# Star Type Wireless Sensor Network for Future Distributed Structural Health Monitoring Applications
## 4 Discussion  
As shown in a typical ringing up pattern of bell ten, which is the heaviest bell in Figure 9, the ringer only increases the angle through which the bell rotates by approximately 4.0\({}^{\circ}\) each time they pull the rope. The nearly linear increase with each pull suggested a very skilled bell ringer. At around 50 s, some data loss could be seen, which was due to the fact that no attempt was made to recover lost packets in the user datagram protocol (UDP). Linear interpolation could be used to recover the data. Similar curves were produced for all of the bells but omitted to avoid repetition. All the small oscillation period values from Table 6 agree within \(\pm\)0.7% of the measurements taken by [PERSON] and \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Bell**} & \(\begin{array}{c}\tau\text{[6]}\\ \text{(s)}\end{array}\) & \multirow{2}{*}{\(\tau\) (s)} & \multirow{2}{*}{**Difference (\%)**} \\ \hline
1 & 1.594 & 1.586 & -0.502 \\ \hline
2 & 1.600 & 1.611 & 0.687 \\ \hline
3 & 1.689 & 1.685 & -0.237 \\ \hline
4 & 1.756 & 1.744 & -0.683 \\ \hline
5 & 1.742 & 1.730 & -0.689 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison with small oscillation period measured in 1993 [6]. Figure 10: The angular rotation of bell ten and six at the beginning of the hand stroke where the ringer pulls upon the rope to displace the bell from its mouth-up position. [PERSON] in 1993 [6]. It is highly likely that the sensor network is more accurate than the methods used by [PERSON] and [PERSON] simply due to the elimination of human error. The sensor produced a data point every 10 ms, whereas the typical reaction time of a human to visual stimuli was 180-200 ms according to [38]. The more than one order of magnitude higher time resolution of the sensors guaranteed a better time accuracy. It can be seen in Figure 10 that the assumption the initial velocity imparted to the bell by the bell ringer is negligible is valid. The velocity at 360\({}^{\circ}\) is clearly negligible compared to the velocity at 310\({}^{\circ}\). These velocities were calculated in Section 3.3. Bell 6 can be seen to overtake bell 10 in terms of angular rotation at \(\sim\)295\({}^{\circ}\), which can be explained by its significantly smaller mass (1425 versus 563 kg). The assumption that the ringer provided negligible initial velocity was widely used in the literature as it greatly simplified the equations used to calculate the forces produced by a bell as a function of angular rotation. This assumption, however, has never been proven experimentally. Every data set collected during this work showed this assumption to be valid. It is therefore correct to assume that the initial angular velocity is negligible for the types of bells measured at Durham Cathedral and take \(p=1\) in Equations (1) and (2). It should be noted that although this assumption is valid for experimental data, the initial velocity should still be taken into account in theoretical studies to avoid timing issues where the angle of the bell in the simulation lags behind the real life angle. Further experimental studies that attempt to correlate N-S and E-W tower vibration with bell forces via angle measurements from each bell will not have to consider the initial velocity of the bell for each rotation. The assumption is only valid once the bell has been rung up to its mouth-up position, not during the ringing up of the bell though. The plot of the forces produced by bell ten in Figure 11 displays abrupt peaks indicating sudden and large increases in forces acting over a few 100s of ms. The plot displayed a rotation of the bell in one direction from 360\({}^{\circ}\) to 0\({}^{\circ}\) then a rotation in the other direction from 0\({}^{\circ}\) to 360\({}^{\circ}\). The vertical forces reached a sharp maximum when the bell was at 180\({}^{\circ}\) (in its mouth-down position), the horizontal forces were momentarily zero as the bell passed through 180\({}^{\circ}\) but had sharp excursions on either side of 180\({}^{\circ}\).