Maximum thrust coefficient

When the nozzle expansion ratio becomes infinity, the pressure ratio pjpa also becomes infinity. The maximum thrust coefficient Cp then becomes... 

If the effect of mixture ratio upon the characteristic velocity and thrust coefficient is examined, additional information is gained over that obtained from consideration of the specific impulse alone. Since the characteristic velocity bears the same dependence upon combustion temperature and molecular weight as does the specific impulse, the optimum characteristic velocity and optimum specific impulse would be expected and are observed to occur at approximately the same mixture ratio, see figure V. A. 6. The failure of these two performance parameters, c andcF. to have maximum values at the same propellant mixture ratio is traceable to their differing dependencies upon the specific heat ratio. The same effect is reflected in the dependency of the thrust coefficient upon the mixture ratio. For optimum expansion and a fixed pressure ratio across the nozzle, the thrust coefficient depends only upon the specific heat ratio. The dependence of the specific heat upon the mixture ratio in turn results in a dependence of the thrust coefficient upon the mixture ratio. Since thrust coefficient increases with decreasing specific heat ratio for a fixed pressure ratio, the maximum thrust coefficient should occur at the mixture ratio of maximum specific heat. The specific heat of the products increases both with temperature and with complexity of the product species. The maximum specific heat is found near the stoichiometric mixture ratio. For equilibrium expansion the specific heat also includes the effect of exothermic recombinations. This later effect is a maximum at the condition of maximum dissociation in the chamber which similarly occurs at the maximum combustion temperature or near the stoichiometric mixture ratio. 

The observations that the thrust coefficient has its maximum value near the stoichiometric mixture ratio, see figure V. A. 6.,is consistent with the foregoing expectations. Since specific impulse is proportional to the product of the characteristic velocity and the thrust coefficient, it is expected and observed that the optimum mixture ratio in terms of the specific impulse should fall between the optimum mixture ratios for the characteristic velocity and for the thrust coefficient. It is noted that the characteristic velocity is the dominant member of the pair, a property which adds further to the utility of the characteristic velocity as a performance parameter to rocket propulsion development. 

---