## 4 Airspeed Indicator or Velocimeter (A.S.I.) (Analog Instrument and Computer Simulation)  
The A.S.I. is the aircraft's velocimeter; nevertheless, speed calculations are a complex problem in terms of aircraft. The A.S.I. also uses the pitot tube and measures the ram air pressure; the indicated airspeed must be corrected for the air density to obtain a true airspeed value. The physical principle is that the airspeed surrounding the aircraft must equal the aircraft's speed moving across the air. Nevertheless, the air density decreases with the altitude and other factors that strongly influence its measurement, such as the wind and weather. Instruments that use barometric principles must be corrected to provide more accurate values. Thus, many concepts concerning aircraft speed have been developed, like the indicated airspeed (I.A.S.), real airspeed (R.A.S.), and true airspeed (T.A.S.). [4; 5; 6; 27; 28; 30; 36; 37; 38; 39; 40; 41; 42; 43].  
To maintain an appropriate airspeed, the A.S.I. is used by the pilots during all flight phases from take-off onward: when the aircraft is climbing or descending, when it is cruising, and when it is landing. Otherwise, each new position of the aircraft is calculated as a function of its instantaneous speed and the previous displacement during simulations.  
The A.S.I. indicates the T.A.S. in our computational simulation and is assumed to be the real aircraft speed; thus, T.A.S. = R.A.S. The rounded A.S.I. dial has 10 main divisions, 5 of which are numbered from 0 to 250 (km/h). The values providing information to the A.S.I. are taken from the aircraft's horizontal speed (v\({}_{\rm{AH}}\)t\({}^{\rm{t+A}}\)t) calculated at each step time (At) [4; 5; 6; 22; 27; 28; 30; 31; 43; 44; 45; 46; 47]. The minimum speed (v\({}_{\rm{AH}}\)t\({}^{\rm{t+A}}\)t = 0) is indicated at 210\({}^{\circ}\) from the left flat horizontal line, and the maximum speed is indicated at \(-\)30\({}^{\circ}\) from this reference line. The A.S.I. uses only one indicator, a needle represented by a line. The following assumptions are used to understand the information displayed:  
1. The velocimeter needle moves counterclockwise to indicate that the aircraft is accelerating.
2. The velocimeter needle remains stationary to indicate that the aircraft's speed is constant.
3. The velocimeter needle moves clockwise to indicate that the aircraft is decelerating.  
Equations (10)-(12) calculate the aircraft's speed at each step time during the simulation; then, Equation (13) calculates the angular position of the indicator. Figure 3a,b show the segmentation and movement zones of the indicators and the final representation on the computer screen, respectively.  
Figure 2: Vertical speed indicator: (**a**) segmentation of the dial and movement regions, and (**b**) instrument developed for the computer simulation.  
\[v_{AH}^{t+\Delta t}=v_{AH}^{n-1}+v_{AH}^{\Delta t} \tag{10}\] \[v_{AH}^{t+\Delta t}=v_{AH}^{n-1}+(v_{AH}^{n}-v_{AH}^{n-1})\] (11) \[v_{AH}^{t+\Delta t}=v_{AH}^{n-1}+(v_{AH}^{n}-v_{AH}^{n-1})\bigg{(} \frac{t_{n}}{ns}\bigg{)}\] (12) \[\alpha_{ASI}=210-v_{AH}^{t+\Delta t}\bigg{(}\frac{240^{*}}{250( km/hr)}\bigg{)} \tag{13}\]  
The pilot establishes the horizontal aircraft speed and heading angles. Thus, the aircraft's path can be calculated by solving Equations (14)-(16) to determine its displacement along the x-, y-, and z-axes as a function of the simulation time. These equations were solved in a previous work by the author and can be nested to provide an accurate representation without the need for any graphical animation [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48].  
\[d_{x}=(v_{x}^{n}-v_{x}^{n-1})(t^{n}-t^{n-1}) \tag{14}\]  
\[d_{y}=(v_{y}^{n}-v_{y}^{n-1})(t^{n}-t^{n-1}) \tag{15}\]  
\[d_{z}=(v_{z}^{n}-v_{z}^{n-1})(t^{n}-t^{n-1}) \tag{16}\]