WOLFRAM SYSTEM MODELER

DouglasDC8

Model of Douglas DC-8 using state-space representation

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)

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)

reference

Type: RefFlightSignalBus

Description: Bus for the real signals of the reference flight conditions

motion

Type: MotionSignalBus

Description: Bus for the real signals of the linear and angular velocity perturbations resolved in the body frame

DdeltaaIn

Type: RealInput

Description: 'input Real' as connector

DdeltaTIn

Type: RealInput

Description: 'input Real' as connector

DdeltaeIn

Type: RealInput

Description: 'input Real' as connector

DdeltarIn

Type: RealInput

Description: 'input Real' as connector

position

Type: PositionSignalBus

Description: Bus for the real signals of position, orientation and velocities resolved in the world frame

Components (21)

trimCalculator

Type: TrimCalculator

Description: Calculates trimmed conditions for given flight conditions

longitudinalMotion

Type: LongitudinalMotion

Description: State space representation of longitudinal motion

lateralMotion

Type: LateralMotion

Description: State space representation of lateral motion

lateralDerivatives

Type: LateralDerivatives

Description: Calculates lateral stability and control derivatives

positionAndOrientation

Type: PositionAndOrientation

Description: Calculates the position, orientation and velocities of the aircraft in the world frame

longitudinalDerivatives

Type: LongitudinalDerivatives

Description: Calculates longitudinal stability and control derivatives

refVtotExpr

Type: RealExpression

Description: Total velocity of reference flight conditions

refAltExpr

Type: RealExpression

Description: Altitude of reference flight conditions

refGammaExpr

Type: RealExpression

Description: Flight path of reference flight conditions

throttleDynamics

Type: CriticalDamping

Description: Damper for simplified model of throttle dynamics

elevatorDynamics

Type: CriticalDamping

Description: Damper for simplified model of elevator dynamics

aileronDynamics

Type: CriticalDamping

Description: Damper for simplified model of aileron dynamics

rudderDynamics

Type: CriticalDamping

Description: Damper for simplified model of rudder dynamics

DeltarLimiter

Type: Limiter

Description: Limits rudder deflection to its assigned limits

DeltaaLimiter

Type: Limiter

Description: Limits aileron deflection to its assigned limits

deltaElvLimiter

Type: VariableLimiter

Description: Limit the range of a signal with variable limits

maxDeltaElv

Type: RealExpression

Description: Upper limit for elevator deflection

minDeltaElv

Type: RealExpression

Description: Lower limit for elevator deflection

maxDeltaThrot

Type: RealExpression

Description: Upper limit for throttle position

minDeltaThrot

Type: RealExpression

Description: Lower limit for throttle position

deltaThrotLimiter

Type: VariableLimiter

Description: Limit the range of a signal with variable limits

Used in Examples (1)

LinearizedStateSpace

Aircraft.Examples

Example for demonstrating the linearized state space modeling environment