Combustion Instability in Gas Rockets

Abstract

T HE objective of the comment by R. H. Smith seems to point out that the controllability limits as given by Refs. 1 and 2 disagree widely because of the difference of practice, and that predictions of the limits of manual control made by Ref. 1 are not capable of yielding the limits of Ref. 2. It is noted at the beginning that we shall confine subsequent discussions to second-order controlled elements with positive static stability, namely, with positive stiffness, unless otherwise stated.Replying to the first part of the comment, we agree that practice is an essential factor for explaining the discrepancy, although it should be remembered that no system input is present in the experiment of Ref. 1, whereas random inputs are present in that of Ref. 2. As mentioned in Ref. 1, we conducted experiments for obtaining the difference between the controllability limits at one trial and at three trials and concluded that the results indicated, evidently, the effect of practicing.The controllability limit of a human operator may depend on many factors such as practice, his naivete, or experience as an airplane pilot, and so forth. Consequently, it is considered indispensable when presenting data on the controllability limit to prescribe conditions fully under which experiments have been conducted. We believe that our data show a controllability limit under the prescribed test program of Ref. 1, namely, a controllability limit at one trial and at three trials. We note that our data agree very well with those obtained by NASA in Ref. 3.On the other hand, we find in Ref. 2 that the two controllability limits, the establishment of which required nearly 900 trial runs, show clearly the effect of heavy practice. This is a controllability limit established by Smith. It seems probable that a more sophisticated technique would further improve the controllability limit established by him. We note here that unpublished data obtained recently at National Aerospace Laboratory of Japan also show that the controllability limit can be improved by heavy practice far beyond that of Ref. 1.In replying to the second part of the comment, we agree that a transfer function, which is more complicated than Eq.(3) of Ref. 1 must be employed in predicting the limits of Ref. 2. The purpose of writing Ref. 1 was this: we assumed that the transfer function of a human pilot was given by Eq.(3) and that the pilot could conduct a self-adaptive control. Then, we made a speculation to find how our prediction could correlate with our experimental data. During the prediction, we were satisfied with obtaining a rough idea of the controllability limit by taking T L = °°, although it was possible to take an assigned value for T L . We believe that Eq. (3) is an appropriate transfer function of a human pilot who is trying to find a controllability limit on a "first-encounter basis.' 7 A brief mention is made here on an operator's behavior under heavy practice. Since there exists a periodicity in transient response of the controlled element with positive static s...