0.1 Type: Real Description: Change in sidewash due to beta |
| CLhtDeltaElv |
Value: CLalphaHT3D * tauElv Type: Real (rad⁻¹) Description: C_L_HT_delta_e (Coefficient for change in the lift coefficient of the horizontal tail due to elevator deflection) |
| ClbetaGamma |
Value: -0.66 Type: Real (rad⁻²) Description: Empirical factor for C_l_beta/gammaWing. -0.66/rad^2 is a decent universal approximation |
| CLdeltae |
Value: SrefHT / SrefWing * etaHT * CLhtDeltaElv Type: Real (rad⁻¹) Description: C_L_delta_e (Coefficient for change in the lift coefficient of entire aircraft due to elevator deflection) |
| CLalpha |
Value: 4.8762 Type: Real (rad⁻¹) Description: Change in the lift coefficient due to alpha |
| CLalphaVT3D |
Value: 4 Type: Real (rad⁻¹) Description: Change in the lift coefficient of the vertical tail due to alpha |
| CDalpha |
Value: 0.212 Type: Real (rad⁻¹) Description: Change in C_D due to alpha |
| CDM |
Value: 0.00208 Type: Real Description: Change in C_D due to Mach number |
| CMM |
Value: -0.002 Type: Real Description: Change in C_M due to Mach number |
| Cmdeltae |
Value: -etaHT * vHT * CLhtDeltaElv Type: Real (rad⁻¹) Description: C_m_delta_e (Coefficient for change in pitch moment due to elevator deflection) |
| Cmq |
Value: Cmalphadot / epsilonAlpha Type: Real (rad⁻¹) Description: C_m_q (Coefficient for change in pitch moment due to pitch rate) |
| Cmalphadot |
Value: -2 * etaHT * CLalphaHT3D * vHT * (lHTcm / cWingMean) * epsilonAlpha Type: Real (rad⁻¹) Description: C_m_alphadot (Coefficient for change in pitch moment due to alphadot) |
| Cmalpha |
Value: -1.5013 Type: Real (rad⁻¹) Description: Change in C_M due to alpha |
| CyDeltaRdr |
Value: SrefVT / SrefWing * tauRdr * CLalphaVT3D Type: Real (rad⁻¹) Description: Y-force due to rudder deflection control derivative |
| ClDeltaAil |
Value: 2 * CLalpha * tauAil / (SrefWing * bWing) * (yAilTip ^ 2 / 2 - yAilRoot ^ 2 / 2) * (cAilWingRoot * 2 / 3 * (1 + cAilWingTip / cAilWingRoot + (cAilWingTip / cAilWingRoot) ^ 2) / (1 + cAilWingTip / cAilWingRoot)) Type: Real (rad⁻¹) Description: Roll moment due to aileron deflection control derivative |
| Cldeltar |
Value: SrefVT / SrefWing * abs(zVTacCM) / bWing * tauRdr * CLalphaVT3D Type: Real (rad⁻¹) Description: C_l_delta_r (Coefficient for change in roll moment due to rudder deflection) |
| Cndeltar |
Value: -vVT * etaVT * tauRdr * CLalphaVT3D Type: Real (rad⁻¹) Description: C_n_delta_r (Coefficient for change in yaw moment due to rudder deflection) |
| CyBeta |
Value: -etaVT * SrefVT / SrefWing * CLalphaVT3D * (1 + sigmaBeta) Type: Real (rad⁻¹) Description: Y-force due to sideslip angle stability derivative |
| Cnr |
Value: -2 * etaVT * vVT * lVTcm / bWing * CLalphaVT3D Type: Real Description: C_n_r (Coefficient for change in yaw moment due to yaw rate) |
| Cyr |
Value: -2 * lVTcm / bWing * CyBeta Type: Real (rad⁻¹) Description: C_y_r (Coefficient for change in Y-force due to yaw rate) |
| ClRoll |
Value: -CLalpha / 12 * (1 + 3 * TRwing) / (1 + TRwing) Type: Real (rad⁻¹) Description: C_l_p (Coefficient for change in roll moment due to roll rate) |
| Cnbeta |
Value: etaVT * vVT * CLalphaVT3D * (1 + sigmaBeta) Type: Real (rad⁻¹) Description: C_n_beta (Coefficient for change in yaw moment due to sideslip angle) |
| Clbeta |
Value: ClbetaGamma * gammaWing Type: Real (rad⁻¹) Description: C_l_beta (Coefficient for change in roll moment due to sideslip angle) |
Connectors (7)
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reference |
Type: RefFlightSignalBus Description: Bus for the real signals of the reference flight conditions |
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motion |
Type: MotionSignalBus Description: Bus for the real signals of the linear and angular velocity perturbations resolved in the body frame |
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DdeltaaIn |
Type: RealInput Description: 'input Real' as connector |
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DdeltaTIn |
Type: RealInput Description: 'input Real' as connector |
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DdeltaeIn |
Type: RealInput Description: 'input Real' as connector |
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DdeltarIn |
Type: RealInput Description: 'input Real' as connector |
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position |
Type: PositionSignalBus Description: Bus for the real signals of position, orientation and velocities resolved in the world frame |
Components (21)
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trimCalculator |
Type: TrimCalculator Description: Calculates trimmed conditions for given flight conditions |
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longitudinalMotion |
Type: LongitudinalMotion Description: State space representation of longitudinal motion |
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lateralMotion |
Type: LateralMotion Description: State space representation of lateral motion |
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lateralDerivatives |
Type: LateralDerivatives Description: Calculates lateral stability and control derivatives |
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positionAndOrientation |
Type: PositionAndOrientation Description: Calculates the position, orientation and velocities of the aircraft in the world frame |
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longitudinalDerivatives |
Type: LongitudinalDerivatives Description: Calculates longitudinal stability and control derivatives |
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refVtotExpr |
Type: RealExpression Description: Total velocity of reference flight conditions |
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refAltExpr |
Type: RealExpression Description: Altitude of reference flight conditions |
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refGammaExpr |
Type: RealExpression Description: Flight path of reference flight conditions |
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throttleDynamics |
Type: CriticalDamping Description: Damper for simplified model of throttle dynamics |
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elevatorDynamics |
Type: CriticalDamping Description: Damper for simplified model of elevator dynamics |
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aileronDynamics |
Type: CriticalDamping Description: Damper for simplified model of aileron dynamics |
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rudderDynamics |
Type: CriticalDamping Description: Damper for simplified model of rudder dynamics |
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DeltarLimiter |
Type: Limiter Description: Limits rudder deflection to its assigned limits |
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DeltaaLimiter |
Type: Limiter Description: Limits aileron deflection to its assigned limits |
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deltaElvLimiter |
Type: VariableLimiter Description: Limit the range of a signal with variable limits |
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maxDeltaElv |
Type: RealExpression Description: Upper limit for elevator deflection |
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minDeltaElv |
Type: RealExpression Description: Lower limit for elevator deflection |
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maxDeltaThrot |
Type: RealExpression Description: Upper limit for throttle position |
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minDeltaThrot |
Type: RealExpression Description: Lower limit for throttle position |
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deltaThrotLimiter |
Type: VariableLimiter Description: Limit the range of a signal with variable limits |
Used in Examples (1)
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Aircraft.Examples Example for demonstrating the linearized state space modeling environment |