## 5 Simulation Results and Discussion  
The energy performance of the protocol is analyzed in terms of two magnitudes: average and total energy consumption by nodes. The algorithms and protocols described in Section 4 have been developed in MATLAB(r). For the simulations, a variable number of nodes, up to 600, have been quasi-randomly located in the scenario, which is a cubic region of side 10 km. Here, quasi means that there is the restriction of a minimum distance between nodes; they that cannot be within 1 km of each other to avoid undesired overlaps. The speed of sound could be calculated with Equation (4). In the simulations, the used value is 1500 m/s. Several transmission ranges have been considered, from 1 km to 8 km. Ten (10) cases were simulated for each value of the transmission range. The detailed summary of parameters used is given in Table 5.  
MATLAB(r) was chosen to implement the protocol. Three average figures vs. transmission range were calculated: average energy consumed per node and per packet (energy/node/packet), average number of hops, and average total energy. First, the impact of the transmission range on the average number of hops has been analyzed. The results are shown in Figures 6-10. It can be observed that average number of hops decreases with increasing transmission range. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Simulation Parameters** & **Value** & **Unit** \\ \hline Speed of sound & 1500 & m/s \\ Data rate & 5000 & bit/s \\ Frequency & 48 & kHz \\ Packet length & 256 & bit \\ Header length & 30 & bit \\ Transmission power & 18 & W \\ Number of nodes & 100 to 600 & - \\ Simulation length & 10 & - \\ Minimum distance & 1 & km \\ Transmission range & 2 to 8 & km \\ \hline \hline \end{tabular}
\end{table} 
Table 5: MATLAB® simulation parameters. Figure 8: Average number of hops for 250 nodes. Figure 6: Average number of hops for 100 nodes. Figure 7: Average number of hops for 175 nodes. As mentioned at the end of the previous section concerning the law of transmission power proportional to the square of the distance, the multi-hop scheme could be more efficient. In addition, and not least, the end-to-end delay increases with the number of hops. For these two reasons, a path with fewer jumps is preferred. Simulations were also carried out to analyze the influence of the transmission range on the energy/node/packet and the average number of hops. When there are fewer nodes in the scenario, the transmission range must be longer, and the opposite. The transmission ranges considered for the different number of nodes are shown in Table 6. The simulation results of the average number of hops vs. transmission range are shown in Figures 6-10. Figures 11-14 show that the energy/node/packet increases with the transmission range, as described above. It can also be observed that the energy decreases with the node density. For instance, with a transmission range of 4 km, the energy/node/packet is 1.9 J with 100 nodes and goes down to 0.71 J with 400 nodes. \begin{table}
\begin{tabular}{c c} \hline \hline
**Number of Nodes** & **Transmission Range (km)** \\ \hline
100 & 4, 5, 6, 7 \\
175 & 3.5, 4.5, 5.5 \\
250 & 3, 4, 5 \\
325 & 2.5, 3.5, 4.5 \\
400 & 2, 3, 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Transmission ranges and number of nodes. Figure 10: Average number of hops for 400 nodes. Figure 9: Average number of hops for 325 nodes. Figure 11: Energy/node/packet for 100 nodes. Figure 12: Energy/node/packet for 200 nodes. Figure 13: Energy/node/packet for 300 nodes. Figure 16 shows the energy/node/packet used vs. the number of nodes, with transmission range as parameter. There is not a clear trend of average consumption vs. number of nodes, but it clearly increases with the transmission range. A good observation from Figure 16 is that, in terms of energy consumption, the network is scalable and stable, that is, the energy used does not show abrupt increments with the network size. Figure 16: Energy/node/packet used vs. number of nodes for different transmission ranges.