[Illustration: RELATIVE AND ABSOLUTE BALLOON VELOCITIES]
[Illustration: FIELD AND SPEED]
An _aerostat_ (non-dirigible balloon), unless anchored, drifts at the
speed of the wind. To the occupants, it seems to stand still, while
the surface of the earth below appears to move in a direction opposite
to that of the wind. In the sketch, if the independent velocity of a
_dirigible_ balloon be _PB_, the wind velocity _PV_, then the actual
course pursued is _PR_, although the balloon always points in the
direction _PB_, as shown at 1 and 2. If the speed of the wind exceed
that of the balloon, there will be some directions in which the latter
cannot progress. Thus, let _PV_ be the wind velocity and _TV_ the
independent speed of the balloon. The tangents _PX_, _PX´_, include the
whole "field of action" possible. The wind direction may change during
flight, so that the initial objective point may become unattainable,
or an initially unattainable point may be brought within the field. The
present need is to increase independent speeds from thirty or forty
to fifty or sixty miles per hour, so that the balloon will be truly
dirigible (even if at low effectiveness) during practically the whole
year.
[Illustration: INFLUENCE OF WIND ON POSSIBLE COURSE]
Suppose a dirigible to start on a trip from New York to Albany,
150 miles away. Let the wind be a twenty-five mile breeze from the
southwest. The wind alone tends to carry the balloon from New York to
the point _d_ in four hours. If the balloon meanwhile be headed due
west, it would need an independent velocity of its own having the same
ratio to that of the wind as that of _de_ to _fd_, or about seventeen
and one-half miles per hour. Suppose its independent speed to be only
twelve and one-half miles; then after four hours it will be at the
position _b_, assuming it to have been continually headed due west, as
indicated at _a_. It will have traveled northward the distance _fe_,
apparently about sixty-nine miles.
[Illustration: COUNT ZEPPELIN]
After this four hours of flight, the wind suddenly changes to
south-southwest. It now tends to carry the balloon to _g_ in the next
four hours. Meanwhile the balloon, heading west, overcomes the easterly
drift, and the balloon actually lands at _c_. Unless there is some
further favorable shift of the wind it cannot reach Albany. If, during
the second four hours, its independent speed could have been increased
to about fifteen and a half miles it would have just made it. The
actual course has been _fbc_: a drifting balloon would have followed
the course _fdh_, _dh_ being a course parallel to _bg_.