## 4 Results and Discussion  
Blockchain-based airspace allocation methodology was tested and validated by relying on our UAS-S4 trajectory database that was generated using a flight dynamics model and its corresponding controller [57]. The UAS-S4 is shown in Figure 8, and Table 1 lists its specifications. We applied our approach within an aerial region, conducting tests with both 100 and 1000 UAS-S4 under the control of an adaptive fuzzy control algorithm [58]. For experimental studies, we took into account a cubic flight area of \(\mathrm{x}=16\;\mathrm{km},\mathrm{y}=16\;\mathrm{km}\), and \(\mathrm{z}=6\;\mathrm{km}\). The UAS-S4s were arranged with predetermined latitudinal and longitudinal coordinates, \begin{table}
\begin{tabular}{c c} \hline \hline
**Specification** & **Value** \\ \hline Wing area & 2.3 m\({}^{2}\) \\ Wingspan & 4.2 m \\ Mean aerodynamic chord & 0.57 m \\ Total length & 2.5 m \\ Maximum take-off weight & 80 kg \\ Empty weight & 50 kg \\ Loitering airspeed & 35 knots \\ Maximum speed & 135 knots \\ Operational range & 120 km \\ Service ceiling & 15,000 ft \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The UAS-S4 geometrical and flight data specifications. Figure 8: Hydra Technologies UAS-S4 Ehccatl [44]. altitudes, and heading angles. The forthcoming paths of the UAS-S4s were then predicted by an autoencoder [43] while the smart contract was validating the allocated airspaces. The utilized validators were following the PoW and PoS consensus strategy. Table 2 provides a comparison of the performance of both algorithms concerning validation time and error rate. As shown in Table 2, consensus algorithms, including Proof of Stake (PoS) and Proof of Work (PoW), are considered. We examined airspace areas with 100 and 1000 UAS-S4. We partitioned each airspace into 4 and 16 shards. Based on the findings presented in Table 2, one can deduce that PoW demonstrated greater accuracy compared to PoS, given its lower error rate with an equivalent number of UAS-S4s. However, PoW exhibited longer validation times compared to PoS. Table 2 illustrates that within a flight region partitioned into four districts and hosting 100 UASs, the error rates were 13.1% for PoS and 7.7% for PoW, while their validation times were 11 ms and 21 ms, respectively. Additionally, it is worth mentioning that an increased quantity of UASs within a flight zone results in higher error rates and longer validation times for a particular consensus mechanism, irrespective of the shard count. For instance, by using the PoS consensus algorithm (considering 16 shards), raising the UAS count from 100 to 1000 leads to a 4.3% increase in the error rate (from 12.6% to 16.9%) and a 93 ms extended validation time (from 8 ms to 101 ms). On the contrary, increasing the shard count (from 4 to 16) and using either PoW or PoS while keeping the UAS quantity constant enhances the algorithm's performance, resulting in decreased error rates and shorter validation times. For example, when employing PoW in a flight area with 1000 UASs, the expansion of shard count from 4 to 16 led to a 0.5% decrease in the error rate (reducing it from 9.3% to 8.8%) and shortened the validation time by 55 ms (from 420 ms to 365 ms). The maximum acceptable error rate was considered 20%. Larger error rates require a reduction in the number of UAS-S4 in districts or an increase in the number of shards. While PoS outperformed PoW in terms of validation time, their performances in terms of error rates need to be evaluated. With this aim, the probability analysis of conflicts between UASs has been carried out, where the lower probability of conflict means the lower error rate of a consensus protocol. Incorporating Gaussian distribution probability functions into the geometrical approach of conflict probability estimation offers a nuanced method to predict UAV conflicts while accounting for uncertainties in UAV positions and velocities.