Viewing page 155 of 212

This transcription has been completed. Contact us with corrections.

57.

narrow, and compact, as possible, the assumption of a cross-section of one square inch for an apparatus weighing one pound will not be unreasonable. A glance at Tables V and VI will show that, for "effective velocities" of 7^[[,]]000 ft/sec. and 3^[[,]]500 ft/sec., the mass at the beginning of any interval (except [[underlined]] s [[/underlined]] [[subscript]] 9 [[/subscript]]) does not greatly exceed one pound –- the mass at the end of each interval being one pound –- so that the computations are in agreement with this assumption of area of cross-section. For the two cases of the adapted Coston rockets, the masses at the beginning of the intervals are much larger; and hence we see that the "total initial masses" in Table VII, large as they are, what have been even larger if a proper value of cross-section had been employed.

The important point is, however, that cross-sectional areas of [[underline]] even less than one square inch should have been used [[/underline]]. The reason for this is obvious when one remembers that in calculating the "total initial masses", when we multiply minimum masses, [[underline]] M [[/underline]], together we are also multiplying the cross-sections in the same ratio. In other words, we are considering numbers of rockets, each of one square inch cross-section, grouped together side by side, into a bundle. But such an arrangement would have its cross-section proportional to its [[underline]] mass [[/underline]] and not to the [[underline]] 2/3rd [[/underline]] power of its mass, as would be the case if the [[underline]] shape of the rocket apparatus were at all times similar to the shape at the start [[/underline]] (as in the ideal rocket, Fig. 1). This constant similarity of shape is, as we have seen (equation 2), one of the conditions for a minimum initial mass. Hence the "total initial masses" that have been calculated are [[underline]] really larger [[/underline]] than the true minima, which would be obtained only by repeating the calculations, assuming a smaller cross-section except