## 2 Materials and Methods
### Tactile Coding Parameters  
A fundamental factor that may affect effectiveness of vibrotactile displays is how this altitude information is encoded [3]. In the this section, several coding parameters that can be used to cue flight attitude are discussed. Figure 1: Vibrotactile actuator. Figure 2: The arrangement of distribution of tactors around the torso and prototype of hlthe designed vibrotactile vest. In frontal of body, five tactors are located on the lower abdomen, upper abdomen, slightly below the chest, middle of chest and below of the clavicle respectively. In back of body, five tactors are located on the hip above, central spine, right shoulder, left shoulder, and cervical spine respectively. In the left or right side of body, five tactors, from down to up, are located on hipbone above, rib, oxter, chest and shoulder respectively. Flight attitude of an aircraft can be divided into four basic states: pitch-down state, pitch-up state, roll-left state and roll-right state. The angle in each state ranges from 0 to 90 degree. The schematic diagram of vibrotactile system, the method of vibrotactile displaying of different flight states, and the graphical definition of flight attitude are illustrated in Figure 3.  
As seen in Figure 3b, the angle of pitch (\(\theta\)) and roll (\(\varphi\)) were be defined as an included angle between the earth-surface inertial reference frame (\(O\), \(x_{g}\), \(y_{g}\), \(z_{g}\)) and aircraft-body coordinate frame (\(O\), \(x_{b}\), \(y_{b}\), \(z_{b}\)). As illustrated in Figure 3b, the state information of aircraft were cued by the vibration on corresponding column or combination of two columns of factors. In order to embody the S-R (stimulus-response) compatibility of space [29], the frontal, back, left and right column of factors were employed to cue angle in pitch-up, pitch-down, roll-left and roll-right state, respectively. When both pitch and roll angles need to be cued, the corresponding columns of factors will simultaneously be activated to vibrate. As illustrated in Table 1, the angle in each flight state was divided into four flight statuses: normal flight ranged in [5; 50] with five degrees apart, acrobatic flight ranged in [50; 90] with 10 degrees apart, fine flight ranged in [0, 5), and emergency \(\geq\)90 degree. In order to distinguish the steady flight from the fault of vibrotactile system, attitude in steady flight was encoded by the tactor placed at the bottom of the corresponding column. Since the aircraft is in steady flight status in most of time, this tactor was controlled to vibrate with weak intensity and short duration considering energy efficiency. An angle of more tha \begin{table}
\begin{tabular}{c c c} \hline \hline
**Group** & **Ranges of Angle (Degree)** & **Flight Status** \\ \hline  & \(\geq\)90 & Emergency \\
5 & [70; 80][80; 90] & Acrobatic flight \\
4 & [50; 60][60; 70] & \\
3 & [35; 40][40; 45][45; 50] & \\
2 & [20; 25][25; 30][30; 35] & Normal flight \\
1 & [05; 10][10; 15][15; 20] & \\  & [0, 5] & Steady flight \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Division of angle range in each flight state. Figure 3: Overview of vibrotactile system for cueing flight attitude. (**a**) System block diagram of vibrotactile TSAS and Tactor arrangement around the torso of pilot. The controller receive flight attitude information from the geomagnetic sensor and activate vibrotactile test to vibrate in the pattern corresponding to the attitude; (**b**) Schematic diagram of encoding flight states for different tactor columns; (**c**) Definition of Flight attitude information of aircraft. simultaneous vibration of all tactors in corresponding column. Thus, the range of angle needed to encode in each flight state is [5; 90] with 14 angle intervals.