Figure 2-10.-Luff upon luff.
luff rig looks like. If you apply the rule by which you
count the parts of the fall going to and from the movable
blocks, you find that block A gives a mechanical
advantage of 3 to 1. Block B has four parts of fall
running to and from it, a mechanical advantage of 4 to 1.
The mechanical advantage of those obtained from A is
multiplied four times in B. The overall mechanical
advantage of a luff upon luff is the product of the two
mechanical advantagesor 12.
Dont make the mistake of adding mechanical
advantages. Always multiply them.
You can easily figure out the mechanical advantage
for the apparatus shown in figure 2-10. Suppose the load
weighs 1,200 pounds. The support is by parts 1, 2, and
3 of the fall running to and from block A. Each part must
be supporting one-third of the load, or 400 pounds. If
part 3 has a pull of 400 pounds on it, part 4made fast
to block Balso has a 400-pound pull on it. There are
four parts of the second fall going to and from block B.
Each of these takes an equal part of the 400pound
pull. Therefore, the hauling part requires a pull of
only 1/4 x 400, or 100 pounds. So, here you have a
100-pound pull raising a 1,200-pound load. Thats a
mechanical advantage of 12.
In shops ashore and aboard ship, you are almost
certain to run into a chain hoist, or differential pulley.
Ordinarily, you suspend these hoists from overhead
trolleys. You use them to lift heavy objects and move
them from one part of the shop to another.
To help you to understand the operation of a chain
hoist, look at the one in figure 2-11. Assume that you
grasp the chain (E) and pull until the large wheel (A) has
Figure 2-11.A chain hoist.
turned around once. Then the distance through which
your effort has moved is equal to the circumference of
that wheel, or 27rr. Again, since C is a single movable
block the downward movement of its center will be
equal to only one-half the length of the chain fed to it,
Of course, C does not move up a distance nl? and
then move down a distance nr. Actually, its steady
movement upward is equal to the difference between the
two, or (nR m). Dont worry about the size of the
movable pulley (C). It doesnt enter into these
calculations. Usually, its diameter is between that of A
and that of B.
The mechanical advantage equals the distance
that moves the effort (E). Its divided by the distance
that moves the load. We call this the velocity ratio,
or theoretical mechanical advantage (T.M.A.). It is
theoretical because the frictional resistance to the
movement of mechanical parts is left out. In practical
uses, all moving parts have frictional resistance.
The equation for theoretical mechanical advantage
may be written