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

**Library:**Aerospace Blockset / Aerodynamics

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

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.

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

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

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

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

to yield the net rotation from body to wind axes:

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

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 | C_{D} | C_{C} | C_{L} |

Stability | — | C_{Y} | C_{L} |

Body | C_{X} | C_{Y} | C
(–_{Z}C)_{N} |

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}).

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

Digital DATCOM Forces and Moments | Dynamic Pressure | Estimate Center of Gravity | Moments About CG Due to Forces