Aerodynamic Forces and Moments

Compute aerodynamic forces and moments using aerodynamic coefficients, dynamic pressure, center of gravity, center of pressure, and velocity

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Libraries:
Aerospace Blockset / Aerodynamics

Description

The Aerodynamic Forces and Moments block computes the aerodynamic forces and moments about the center of gravity.

The Aerodynamic Forces and Moments block port labels change based on the coordinate system selected from the Input axes, Force axes, and Moment axes list.

Examples

HL-20 with Flight Instrument Blocks and Visualization Using Unreal Engine

Model NASA HL-20 lifting body and controller modeled in Simulink^® and Aerospace Blockset™, using Unreal Engine^® for visualization.

• Open Live Script

Limitations

• The default state of the block hides the V_b input port and assumes that the transformation is body-body.

• The center of gravity and the center of pressure are assumed to be in body axes.

• While this block has the ability to output forces and/or moments in the stability axes, the blocks in the Equations of Motion library are currently designed to accept forces and moments in either the body or wind axes only.

Ports

Input

Coef — Aerodynamic coefficients

six-element vector

Aerodynamic coefficients (in the chosen input axes) for forces and moments, specified as a vector. These coefficients are ordered into a vector depending on the choice of axes:

Input Axes	Input Vector
Body	(axial force Cx, side force Cy, normal force Cz, rolling moment Cl, pitching moment Cm, yawing moment Cn)
Stability	(drag force CD(β=0), side force Cy, lift force CL, rolling moment Cl, pitching moment Cm, yawing moment Cn)
Wind	(drag force CD, cross-wind force Cc, lift force CL, rolling moment Cl, pitching moment Cm, yawing moment Cn)

Data Types: double

q_bar — Dynamic pressure

scalar | three-element vector

Dynamic pressure, specified as a 1-by-3 array.

Data Types: double

CG — Center of gravity

three-element vector

Center of gravity, specified as a 1-by-3 vector.

Data Types: double

CP — Center of pressure

three-element vector

Center of pressure, specified as a 1-by-3 vector. This can also be taken as any general moment reference point as long as the rest of the model reflects the use of the moment reference point.

Data Types: double

V_b — Velocity in the body axes

three-element vector

Velocity in the body axes. specified as a 1-by-3 vector.

Dependencies

This port is enabled if the Input axes parameter is set to Wind or Stability.

Data Types: double

Output

F — Aerodynamic forces

three-element vector

Aerodynamic forces (in the chosen output axes), returned as three-element vector, at the center of gravity in x-, y-, and z-axes.

Data Types: double

M — Aerodynamic moments

three-element vector

Aerodynamic moments (in the chosen output axes), returned as three-element vector, at the center of gravity in x-, y-, and z-axes.

Data Types: double

Parameters

Input axes — Coordinate system for input coefficients

Body (default) | Stability | Wind

Coordinate system for input coefficients, specified as Body (default), Stability, or Wind.

Dependencies

Selecting Stability or Wind enables input port Port_5.

Programmatic Use

Block Parameter: inputAxes

Type: character vector

Values: 'Body' | 'Stability' | 'Wind'

Default: 'Body'

Force axes — Coordinate system for aerodynamic force

Body (default) | Stability | Wind

Coordinate system for aerodynamic force, specified as Body (default), Stability, or Wind.

Dependencies

Selecting Stability or Wind enables input port Port_5.

Programmatic Use

Block Parameter: outputForcesAxes

Type: character vector

Values: 'Body' | 'Stability' | 'Wind'

Default: 'Body'

Moment axes — Coordinate system for aerodynamic moment

Body (default) | Stability | Wind

Coordinate system for aerodynamic moment, specified as Body (default), Stability, or Wind.

Dependencies

Selecting Stability or Wind enables input port Port_5.

Programmatic Use

Block Parameter: outputMomentAxes

Type: character vector

Values: 'Body' | 'Stability' | 'Wind'

Default: 'Body'

Reference area — Reference area

1 (default) | any double value

Reference area for calculating aerodynamic forces and moments, specified as any double value.

Programmatic Use

Block Parameter: S

Type: character vector

Values: any double value

Default: '1'

Reference span — Reference span

1 (default) | any double value

Reference span for calculating aerodynamic moments in x-axes and z-axes, specified as any double value.

Programmatic Use

Block Parameter: b

Type: character vector

Values: any double value

Default: '1'

Reference length — Reference length

1 (default) | any double value

Reference length for calculating aerodynamic moment in the y-axes, specified as any double value.

Programmatic Use

Block Parameter: cbar

Type: character vector

Values: any double value

Default: '1'

Algorithms

Let α be the angle of attack and β the sideslip. The rotation from body to stability axes:

$$C_{s\leftarrow b}=\left[\begin{array}{ccc}\cos (\alpha )& 0& \sin (\alpha )\\ 0& 1& 0\\ -\sin (\alpha )& 0& \cos (\alpha )\end{array}\right]$$

can be combined with the rotation from stability to wind axes:

$$C_{w\leftarrow s}=\left[\begin{array}{ccc}\cos (\beta )& \sin (\beta )& 0\\ -\sin (\beta )& \cos (\beta )& 0\\ 0& 0& 1\end{array}\right]$$

to yield the net rotation from body to wind axes:

$$C_{w\leftarrow b}=\left[\begin{array}{ccc}\cos (\alpha )\cos (\beta )& \sin (\beta )& \sin (\alpha )\cos (\beta )\\ -\cos (\alpha )\sin (\beta )& \cos (\beta )& -\sin (\alpha )\sin (\beta )\\ -\sin (\alpha )& 0& \cos (\alpha )\end{array}\right]$$

Moment coefficients have the same notation in all systems. Force coefficients are given below. Note there are no specific symbols for stability-axes force components. However, the stability axes have two components that are unchanged from the other axes.

$$F_A^w\equiv \left[\begin{array}{c}-D\\ -C\\ -L\end{array}\right]=C_{w\leftarrow b}\cdot \left[\begin{array}{c}{X}_A\\ Y_A\\ Z_A\end{array}\right]\equiv C_{w\leftarrow b}\cdot F_A^b$$

Components/Axes	x	y	z
Wind	CD	CC	CL
Stability	—	CY	CL
Body	CX	CY	CZ (–CN)

Given these definitions, to account for the standard definitions of D, C, Y (where Y = -C), and L, force coefficients in the wind axes are multiplied by the negative identity diag(-1, -1, -1). Forces coefficients in the stability axes are multiplied by diag(-1, 1, -1). C_N and C_X are, respectively, the normal and axial force coefficients (C_N = -C_Z).

References

[1] Stevens, B. L., and F. L. Lewis, Aircraft Control and Simulation, John Wiley & Sons, New York, 1992

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a