3DOF (Wind Axes)

A model of plane longitudinal motion in a high-speed coordinate system.

blockType: SubSystem

Path in the library:

/Aerospace/Equations of Motion/3DOF/3DOF (Wind Axes)

Description

Block 3DOF (Wind Axes) implements a model of the plane longitudinal motion of an aircraft, taking into account the rotation of the vertical plane of the velocity coordinate system relative to the Earth’s coordinate system.

The equations of motion have the form:

Block 3DOF (Wind Axes) it works in SI units.

The block uses coordinate systems according to the international standard ISO 1151.

Ports

Input

# F_x (N) — projection of the applied force on the OX axis
scalar

Details

Projection of the applied force on the axis velocity coordinate system, N.

Data types	`Float64`
Complex numbers support	No

# F_z (N) — projection of the applied force on the OZ axis
scalar

Details

Projection of the applied force on the axis velocity coordinate system, N.

Data types	`Float64`
Complex numbers support	No

# M (N-m) — pitch moment
scalar

Details

Pitch moment, NM.

Data types	`Float64`
Complex numbers support	No

Output

# γ (rad) — trajectory tilt angle
scalar

Details

The angle of the trajectory, rad. The value is in the range .

Data types	`Float64`
Complex numbers support	No

# q (rad/s) — pitch speed
scalar

Details

Pitch velocity, rad/s.

Data types	`Float64`
Complex numbers support	No

# dq/dt (rad/s²) — pitch velocity change
scalar

Details

Pitch velocity change, rad/s².

Data types	`Float64`
Complex numbers support	No

# X_e Z_e (m) — position relative to the Earth’s coordinate system
A 2-by-1 vector

Details

The coordinates of the aircraft relative to the Earth’s coordinate system, m. Are set as a vector.

Data types	`Float64`
Complex numbers support	No

# V_w (m/s) — the speed of the aircraft
The vector is 2 by 1

Details

Components of the speed of the aircraft along the axes and accordingly, m/s. They are set as a vector.

Data types	`Float64`
Complex numbers support	No

# A_xb A_zb (m/s²) — acceleration of an aircraft in a connected coordinate system
A 2-by-1 vector

Details

Components of the acceleration of an aircraft in a connected coordinate system along the axes and accordingly, m/s ². They are set as a vector.

Data types	`Float64`
Complex numbers support	No

# α (rad) — Angle of attack
scalar

Details

Angle of attack, rad.

Data types	`Float64`
Complex numbers support	No

# A_xe A_ze (m/s²) — acceleration of the aircraft relative to the Earth’s coordinate system
A 2-by-1 vector

Details

Components of the acceleration of an aircraft relative to the Earth’s coordinate system along the axes and accordingly, m/s ². They are set as a vector.

Data types	`Float64`
Complex numbers support	No

Parameters

# Initial airspeed — initial airspeed

Details

The initial airspeed of the aircraft, rad /s. The value must be higher 0.

Default value	`100.0`
Program usage name	`v_ini`
Tunable	No
Evaluatable	Yes

# Initial flight path angle — the initial angle of the trajectory

Details

The initial angle of inclination of the trajectory, rad.

Default value	`0.0`
Program usage name	`gamma_ini`
Tunable	No
Evaluatable	Yes

# Initial body rotation rate — initial pitch velocity change

Details

The initial change in pitch velocity, rad/s ².

Default value	`0.0`
Program usage name	`q_ini`
Tunable	No
Evaluatable	Yes

# Initial incidence — initial angle of attack

Details

Initial angle of attack, rad.

Default value	`0.0`
Program usage name	`alpha_ini`
Tunable	No
Evaluatable	Yes

# Initial position (x,z) — initial position relative to the Earth’s coordinate system

Details

The initial coordinates of the aircraft relative to the Earth’s coordinate system, m. Are set as a vector.

Default value	`[0.0, 0.0]`
Program usage name	`pos_ini`
Tunable	No
Evaluatable	Yes

# Initial mass — weight

Details

Weight of the aircraft, kg.

Default value	`1.0`
Program usage name	`mass`
Tunable	No
Evaluatable	Yes

# Inertia body axes — moment of inertia

Details

The moment of inertia of the aircraft relative to the axis , kg⋅m².

Default value	`1.0`
Program usage name	`Iyy`
Tunable	No
Evaluatable	Yes

# Acceleration due to gravity — acceleration of free fall

Details

Acceleration of gravity, m/s ². The value can be zero if the effect of gravity on the aircraft can be ignored.

Default value	`9.81`
Program usage name	`g`
Tunable	No
Evaluatable	Yes