1. In fact, for SRMs designed to operate in atmosphere, i.e. first stages or boosters, the nozzle erosion has not a strong impact on the SRM performance, since they are designed with high operative pressures, but also with high nozzle throat areas, in order to have high thrust. Therefore, the high throat area, for the same nozzle throat erosion rate and combustion time, implies a small percentage increment of the nozzle throat area during the firing (within 5-20 % of its initial value) and, hence, a small variation in the nozzle throat expansion ratio. In every case, for SRMs operating in the atmosphere, the major constraint to high performance is represented by the limitation on the thrust coefficient, due to the atmospheric pressure. Therefore, the effects of the nozzle erosion does not represent a strong limitation in motor performance.
2. For SRMs/stages operating in vacuum, instead, the scenario is completely different and the limitation on the performance due to nozzle throat erosion becomes significant. In fact, upper stage SRMs have smaller sizes of the nozzle with respect to the first stages ones, since they need to have smaller thrusts. Hence, for erosion rates and combustion times similar to the first stages, they are prone to relevant nozzle throat area increase during time, even greater than 50-60 %, which implies a strong reduction of the nozzle expansion ratio during the firing. In turn, this reduction of the expansion ratio brings to high losses in the delivered specific impulse, because of a strong reduction in the thrust coefficient, which is the main responsible for the high specific impulse realized by upper SRM stages with respect to lower stages (the characteristic velocity is, instead, limited by the propellant formulation and the maximum operative pressures typical for SRMs). A simple assessment of the losses in the SRM specific impulse, for variation of the stage design and typical design parameters of SRMs is presented in Ref. 1.
3. The reference cases are three upper stage SRMs designed tentatively with some reference to the second and third VEGA solid stages, Zefiro 23 (Z23) and Zefiro 9A (Z9A), and the technological demonstrator for the VEGA Evolution Program presented by AVIO in Ref. 2, Zefiro 40 (Z40), candidate for the evolution of the VEGA second stage Zefiro 23. The SRMs share the same finocyl configuration, the same propellant formulation HTPB 1912 (19 % aluminum - 12 % HTPB), the same design characteristics and technologies, but have different sizes and performance2-4, due to their different mission profiles.
4. In facts, this study represents the finalization of the work presented in Ref. 7 by the same authors, in which a first analysis of the effect of different kind of propellant formulations was presented for Z9A. The main outcome of the analysis performed in Ref. 7, here briefly recalled, is that a strong reduction of the nozzle throat erosion can be obtained in two ways: by moving the ratio between binder and ammonium perchlorate (e.g. HTPB 1517) with a reduction of the aluminum in the compound, or by increasing the aluminum loading (e.g. HTPB 2012 - HTPB 2112) of the propellant composition. The first one allows a larger reduction of the nozzle throat erosion in comparison to the latter, principally due to the lower presence of the oxidizing species in the resultant combustion products, which chemically attack the carbon-carbon insert of the throat. Notwithstanding, the different approaches bring about different impacts on the SRM performance. In fact, the beneficial effect of nozzle throat erosion reduction for HTPB 1517 propellants is completely out-matched by the reduction of the thrust coefficient due to a higher specific heat ratio of the combustion products. Hence, for such family of propellants, a lower performance of the SRM is obtained with respect to the baseline. By the other side, the propellants with higher content of aluminum in the compound present two superposed beneficial effects on SRM performance: a reduced nozzle throat erosion and a higher thrust coefficient due to a lower specific heat ratio of the combustion products.