Ærial Navigation.

ATMOSPHERIC RESISTANCE.—We shall now indeavour to show the practicability of propelling a balloon of the dimensions specified in a former number, with the proposed velocity of 100 miles per hour, independently of any atmospheric current. The atmospheric resistance presented to a plain surface, as the end of a cylinder, while passing through the air with a velocity of 100 miles per hour, is according to Dr. Arnot, and nearly according with some experiments of our own, about three pounds per square foot. On this calculation the atmospheric resistance against the end of a cylinder 35 feet in Diameter, while moving with a velocity of 100 miles per hour, would be about 3000 pounds, and would require 1600 horse power to propel it. What constitutes this atmospheric resistance, is the inertia of the air, 1000 cubic feet of which, must be put into as rapid a motion as that of the cylinder during each foot of the progress thereof. And if the length of the cylinder is equal to that of the proposed balloon,—350 feet,—then in moving half its length, or 175 feet, 175,000 cubic feet of atmospheric air must be put into this rapid motion during this portion of its progress. With the elliptical or revoloidal spindle form, the case is different: for although an equal quantity of air must be displaced during an equal progress of the balloon, yet the motion of the air being comparatively moderate, the resistance of inertia is less. It will be seen that at and near the point of the balloon, where the surface forms the greatest angle with the direction of its motion, the diameter is small, and consequently, but a small portion of surface encounters atmospheric resistance, in that section: but where the diameter and surface are larger, the angle is less and the resistance is less in proportion to the surface. The greatest resistance may be therefore supposed to be at about 160 feet from the point, at which place the circumference of the balloon is about 80 feet. The angle between the surface and the direction of motion at this point is about 5 degrees, or about one foot rise to fifteen feet in length. Then if the balloon is moving, as supposed, nearly 150 feet per second, the motion of the displaced air is about 10 feet per second, and its resistance will be about one fourth of an ounce per square foot. And as the surface of the first half of the balloon is about 10,000 square feet, we may estimate the resistance at 156 lbs. But it must be observed that this resistance is not directly against the motion of the balloon, but only obliquely as it presses on the surface: and the average angle or inclination on which it presses, being as about one to fifteen, the actual resistance is reduced to about ten lbs. Therefore, as 10 horse powers are sufficient to drive a resistance of 33 lbs., 150 feet per second, it is a reasonable conclusion that the difference between 33 lbs. force and 10 lbs. resistance, is sufficient to balance the loss of power by the imperfect resistance of the air against the fans of the spiral fan-wheel. These calculations have not been drawn with mathematical accuracy, because our limits would not admit of it: but we have kept on the liberal side of the estimates, and if we have fallen into any material errors, shall be glad to be corrected.