Resistance of Dirigibles
If the bow of a balloon were cut off square, its head end resistance would be that given by the rule already cited (page [19]): one three-hundredth pound per square foot, multiplied by the square of the velocity. But by pointing the bow an enormous reduction of this pressure is possible. If the head end is a hemisphere (as in the English military dirigible), the reduction is about one-third. If it is a sharp cone, the reduction may be as much as four-fifths. Unless the stern is also tapered, however, there will be a considerable eddy resistance at that point.
Head End Shapes
If head end resistance were the only consideration, then for a balloon of given diameter and end shape it would be independent of the length and capacity. The longer the balloon, the better. Again, since the volume of any solid body increases more rapidly than its surface (as the linear dimensions are increased), large balloons would have a distinct advantage over small ones. The smallest dirigible ever built was that of Santos-Dumont, of about 5000 cubic feet.
Large balloons, however, are structurally weak: and more is lost by the extra bracing necessary than is gained by reduction of head end resistance. It is probable that the Zeppelin represents the limit of progress in this direction; and even in that balloon, if it had not been that the adoption of a rigid type necessitated great structural strength, it is doubtful if as great a length would have been fixed upon, in proportion to the diameter.
The frictional resistance of the air gliding along the surface of the envelope, moreover, invalidates any too arbitrary conclusions. This, as in the aeroplane, varies nearly as the square of the velocity, and is usually considerably greater than the direct head end resistance. Should the steering gear break, however, and the wind strike the side of the balloon, the pressure of the wind against this greatly increased area would absolutely deprive it of dirigibility.
A stationary, drifting, or “sailing” balloon may as well have the spherical as well as any other shape: it makes the wind a friend instead of a foe and requires nothing in the way of control other than regulation of altitude.
Independent Speed and Time Table
The air pressure, direct and frictional resistances, and power depend upon the relative velocity of flying machine and air. It is this relative velocity, not the velocity of the balloon as compared with a point on the earth’s surface, that marks the limit of progression. Hence the speed of the wind is an overwhelming factor to be reckoned with in developing an aerial time table. If we wish to travel east at an effective speed of thirty miles per hour, while the wind is blowing due west at a speed of ten miles, our machine must have an independent speed of forty miles. On the other hand, if we wish to travel west, an independent speed of twenty miles per hour will answer.