## 2 Materials and Methods
### Tactile Coding Parameters
The parameters that can be used to encode angle and flight state include spatial location, intensity, rhythm and mode of vibration, which can be classified into two categories according to the number of vibrating tactors as illustrated in Table 2.  
Spatial characteristics of a vibrotactile sensation is determined by the location of vibration stimulus on a vibrotactile display [30]. Of the four coding parameters shown in Table 2, the parameter of location is therefore mandatory to encode attitude information. However, it is not enough to encode 56 (14 \(\times\) 4) angle intervals with 20 tactors only using parameter of location. Thus, there are other parameters in Table 2. They should be selected to combine with location for cueing all the angle intervals. There are about three identifiable levels for intensity of vibration on torso according to the results according to our previous psychophysical test for actuators [31]. Thus, the identifiable levels of intensity can be used to cue angle information more precisely. For instance, the weak, middle and strong vibration intensity of a tactor can be employed to indicate the three different angle intervals of a group in Table 1. However, the coding capacity of cueing information with intensity is limited, since there are only three tactor amplitude intensities that can be easily identified [32]. The rhythm of vibration is a time-domain parameter that can also be used to improve the precision of cueing angle. As is similar with the parameter of intensity, different times or duration lengths of vibration can be used to cue different angle intervals in a group. Activating multiple tactors in vibration modes is another useful coding strategy. The three main parameters that control the feeling of different vibration modes are the duration of stimulus (DOS), stimulus onset asynchrony (SOA) and the inter-stimulus interval (ISI) [33]. By adjusting the parameter of DOS and ISI, we can make multiple tactors to be perceived as different vibrating modes as illustrated in Figure 4. The simultaneous vibration is also called tactile funnelling illusion: when two tactors vibrate simultaneously on skin, the perceived vibration of a virtual tactor located between the tactors will be felt [34]. The continuous vibration is also called \"vibrotactile apparent movement\": When activating two or more tactors sequentially with a certain timing, the stimulation point is perceived as if it is moving continuously from one location to another, although the real stimulating sites are discrete [35]. Discrete motion will be perceived when the adjacent tactors are activated sequentially with an inter-stimulus interval (ISI). From what is described above, the flight attitude can be displayed using coding methods with combination of two parameters or three parameters in Table 2. Therefore, two psychophysical experiments were designed to investigate the preferred combination of two and three parameters respectively. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters for Single Tactor** & Vibrating location (P), Intensity (I), Rhythm (R) \\ \hline
**Parameters for Multiple Tactors** & Vibrating mode (M) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coding parameters for tactors. Figure 4: Schematic diagram of tactile apparent motion.