Sec. XXVIII. Observations on Rockets.
The following remarks on the subject of rockets by M. Bigot, (Traité d'Artifice de Guerre, p. 131,) may be interesting to the reader.
Authors, who have written on rockets, are of opinion, that the height of the different kinds of rockets should not be increased on account of their diameter; because, as the diameter increases, the rocket also increases in weight and surface; and if augmented in height in the same ratio, its power of ascension would be feeble. It is from this reasoning, together with practice, that they have determined the height of empty cases. Some have given the proportion of six times their exterior diameter, and others again have made them a third longer than the piercer. There has resulted from this difference of opinion, such an irregularity in the formation of rockets, that artificers or fire-workers were left in uncertainty as to the best mode to be pursued. To avoid, however, this embarrassment, if we consider the diameter of the base of the piercer of any kind of rocket as one-third of the exterior diameter of the case, the small end must be the one-sixth part of it; and the piercer and the cone are of the same diameter, and the surface of the one is equal to the surface of the other. We might conclude, accordingly, that the increase of the height of the case, should be the same with all kinds of rockets. It appears by different authors, that the ancient and modern fire-workers have fixed the dimensions of rockets and their piercers, by various experiments. If we take for granted all the heights of the piercers, or the rockets themselves, we obtain a curve of double or treble reflection, which is very evidently in opposition to the above principles, and of the law which results from them.
Experiments prove, that to make a good rocket of half an inch in diameter, the piercer must be five times and a third of the same diameter; and for a rocket of three inches, the piercer, or broach, as it is sometimes called, is only four times the diameter in height. To determine, however, the height of the piercer in general, greater than the preceding, it is found necessary to have some satisfactory result, in order to employ, mathematically speaking, less times of the exterior diameter of the rocket. The half-inch and three-inch rocket are the extremes of an increasing arithmetical progression; and their equivalents, 51/3 and 4 diameters is the extreme of a similar, but decreasing progress; but if we insert the same number of arithmetical mean between the two extremes of each of these two progressions, and then continue them indifferently, the terms of the first will express the diameter of as many different cases; and those of the second, the height of the corresponding piercers. They will be, for instance, in the two following proportions:
| ÷ | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14, | &c. | 36. |
| ÷ | 514/45 | 512/45 | 511/45 | 59/45 | 57/45 | 57/45 | 52/45 | 51/45 | 444/45 | &c. | 4. |
The first of which has unity for its common difference. It has been found, that, by inserting in each, a mean of 29, the height of the piercers will correspond with the superior diameter, which is less, or regulated by their respective diameters. Besides, as the diameters go on augmenting, the rockets are proportionably increased in height, but only in an inverse order, until the 58th term included, and beyond which they decrease, until they become negative, which appears to indicate that the term appertains to the diameter of the rocket, and without any uncertainty.
It results from the intimate relation of these two progressions, that, in stopping at the 58th term, if we bring back on an axis as it were, the height of the piercers, we obtain a straight instead of a curved line.
Bigot has given two tables relative to the construction of rockets, and, as their use is seen by mere inspection, we here introduce them without remark.
They comprehend the dimensions of rockets of different calibers, compared with the exterior and respective diameter of each kind; and relative to the dimensions of the tools of sky-rockets of different calibers, and also compared with the exterior and respective diameter of each.
It will be seen, on an examination of these tables, that all the data are satisfactorily given; so that, in the construction of rockets, the artificer will find them extremely useful, if not absolutely necessary.