Aerospace Blockset™

Aerodynamic Forces and Moments

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

Library

Aerodynamics

Description

The Aerodynamic Forces and Moments block computes the aerodynamic forces and moments about the center of gravity. By default, the inputs and outputs are represented in the body axes.

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

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

to yield the net rotation from body to wind axes:

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.

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).

Dialog Box

Input Axes: Specifies coordinate system for input coefficients: Body (default), Stability, or Wind.
Force Axes: Specifies coordinate system for aerodynamic force: Body (default), Stability, or Wind.
Moment Axes: Specifies coordinate system for aerodynamic moment: Body (default), Stability, or Wind.
Reference area: Specifies the reference area for calculating aerodynamic forces and moments.
Reference span: Specifies the reference span for calculating aerodynamic moments in x-axes and z-axes.
Reference length: Specifies the reference length for calculating aerodynamic moment in the y-axes.

Inputs and Outputs

The first input consists of aerodynamic coefficients (in the chosen input axes) for forces and moments. These coefficients are ordered into a vector depending on the choice of axes:

Input Axes	Input Vector
Body	(axial force C_x, side force C_y, normal force C_z, rolling moment C_l, pitching moment C_m, yawing moment C_n)
Stability	(drag force C_D(β=0), side force C_y, lift force C_L, rolling moment C_l, pitching moment C_m, yawing moment C_n)
Wind	(drag force C_D, cross-wind force C_c, lift force C_L, rolling moment C_l, pitching moment C_m, yawing moment C_n)

Input	Dimension Type	Description
Second		Contains the dynamic pressure.
Third		Contains the center of gravity.
Fourth		Contains the center of pressure. 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.
Fifth (For inputs or outputs in stability or wind axes)	Three-element vector	Contains the velocity in the body axes.

Output	Dimension Type	Description
First		Contains the aerodynamic forces (in the chosen output axes) at the center of gravity in x-, y-, and z-axes.
Second		Contains the aerodynamic moments (in the chosen output axes) at the center of gravity in x-, y-, and z-axes.

Assumptions and 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.

Examples

See Airframe in the aeroblk_HL20 demo for an example of this block.

Reference

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