Aerospace Blockset™

3DoF (Wind Axes)

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

Library

Equations of Motion/3DoF

Description

The 3DoF (Wind Axes) block considers the rotation in the vertical plane of a wind-fixed coordinate frame about an Earth-fixed reference frame.

The equations of motion are

where the applied forces are assumed to act at the center of gravity of the body.

Dialog Box

Units

Specifies the input and output units:

Units	Forces	Moment	Acceleration	Velocity	Position	Mass	Inertia
`Metric (MKS)`	Newton	Newton meter	Meters per second squared	Meters per second	Meters	Kilogram	Kilogram meter squared
`English (Velocity in ft/s)`	Pound	Foot pound	Feet per second squared	Feet per second	Feet	Slug	Slug foot squared
`English (Velocity in kts)`	Pound	Foot pound	Feet per second squared	Knots	Feet	Slug	Slug foot squared

Mass Type

Select the type of mass to use:

`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.

Initial airspeed

A scalar value for the initial velocity of the body, (V₀).

Initial flight path angle

A scalar value for the initial flight path angle of the body, .

Initial incidence

A scalar value for the initial angle between the velocity vector and the body, .

Initial body rotation rate

A scalar value for the initial body rotation rate, (q₀).

Initial position (x,z)

A two-element vector containing the initial location of the body in the Earth-fixed reference frame.

Initial Mass

A scalar value for the mass of the body.

Inertia body axes

A scalar value for the inertia of the body.

Gravity Source

Specify source of gravity:

`External`	Variable gravity input to block
`Internal`	Constant gravity specified in mask

Acceleration due to gravity

A scalar value for the acceleration due to gravity used if internal gravity source is selected. If gravity is to be neglected in the simulation, this value can be set to 0.

Inputs and Outputs

Input	Dimension Type	Description
First		Contains the force acting along the wind x-axis, .
Second		Contains the force acting along the wind z-axis, .
Third		Contains the applied pitch moment in body axes, (M).
Fourth (Optional)		Contains the block is gravity in the selected units.

Output	Dimension Type	Description
First		Contains the flight path angle, in radians .
Second		Contains the pitch angular rate, in radians per second .
Third		Contains the pitch angular acceleration, in radians per second squared .
Fourth	Two-element vector	Contains the location of the body, in the Earth-fixed reference frame, (Xe,Ze).
Fifth	Two-element vector	Contains the velocity of the body resolved into the wind-fixed coordinate frame, (V,0).
Sixth	Two-element vector	Contains the acceleration of the body resolved into the body-fixed coordinate frame, (Ax,Az).
Seventh	Scalar	Contains the angle of attack, .

Assumptions and Limitations

The block assumes that the applied forces are acting at the center of gravity of the body, and that the mass and inertia are constant.

Reference

Stevens, B. L., and F. L. Lewis, Aircraft Control and Simulation, John Wiley & Sons, New York, 1992.