The manner in which the flame, and, consequently, the gases are expelled from the orifice of a rocket, resembles the operation of an æolipile, which throws out the vapour of water, and sets in motion the air in its vicinity. As the more flexible must yield to the more solid body, so, in this respect, the gases produced are repelled by the air in contact with the orifice of the rocket. Thus it follows, that the rocket displaces a volume of air of a much greater weight than itself. The rocket then has upon the air, reasoning a priori, the same effect as the oars of a boat have upon water; and hence, the greater the volume of fire from the rocket, the greater is its velocity and ascent. The impelling force also increases as it consumes, being a uniformly accelerated motion.
It also appears, that a rocket sent in an horizontal direction will not pass over so great a distance, as when its motion is vertical; for, a rocket, directed in a line parallel to the horizon, passes through a medium of equal density, but if directed perpendicular to the horizon, from the moment it leaves the ground till it arrives at its greatest height, it penetrates and passes through an atmosphere whose density is continually decreasing, and consequently its impelling force meets with less resistance. But when we consider the increase of the force of the rocket, there is no comparison between that force, and the diminution of the density of the air.
From these premises it follows, that the ascension of rockets of all kinds is governed by one principle, namely, the disengagement of gaseous fluids and caloric, which displacing an equal volume of atmospheric air, operates by mutual contact.
Since, however, the air is heavier than the gases produced by the rocket, as the latter are greatly expanded, it is evident, that the gases will ascend; their specific gravity at the time of dilatation being less than that of the air.
The gases proceeding from the interior of the rocket, act therefore upon the air in the immediate vicinity of the orifice, and the rocket is consequently propelled, the stick guiding it in the direction given to it. If it were not for the rocket-stick or balance, its direction would be neither regular nor certain. Considering then, that, by the rocket-stick, the centre of gravity is changed from the rocket itself to the stick, the motion is regulated in its perpendicular flight by the stick. The rocket-stick must be always of a proportionate length and weight to the rocket.
The motion given to rockets is always to be considered, for this depends upon the direction at first imparted; but the force of ascension is regulated by the size, and other circumstances which we have mentioned.
Assuming the principle of constant force acting upon the rocket, its velocity will increase with the time, and will be as the squares of the time, according to the principles of uniform accelerated motion; but if the force varies from uniformity, then the velocity and spaces will proportionably vary.
As action and re-action must be equal, the repulsion produced by the action of the gases upon the air is equal to the force impelling the rocket. The constant action produces equal acceleration of the motion.
On the subject of the condensation and dilatation of air, and the different pressures at a mean temperature, which is more or less connected with this inquiry, the reader may consult with advantage, the work of Mr. Biot, (Traité de Physique, &c. tome i, p. 110, and 141.) The conclusions of Mr. Robins on the gaseous products of gunpowder, and the elasticity of those products, may be seen by referring to the article on gunpowder.
It must be confessed, that the theory of rockets differs in many essential particulars from that of the usual projectiles; for the motion of rockets is more complicated than that of common projectiles, and is described to partake of all the anomalies that attend the accelerated motion arising from the rocket composition, and the uniform motion of the rocket-case, after the composition is expended. It is a fact, which appears to be established, that little or no advantage has yet been gained from the experiments that have been made with cannon, even where the angle of elevation, and the initial velocity of the ball were both accurately known. It seems totally useless to look for mathematical investigations, with respect to determining the ranges, &c. of military rockets; because, if we could determine, with the greatest accuracy, the point, position, and velocity of the rocket, at the moment when the composition was expended, the remaining part of its track would still be subject to all the inequalities attending on common projectiles. During the burning of the rocket, however, its motion might, by a series of experiments, be reduced to precise rules. As the principles of gunnery, or rather of projectiles, involve a number of collateral circumstances, such as the exact momentum of any given ball when projected with a given velocity, and from a given distance, the subject is still not fully settled; but they are so far conclusive, that the resistance of the air to the same ball is as some function of the velocity. The remarks of Dr. Hutton on this head would be too lengthy. A rocket, however, is very different. The very medium, in this case, is the principal agent in producing the motion; and being enabled to ascertain all the successive energies of the propelling power, and the resisting force, we may thus far determine correctly. It is suggested, that a rocket fixed to the ballistic pendulum would determine its whole energy; but, in order to make the experiment more perfect, it is proposed to attach it to a wheel, or revolving body, and then to measure its successive energies by the motion of some weight attached to the revolving axis of the machine. It is worthy of remark, that it is impossible to accommodate or determine the motion of rockets by other projectiles; and, therefore, to ascertain their momentum, such a contrivance would be eminently useful.