Documentation |
Calculate fourth-order point mass
The 4th Order Point Mass (Longitudinal) block performs the calculations for the translational motion of a single point mass or multiple point masses.
The translational motions of the point mass [X_{East} X_{Up}]^{T }are functions of airspeed (V ) and flight path angle (γ),
$$\begin{array}{c}{F}_{x}=m\dot{V}\\ {F}_{z}=mV\dot{\gamma}\\ {\dot{X}}_{East}=V\mathrm{cos}\gamma \\ {\dot{X}}_{Up}=V\mathrm{sin}\gamma \end{array}$$
where the applied forces [F_{x} F_{z}]^{T }are in a system defined as follows: x-axis is in the direction of vehicle velocity relative to air, z-axis is upward, and y-axis completes the right-handed frame. The mass of the body m is assumed constant.
Specifies the input and output units:
Units | Forces | Velocity | Position |
---|---|---|---|
Metric (MKS) | Newton | Meters per second | Meters |
English (Velocity in ft/s) | Pound | Feet per second | Feet |
English (Velocity in kts) | Pound | Knots | Feet |
The scalar or vector containing the initial flight path angle of the point mass(es).
The scalar or vector containing the initial airspeed of the point mass(es).
The scalar or vector containing the initial downrange of the point mass(es).
The scalar or vector containing the initial altitude of the point mass(es).
The scalar or vector containing the mass of the point mass(es).
Input | Dimension Type | Description |
---|---|---|
First | Contains the force in x-axis in selected units. | |
Second | Contains the force in z-axis in selected units. |
Output | Dimension Type | Description |
---|---|---|
First | Contains the flight path angle in radians. | |
Second | Contains the airspeed in selected units. | |
Third | Contains the downrange or amount traveled East in selected units. | |
Fourth | Contains the altitude or amount traveled Up in selected units. |
The flat Earth reference frame is considered inertial, an excellent approximation that allows the forces due to the Earth's motion relative to the "fixed stars" to be neglected.