Among the principal causes of variation in range and deviation in direction of flight of rifled projectiles, independent of the errors of the gun itself, are the influence of the wind and the motion of the gun. The motion of the target, if not allowed for, also affects accuracy of fire.
It will perhaps be admitted that errors in gunnery practice due to the above causes should be eliminated so far as is possible, and that this should be the duty of the officer directing the firing.
In the Ordnance Instructions for the U. S. Navy, Articles 766 to 772, are general instructions in regard to "corrections for speed, wind," etc., and in this paper an attempt will be made to show how these instructions may be carried out in detail, how officers commanding divisions of guns may construct for their use simple tables, by which the sight-bar and sliding leaf may be set to allow for these corrections, leaving the gun captain free to point his gun directly at the target, and to fire when his line of sight and the point to be hit coincide.
In these days of high-powered guns and high speed of modern ships, much valuable time would be lost in trying to find the amount of the corrections necessary to apply to the range and direction of flight by trial shots alone, especially if the guns and target are in motion and if a ship's battery is composed of guns of different caliber and class ; and it is believed also that with expensive ammunition, of which but a limited supply can be carried, owing to its weight and the space necessary for stowage, a great saving would result if approximate corrections were applied to the first trial shot, even if the plan was not followed thereafter.
The speed, distance and direction of motion of the target, and the force and direction of the wind, are subject to the errors of estimation or of observation in any case ; and the estimations or observations having been made, the tables, if easy of application, furnish on the one hand a quick and approximately accurate solution of what is largely attempted by guesswork on the other hand.
It is claimed also that by practice officers can soon become very expert in the use of tables to apply corrections, and the time thus expended cannot in these days be used to greater advantage if it will lead to any improvement in gunnery practice.
The mathematical work necessary to show on what foundation the formulae used in the construction of the tables rest, is here given; but it is not at all necessary to a proper understanding of their construction and use.
It must not be supposed that the formulae as finally reached furnish a rigid solution of the problems, but they give a close approximation to the truth, and will suffice for nearly all cases which are likely to happen in firing guns at sea.
Let us now consider in detail the three causes before mentioned.
The Influence of the Wind.
The method followed is that of M. Helie, Professeur a l'Ecole d'Artillerie de la Marine, in a pamphlet on this subject published in 1874, somewhat abridged.
Let Fig. I represent the horizontal plane passing through the point O.
OB direction of line of fire.
B point of fall of the projectile when the gun is fired in a calm atmosphere and at an angle of elevation a, the gun being at O.
AA' direction of the wind with respect to the line of fire.
Vcos a horizontal component of the initial velocity V.
W velocity of the wind.
Didion in his Trait6 de Balistique shows that if we suppose the whole system—gun, projectile, atmosphere, etc.—to have a horizontal motion equal to and opposite to that of the wind, that is to say, if in the figure the wind is from A'O, if we suppose the whole system to have motion equal to that of the wind and in an opposite sense, the absolute velocity of the wind reduces to zero, and, so fat as the relative positions of the parts of the system are concerned, we would have the condition of a calm atmosphere. On this hypothesis we suppose the system to have at the instant of firing a velocity equal to W and toward A' from O, then the projectile on leaving the gun has a resultant velocity of which the horizontal component is V the direction of which is the resultant of V cos a and W.
At the end of a given time T the projectile will fall at some point C, but the points O and B at the end of the same time have, owing to the motion given to the system, moved to the new positions O' and B', the line OB' parallel to OB, and the relative positions of the gun, point of fall and line of fire will be represented by the triangle O'CB'.
(Corresponding figures are available in the PDF.)