WOLFRAM SYSTEM MODELER

Conventional

Model of system of surfaces in conventional wing configuration

Diagram

Wolfram Language

In[1]:=
SystemModel["Aircraft.Physical.FixedWing.Parts.Surfaces.Conventional"]
Out[1]:=

Information

This model compiles the WingBody, Ailerons, HorizontalTail and VerticalTail components into a system of surfaces of an aircraft with conventional wing configuration for modeling the aerodynamic forces and moments due to the presence of the surfaces and the deflection of the control suraces. The magnitude of the aerodynamic forces and moments are indeed solved in their respective individual surface models, but they require input from one another, and this model serves for distributing the signal between the surface models.

This model also propagates the required parameters and the variables of the flight conditions from the AircraftBase model further into the surface models. Additionally, if the weight estimation method is used, the calculations to estimate the mass properties of the main wing and the tail are performed in the respective models.

The inputs to this model are the control surface deflections, namely the elevator delflection (δe, deltaElvCmd), ailerons deflection (δa, deltaAilCmd) and rudder deflection (δr, deltaRdrCmd). Figure 1 shows the positive directions of control surface deflection angles as well as the body angular velocities and moments. All surface models are connected here to the aircraft reference point frame (aircraftRP), and the translations and rotations of each surface with respect to the aircraft reference point are included in the respective surface models.


Figure 1: Sign convention of control surface deflections, body angular velocities and moments [1].

For the horizontal and vertical tails, the contributions from their control surfaces, i.e. elevator and rudder, are integrated into the calculations of their aerodynamic forces, whereas the ailerons have their dedicated model to calculate their contribution to aerodynamic forces and moments.

References

[1]  Erä-Esko, N. (2022). "Development and Use of System Modeler 6DOF Flight Mechanics Model in Aircraft Conceptual Design."
      Available atmodelica://Aircraft/Resources/Documents/EraeEskoThesis.pdf.

 

Parameters (105)

weightEst

Value:

Type: Boolean

Description: true, if weight estimation method is used for masses, center of mass location and inertia tensor

xCMdry

Value:

Type: Length (m)

Description: Aircraft center of mass x-coordinate w.r.t. fuselage reference point (with total mass for electric aircraft and gliders, positive x-axis towards nose)

zCMdry

Value:

Type: Length (m)

Description: Aircraft center of mass z-coordinate w.r.t. fuselage reference point (with total mass for electric aircraft and gliders, positive z-axis towards ground)

MTOMdes

Value:

Type: Mass (kg)

Description: Design maximum take-off mass

machDes

Value:

Type: Real

Description: Design Mach number

compMat

Value:

Type: Boolean

Description: true, if composite materials are used in structures

qMax

Value:

Type: Pressure (Pa)

Description: Maximum dynamic pressure

nMax

Value:

Type: Real

Description: Maximum load factor

lFus

Value:

Type: Length (m)

Description: Fuselage length

wFus

Value:

Type: Length (m)

Description: Fuselage maximum width

hFus

Value:

Type: Length (m)

Description: Fuselage maximum height

dFusHT

Value:

Type: Length (m)

Description: Fuselage diameter at horizontal tail 1/4 chord

SwetFus

Value:

Type: Area (m²)

Description: Fuselage wetted area

FFfus

Value:

Type: Real

Description: Fuselage form factor

bWing

Value:

Type: Length (m)

Description: Main wing span

cWingRoot

Value:

Type: Length (m)

Description: Main wing root chord (where wing intersects with fuselage)

cWingTip

Value:

Type: Length (m)

Description: Main wing tip chord

tWingRoot

Value:

Type: Length (m)

Description: Main wing root thickness

xWingRootLE

Value:

Type: Length (m)

Description: Main wing root leading edge x-coordinate w.r.t. fuselage reference point (positive x-axis towards nose)

zWingRootLE

Value:

Type: Length (m)

Description: Main wing root leading edge z-coordinate w.r.t. fuselage reference point (positive z-axis towards ground)

lambdaWing

Value:

Type: Angle (rad)

Description: Main wing sweep angle at 1/4 chord

gammaWing

Value:

Type: Angle (rad)

Description: Main wing dihedral angle

iWing

Value:

Type: Angle (rad)

Description: Main wing incidence angle

SrefWing

Value:

Type: Area (m²)

Description: Main wing reference area

ARwing

Value:

Type: Real

Description: Main wing aspect ratio

TRwing

Value:

Type: Real

Description: Main wing taper ratio

cWingMean

Value:

Type: Length (m)

Description: Main wing mean chord length

xWingAC

Value:

Type: Length (m)

Description: Main wing aerodynamic center from wing leading edge at mean chord (positive x-axis towards nose)

yWingAC

Value:

Type: Length (m)

Description: Main wing aerodynamic center from fuselage centerline (y-coordinate w.r.t. fuselage centerline of mean chord)

SwetWing

Value:

Type: Area (m²)

Description: Main wing wetted area

lambdaWingLE

Value:

Type: Angle (rad)

Description: Main wing leading edge sweep angle

lambdaWingHC

Value:

Type: Angle (rad)

Description: Main wing half-chord sweep angle

lambdaWingTE

Value:

Type: Angle (rad)

Description: Main wing trailing edge sweep angle

FFwing

Value:

Type: Real

Description: Main wing form factor

sdWing

Value:

Type: Real

Description: Fuselage drag factor for main wing

kdWing

Value:

Type: Real

Description: Empirical constant for Oswald efficiency factor for main wing

cAil

Value:

Type: Length (m)

Description: Aileron average chord

yAilRoot

Value:

Type: Length (m)

Description: Aileron root y-coordinate w.r.t. fuselage centerline

yAilTip

Value:

Type: Length (m)

Description: Aileron tip y-coordinate w.r.t. fuselage centerline

yAilAC

Value:

Type: Length (m)

Description: Aileron aerodynamic center y-coordinate w.r.t. fuselage centerline

cAilWingRoot

Value:

Type: Length (m)

Description: Local main wing chord at aileron root

cAilWingTip

Value:

Type: Length (m)

Description: Local main wing chord at aileron tip

kCnDeltaAil

Value:

Type: Real

Description: Empirical factor for the yaw moment derivative due to ailerons

tauAil

Value:

Type: Real

Description: Aileron effectiveness parameter

bHT

Value:

Type: Length (m)

Description: Horizontal tail span

cHTroot

Value:

Type: Length (m)

Description: Horizontal tail root chord

cHTtip

Value:

Type: Length (m)

Description: Horizontal tail tip chord

tHTroot

Value:

Type: Length (m)

Description: Horizontal tail root thickness

zHTrootLE

Value:

Type: Length (m)

Description: Horizontal tail root leading edge z-coordinate w.r.t. fuselage reference point (positive z-axis towards ground)

lambdaHT

Value:

Type: Angle (rad)

Description: Horizontal tail sweep angle at 1/4 chord

iHT

Value:

Type: Angle (rad)

Description: Horizontal tail incidence angle

Selv

Value:

Type: Area (m²)

Description: Elevator area

SrefHT

Value:

Type: Area (m²)

Description: Horizontal tail reference area

ARht

Value:

Type: Real

Description: Aspect ratio of horizontal tail

TRht

Value:

Type: Real

Description: Taper ratio of horizontal tail

cHTmean

Value:

Type: Length (m)

Description: Horizontal tail mean chord

lHTcm

Value:

Type: Length (m)

Description: Horizontal tail arm length (from aircraft center of mass to horizontal tail 1/4 chord)

lHTwingAC

Value:

Type: Length (m)

Description: Horizontal tail arm length (from wing aerodynamic center to horizontal tail 1/4 chord)

SwetHT

Value:

Type: Area (m²)

Description: Horizontal tail wetted area

lambdaHTle

Value:

Type: Angle (rad)

Description: Horizontal tail leading edge sweep angle

FFht

Value:

Type: Real

Description: Horizontal tail form factor

sdHT

Value:

Type: Real

Description: Fuselage drag factor for horizontal tail

kdHT

Value:

Type: Real

Description: Empirical constant for Oswald efficiency factor for horizontal tail

tauElv

Value:

Type: Real

Description: Elevator effectiveness parameter

bVT

Value:

Type: Length (m)

Description: Vertical tail span

cVTroot

Value:

Type: Length (m)

Description: Vertical tail root chord

cVTtip

Value:

Type: Length (m)

Description: Vertical tail tip chord

tVTroot

Value:

Type: Length (m)

Description: Vertical tail root thickness

zVTroot

Value:

Type: Length (m)

Description: Vertical tail root z-coordinate w.r.t fuselage reference point

lambdaVT

Value:

Type: Angle (rad)

Description: Vertical tail sweep angle at 1/4 chord

Srdr

Value:

Type: Area (m²)

Description: Rudder area

SrefVT

Value:

Type: Area (m²)

Description: Vertical tail reference area

ARvt

Value:

Type: Real

Description: Aspect ratio of vertical tail

TRvt

Value:

Type: Real

Description: Taper ratio of vertical tail

cVTmean

Value:

Type: Length (m)

Description: Vertical tail mean chord

lVTcm

Value:

Type: Length (m)

Description: Vertical tail arm length (from aircraft center of mass to vertical tail 1/4 chord)

lVTwingAC

Value:

Type: Length (m)

Description: Vertical tail arm length (from wing aerodynamic center to vertical tail aerodynamic center)

zVTac

Value:

Type: Length (m)

Description: Vertical tail center of pressure z-coordinate w.r.t. fuselage reference point

SwetVT

Value:

Type: Area (m²)

Description: Vertical tail wetted area

lambdaVTle

Value:

Type: Angle (rad)

Description: Vertical tail leading edge sweep angle

FFvt

Value:

Type: Real

Description: Vertical tail form factor

sdVT

Value:

Type: Real

Description: Fuselage drag factor for vertical tail

kdVT

Value:

Type: Real

Description: Empirical constant for Oswald efficiency factor for vertical tail

tauRdr

Value:

Type: Real

Description: Rudder effectiveness parameter

sigmaBeta

Value:

Type: Real

Description: Change in sidewash due to beta

kSkinFus

Value:

Type: Length (m)

Description: Fuselage surface roughness height

CDmaxFus

Value:

Type: Real

Description: Maximum drag coefficient of the fuselage

kSkinWing

Value:

Type: Length (m)

Description: Main Wing surface roughness height

ClAlphaWing2D

Value:

Type: CurveSlope (rad⁻¹)

Description: Change in the section lift coefficient of the main wing airfoil (2D) due to alpha

alpha0Wing2D

Value:

Type: Angle (rad)

Description: Zero-lift angle of attack of the main wing airfoil (2D)

CLmaxWing3D

Value:

Type: Real

Description: Maximum lift coefficient of the main wing (3D)

CDmaxWing3D

Value:

Type: Real

Description: Maximum drag coefficient of the main wing (3D)

kSkinHT

Value:

Type: Length (m)

Description: Horizontal tail surface roughness height

ClAlphaHT2D

Value:

Type: CurveSlope (rad⁻¹)

Description: Change in the section lift coefficient of the horizontal tail airfoil (2D) due to alpha

alpha0HT2D

Value:

Type: Angle (rad)

Description: Zero-lift angle of attack of the horizontal tail airfoil (2D)

CLmaxHT3D

Value:

Type: Real

Description: Maximum lift coefficient of the horizontal tail (3D)

CDmaxHT3D

Value:

Type: Real

Description: Maximum drag coefficient of the horizontal tail (3D)*(SrefHT/SrefWing)

kSkinVT

Value:

Type: Length (m)

Description: Vertical tail surface roughness height

ClAlphaVT2D

Value:

Type: CurveSlope (rad⁻¹)

Description: Change in the section lift coefficient of the vertical tail airfoil (2D) due to alpha

deltaElvMax

Value:

Type: Angle (rad)

Description: Maximum elevator deflection

deltaAilMax

Value:

Type: Angle (rad)

Description: Maximum aileron deflection

deltaRdrMax

Value:

Type: Angle (rad)

Description: Maximum rudder deflection

CADshapes

Value:

Type: Boolean

Description: true, if external CAD files are used for animation

rho0

Value:

Type: Density (kg/m³)

Description: Air density at sea-level

a0

Value:

Type: Velocity (m/s)

Description: Speed of sound at sea-level

Inputs (1)

flightData

Type: FlightData

Description: Global flight data variables

Connectors (4)

aircraftRP

Type: Frame_b

Description: Connector to aircraft reference point

deltaElvCmd

Type: RealInput

Description: Elevator deflection command

deltaAilCmd

Type: RealInput

Description: Ailerons deflection command

deltaRdrCmd

Type: RealInput

Description: Rudder deflection command

Components (6)

flightData

Type: FlightData

Description: Global flight data variables

wingBody

Type: WingBody

Description: Model for drag and lift forces due to main wing and fuselage

horizontalTail

Type: HorizontalTail

Description: Model for lift and drag forces due to horizontal tail and elevator

verticalTail

Type: VerticalTail

Description: Model for lift and drag forces due to vertical tail and rudder

ailerons

Type: Ailerons

Description: Model for lift and drag forces due to ailerons

totalLift

Type: Add

Description: Summing of the lift force components

Used in Components (1)

AircraftBase

Aircraft.Physical.FixedWing.Interfaces

Interface for a complete aircraft model