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Fixed-Wing UAV Point Mass

Integrate fourth- or sixth-order point mass equations of motion in coordinated flight

  • Library:
  • UAV Toolbox / Algorithms

    Aerospace Blockset / Equations of Motion / Point Mass

  • Fixed-Wing Point Mass block

Description

The Fixed-Wing Point Mass block integrates fourth- or sixth-order point mass equations of motion in coordinated flight.

Limitations

  • The flat Earth reference frame is considered inertial, an approximation that allows the forces due to the Earth's motion relative to the "fixed stars" to be neglected.

  • The block assumes that there is fully coordinated flight, that is, there is no side force (wind axes) and sideslip is always zero.

Ports

Input

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Lift, specified as a scalar in units of force.

Data Types: double

Drag, specified as a scalar in units of force.

Data Types: double

Weight, specified as a scalar in units of force.

Data Types: double

Thrust, specified as a scalar in units of force.

Data Types: double

Flight path angle relative to the air mass, specified as a scalar in radians.

Data Types: double

Bank angle, specified as a scalar in radians.

Data Types: double

Angle of attack, specified as a scalar in radians.

Data Types: double

Wind vector in the direction in which the air mass is moving, specified as a three-element vector.

Data Types: double

Output

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Airspeed, returned as a scalar.

Data Types: double

Ground speed over the Earth (speed of motion over the ground), returned as a scalar.

Data Types: double

Velocity vector relative to the air mass, returned as a three-element vector.

Data Types: double

Velocity vector relative to Earth with [North East Down] orientation, returned as a three-element vector.

Dependencies

To enable this port, set Reference frame orientation to [North East Down].

Data Types: double

Velocity vector relative to Earth with [East North Up] orientation, returned as a three-element vector.

Dependencies

To enable this port, set Reference frame orientation to [East North Up].

Data Types: double

Position vector relative to Earth with [North East Down] orientation, returned as a three-element vector.

Dependencies

To enable this port, set Reference frame orientation to [North East Down].

Data Types: double

Position vector relative to Earth with [East North Up] orientation, returned as a three-element vector.

Dependencies

To enable this port, set Reference frame orientation to [East North Up].

Data Types: double

Flight path angle relative to the air mass, returned as a scalar.

Data Types: double

Flight path angle relative to Earth, returned as a scalar.

Data Types: double

Heading angle relative to air mass, returned as a scalar.

Dependencies

To enable this port, set Degrees of Freedom to 6th Order (Coordinated Flight).

Data Types: double

Heading angle relative to Earth, returned as a scalar.

Dependencies

To enable this port, set Degrees of Freedom to 6th Order (Coordinated Flight).

Data Types: double

Parameters

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Input and output units, specified as follows:

Units

Forces

Velocity

Position

Mass

Metric (MKS)

newtons

meters per second

meters

kilograms

English (velocity in ft/s)

pounds

feet per second

feet

slugs

English (velocity in kts)

pounds

knots

feet

slugs

Programmatic Use

Block Parameter: units
Type: character vector
Values: 'Metric (MKS)' | 'English (velocity in ft/s)' | 'English (velocity in kts)'
Default: 'Metric (MKS)'

Reference frames used for input ports and output ports, specified as [East North Up] or [North East Down].

Programmatic Use

Block Parameter: frame
Type: character vector
Values: '[East North Up]' | '[North East Down]'
Default: '[North East Down]'

Degrees of freedom, specified as 4th Order (Longitudinal) or 6th Order (Coordinated Flight).

Programmatic Use

Block Parameter: order
Type: character vector
Values: '4th Order (Longitudinal)' | '6th Order (Coordinated Flight)'
Default: '6th Order (Coordinated Flight)'

Initial East (Earth) location in the [North East Down] orientation, specified as a scalar.

Dependencies

The direction specification of this parameter depends on the Reference frame orientation and Degrees of Freedom setting:

Initial crossrangeReference frame orientationDegrees of freedom

East

[North East Down]

6th Order (Coordinated Flight)

North

[East North Up]

6th Order (Coordinated Flight)

Programmatic Use

Block Parameter: east
Type: character vector
Values: scalar
Default: '0'

Initial North (Earth) downrange of the point mass, specified as a scalar.

Dependencies

The direction specification of this parameter depends on the Reference frame orientation and Degrees of Freedom setting:

Initial downrangeReference frame orientationDegrees of freedom

North

[North East Down]

6th Order (Coordinated Flight)

North

[North East Down]

4th Order (Longitudinal)

East

[East North Up]

6th Order (Coordinated Flight)

East

[East North Up]

4th Order (Longitudinal)

Programmatic Use

Block Parameter: north
Type: character vector
Values: scalar
Default: '0'

Initial altitude of the point mass, specified as a scalar.

Programmatic Use

Block Parameter: altitude
Type: character vector
Values: scalar
Default: '0'

Initial airspeed of the point mass, specified as a scalar.

Programmatic Use

Block Parameter: 'airspeed'
Type: character vector
Values: scalar
Default: '50'

Initial flight path angle of the point mass, specified as a scalar.

Programmatic Use

Block Parameter: gamma
Type: character vector
Values: scalar
Default: '0'

Initial heading angle of the point mass, specified as a scalar.

Dependencies

To enable this parameter, set Degrees of Freedom to 6th Order (Coordinated Flight).

Programmatic Use

Block Parameter: chi
Type: character vector
Values: scalar
Default: '0'

Mass of the point mass, specified as a scalar.

Programmatic Use

Block Parameter: mass
Type: character vector
Values: scalar
Default: '10'

Algorithms

The integrated equations of motion for the point mass are:

V˙=(TcosαDWsinγai)/mγ˙a=((L+Tsinα)cosμWcosγai)/(mV)X˙e=Va+Vw

6th order equations:

X˙a=((L+Tsinα)sinμ)/(mVcosγa)X˙a|East=VcosχacosγaX˙a|North=VsinχacosγaX˙a|Up=Vsinγa

4th order equations:

χ˙a=0X˙a|East=VcosγaX˙a|North=0X˙a|Up=Vsinγa

where:

  • m — Mass.

  • g — Gravitational acceleration.

  • W — Weight ( m*g).

  • L — Lift force.

  • D — Drag force.

  • T — Thrust force.

  • α — Angle of attack.

  • μ — Angle of bank.

  • γai — Input port value for the flight path angle.

  • V — Airspeed, as measured on the aircraft, with respect to the air mass. It is also the magnitude of vector Va.

  • Vw — Steady wind vector.

  • Subscript a — For the variables, denotes that they are with respect to the steadily moving air mass:

    • γa — Flight path angle.

    • χa — Heading angle.

    • Xa — Position [East, North, Up].

  • Subscript e — Flat Earth inertial frame such that so Xe is the position on the Earth after correcting Xa for the air mass movement.

Additional outputs are:

G=(Ve|East2+Ve|North2)γ=sin1(Ve|UpVe¯)χ=tan1(Ve|NorthVe|East)

where:

  • The four-quadrant inverse tangent (atan2) calculates the heading angle.

  • The groundspeed, G, is the speed over the flat Earth (a 2-D projection).

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Introduced in R2021a