303 Example 1. The 80-ton gun fires at a vessel in motion at a range of 2000 yards. The muzzle velocity is 1580 f . s., the calibre 16 inches, and the weight of projectile 1700 lb. Required the velocity on im pact, and the time of flight. Here ^-^=0-1506 w 1700 0-1506x6000 ft. =903 ft. Selecting the m. v. 1580 f. s. in the first column, the second column shows 23,519 ft. Subtracting, 23,519 - 903 = 22,616. Running up the second column and using proportional parts, this number corresponds to a velocity of 1383 f. s. , which is the velocity on impact, showing the projectile to have lost 197 f. s. of its velo city during flight. In the third column, opposite 22,616 feet, we find 31 929 seconds. Subtracting this from the time opposite 1580 cP feet, and dividing by --, we have t- ^-(32-544-31-929) = 4 084 seconds. Example 2. -An observer in an earthwork notes the flash of a hostile gun ; in 3} seconds the shell (blind) buries itself in the parapet, followed in half a second by the report of the gun. The shell is dug out, and found to weigh 60 lb, and to measure 15 centi metres in diameter. Required the range, the muzzle velocity, and the striking velocity. The range is here given by the velocity of sound, which travels through air at an average rate of 1140 feet per second; so that r= 3 75x1140 -4275 ft.; c_(15 cm. ) 2 ^ (5 91 " ls -) 2 = 60 60 r -2488 ft, and -- = 1-892 sec. w w We have now to consider what muzzle velocity will cause the pro jectile to traverse the given distance in the given time. It must move at a mean speed of 1315 f. s. Assume the muzzle velocity to be 1600 f. s. ; corresponding to this are found 23,607 feet and 32 599 seconds. Subtracting from these the reduced range and time, we have 21,119 feet and 30707 seconds; if the velocity has been correctly assumed, it is clear that the range and the time of flight should result in the same terminal velocity. In the pre sent instance, opposite 21,119 feet stands 1130 f. s., while opposite 30 707 seconds stands 1125 f. s. Thus it appears that the velocity has diminished more rapidly in the time travelled than in the dis tance travelled. This shows that it is assumed too high. Trying 1584 f. s. , and proceeding as before, each column indicates 1120 f. s. , which therefore is the terminal velocity, showing that the projectile has lost 464 f. s. of its speed during flight. Drift. Projectiles fired from rifled guns do not move in a vertical plane, but deviate to the right or to the left according to the direction of their rotation. All nations have adopted the right-handed twist, probably because it happened to be selected first. If the observer stands in rear of the piece and looks at the gun when fired, the pro jectile rotates in the same direction as the hands of a watch. ft or It then steadily bears away to the right. The reason of exion. fa[ s j g no very clearly understood ; in fact, two rival theories are put forward to account for it. If there were no resistance of the air, the path of the shot would be a parabola, and the axis of an elongated projectile would remain parallel to its original direction. The resistance offered by the air causes the axis to tend to assume a position tangential to the trajectory. On leaving the gun the projectile moves in the direction of its axis, which is also the direction of the axis of the gun. The action of gravity soon causes the path of the shot to make a small angle with the original direction of the axis ; that is, the trajectory soon deviates from a straight line ; the axis of the projectile is urged by the resistance of the air to accommodate itself to the new path, but as the path is constantly changing, the axis is always too late, since the rotation tends to preserve its parallelism. Thus there is always an angle depending in amount on the velocities of rotation and translation, weight of shot, and density of the air between the axis of the shot GB and the trajectory CD (fig. 16). Thus far both theories agree as to the facts, but they differ as to the deductions. The first view is that the resultant resistance of the air, which has the effect of a force in the direction DC, tends to turn the shot about an axis passing through G, and per pendicular to the plane containing BGD, so that if the shot had no rotation, it would turn end over end. But as it has a right-handed twist, this motion is combined with that which the resistance of the air tends to impart to the shot, and the point A is therefore slightly deflected to the right at first. Continuing the action, the axis GA describes a cone about CD, rotating in the same direction as the shot rotates about its own axis. The resultant of the air s resistance tends to increase the angle BGD, therefore the shot will have a sinuous motion ; but as the first deflexion Fig. 16. is to the right, and afterwards the point is more to the right than to the left, the deviation will on the whole be to the right. The other view is that, as the axis of the shot is always directed a little above the trajectory, the resistance of the air meets the surface on the under side, on which therefore there is more pressure than on the upper side. The consequence of this is that the friction of the air with the rotating surface is greater below than above, and there fore causes the projectile to roll bodily to the right while travelling forward. The path thus curves away from the vertical plane, and the resistance of the air tends to cause the axis to lose its parallelism with that vertical plane, though it is, as before, too slow in altering its direction to FIG. 17. Correction for deflexion. become tangential to the curve described. Crucial experi ments to set this point at rest are as yet wanting. The "drift" or "deflexion" is usually corrected in the British service by inclining the tangent sight. The result of this is that as the range increases, the higher the sight is raised, and the farther is the eye-notch to the left of the vertical plane containing the axis of the gun. In the German service the tangent sight is placed vertically in the gun, and the deflexion is allowed" for by a graduated sliding leaf in the head. The same arrangement is used in those British guns, as the howitzers, which fire variable charges, as the slope of the tangent sight will accurately suit only one muzzle velocity. To ascertain the correct slope, the actual deflexion is deter mined for each gun on the practice ground at various ranges with a vertical sight; then, in fig. 17, AD is the line of sight when the axis of the gun is horizontal. CD is the line of sight with a vertical tangent sight set at the angle of eleva tion ADC required for the range DF. Since the projectile deflects to the right, it is necessary that the line CD should point to E in order to hit F. This is accomplished by inclin ing the tangent sight AB, so that EC shall give the requisite
allowance. The relation is thus established. By similar triangles,