trailing span
at the moment before it reaches the circumference of the drum. It is
mounted on a screwed spindle, which is depressed by a nut, and thus makes
the wet rope grip the outside of the drum in a thoroughly efficacious
manner.
The author has made a theoretical investigation of the power which may be
developed by the system, and has worked out tables by which, when the
velocity of the current and the other elements of the problem are known,
the power developed by any given number of parachutes can be at once
determined. We do not reproduce this investigation, which takes account of
the resistance of the returning parachutes and other circumstances, but
will content ourselves with quoting the final equation, which is as
follows: T = 0.328 S V cubed. Here T is the work done in H.P., S is the total
working area in sq. m., and V is the velocity of the current in m. per
sec. Taking V = 1, and S = 1 sq. m., which is by no means an impracticable
quantity, we have T = 0.328 H.P. per sq. m. We may check this result by
the equation given, in English measures, by Rankine--"Applied Mechanics,"
p. 398--for the pressure of a current upon a solid body immersed in it.
This equation, F = 1.8 m A v squared / 2g, where m is the weight of a unit of
volume of the fluid--say 62 lb.--A is the area exposed, and v the relative
velocity of the current. Mr. Jagn finds that the maximum of efficiency is
obtained when the rope moves at one-third the velocity of the stream. If
this velocity be 3 feet per second, we shall have v = 2. and we then get F
= 7 lb. per sq. ft. very nearly. Now 1 sq. meter = 10.76 sq. ft., and a
speed of 1 ft. per second (which is that of the rope) is 60 ft. per
minute. Hence the H.P. realized in the same case as that taken above will
be 7 x 10.76 x 60 / 33,000 = 0.137 H.P. The difference between the two
values is very large, but Rankine, of course, depends entirely on the
value of the constant 1.8, which is quite empirical, and is for a flat
band instead of a hollow parachute. Taking, however, his smaller figure,
and an area of 544 square inches, which Mr. Jagn has actually employed, we
get a gross power of = 0.137 x 544 = 7.43 H.P. Hence it will be seen that
the amount of power which can be realized by the system is far from being
inconsiderable.
Lastly, we may point out that the durability of the apparatus will be
considerable. There is no wear except at the moment when the rope is
passing round the drum, and e
|