Stability Criteria of Rocket Motor

When a propellant burns in a rocket motor as shown in Fig. 9-4, the mass generation rate in the chamber, mg, is given by 

One assumes that Vc and Tc are constant, and the burning rate is expressed by Eq. (3.68) during a pressure transient in a rocket motor. Eq. (9.4) is represented by141 

Substituting Eq. (3.68) into Eq. (9.7), one gets the chamber pressure under steady state conditions as 

As shown in Fig. 9-5, the chamber pressure is given as a crossover point ritg and md in a pressure versus mg or md plot. It is evident that stable combustion occurs only under the condition of 

The characteristic time in combustion chamber xc is defined, based on Eq. (9.6), as 

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