## 7 Analysis of Flights Simulated  
A validation for 3 flights was performed, analyzing the errors as a function of the step time (\(\Delta t\)) used. The information for the simulated flights is shown in the Table 1; here, some values were included to assess the rolling movement in the attitude indicator and some displays of the fight simulator were snapped from the computer screen [24; 25; 26; 27; 28; 29; 34; 35; 36; 37; 38; 39]. Figure 10a-c show the instruments' behavior in a virtual panel for flight 1. Figures 11 and 12 show the speed and displacement curves along every axis for the simulated flights. Aircraft instantaneous acceleration is calculated using Equations (11) to (13) as a function of horizontal aircraft speed [47]. These equations can be nested in computational loops in order to be solved at every step time (\(t+\Delta t\)). This is performed by obtaining dividing the manoeuvre time between the number of steps undergoing analysis (np). \[a_{x}=\frac{(v_{x}^{n}-v_{x}^{n-1})}{(t^{n}-t^{n-1})} \tag{11}\]  
\[a_{y}=\frac{(v_{y}^{n}-v_{y}^{n-1})}{(t^{n}-t^{n-1})} \tag{12}\]  
\[a_{z}=\frac{(v_{z}^{n}-v_{z}^{n-1})}{(t^{n}-t^{n-1})} \tag{13}\]  
Then, the aircraft instantaneous displacement is calculated using Equations (14) to (16) inside the same nested loops and the step time (\(\Delta t\)) is calculated as a function of the step defined, according with the Equation (17), and Equation (18) is used to calculate the aircraft displacement, considering the original position of the aircraft. \[x=(v_{x}^{n}-v_{x}^{n-1})(t^{n}-t^{n-1}) \tag{14}\]  
\[y=(v_{y}^{n}-v_{y}^{n-1})(t^{n}-t^{n-1}) \tag{15}\]  
\[z=(v_{z}^{n}-v_{z}^{n-1})(t^{n}-t^{n-1}) \tag{16}\]  
\[\Delta t=\left(\frac{t_{manuvre}}{steps}\right)=\left(tp/np\right) \tag{17}\]  
\[d^{n}=\sqrt{\left(x^{n}-x^{n-1}\right)^{2}+\left(y^{n}-y^{n-1}\right)^{2}+ \left(z^{n}-z^{n-1}\right)^{2}} \tag{18}\]  
Then, the aircraft longest displacements are used to fit the flight at an appropriate scale onto the computer screen (\(\text{D}_{\text{x\, scale}}\), \(\text{D}_{\text{y\, scale}}\), \(\text{D}_{\text{z\, scale}}\)); these can be obtained from Equations (19) to (21). \[\text{D}_{\text{X\, scale}}=\text{d}_{\text{x\, max}}-\text{d}_{\text{X\, min}} \tag{19}\]  
\[\text{D}_{\text{y\, scale}}=\text{d}_{\text{y\, max}}-\text{d}_{\text{Y\, min}} \tag{20}\]  
\[a_{y}=\frac{(v_{y}^{n}-v_{y}^{n-1})}{(t^{n}-t^{n-1})} \tag{12}\]0  
Figure 10a-c show the aircraft instruments' cockpit. In the left side, there are 3 instrument dials for the measurement of the fuel reserve as a function of consumption. These are just below the RPM indicator and the speed indicator velocimeter, which is measured as a function of the true air speed using the information input; then at the bottom, a pair of bar indicators is shown; here, the values of temperature and pressure are shown; these values are calculated as a function of the aircraft vertical speed and compared with those of International Standard Atmosphere [27; 28; 29; 47]. On the right side, the following instruments and measurements are shown: an altimeter, vertical air speed, a turn-and-slip indicator, a magnetic compass, an attitude indicator, and a Machmeter. Figure 10a shows all indicators at the beginning of the simulation when stationary conditions were assumed. Then, it is possible to appreciate the following facts:Every indicator has a particular movement and moves according to the data input, as is shown in Figure 10b,\(c\). Both figures show a light level of fuel consumption after some minutes of flight; the RPM and velocimeter have measurements; and the altimeter shows an altitude because of a positive vertical air speed. There are slips and turns according to the data input. The aircraft flight direction, as a function of the heading angle and the attitude indicator, shows ground movement as a function of the rolling movement condition [8; 9; 10; 11; 12; 26; 39; 40; 41; 42; 43].