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3DOF (Wind Axes)

Implement three-degrees-of-freedom equations of motion with respect to wind axes

  • Library:
  • Aerospace Blockset / Equations of Motion / 3DOF

  • 3DOF (Wind Axes) block

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

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Applied force along the body x-axis, specified as a scalar, in the units selected in Units.

Data Types: double

Applied force along the body z-axis, specified as a scalar.

Data Types: double

Applied pitch moment, specified as a scalar.

Data Types: double

Gravity, specified as a scalar.

Dependencies

To enable this port, set Gravity source to External.

Data Types: double

Output

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Flight path angle, within ±pi, returned as a scalar, in radians.

Data Types: double

Pitch angular rate, specified as a scalar, in radians per second.

Data Types: double

Pitch angular acceleration, returned as a scalar, in radians per second squared.

Data Types: double

Location of the body in the flat Earth reference frame, (Xe, Ze), returned as a two-element vector.

Data Types: double

Velocity of the body resolved into the wind-fixed coordinate frame, (V, 0), returned as a two-element vector.

Data Types: double

Acceleration of the body with respect to the body-fixed coordinate frame, (Ax, Az), returned as a two-element vector.

Data Types: double

Angle of attack, returned as a scalar, in radians.

Data Types: double

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

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Main

Input and output units, specified as Metric (MKS), English (Velocity in ft/s), or English (Velocity in kts).

UnitsForcesMomentAccelerationVelocityPositionMassInertia
Metric (MKS) NewtonNewton-meterMeters per second squaredMeters per secondMetersKilogramKilogram meter squared
English (Velocity in ft/s) PoundFoot-poundFeet per second squaredFeet per secondFeetSlugSlug foot squared
English (Velocity in kts) PoundFoot-poundFeet per second squaredKnotsFeetSlugSlug 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, specified according to the following table.

Mass TypeDescriptionDefault 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 speed of the body, (V0), specified as a scalar.

Programmatic Use

Block Parameter: V_ini
Type: character vector
Values: '100' | scalar
Default: '100'

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 of the body, (γ0), specified as a scalar.

Programmatic Use

Block Parameter: gamma_ini
Type: character vector
Values: '0' | scalar
Default: '0'

Initial pitch rotation rate, (q0), specified as a scalar.

Programmatic Use

Block Parameter: q_ini
Type: character vector
Values: '0' | scalar
Default: '0'

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 of the rigid body, specified as a scalar.

Programmatic Use

Block Parameter: mass
Type: character vector
Values: '1.0' | scalar
Default: '1.0'

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, 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, 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'

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 state name, specified as a character vector.

Programmatic Use

Block Parameter: V_statename
Type: character vector
Values: '' | scalar
Default: ''

Incidence angle state name, specified as a scalar.

Programmatic Use

Block Parameter: alpha_statename
Type: character vector
Values: '' | scalar
Default: ''

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 state names, specified as a character vector.

Programmatic Use

Block Parameter: q_statename
Type: character vector
Values: '' | scalar
Default: ''

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.

Graphical view of rotation in the vertical plane of a body-fixed coordinate frame about a flat Earth reference frame.

The equations of motion are

V˙=Fxwindmgsinγα˙=FzwindmVcosβ+q+gVcosβcosγq˙=θ˙=MybodyIyyγ˙=qα˙Abe=[AxeAze]=DCMwb[Fwmgsinγ]Abb=[u˙bw˙b]=DCMwb[Fwmgsinγω¯w×V¯w]F¯w=[FxwindFzwind],V¯w=[VxwindVzwind],ω¯w=q

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™.

Introduced in R2006a