Fixed-Wing UAV Point Mass

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

Since R2021a

• 

Libraries:
UAV Toolbox / Algorithms
Aerospace Blockset / Equations of Motion / Point Mass

Description

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

Examples

Transition from Low- to High-Fidelity UAV Models in Three Stages

Evolve your UAV plant model continuously to stay in sync with the latest information available.

• Open Live Script

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

Lift — Lift

scalar

Lift, specified as a scalar in units of force.

Data Types: double

Drag — Drag

scalar

Drag, specified as a scalar in units of force.

Data Types: double

Weight — Weight

scalar

Weight, specified as a scalar in units of force.

Data Types: double

Thrust — Thrust

scalar

Thrust, specified as a scalar in units of force.

Data Types: double

ɣ_a — Flight path angle relative to the air mass

scalar

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

Data Types: double

μ — Bank angle

scalar

Bank angle, specified as a scalar in radians.

Data Types: double

ɑ — Angle of attack

scalar

Angle of attack, specified as a scalar in radians.

Data Types: double

V_wind — Wind vector

three-element vector

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

Data Types: double

Output

V — Airspeed

scalar

Airspeed, returned as a scalar.

Data Types: double

G — Ground speed projection

scalar

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

Data Types: double

V_a — Velocity vector relative to air mass

three-element vector

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

Data Types: double

V_e — Velocity vector relative to Earth with [North East Down] orientation

three-element vector

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

V_ENU — Velocity vector relative to Earth

three-element vector

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

X_e — Position vector relative to Earth

three-element vector

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

X_ENU — Position vector relative to Earth

three-element vector

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

γ_a — Flight path angle relative to air mass

scalar

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

Data Types: double

γ — Flight path angle relative to Earth

scalar

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

Data Types: double

χ_a — Heading angle relative to air mass

scalar

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

χ — Heading angle relative to Earth

scalar

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

Units — Units

Metric (MKS) (default) | English (velocity in ft/s) | English (velocity in kts)

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 frame orientation — Reference frames

[North East Down] (default) | [East North Up]

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 — Degrees of freedom

6th Order (Coordinated Flight) (default) | 4th Order (Longitudinal)

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 crossrange — Initial East (Earth) crossrange location

0 (default) | scalar

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 crossrange	Reference frame orientation	Degrees 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 downrange — Initial North (Earth) downrange

0 (default) | scalar

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 downrange	Reference frame orientation	Degrees 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 — Initial altitude

0 (default) | scalar

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

Programmatic Use

Block Parameter: altitude

Type: character vector

Values: scalar

Default: '0'

Initial airspeed — Initial airspeed

50 (default) | scalar

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 — Initial flight path angle

0 (default) | scalar

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 — Initial heading angle

0 (default) | scalar

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 — Point mass

10 (default) | scalar

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:

$$\begin{array}{l}\dot{V}=(T\cos \alpha -D-W\sin {\gamma }_{ai})/m\\ {\dot{\gamma }}_a=((L+T\sin \alpha )\cos \mu -W\cos {\gamma }_{ai})/(mV)\\ {\dot{X}}_e=V_a+V_w\end{array}$$

6th order equations:

$$\begin{array}{l}{\dot{X}}_a=((L+T\sin \alpha )\sin \mu )/(mV\cos {\gamma }_a)\\ {{\dot{X}}_a|}_{East}=V\cos {\chi }_a\cos {\gamma }_a\\ {{\dot{X}}_a|}_{North}=V\sin {\chi }_a\cos {\gamma }_a\\ {{\dot{X}}_a|}_{Up}=V\sin {\gamma }_a\end{array}$$

4th order equations:

$$\begin{array}{l}{\dot{\chi }}_a=0\\ {{\dot{X}}_a|}_{East}=V\cos {\gamma }_a\\ {{\dot{X}}_a|}_{North}=0\\ {{\dot{X}}_a|}_{Up}=V\sin {\gamma }_a\end{array}$$

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.

• γ_ai — 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 V_a.

• V_w — Steady wind vector.

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

  • γ_a — Flight path angle.

  • χ_a — Heading angle.

  • X_a — Position [East, North, Up].

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

Additional outputs are:

$$\begin{array}{l}G=\sqrt{({V_e|}_{Eas{t}^2}+{V_e|}_{Nort{h}^2})}\\ \gamma ={\sin }^{-1}\left(\frac{{V_e|}_{Up}}{\Vert \underset{¯}{V_e}\Vert }\right)\\ \chi ={\tan }^{-1}\left(\frac{{V_e|}_{North}}{{V_e|}_{East}}\right)\end{array}$$

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™.

Version History

Introduced in R2021a