Longitudinal Movement in Overloads#

This block is based on the equations of full longitudinal motion, written in a semi-connected coordinate system in the form of the so-called equations in “overloads”. A switch Swfg is introduced as a parameter in this block, which controls the accounting of fugoid motion. At Swfg = 1 full longitudinal motion is considered. At Swfg = 0, short period motion is considered. The transition to short-period equations is carried out by disabling the integration of equations for speed and altitude.

Swfg = 1

\[\begin{split} \begin{cases} \dot {\omega}_z= \bar M_z \\ \dot {\theta}=\frac{g}{V}\cdot (n_y-cos\theta) \\ \dot{V}=g \cdot(n_x - sin \theta) \\ \dot {\upsilon} = \omega_z \\ \dot{H}=V \cdot sin \theta\end{cases} \end{split}\]

Swfg = 0

\[\begin{split} \begin{cases} \dot {\omega}_z= \bar M_z \\ \dot {\theta}=\frac{g}{V}\cdot (n_e-1) \\ \dot{V}=0 \\ \dot {\upsilon} = \omega_z \\ \dot{H}=0\end{cases} \end{split}\]

where:

\(\upsilon\) - pitch angle;

\(\omega_z\) - angular pitch speed;

\( heta\) - flight-path angle.

The right parts of the equations of motion (block inputs) can be calculated, for example, using the following formulas (1), (2) and (3):

(1)#\[\bar M_z=(M_{za}-T \cdot x_{eng}\cdot sin(\phi_{eng+ \Delta \phi_{Thr}}))/I_z\]

(2)#\[n_y=(Y_a+T \cdot sin (\alpha + \phi_{eng} +\Delta \phi_{Thr}))/G\]

(3)#\[n_x=(-X_a+T \cdot cos (\alpha + \phi_{eng} +\Delta \phi_{Thr}))/G\]

where:

T - total thrust of engines;

\(\phi_{eng}\) - angle of engine “jamming”;

\(\Delta \phi_{Thr}\) - angle of thrust vector rotation;

\(x_{eng}\) - “arm” of engine thrust relative to aircraft center of gravity.

1. Properties#

Property	Default Value	Description	Units of measurement
Initial value of pitch angular velocity	0	-	rad/s
Initial value of flight speed	0	-	m/s
Initial height value	0	-	m
Initial range value	0	-	m
Initial value of the trajectory inclination angle	57.295779513082323	-	rad
Pitch angle initial value	0	-	rad
Switch to move from full equations of motion (1) to equations of short period motion (0)	0	-	-

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
\(M_{zs}\)	Input	Relative pitching moment \(M_{zs}=M_z/l_z\)	N\(\cdot\)m	Automation
n\(_y\)	Input	Overload vector projection on the Y axis of a semi-connected coordinate system	deg	Automation
n\(_x\)	Input	Projection of the overload vector on the X axis of a semi-connected coordinate system	deg	Automation
\(\omega_{z}\)	Output	Angular pitch speed	rad/s	Automation
H	Output	Flight altitude	m	Automation
L	Output	Range	m	Automation
\(v\)	Output	Flight speed	m/s	Automation
Alpha_dot (\(\dot \alpha\))	Output	Attack angle derivative	rad	Automation
theta (\(\theta\))	Output	Flight-path angle	rad	Automation
Alpha (\(\alpha\))	Output	Attack angle	rad	Automation
Tang (\(\upsilon\))	Output	Pitch angle	rad	Automation

In order to see the connection capabilities of the block, you need to go to page Description of block ports