Figure 2-10.-Luff upon luff.luff rig looks like. If you apply the rule by which youcount the parts of the fall going to and from the movableblocks, you find that block A gives a mechanicaladvantage of 3 to 1. Block B has four parts of fallrunning to and from it, a mechanical advantage of 4 to 1.The mechanical advantage of those obtained from A ismultiplied four times in B. The overall mechanicaladvantage of a luff upon luff is the product of the twomechanical advantages—or 12.Don’t make the mistake of adding mechanicaladvantages. Always multiply them.You can easily figure out the mechanical advantagefor the apparatus shown in figure 2-10. Suppose the loadweighs 1,200 pounds. The support is by parts 1, 2, and3 of the fall running to and from block A. Each part mustbe supporting one-third of the load, or 400 pounds. Ifpart 3 has a pull of 400 pounds on it, part 4—made fastto block B—also has a 400-pound pull on it. There arefour parts of the second fall going to and from block B.Each of these takes an equal part of the 400—poundpull. Therefore, the hauling part requires a pull ofonly 1/4 x 400, or 100 pounds. So, here you have a100-pound pull raising a 1,200-pound load. That’s amechanical advantage of 12.In shops ashore and aboard ship, you are almostcertain to run into a chain hoist, or differential pulley.Ordinarily, you suspend these hoists from overheadtrolleys. You use them to lift heavy objects and movethem from one part of the shop to another.To help you to understand the operation of a chainhoist, look at the one in figure 2-11. Assume that yougrasp the chain (E) and pull until the large wheel (A) hasFigure 2-11.—A chain hoist.turned around once. Then the distance through whichyour effort has moved is equal to the circumference ofthat wheel, or 27rr. Again, since C is a single movableblock the downward movement of its center will beequal to only one-half the length of the chain fed to it,or xr.Of course, C does not move up a distance nl? andthen move down a distance nr. Actually, its steadymovement upward is equal to the difference between thetwo, or (nR – m). Don’t worry about the size of themovable pulley (C). It doesn’t enter into thesecalculations. Usually, its diameter is between that of Aand that of B.The mechanical advantage equals the distancethat moves the effort (E). It’s divided by the distancethat moves the load. We call this the velocity ratio,or theoretical mechanical advantage (T.M.A.). It istheoretical because the frictional resistance to themovement of mechanical parts is left out. In practicaluses, all moving parts have frictional resistance.The equation for theoretical mechanical advantagemay be written2-5
Integrated Publishing, Inc. - A (SDVOSB) Service Disabled Veteran Owned Small Business