338. It will be useful to contrast the wheel and axle on which we
have experimented (Art. 304) with the differential pulley (Art. 209).
The velocity ratio of the former machine is nearly double that of
the latter, and its mechanical efficiency is nearly four times as
great. Less than half the applied power is wasted in the wheel and
axle, while more than half is wasted in the differential pulley. This
makes the wheel and axle both a more powerful machine, and a more
economical machine than the differential pulley. On the other hand, the
greater compactness of the latter, its facility of application, and
the practical conveniences arising from the property of not allowing
the load to run down, do often more than compensate for the superior
mechanical advantage of the wheel and axle.
339. We may also contrast the wheel and axle with the screw (Art.
277). The screw is remarkable among the mechanical powers for its very
high velocity ratio, and its excessive friction. Thus we have seen in
Art. 291 how the velocity ratio of a screw-jack with an arm attached
amounted to 414, while its mechanical efficiency was little more than
one-fourth as great. No _single_ wheel and axle could conveniently
be made to give a mechanical efficiency of 116; but from Art. 337 we
could easily design a _combination_ of wheels and axles to yield an
efficiency of quite this amount. The friction in the wheel and axle is
very much less than in the screw, and consequently energy is saved by
the use of the former machine.
340. In practice, however, it generally happens that economy of
energy does not weigh much in the selection of a mechanical power
for any purpose, as there are always other considerations of greater
consequence.
341. For example, let us take the case of a lifting crane employed in
loading or unloading a vessel, and inquire why it is that a train of
wheels is generally used for the purpose of producing the requisite
power. The answer is simple, the train of wheels is convenient,
for by their aid any length of chain can be wound upon the barrel;
whereas if a screw were used, we should require a screw as long as the
greatest height of lift. This screw would be inconvenient, and indeed
impracticable, and the additional circumstance that a train of wheels
is more economical of energy than a screw has no influence in the
matter.
342. On the other hand, suppose that a very heavy load has to be
overcome for a short distance, as for example in starting a ship
launch, a screw-jack is evidently the proper machine to employ; it
is easily applied, and has a high mechanical efficiency. The want of
economy of energy is of no consequence in such an operation.
LECTURE XI.
_THE MECHANICAL PROPERTIES OF TIMBER._
Introduction.—The General Properties of
Timber.—Resistance to Extension.—Resistance to
Compression.—Condition of a Beam strained by a
Transverse Force.