3DOF (Wind Axes)
Implement three-degrees-of-freedom equations of motion with respect to wind axes
- Library:
Aerospace Blockset / Equations of Motion / 3DOF
Description
The 3DOF (Wind Axes) block implements three-degrees-of-freedom equations of motion with respect to wind axes. It considers the rotation in the vertical plane of a wind-fixed coordinate frame about a flat Earth reference frame. For more information about the rotation and equations of motion, see Algorithms.
Limitations
The block assumes that the applied forces act at the center of gravity of the body, and that the mass and inertia are constant.
Ports
Input
Fx — Applied force along x-axis
scalar
Applied force along the body x-axis, specified as a scalar, in the units selected in Units.
Data Types: double
Fz — Applied force along z-axis
scalar
Applied force along the body z-axis, specified as a scalar.
Data Types: double
M — Applied pitch moment
scalar
Applied pitch moment, specified as a scalar.
Data Types: double
g — Gravity
scalar
Gravity, specified as a scalar.
Dependencies
To enable this port, set Gravity source to
External.
Data Types: double
Output
γ — Flight path angle
scalar
Flight path angle, within ±pi, returned as a scalar, in radians.
Data Types: double
ωy (rad/s) — Pitch angular rate
scalar
Pitch angular rate, specified as a scalar, in radians per second.
Data Types: double
dωy/dt — Pitch angular acceleration
scalar
Pitch angular acceleration, returned as a scalar, in radians per second squared.
Data Types: double
XeZe — Location of body
two-element vector
Location of the body in the flat Earth reference frame, (Xe, Ze), returned as a two-element vector.
Data Types: double
Vw — Velocity in wind-fixed frame
two-element vector
Velocity of the body resolved into the wind-fixed coordinate frame, (V, 0), returned as a two-element vector.
Data Types: double
AxbAzb — Acceleration of body
two-element vector
Acceleration of the body with respect to the body-fixed coordinate frame, (Ax, Az), returned as a two-element vector.
Data Types: double
α — Angle of attack
scalar
Angle of attack, returned as a scalar, in radians.
Data Types: double
AxeAze — Acceleration of body
two-element vector
Accelerations of the body with respect to the inertial (flat Earth) coordinate frame, returned as a two-element vector. You typically connect this signal to the accelerometer.
Dependencies
To enable this port, select the Include inertial acceleration check box.
Data Types: double
Parameters
Main
Units — Input and output units
Metric (MKS) (default) | English (Velocity in ft/s) | English (Velocity in kts)
Input and output units, specified as Metric (MKS), English (Velocity in ft/s), or English (Velocity in kts).
| Units | Forces | Moment | Acceleration | Velocity | Position | Mass | Inertia |
|---|---|---|---|---|---|---|---|
Metric (MKS) | Newton | Newton-meter | Meters per second squared | Meters per second | Meters | Kilogram | Kilogram meter squared |
English (Velocity in ft/s) | Pound | Foot-pound | Feet per second squared | Feet per second | Feet | Slug | Slug foot squared |
English (Velocity in kts) | Pound | Foot-pound | Feet per second squared | Knots | Feet | Slug | Slug foot squared |
Programmatic Use
Block Parameter:
units |
| Type: character vector |
Values: Metric (MKS) | English (Velocity in ft/s) | English (Velocity in kts) |
Default: Metric (MKS) |
Mass type — Mass type
Fixed (default) | Simple Variable | Custom Variable
Mass type, specified according to the following table.
| Mass Type | Description | Default for |
|---|---|---|
Fixed | Mass is constant throughout the simulation. | |
Simple Variable | Mass and inertia vary linearly as a function of mass rate. | |
Custom Variable | Mass and inertia variations are customizable. |
The Fixed selection conforms to the previously
described equations of motion.
Programmatic Use
Block Parameter:
mtype |
| Type: character vector |
Values:
Fixed | Simple Variable |
Custom Variable |
Default:
'Fixed' |
Initial airspeed — Initial speed
100 (default) | scalar
Initial speed of the body, (V0), specified as a scalar.
Programmatic Use
Block
Parameter:
V_ini |
| Type: character vector |
Values:
'100' | scalar |
Default:
'100' |
Initial incidence — Initial angle
0 (default) | scalar
Initial angle between the velocity vector and the body, (α0), specified as a scalar.
Programmatic Use
Block Parameter: alpha_ini |
| Type: character vector |
Values:
'0' | scalar |
Default: '0' |
Initial flight path angle — Initial flight path angle
0 (default) | scalar
Initial flight path angle of the body, (γ0), specified as a scalar.
Programmatic Use
Block Parameter: gamma_ini |
| Type: character vector |
Values:
'0' | scalar |
Default: '0' |
Initial body rotation rate — Initial pitch rotation rate
0 (default) | scalar
Initial pitch rotation rate, (q0), specified as a scalar.
Programmatic Use
Block
Parameter:
q_ini |
| Type: character vector |
Values:
'0' | scalar |
Default:
'0' |
Initial position (x,z) — Initial location
[0 0] (default) | two-element vector
Initial location of the body in the flat Earth reference frame, specified as a two-element vector.
Programmatic Use
Block Parameter:
pos_ini |
| Type: character vector |
Values:
'[0 0]' | two-element vector |
Default:
'[0 0]' |
Initial mass — Initial mass
1.0 (default) | scalar
Initial mass of the rigid body, specified as a scalar.
Programmatic Use
Block Parameter: mass |
| Type: character vector |
Values:
'1.0' | scalar |
Default:
'1.0' |
Inertia body axes — Inertia of body
1.0 (default) | scalar
Inertia of the body, specified as a scalar.
Dependencies
To enable this parameter, set Mass type to Fixed.
Programmatic Use
Block Parameter: Iyy |
| Type: character vector |
Values:
'1.0' | scalar |
Default:
'1.0' |
Gravity Source — Gravity source
Internal (default) | External
Gravity source, specified as:
External | Variable gravity input to block |
Internal | Constant gravity specified in mask |
Programmatic Use
Block Parameter: g_in |
| Type: character vector |
Values: 'Internal' | 'External' |
Default: 'Internal' |
Acceleration due to gravity — Gravity source
9.81 (default) | scalar
Acceleration due to gravity, specified as a double scalar and used if internal gravity source
is selected. If gravity is to be neglected in the simulation, this value can be set to
0.
Dependencies
To enable this parameter, set Gravity Source to
Internal.
Programmatic Use
Block Parameter: g |
| Type: character vector |
Values:
'9.81' | scalar |
Default: '9.81' |
Include inertial acceleration — Include inertial acceleration port
off (default) | on
Select this check box to add an inertial acceleration in flat Earth frame output port. You typically connect this signal to the accelerometer.
Dependencies
To enable the AxeAze port, select this parameter.
Programmatic Use
Block Parameter: abi_flag |
| Type: character vector |
Values:
'off' |
'on' |
Default:
'off' |
State Attributes
Velocity: e.g., 'V' — Velocity state name
'' (default) | character vector
Velocity state name, specified as a character vector.
Programmatic Use
Block Parameter: V_statename |
| Type: character vector |
Values:
'' | scalar |
Default: '' |
Incidence angle e.g., 'alpha' — Incidence angle state name
'' (default) | scalar
Incidence angle state name, specified as a scalar.
Programmatic Use
Block
Parameter:
alpha_statename |
| Type: character vector |
Values:
'' | scalar |
Default:
'' |
Flight path angle: e.g., 'gamma' — Flight path angle state name
'' (default) | character vector
Flight path angle state name, specified as a character vector.
Programmatic Use
Block Parameter: gamma_statename |
| Type: character vector |
Values:
'' | scalar |
Default: '' |
Body rotation rate: e.g., 'q' — Body rotation state name
'' (default) | scalar
Body rotation rate state names, specified as a character vector.
Programmatic Use
Block Parameter: q_statename |
| Type: character vector |
Values:
'' | scalar |
Default: '' |
Position: e.g., {'Xe', 'Ze'} — Position state name
'' (default) | comma-separated list surrounded by braces
Position state names, specified as a comma-separated list surrounded by braces.
Programmatic Use
Block Parameter: pos_statename |
| Type: character vector |
Values:
'' | comma-separated list surrounded by braces |
Default: '' |
Algorithms
The block considers the rotation in the vertical plane of a wind-fixed coordinate frame about a flat Earth reference frame.
The equations of motion are
where the applied forces are assumed to act at the center of gravity of the body.
References
[1] Stevens, Brian, and Frank Lewis. Aircraft Control and Simulation. New York: John Wiley & Sons, 1992.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
See Also
3DOF (Body Axes) | 4th Order Point Mass (Longitudinal) | Custom Variable Mass 3DOF (Body Axes) | Custom Variable Mass 3DOF (Wind Axes) | Simple Variable Mass 3DOF (Body Axes) | Simple Variable Mass 3DOF (Wind Axes)