577 



GUNNERY. 



GUNNERY. 



878 



The effects of shot in penetrating any material form a subject of 

 great importance in military engineering, as a knowledge of those 

 effects can alone afford data for constructing walls and roofs capable of 

 resisting the momenta of the vast masses which, during a siege, may 

 descend upon or be projected against them. And in order that such 

 effects may be made the objects of scientific investigation, the resist- 

 ance which the material opposes must be considered as a uniformly 

 retarding force, like that which gravity would exert against a shot 

 fired vertically upwards : then the depth penetrated will correspond to 

 the space which would be described by a body, when subject to an 

 accelerative force equal to that retardative force, in the time that it 

 would acquire a velocity equal to that of the impact, and the time of 

 the penetration may be considered as equal to that in which such 

 velocity would be acquired. By the theorem of uniformly accelerated 



V. V" 



motions we have F varies as (where F is the accelerative or retar- 

 dative force, w is the weight of the body, v the velocity with which 

 it is moving, and i the space moved through). 

 Now, if o represent the force of gravity : 



g 32| feet, or the velocity generated in one second by the force 

 of gravity, 



o = the space or height due to that velocity, 



v = the given velocity of impact, 



s = the depth of the impression. Then 



VI y* 10 * *G 



G : : : r : ; whence F = ~- which is the force of resistance 



2 

 exercised by the material. 



* 

 If G be supposed to be equal to unity, we shall have F = 5- and 



this value of F expresses the ratio of the retardative force to that of 

 gravity ; consequently, representing the latter by the weight v> of the 



ic r 1 

 shot, the force of resistance should be expressed by j^7 . 



In Sir Howard Douglas's ' Treatise on Naval Gunnery ' there are 

 recorded the following results of experiments on the penetration of an 

 18-pounder shot into a butt made of beams of oak ; namely, with charged 

 of 6 lb., 3 Ibs., 2J Ibs., and 1 lb., the depths of the penetrations were 

 42 inches, 30 inches, 28 inches, and 1 5 inches respectively ; the velocities 

 are 1600 feet, 1130 feet, 1024 feet, and 656 feet respectively ; and from 

 these data the mean value of F will be found to be 138701. This 

 number expresses the resistance of the oak, in pounds, against a surface 

 equal to the area of a section through the centre of the shot ; and, by 

 reduction, it becomes equivalent to 912190 pounds exerted on one 

 square foot. 



Similar experiments made at Metz by firing 24-pounder shot against 

 butts of fir (the numbers being reduced to English denominations) 

 gave 475070 pounds for the resistance exerted on a square foot. 



At Woolwich, in 1835, two 24-pounder shot were fired with a velocity 

 of 1390 feet per second against a wall of concrete, into which they 

 penetrated to the mean depth of 3 feet 10 inches; whence, by the 

 above formula, we have F = 188047 pounds; and, consequently, the 

 resistance on a square foot is equal to 1013730 pounds. From n like 

 experiment made at Metz it was found that the resistance opposed by 

 a wall of oolitic stone might be expressed by 1394800 pounds (English) 

 on an equal surface. 



The French engineers, agreeably to the theoretical determination of 

 M. Prony, suppose the volume, instead of the depth, of the space pene- 

 trated to be proportional to the term vrv* ; but when that space is 

 cylindrical, the hypothesis will evidently be identical with that which 

 has been above stated. Dr. Button finds that, on firing into wood, the 

 depths of penetration, when high charges are employed, are in a lower 

 ratio than the squares of the velocities, and nearly proportional to the 

 velocities simply : this he supposes to depend on the resistance caused 

 by the elasticity of the fibres which are driven before the ball during 

 the time of penetration. 



Mr. Robins, in his work and various tracts on gunnery, was the first 

 to point out the important effects of rotation in producing deviations 

 in the line of flight of cannon balls. This rotation may be caused both 

 by the balls not fitting exactly to the bore of the gun, when the friction 

 being greater on one side than on the other would offer a greater 

 resistance to its motion on that side, and, secondly, by the density of 

 the ball not being uniform. When the centres of gravity and figure do 

 not coincide, the forces, that is, the pressure of the gases generated by 

 the powder, acting on the ball to move it, would act unequally on each 

 side of the centre of gravity, except when the line joining the centres 

 of gravity and figure is coincident with the axis of the bore, and would, 

 by the theory of parallel pressures, produce (besides exerting its whole 

 pressure in the motion of translation in a line through the centre of 

 gravity parallel to the axis of the bore) a motion of rotation round a 

 horizontal axis passing through the centre of gravity, due to the couple 

 whose arm is the line joining the centre of gravity and centre of the 

 figure, and whose force is the same pressure acting through the centre 

 of the figure. Though the constraint due to the bore of the gun 



ARTS AM) SCI. DIV. VOL. IV. 



would cause the direction of the rotation to be that in which the centre 

 of form was moving relatively to the centre of gravity (which latter 

 while passing through the bore must be performing equal oscillations 

 about the centre of form in a plane containing the centre of gravity 

 and axis of the bore) at the moment of leaving the bore, depending 

 therefore on its length ; yet as from the velocity of rotation being 

 proportionately small to the velocity of translation, there is not time 

 for a complete oscillation in the length of the bore, in practice the 

 direction of rotation depends entirely on the relative positions of these 

 points when placed in the bore of the gun. Thus, if when the ball is 

 first acted on, the centre of gravity is in a vertical Hue below the 

 centre of form, the rotation in leaving the bore will be round a hori- 

 zontal axis passing through the centre of gravity, and causing the 

 anterior part to move downwards. If the positions of the centres of 

 gravity and form be reversed, the motion of the anterior part of the 

 ball will be upwards, and in the same way to the right or left. 



If a perfectly smooth homogeneous sphere rotate in the air, there is 

 nothing to produce movement in the position of its centre of gravity 

 on an axis through which it is rotating ; and when rotation is com- 

 bined with translation there is nothing to cause deflection from the 

 line in which it is translated. But if the surface be not smooth, when 

 being translated, the air being denser in front than behind, depending 

 on the velocity of translation, the friction will not be symmetrical on 

 both sides the axis of rotation, but being greater on the anterior sur- 

 face will tend to produce deflection in the centre of the sphere in a 

 direction contrary to the one in which this surface is moving. But 

 on the other hand, one half of the surface is rotating in a direction 

 with, and the other half in a direction contrary to, the motion of trans- 

 lation, and the actual velocity of the former half through the air being 

 greater than that of the latter from its position, prevents its escape, 

 and causes a greater density in the air on that side. The resistance to 

 motion being greater in this direction than in the other, there is a 

 tendency to produce deflection in the centre of the sphere in the 

 direction in which the surface is rotating contrary to the motion of 

 translation ; that is, in the direction in which the anterior surface is 

 rotating, and this latter tendency is found in practice to overcome ths 

 former, and the shot is deflected in the direction in which the anterior 

 surface is rotating. When a shot is excentric, that is, where the centres 

 of gravity and figure do not coincide, and the ball is rotating round an 

 axis through the centre of gravity, there is not only this friction, but a 

 displacement of air equal to the figure contained between the sphere 

 whose radius is the shortest distance from the centre of gravity to the 

 exterior and the figure of the shot itself. The above described effect 

 is then immensely exaggerated ; in fact, if there were no friction, the 

 resultant normal pressures would in this case make an angle with the 

 direction of translation, and therefore cause deflection. Experiments 

 were made in 1851, at Shoeburyness, with shot and shell made excentric 

 by removing portions of the metal and replacing them with a heavier 

 or lighter body. The direction of the line joining the centre of gravity 

 and centre of figure was then determined by floating the shot in 

 mercury. By this means they could be strapped to wooden bottoms 

 in any position desired. An increase of upwards of 900 yards in the 

 range was obtained with these excentric projectiles over concentric 

 ones at angles of 20 to 28 and 32, and deflections proportionally 

 large according to the relative positions of the centre of gravity and 

 figure of the shot when placed in the bore of the gun as above described. 

 It is evident that the deflection of spherical shot from smooth bored 

 guns is principally, if not wholly, due to the varying rotations which 

 arise, and which produce deflections not in planes making angles with 

 the direction of the piece when the deflection would be proportionate 

 to the distance, but in incurvated lines, as stated by Kobins and proved 

 by his experiment with the bent barrel. In a rifle [RIFLE] we have 

 the means of impressing on the projectile a rotation round an axis 

 coincident with the line of flight ; when the resistances being equal 

 round the pole of rotation/no deflection can be produced while the axis 

 remains coincident, and any casual irregularity on the point or surface 

 is compensated for by being constantly shifted round from one side to 

 the other. Rifling, again, gives us the power of using elongated bullets 

 (cylindrp-conical), which .are kept point foremost by their rapid rota- 

 tion, which has the tendency of always keeping the axis of rotation 

 parallel to its original direction ; and it will be easily seen from the 

 previous investigations on the resistance of the air, what a greatly 

 increased power of maintaining its initial velocity is possessed by a 

 ball which, with the same surface of resistance, has double or treble 

 the weight of another. These are the reasons for the enormously 

 increased ranges and accuracy obtained with the Whitworth and 

 Armstrong guns, to which we shall have again occasion to refer under 

 KIKI.I;. 



(Colliado, Prattica Manuate dell' Artirjlieria, Milan, 1606; Ufano, 

 Vraye Instruction de I'Artillerie, Frankfort, 1614; Belidor, Le Bom,- 

 bardier Francois, Paris, 1731; Le Blond, Traite de /'^rti'tfm'e, Paris, 

 1743; Du Paget, Estai sur I' Usage de I'Artillerie, Amsterdam, 1771 ; 

 Lombard, Tables du Tir des Canons, &c., Auxonne, 1787 ; D'Antoni, 

 On Gunpowder and Fire-arms, translated by Capt. Thomson, London, 

 1789 ; Bezout, Court de MathCmatiquea it V i'sage du Corps d'Artillerie, 

 Paris, 1797; Robins, New Principles of d'unncry, London, 1805; 

 Hutton, Tracts, London, 1812 ; Robison, Mechanical Philosophy, 

 London, 1822; Sir Howard Douglas, Treatise on Naval Gunnery; 



P v 



