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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 (V_tot), 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 (T_ref), thrust available at reference altitude is first calculated as a function of air density, and T_ref 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	Type: Real Description: Drag coefficient of wing-body at zero lift
CmW0	Type: Real Description: Moment coefficient of wing-body at alpha = 0 (required only for state space model)
CLalphaWing3D	Type: Real (rad⁻¹) Description: Change in the lift coefficient of the wing-body due to alpha
mAC	Type: Mass (kg) Description: Aircraft mass
xCMdry	Type: Length (m) Description: Aircraft center of mass from wing leading edge at mean chord (positive x-axis towards nose)
Kw	Type: Real Description: Induced drag factor for main wing
alphaw0	Type: Angle (rad) Description: Zero-lift angle of attack of wing
SrefWing	Type: Area (m²) Description: Main wing reference area
xWingAC	Type: Length (m) Description: Main wing aerodynamic center from wing leading edge at mean chord (positive x-axis towards nose)
iWing	Type: Angle (rad) Description: Main wing incidence angle
cWingMean	Type: Length (m) Description: Main wing mean chord length
epsilon0	Type: Angle (rad) Description: Zero-lift downwash angle
CDHT0	Type: Real Description: Drag coefficient of horizontal tail at zero lift
vHT	Type: Real Description: Horizontal tail volume coefficient
CLalphaHT3D	Type: Real (rad⁻¹) Description: Change in the lift coefficient of the horizontal tail due to alpha
SrefHT	Type: Area (m²) Description: Horizontal tail reference area
iHT	Type: Angle (rad) Description: Horizontal tail incidence angle
nEng	Type: Integer Description: Number of engines
zTauTotal	Type: Length (m) Description: z-coordinate of thrust line
Tstatic	Type: Force (N) Description: Static thrust of one engine at sea level
kappa	Type: Angle (rad) Description: Engine thrust line angle for side (#2-5) engines and single engine
CLhtDeltaElv	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	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