WOLFRAM SYSTEM MODELER

TrimCalculator

Calculates trimmed conditions for given flight conditions

Diagram

Wolfram Language

In[1]:=
SystemModel["Aircraft.StateSpace.FixedWing.Blocks.TrimCalculator"]
Out[1]:=

Information

This block calculates trimmed flight conditions for any given total velocity (Vtot), altitude (h) and flight path angle angle (γ) that are the inputs to this block. The outputs from this block are the trimmed flight conditions through the subRefFlightCondBus connector that are to be used as reference flight conditions around which the linearization of the state space representation of the aircraft equations of motion are done.

By using the Atmospheres functions, the atmospheric properties and dynamic pressure are calculated at the reference altitude. In order to solve the reference throttle position value (Tref), thrust available at reference altitude is first calculated as a function of air density, and Tref is assigned to be thrust required at trimmed conditions divided by thrust available at reference altitude, which naturally must be ≤ 1. An error is triggered with a message given if this condition is not fulfilled.

The equations used here to calculate trimmed conditions are based on the trim calculator presented by Cook [1]. Currently, only level flights and flights with constant climb angle can be modeled as the reference flight conditions. Thus, the reference values for side velocity, angular velocities, roll angle and yaw angle are always zero.

References

[1]  Cook, M. (2012). Flight Dynamics Principles. 3rd ed. Elsevier.

Parameters (23)

CDW0

Value:

Type: Real

Description: Drag coefficient of wing-body at zero lift

CmW0

Value:

Type: Real

Description: Moment coefficient of wing-body at alpha = 0 (required only for state space model)

CLalphaWing3D

Value:

Type: Real (rad⁻¹)

Description: Change in the lift coefficient of the wing-body due to alpha

mAC

Value:

Type: Mass (kg)

Description: Aircraft mass

xCMdry

Value:

Type: Length (m)

Description: Aircraft center of mass from wing leading edge at mean chord (positive x-axis towards nose)

Kw

Value:

Type: Real

Description: Induced drag factor for main wing

alphaw0

Value:

Type: Angle (rad)

Description: Zero-lift angle of attack of wing

SrefWing

Value:

Type: Area (m²)

Description: Main wing reference area

xWingAC

Value:

Type: Length (m)

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

iWing

Value:

Type: Angle (rad)

Description: Main wing incidence angle

cWingMean

Value:

Type: Length (m)

Description: Main wing mean chord length

epsilon0

Value:

Type: Angle (rad)

Description: Zero-lift downwash angle

CDHT0

Value:

Type: Real

Description: Drag coefficient of horizontal tail at zero lift

vHT

Value:

Type: Real

Description: Horizontal tail volume coefficient

CLalphaHT3D

Value:

Type: Real (rad⁻¹)

Description: Change in the lift coefficient of the horizontal tail due to alpha

SrefHT

Value:

Type: Area (m²)

Description: Horizontal tail reference area

iHT

Value:

Type: Angle (rad)

Description: Horizontal tail incidence angle

nEng

Value:

Type: Integer

Description: Number of engines

zTauTotal

Value:

Type: Length (m)

Description: z-coordinate of thrust line

Tstatic

Value:

Type: Force (N)

Description: Static thrust of one engine at sea level

kappa

Value:

Type: Angle (rad)

Description: Engine thrust line angle for side (#2-5) engines and single engine

CLhtDeltaElv

Value:

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)

epsilonAlpha

Value:

Type: Real

Description: Change in downwash due to alpha

Connectors (4)

subRefFlightCondBus

Type: RefFlightSignalBus

Description: Bus port for reference flight conditions input

VtotTrimIn

Type: RealInput

Description: Total velocity input

gammaeIn

Type: RealInput

Description: Flight path angle input

hGIn

Type: RealInput

Description: Geometric altitude input

Components (16)

u0Expr

Type: RealExpression

Description: Set output signal to a time varying Real expression

v0Expr

Type: RealExpression

Description: Set output signal to a time varying Real expression

w0Expr

Type: RealExpression

Description: Set output signal to a time varying Real expression

p0Expr

Type: RealExpression

Description: Set output signal to a time varying Real expression

q0Expr

Type: RealExpression

Description: Set output signal to a time varying Real expression

r0Expr

Type: RealExpression

Description: Set output signal to a time varying Real expression

phi0Expr

Type: RealExpression

Description: Set output signal to a time varying Real expression

theta0Expr

Type: RealExpression

Description: Set output signal to a time varying Real expression

psi0Expr

Type: RealExpression

Description: Set output signal to a time varying Real expression

h0Expr

Type: RealExpression

Description: Set output signal to a time varying Real expression

Vtot0Expr

Type: RealExpression

Description: Set output signal to a time varying Real expression

CL0Expr

Type: RealExpression

Description: Set output signal to a time varying Real expression

CD0Expr

Type: RealExpression

Description: Set output signal to a time varying Real expression

deltae0Expr

Type: RealExpression

Description: Set output signal to a time varying Real expression

deltaT0Expr

Type: RealExpression

Description: Set output signal to a time varying Real expression

TAvail0Expr

Type: RealExpression

Description: Set output signal to a time varying Real expression

Used in Components (1)

DefaultAircraft

Aircraft.StateSpace.FixedWing

Aircraft model using state-space representation