Compute aerodynamic forces and moments using Digital DATCOM static and dynamic stability derivatives

Aerodynamics

The Digital DATCOM Forces and Moments block computes the aerodynamic forces and moments about the center of gravity using aerodynamic coefficients from Digital DATCOM.

Algorithms for calculating forces and moments build up the overall
aerodynamic forces and moments (** F** and

** F** =

** M** =

*F*_{static} and *M*_{static} are the static
contribution, and *F*_{dyn} and *M*_{dyn} the dynamic contribution,
to the aerodynamic coefficients. If the dynamic characteristics are
not contained in the **Digital DATCOM structure** parameter,
their contribution is set to zero.

Static stability characteristics include the following.

Coefficient | Meaning |
---|---|

C_{D} | Matrix of drag coefficients. These coefficients are defined positive for an aft-acting load. |

C_{L} | Matrix of lift coefficients. These coefficients are defined positive for an up-acting load. |

C_{m} | Matrix of pitching-moment coefficients. These coefficients are defined positive for a nose-up rotation. |

C_{Yβ} | Matrix of derivatives of side-force coefficients with respect to sideslip angle |

C_{nβ} | Matrix of derivatives of yawing-moment coefficients with respect to sideslip angle |

C_{lβ} | Matrix of derivatives of rolling-moment coefficients with respect to sideslip angle |

These are the static contributions to the aerodynamic coefficients in stability axes.

*C*_{D static} = *C*_{D}

*C*_{y static} = *C*_{Yβ}β

*C*_{L static} = *C*_{L}

*C*_{l static} = *C*_{lβ}β

*C*_{m static} = *C*_{M}

*C*_{n static} = *C*_{nβ}β

Dynamic stability characteristics include the following.

Coefficient | Meaning |
---|---|

C_{lq} | Matrix of rolling-moment derivatives due to pitch rate |

C_{mq} | Matrix of pitching-moment derivatives due to pitch rate |

C_{Ldα/dt} | Matrix of lift force derivatives due to rate of angle of attack |

C_{mdα/dt} | Matrix of pitching-moment derivatives due to rate of angle of attack |

C_{lp} | Matrix of rolling-moment derivatives due to roll rate |

C_{Yp} | Matrix of lateral force derivatives due to roll rate |

C_{np} | Matrix of yawing-moment derivatives due to roll rate |

C_{nr} | Matrix of yawing-moment derivatives due to yaw rate |

C_{lr} | Matrix of rolling-moment derivatives due to yaw rate |

These are the dynamic contributions to the aerodynamic coefficients in stability axes.

$$\begin{array}{l}{C}_{\text{D}}{\text{}}_{\text{dyn}}=0\\ {C}_{\text{y}}{\text{}}_{\text{dyn}}={C}_{\text{yp}}p({b}_{\text{ref}}/2V)\\ {C}_{\text{L}}{\text{}}_{\text{dyn}}={C}_{\text{L}}\dot{a}({c}_{\text{bar}}/2V)\\ {C}_{\text{l}}{\text{}}_{\text{dyn}}=({C}_{\text{lp}}p+{C}_{\text{lq}}q+{C}_{\text{lr}}r)({b}_{\text{ref}}/2V)\\ {C}_{\text{m}}{\text{}}_{\text{dyn}}=({C}_{\text{mq}}q+{C}_{\text{m}}\dot{a})({c}_{\text{bar}}/2V)\\ {C}_{\text{n}}{\text{}}_{\text{dyn}}=({C}_{\text{np}}p+{C}_{\text{nr}}r)({b}_{\text{ref}}/2V)\end{array}$$

**Units**Specifies the input and output units:

Units

Force

Moment

Length

Velocity

Pressure

`Metric (MKS)`

Newton

Newton-

meterMeters

Meters per second

Pascal

`English (Velocity in ft/s)`

Pound

Foot-pound

Feet

Feet per second

Pound per square inch

`English (Velocity in kts)`

Pound

Foot-pound

Feet

Knots

Pound per square inch

**Digital DATCOM structure**Specifies the MATLAB

^{®}structure containing the digital DATCOM data. This structure is generated by the Aerospace Toolbox function`datcomimport`

. The Digital DATCOM Forces and Moments block supports only Digital DATCOM, which is the 1976 version of DATCOM.**Force axes**Specifies coordinate system for aerodynamic force:

`Body`

or`Wind`

.**Interpolation method**`None (flat)`

or`Linear`

**Extrapolation method**`None (clip)`

or`Linear`

**Process out of range input**Specifies how to handle out-of-range input:

`Linear Extrapolation`

or`Clip to Range`

.**Action for out of range input**Specifies if out-of-range input invokes a warning, an error, or no action.

Input | Dimension Type | Description |
---|---|---|

First | 3-by-3 matrix | Contains the angle of attack. |

Second | Contains the sideslip angle, in radians. | |

Third | Contains the Mach number. | |

Fourth | Contains the altitude, in selected length units. | |

Fifth | Contains the dynamic pressure, in selected pressure units. | |

Sixth | Contains the velocity, selected velocity units and selected force axes. | |

Seventh (Optional) | Contains the angle of attack rate, in radians per second. Appears when DAMP Control Card is used in input to Digital DATCOM. | |

Eight (Optional) | Contains the body angular rates, in radians per second. Appears when DAMP Control Card is used in input to Digital DATCOM. | |

Ninth (Optional) | Contains the ground height, in select units of length. Appears when GRNDEF Namelist is used in input to Digital DATCOM. | |

Tenth (Optional) | Contains the control surface deflections, radians. Appears when ASYFLP or SYMFLP and GRNDEF namelists are used in input to Digital DATCOM. |

Output | Dimension Type | Description |
---|---|---|

First | Contains the aerodynamic forces at the center of gravity in
selected coordinate system: Body (F_{x}, F_{y},
and F_{z}), or Wind (F_{D}, F_{y},
and F_{L}). | |

Second | Contains the aerodynamic moments at the center of gravity in
body coordinates (M_{x}, M_{y},
and M_{z}). |

The operational limitations of Digital DATCOM apply to the data
contained in the **Digital DATCOM structure** parameter.
For more information on Digital DATCOM limitations, see Section 2.4.5
of reference [1].

The **Digital DATCOM structure** parameters `alpha`

, `mach`

, `alt`

, `grndht`

,
and `delta`

must be strictly monotonically increasing
to be used with the Digital DATCOM Forces and Moments block.

The **Digital DATCOM structure** coefficients
must correspond to the dimensions of the breakpoints (`alpha`

, `mach`

, `alt`

, `grndht`

,
and `delta`

) to be used with the Digital DATCOM Forces
and Moments block.

[1] *The USAF Stability and Control
Digital Datcom*, AFFDL-TR-79-3032, 1979.

[2] Etkin, B., and L. D. Reid, *Dynamics
of Flight Stability and Control,* John Wiley & Sons,
New York, 1996.

[3] Roskam, J., "Airplane Design Part VI: Preliminary Calculation of Aerodynamic, Thrust and Power Characteristics," Roskam Aviation and Engineering Corporation, Ottawa, Kansas, 1987.

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

See `asbSkyHogg`

`asbSkyHogg`

for
an example of this block.

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