## 3 Experimental Activity and Results
### Eldred Model Results
On the other hand, considering the case of fully coherent and in-phase signals (OASPL-6 dB) compared to [PERSON]'s prediction assuming an acoustic efficiency of 0.5% (lower limit), the same previous trend in the sound pressure spectrum curves is observed (all curves are simply shifted by 3 dB). In fact, the difference from the previous comparison is a factor of 0.5 in Equation (2). This results in \(-3\) dB of the overall sound power level (\(20 log_{10}[1/2]\)). Therefore, as shown in Table 4, the lower limit case outcomes can be obtained by merely subtracting 3 dB from the already calculated OASPLs. This also means that the results for the \(\Delta\)OASPLs do not change from the previous case. In summary, assuming an acoustic efficiency ranging from 0.5% to 1%, [PERSON]'s prediction recovers the expected experimental SPL in both limit cases. Specifically, due to the unknown amount of reflected energy, the above comparisons do not allow for a fully accurate acoustic characterization of the HRE under investigation; nevertheless, it can be stated that the value of its acoustic efficiency falls within the common range for conventional rocket engines, namely 0.2-1% [11]. These results are quite general, as a generic hybrid propulsion system has roughly similar features compared to the one analyzed here, so it is reasonable to assume that even other low-thrust hybrid rocket engines convert less than 1% of their mechanical power into acoustic energy. Furthermore, it should be emphasized that [PERSON]'s technique cannot account for the SPL peaks due to the coupled modes of cavities resonance. Nevertheless, even without implementing corrections, the predicted OASPL is in agreement with the experimentally measured (within 4 dB [11]). The model consistency can thus be exploited to support the goodness of noise level estimation for nearby regions. For example, to assess the noise impact on local communities as a function of sound power distribution along the jet, or simply to estimate the noise load on the rocket or launch pad. To illustrate this possibility, OASPLs were calculated for an area of 70 \(\times\) 100 m (Figure 14): \begin{table}
\begin{tabular}{c c c c} \hline
**Frequency** & **Predicted OASPL** & **Experimental** & \\
**Weighting** & **(dB)** & **OASPL (dB)** & **\(\Delta\)OASPL (dB)** \\ \hline Un-weighted & 121.35 & 123.55 & 2.20 \\ A-weighted & 121.39 & 124.07 & 2.68 \\ \hline \end{tabular}
\end{table} 
Table 4: Assumption of coherent signals (OASPL-6 dB) compared to the prediction considering 0.5% of the acoustic efficiency. \begin{table}
\begin{tabular}{c c c c} \hline
**Frequency** & **Predicted OASPL** & **Experimental** & \\
**Weighting** & **(dB)** & **OASPL (dB)** & **\(\Delta\)OASPL (dB)** \\ \hline Un-weighted & 124.35 & 126.55 & 2.20 \\ A-weighted & 124.39 & 127.07 & 2.68 \\ \hline \end{tabular}
\end{table} 
Table 3: Assumption of incoherent signals (OASPL-3 dB) compared to the prediction considering 1% of the acoustic efficiency. As presented in the previous section, [PERSON] method [11] involves the use of empirically determined frequency-dependent directivity indices for a standard chemical rocket engine. Therefore, the simulated directional characteristics of the noise produced by low-thrust HREs exhibit a critical zone along a line inclined approximately 45\({}^{\circ}\) from the jet plume, as for conventional propulsion systems. Although these are probably the most appropriate values to use even for HRE, their accuracy is generally questionable.