4.4.2 Mathematical model of the vertical velocity

According to [21–23], the lift force generates the vertical displacement of the airplane. This displacement could be explained by using the classical physical laws considering the lift force like a punctual force applied to the mass of the airplane. The following equation is obtained:

A New Real-Time Flight Simulator for Military Training Using Mechatronics and Cyber… DOI: http://dx.doi.org/10.5772/intechopen.86586

$$V\_V = V\_{vt} \frac{t \cdot \left( \left( \rho \left( V\_{t\chi} + \left( \frac{V\_\sigma + k\_h}{m\_a} \right) \cdot t \right)^2 \right) \cdot \mathcal{S}\_W \cdot \mathcal{C}\_L \cdot \cos(a\_t) - \mathcal{W}\_a \right)}{m\_a} \tag{8}$$

where Vv is the vertical velocity of an airplane; Vvi is the initial vertical velocity of an airplane; Vix is the initial velocity of the airplane; Ve is the engine velocity of the airplane; kh is the trust constant; ma is the mass of an airplane; t is the flight time; Sw is the wing surface; CL is the coefficient of lift; α<sup>t</sup> is the angle of rotation; and Wa is the weight of an airplane.

#### 4.4.3 Mathematical model of lateral velocity

According to [21–23], the resultant force Ly of the sinusoidal component of the lift is responsible for generating the speed of lateral displacement of the aircraft. The following equation is obtained:

$$V\_L = V\_{iy} \frac{\mathbf{t} \cdot \left( \left( \rho \left( V\_{tx} + \left( \frac{V\_o + k\_h}{m\_a} \right) \cdot \mathbf{t} \right)^2 \right) \cdot \mathcal{S}\_W \cdot \mathcal{C}\_L \cdot \sin(\alpha\_t) \right)}{m\_a} \tag{9}$$

where VL is the lateral velocity of an airplane; Viy is the initial velocity on the y-axis of an airplane; Vix is the initial velocity on the x-axis of the airplane; Ve is the engine velocity of an airplane; kh is the trust constant; ma is the mass of an airplane; t is the flight time; Sw is the wing surface; CL is the lift coefficient; and α<sup>t</sup> is the angle of rotation.

#### 4.5 Implementation and testing

The CPS complied with a development process for the flight simulator based on the XP cycle that performs iterative and incremental tasks [24, 25]. According to the XP methodology, the work team completed incremental delivery of the software products, based on the following iterations: (1) computational iteration—in this iteration, mathematical models were developed, aerodynamics in physics, management of threads and the design of delegates instance to control the airplane of the virtual world; (2) communication iteration—in this iteration, the processing and transfer of data referring to roll, pitch, and yaw was performed using text files, sockets and a local network; and (3) control iteration—in this iteration, the control system of the Stewart platform was programmed to reproduce the movements of the flight simulator. A multidisciplinary approach supported by the system design engineering allowed the integration of all the modules of the complex dynamic system for its correct operation. Figure 7 shows the iterations of the CPS based on the XP methodology, applying the model proposed by Drake et al. [26].

Unitary tests were performed on the cyber-physical system that included the computational, communication and control subsystems, both at the software level and at the hardware level. Acceptance tests were also carried out with a group of 40 aircraft pilots, to evaluate the proper functioning of the software application at the end of each iterations. Figure 8 shows the graphical user interface of the flight simulator developed with the Unity 3D framework, where it is possible to observe the cockpit of a Cessna 172 aircraft operated by a joystick, where the plane is flying over the city of Manta in Ecuador, where the main military aviation schools of the country are located.

flight simulator was programmed with the UNITY 3D framework in computer 1, where the frontal velocity, vertical velocity and lateral velocity are considered allowing the airplane to move in the virtual world as it would be in the real world.

In this research, we developed three basic mathematical models for the correct operation of the flight simulator, considering that an aircraft is a mass subjected to different forces such as weight (W), lift (L), thrust (T), and drag (D). In this sense, an analysis of each of these forces and the causes that produce them was made. This allowed the flight simulator to work according to the physical laws that are produced in the air and that the pilot know to properly control of an airplane.

According to [21–23], the thrust force generates the frontal displacement of the airplane. This displacement can be explained using the classical physical laws considering to Ft like a punctual force applied to the mass of the airplane. The following

where Ft is the thrust force; Ve is the engine speed or helix; kh is the thrust constant; ma is the mass of the airplane; Vx is the front speed; Vix is the initial

According to [21–23], the lift force generates the vertical displacement of the airplane. This displacement could be explained by using the classical physical laws considering the lift force like a punctual force applied to the mass of the airplane.

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4.4 Mathematical model

Figure 6.

Military Engineering

4.4.1.1 Front velocity

equation is obtained:

4.4.1 Mathematical model of the front velocity

Infographic of the electric and mechanical diagram of Stewart platform.

velocity of the airplane; and t is the time.

The following equation is obtained:

82

4.4.2 Mathematical model of the vertical velocity

Figure 9 shows the control front panel of the Stewart platform, where the behavior of the input and output values of the control system developed in

A New Real-Time Flight Simulator for Military Training Using Mechatronics and Cyber…

LabVIEW can be seen, which reproduces the movements of the flight simulator by integrating a network of two computers that use communication threads with sockets and flat text files, where the information of the three angles of maneuverability of the airplane are found, including: the direction (heading or yaw),

For a proof of concept related to the operation of the flight simulator with the Stewart platform at scale, please access the following links available at: https://

A total population of 40 pilots belonging to the aviation schools of the Armed Forces located in the city of Manta in Ecuador have been chosen to use, test and fly in the developed flight simulator. Of the 40 pilots, 15 correspond to the area of instructors and 25 correspond to the area of students of the aviation schools. After testing the constructed flight simulator, we proceeded to execute the statistical processing, for which we compared six basic characteristics of a flight simulator such as: (a) maneuverability capabilities; (b) motion detection (roll, pitch, yaw); (c) change of plane on the stage; (d) aerodynamic performance; (e) interaction with the virtual simulator; (f) control of the pilot board. These characteristics have

been compared with the Microsoft Flight Simulator commercial simulator,

Figure 10, documents the results obtained from a sample of 40 pilots, as indicated above. The reference point has been executed in such a way that a pilot has been tested only in the environment of the flight simulator, being saved of expressing any comment of the experience of testing the simulator with the companions of the aviation schools. Consequently, each evaluation performed by each instructor or apprentice pilot has been free of mutual influence, which leads that the collected data have been an adequate indicator of the perception of the pilots of the

In this version of the flight simulator, the lowest value in the characteristics of the simulator corresponds to the control of the pilot's board, since the design and development of three of the six basic flight instruments is almost complete: (a) altimeter; (b) airspeed indicator; (c) vertical speed indicator; (d) attitude indicator; (e) heading indicator; (f) turn indicator. Actually, the simulator is 90% ready and

Average scores of the characteristics of the selected reference points applied for the tests of the flight simulator

elevation (pitch), and angle of bank (roll).

DOI: http://dx.doi.org/10.5772/intechopen.86586

5. Experimental results and discussion

obtaining the results indicated in Figure 10.

flight simulator as a perceptive experience.

Figure 10.

pilots.

85

youtu.be/pyXP5FlyJYU, https://youtu.be/13d4mFDglmM.

Figure 7.

The Xtreme programming CPS iterations.

Figure 8. Graphical user interface of the flight simulator.

#### Figure 9.

Control front panel of the Stewart platform.

A New Real-Time Flight Simulator for Military Training Using Mechatronics and Cyber… DOI: http://dx.doi.org/10.5772/intechopen.86586

Figure 9 shows the control front panel of the Stewart platform, where the behavior of the input and output values of the control system developed in LabVIEW can be seen, which reproduces the movements of the flight simulator by integrating a network of two computers that use communication threads with sockets and flat text files, where the information of the three angles of maneuverability of the airplane are found, including: the direction (heading or yaw), elevation (pitch), and angle of bank (roll).

For a proof of concept related to the operation of the flight simulator with the Stewart platform at scale, please access the following links available at: https:// youtu.be/pyXP5FlyJYU, https://youtu.be/13d4mFDglmM.
