Figure 2-10.-Luff upon luff.

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 advantages—or 12. Don’t 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 4—made fast to block B—also 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 400—pound 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. That’s 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, or xr. 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). Don’t worry about the size of the movable pulley (C). It doesn’t 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). It’s 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 2-5