## 7 International Standard Atmosphere  
The International Standard Atmosphere (I.S.A.) is an atmospheric model of ways in which the pressure, temperature, density, and viscosity of the Earth's atmosphere change over a wide range of altitudes and terrain elevations [4; 11; 25; 26; 27; 43; 44; 45; 46; 47; 48; 49]. It was established to provide a common reference for temperature and pressure and consists of tables with values at various altitudes, including the formulas through which those values were derived [11; 25; 26; 27]. The International Organization for Standardization (ISO) publishes the I.S.A. as an international standard, ISO 2533:1975 [25; 26; 27; 28]. Other standards organizations, such as the International Civil Aviation Organization (ICAO) and the United States Government, publish extensions or subsets of the same atmospheric model under their own standards-making authorities [11; 25; 26; 27]. The I.S.A. model divides the atmosphere into layers with linear temperature distributions [26; 27; 28]. The other values are computed from basic physical constants and relationships. Figure 5: Fuel indicator: (**a**) segmentation of the dial and movement regions, and (**b**) instrument developed for the computer simulation. For example, at sea level, the standard provides a pressure of 1013.25 hPa (1 atm), a temperature of 15 \({}^{\circ}\)C, and an initial lapse rate of \(-6.5\) \({}^{\circ}\)C/km (roughly \(-2\) \({}^{\circ}\)C/1000 ft). The tabulation continues to 11 km, where the pressure falls to 226.32 hPa and the temperature to \(-56.5\) \({}^{\circ}\)C. Between 11 km and 20 km, the temperature remains almost constant [11; 25; 26; 27]. All the instruments developed in this work are calibrated with the assumption that they are operating at sea level in the international standard atmosphere, where the air density is 1.225 kg/m\({}^{3}\). Finally, as noted, the altitude values depend on the atmospheric pressure and temperature in relation to real flight instruments. Thus, we decided to incorporate these temperature values according to the I.S.A. rules. The equations are established according to the aircraft flight altitude using conditional sentences: for an aircraft flying under 11 km, Equations (24) and (25) are used; for an aircraft flying above 11 km, \(-56.5\) \({}^{\circ}\)C and 226.32 hPa are assumed. These equations are included in the same calculation process; thus, these are also solved simultaneously during the simulation, and bar graphics are used to display the temperature and pressure values. \[T_{l}^{t+\Delta t}=15-6.5*d_{z}^{t+\Delta t} \tag{24}\]  
\[P^{t+\Delta t}=101.33-(1-0.00022585)^{5.26} \tag{25}\]  
Figure 6a shows the algorithm for calculating the aircraft's speed components along the x- and y-axes as a function of the horizontal aircraft speed and the heading angle. The horizontal speed, total aircraft speed, and displacement are calculated as a function of this algorithm, including the climbing angle (\(\beta\)), as described in Figure 6b. The instantaneous speed and displacement can also be calculated as a function of the aircraft speed using Equations (26)-(28) and by solving Equations (29)-(31) for the x-, y-, and z-axes, respectively. Finally, Equation (32) determines the total displacement. The Runge-Kutta iterative numerical method solves the ordinary derivative equations, and the approach can be improved in this way by increasing the step number (ns). The information obtained at the end of this calculation procedure is used to create a dynamic animation of the instrument indicators. The animation draws the indicators, which remain on the screen for a short time, and then erases them to repeat the process for the next simulation (t + \(\Delta\)t). The animation can be shorter or longer as a function of the step used for the calculation. The time the indicators remain on the screen can be between 0.05 and 0.20 s, which is considered appropriate for good visualization.