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.
[Illustration: 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.