Fixed-Wing Point Mass

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

Since R2021a

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

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 — 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

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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

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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:

$\begin{array}{l} \dot{V} = (T \cos α - D - W \sin γ_{a i}) / m \\ {\dot{γ}}_{a} = ((L + T \sin α) \cos μ - W \cos γ_{a i}) / (m V) \\ {\dot{X}}_{e} = V_{a} + V_{w} \end{array}$

6th order equations:

$\begin{array}{l} {\dot{X}}_{a} = ((L + T \sin α) \sin μ) / (m V \cos γ_{a}) \\ {{\dot{X}}_{a} |}_{E a s t} = V \cos χ_{a} \cos γ_{a} \\ {{\dot{X}}_{a} |}_{N o r t h} = V \sin χ_{a} \cos γ_{a} \\ {{\dot{X}}_{a} |}_{U p} = V \sin γ_{a} \end{array}$

4th order equations:

$\begin{array}{l} {\dot{χ}}_{a} = 0 \\ {{\dot{X}}_{a} |}_{E a s t} = V \cos γ_{a} \\ {{\dot{X}}_{a} |}_{N o r t h} = 0 \\ {{\dot{X}}_{a} |}_{U p} = V \sin γ_{a} \end{array}$

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:

$\begin{array}{l} G = \sqrt{({V_{e} |}_{E a s t^{2}} + {V_{e} |}_{N o r t h^{2}})} \\ γ = \sin^{- 1} (\frac{{V_{e} |}_{U p}}{‖ \underline{V_{e}} ‖}) \\ χ = \tan^{- 1} (\frac{{V_{e} |}_{N o r t h}}{{V_{e} |}_{E a s t}}) \end{array}$

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

Fixed-Wing Point Mass

Description

Limitations

Ports

Input

Lift — Lift scalar

Drag — Drag scalar

Weight — Weight scalar

Thrust — Thrust scalar

ɣa — Flight path angle relative to the air mass scalar

μ — Bank angle scalar

ɑ — Angle of attack scalar

Vwind — Wind vector three-element vector

Output

V — Airspeed scalar

G — Ground speed projection scalar

Va — Velocity vector relative to air mass three-element vector

Ve — Velocity vector relative to Earth with [North East Down] orientation three-element vector

Dependencies

VENU — Velocity vector relative to Earth three-element vector

Dependencies

Xe — Position vector relative to Earth three-element vector

Dependencies

XENU — Position vector relative to Earth three-element vector

Dependencies

γa — Flight path angle relative to air mass scalar

γ — Flight path angle relative to Earth scalar

χa — Heading angle relative to air mass scalar

Dependencies

χ — Heading angle relative to Earth scalar

Dependencies

Parameters

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

Programmatic Use

Reference frame orientation — Reference frames [North East Down] (default) | [East North Up]

Programmatic Use

Degrees of freedom — Degrees of freedom 6th Order (Coordinated Flight) (default) | 4th Order (Longitudinal)

Programmatic Use

Initial crossrange — Initial East (Earth) crossrange location 0 (default) | scalar

Dependencies

Programmatic Use

Initial downrange — Initial North (Earth) downrange 0 (default) | scalar

Dependencies

Programmatic Use

Initial altitude — Initial altitude 0 (default) | scalar

Programmatic Use

Initial airspeed — Initial airspeed 50 (default) | scalar

Programmatic Use

Initial flight path angle — Initial flight path angle 0 (default) | scalar

Programmatic Use

Initial heading angle — Initial heading angle 0 (default) | scalar

Dependencies

Programmatic Use

Mass — Point mass 10 (default) | scalar

Programmatic Use

Algorithms

Extended Capabilities

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

Version History

See Also

Lift — Lift
scalar

Drag — Drag
scalar

Weight — Weight
scalar

Thrust — Thrust
scalar

ɣ_a — Flight path angle relative to the air mass
scalar

μ — Bank angle
scalar

ɑ — Angle of attack
scalar

V_wind — Wind vector
three-element vector

V — Airspeed
scalar

G — Ground speed projection
scalar

V_a — Velocity vector relative to air mass
three-element vector

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

V_ENU — Velocity vector relative to Earth
three-element vector

X_e — Position vector relative to Earth
three-element vector

X_ENU — Position vector relative to Earth
three-element vector

γ_a — Flight path angle relative to air mass
scalar

γ — Flight path angle relative to Earth
scalar

χ_a — Heading angle relative to air mass
scalar

χ — Heading angle relative to Earth
scalar

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

Reference frame orientation — Reference frames
`[North East Down]` (default) | `[East North Up]`

Degrees of freedom — Degrees of freedom
`6th Order (Coordinated Flight)` (default) | `4th Order (Longitudinal)`

Initial crossrange — Initial East (Earth) crossrange location
`0` (default) | scalar

Initial downrange — Initial North (Earth) downrange
`0` (default) | scalar

Initial altitude — Initial altitude
`0` (default) | scalar

Initial airspeed — Initial airspeed
`50` (default) | scalar

Initial flight path angle — Initial flight path angle
`0` (default) | scalar

Initial heading angle — Initial heading angle
`0` (default) | scalar

Mass — Point mass
`10` (default) | scalar

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