Firing a Gun in a Vacuum
When firing in vacuum, the trajectory is easily traced and its properties simply discussed. Considering its position with reference to the line of sight it will be seen that near the muzzle it is below the line of sight for some distance, then it cuts it; beyond this point it rises above the line of sight for some distance, then falls and cuts it again. This second point of intersection is the point blank and determines the point blank range. With a good rifle, up to 175 or even 200 yards, the line of fire will not cut the line of sight; or, in other words, it will not shoot high.
The progressive velocity of fall of the bullet being so much less than its initial velocity, the air resistance opposed to its descent will be inappreciably small in comparison with that in the direction of its motion of translation (the resistances being proportional to the squares of the velocities). Hence, when the bullet would have been at certain points, in vacuum, it will in reality be at points below and in rear of them, by distances increasing from the point of departure (since the resistance of air causes the spaces passed over in equal times to become progressively smaller and smaller), thus causing the trajectory in air to be constantly below and in rear of its place in vacuum and changing its curvature, so that the left branch presents a flattened form while the right branch approaches the vertical. From thus destroying the symmetry of this curve, there results that the angle of fall is greater than the angle of ascent, and more considerably so as it is distant from the origin, that the point of culmination is lowered, and that the range is greatly diminished. In practice the object aimed at has a certain height; hence, it will not only be struck when at point blank, but also when at points in rear or in front of the point blank where the vertical distances of the trajectory from such points shall be equal to or less than the height of the object. This distance between these two points, known as the dangerous space, is greater as the trajectory is flattened or as the height of the object is greater. An object may also be struck when in rear of the point blank. The sum of the distances in front and rear of the point blank, at which the object could be struck at its bottom and top, is the dangerous space. This permits us to make slight errors in estimating distances; we can either over or underestimate them so long as the errors do not exceed the limits of the dangerous space.
Farrow, Edward S. American Small Arms; a Veritable Encyclopedia of Knowledge for Sportsmen and Military Men. New York: Bradford, 1904. Print.
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