## 4 Conclusions  
A semi-empirical method proposed by [PERSON] for predicting rocket jet noise was described and applied to the low-thrust hybrid rocket engine (paraffin-oxygen based) developed as part of the Italian Aerospace Research Centre's HYPROB project. Such an approach utilizes empirical curves, derived from a series of measurements carried out during the Apollo era, to distribute the overall acoustic power along the plume axis into multiple acoustic monopoles, and then uses the acoustic propagation theory to predict the radiated sound levels as a function of frequency, distance, and direction from the plume. Since the method is based on past experimental data, good results are generally obtained for nozzle design, exhaust flow characteristics, and thrusts typical of high-thrust liquid/solid rocket engines. Therefore, the experimental data gathered during a firing test campaign, conducted by CIRA, were valuable to asses the potential of extending current empirical methods to rocket engine concepts significantly different from existing configurations, i.e., low-thrust hybrid rocket engines. The experimental activity was carried out at the military outdoor firing range located at the Grazzanise Air Force Base. Acoustic data were recorded with a \(1/2\)\" free-field prepolarized condenser microphone, while data acquisition was handled with a sound level integrator and analyzer (sampling rate 51.2 kHz per channel). Specifically, the acoustic sensor was deployed 22 m from the nozzle exit and at an angle of 35\({}^{\circ}\) to the plume exhaust axis. The experimental sound pressure level was computed performing a Fourier transform of the 5-s jet noise signal and adjusted to account for the effect of large reflective surfaces, such as the concrete ground parallel to the engine under test. In this scenario (i.e., the presence of reflective surfaces), according to [PERSON]'s work, it is reasonable to expect an increase in sound field levels of 3-6 dB. Therefore, in order to exclude the energy component due to the reflection phenomenon, an expected experimental sound pressure level range (original SPL-3 dB and original SPL-6 dB) was established. The presence of 3 dB range prevented a fully accurate acoustic characterization of the HRE under investigation; nevertheless, it was possible to determine that its acoustic efficiency (between 0.5 and 1%) falls within the common range for conventional rocket engines (between 0.2 and 1%). Moreover, since a generic hybrid propulsion system has roughly  
Figure 14: Acoustic field estimated on an area 70 \(\times\) 100 m (1% of acoustic efficiency). The engine is located at the origin of the axes (0,0), while the plume is oriented along the positive x-coordinate. (**a**) Un-weighted OASPL. (**b**) A-weighted OASPL. similar features compared to the one analyzed here, these results are reasonably quite general. In summary, the powerful features of the [PERSON] model (prediction of noise levels in nearby regions, or simple estimation of acoustic loads on the rocket or launch pad) appear to be applicable to low-thrust hybrid rocket engines as well. Besides the main activity, a simple study on resonant cavity modes was undertaken to explain some of the anomalies observed in the measured jet noise spectrum (unexpected spike). The size of the combustion and post-combustion chambers has been identified as the cause of longitudinal modes coupling. In particular, this phenomenon can manifest itself as an increase in the acoustic efficiency for some frequencies of the spectrum. These types of couplings can also induce large amplitude structural vibrations, with consequent detrimental effects on both engine operation and durability; therefore, identifying the occurrence of such phenomena and reducing or eliminating them is a critical step in rocket engine design. Acoustic analysis also revealed that certain modes couplings in the hybrid engine are unusual for conventional liquid rocket engines.