WOLFRAM SYSTEM MODELER

# TrimCalculator

Calculates trimmed conditions for given flight conditions

# 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 Value: Type: Real Description: Moment coefficient of wing-body at alpha = 0 (required only for state space model) Value: Type: Real (rad⁻¹) Description: Change in the lift coefficient of the wing-body due to alpha Value: Type: Mass (kg) Description: Aircraft mass Value: Type: Length (m) Description: Aircraft center of mass from wing leading edge at mean chord (positive x-axis towards nose) Value: Type: Real Description: Induced drag factor for main wing Value: Type: Angle (rad) Description: Zero-lift angle of attack of wing Value: Type: Area (m²) Description: Main wing reference area Value: Type: Length (m) Description: Main wing aerodynamic center from wing leading edge at mean chord (positive x-axis towards nose) Value: Type: Angle (rad) Description: Main wing incidence angle Value: Type: Length (m) Description: Main wing mean chord length Value: Type: Angle (rad) Description: Zero-lift downwash angle Value: Type: Real Description: Drag coefficient of horizontal tail at zero lift Value: Type: Real Description: Horizontal tail volume coefficient Value: Type: Real (rad⁻¹) Description: Change in the lift coefficient of the horizontal tail due to alpha Value: Type: Area (m²) Description: Horizontal tail reference area Value: Type: Angle (rad) Description: Horizontal tail incidence angle Value: Type: Integer Description: Number of engines Value: Type: Length (m) Description: z-coordinate of thrust line Value: Type: Force (N) Description: Static thrust of one engine at sea level Value: Type: Angle (rad) Description: Engine thrust line angle for side (#2-5) engines and single engine 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) Value: Type: Real Description: Change in downwash due to alpha

# Connectors (4)

subRefFlightCondBus Type: RefFlightSignalBus Description: Bus port for reference flight conditions input Type: RealInput Description: Total velocity input Type: RealInput Description: Flight path angle input Type: RealInput Description: Geometric altitude input

# Components (16)

u0Expr Type: RealExpression Description: Set output signal to a time varying Real expression Type: RealExpression Description: Set output signal to a time varying Real expression Type: RealExpression Description: Set output signal to a time varying Real expression Type: RealExpression Description: Set output signal to a time varying Real expression Type: RealExpression Description: Set output signal to a time varying Real expression Type: RealExpression Description: Set output signal to a time varying Real expression Type: RealExpression Description: Set output signal to a time varying Real expression Type: RealExpression Description: Set output signal to a time varying Real expression Type: RealExpression Description: Set output signal to a time varying Real expression Type: RealExpression Description: Set output signal to a time varying Real expression Type: RealExpression Description: Set output signal to a time varying Real expression Type: RealExpression Description: Set output signal to a time varying Real expression Type: RealExpression Description: Set output signal to a time varying Real expression Type: RealExpression Description: Set output signal to a time varying Real expression Type: RealExpression Description: Set output signal to a time varying Real expression 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