RESULTS OF EXPERIMENTS WITH SLOW MOTIONS.
Resistance in proportion to surface.
1st. It appears from the various experiments that have been made upon bodies moving in the atmosphere, that the resistance is nearly as the surface, increasing a very little above that proportion in the greater surfaces.
Resistance as squares of velocity.
2nd. That the resistance to the same surface with different velocities, is in slow motions nearly as the squares of the velocity, but gradually increasing more and more in proportion as the velocities increase.
Rounded and pointed ends suffer less resistance.
3rd. The round ends, and sharp ends of solids, suffer less resistance than the flat or plane ends of the same diameter. Hence the flat end of the cylinder and of a hemisphere, or of a cone, suffer more resistance than the round or sharp ends of the same.
Sharp ends not always least resistance.
4th. The sharper ends have not always the smaller resistances; for instance, the round end of a hemisphere has less resistance than the pointed end of a cone, whose angle with the axis is 25° 42′.
Form of base affects resistance.
5th. When the hinder parts of bodies are of different forms, the resistances are different, though the fore parts are the same. Hence the resistance to the fore part of a cylinder is less than that on the equally flat surface of the cone or hemisphere, owing to the shape of the base of the cylinder. The base of the hemisphere has less resistance than the cone, and the round side of the hemisphere less than that of the whole sphere.
Only proved for slow motions.
The above refers only to slow motions, and the results given, from experiments with very small velocities; and it is to be expected, that with very rapid motions the form of the fore, as well as the hind part, of the projectile, will influence the amount of resistance in a much higher degree.
Form of hind part.
That form for the hind part will be best which has the greatest pressure upon it, when moving with a certain velocity.
Best shape for fore and hind part.
The ogivale form seems, from experiment, to fulfil the former condition. The best form for the hind part, for rapid motions, has not been determined; it may, however, be considered to be of much less importance than the shape of the fore part.
Form determined by extent of range.
Of course the best form can be determined by extent of range, but deductions from this will depend upon such a variety of circumstances, the effects of some of which must be entirely hypothetical, that the correctness of any formulæ obtained in this manner must be very uncertain.
Form suggested by Sir I. Newton.
Sir Isaac Newton, in his “Principia,” has given an indication of that form of body, which, in passing through a fluid, would experience less resistance than a solid body of equal magnitude of any other form. It is elongated.
Axis of elongated bodies must be fixed.
It is plain, however, that the minimum of resistance would not be obtained with a shot of an elongated form, unless the axis can be kept in the direction of the trajectory; as not only will the axis perpetually deviate from the true direction, but the projectile will turn over and rotate round its shorter axis, that is, if fired out of a smooth bore.
Advantages of conical bullets.
Conical bullets have an advantage, from their pointed end, which enables them to pass through the air with greater facility; and for the same reason they are better calculated to penetrate into any matter than spherical ones.
Disadvantages of conical bullets.
A solid bullet cannot be pointed without sending backward the centre of gravity. The sharper the point, the more it is liable to injury, and if the apex of the cone does not lie true, in the axis of the projectile, then such an imperfection of figure is calculated to cause greater deflections in the flight than any injury which a round surface is likely to sustain. In penetrating into solid bodies, it is also important that the centre of gravity should be near its work.