allowance for friction, you multiply this result by 10,and then divide what you get by 10 plus the number ofsheaves in the system.Suppose you have a threefold purchase, amechanical advantage of 6, reeved with a line that hasa safe working load of 2 tons. Disregarding friction, 6times 2, or 12 tons, should be the safe working load ofthis setup. To make the necessary allowance forfriction, however, you first multiply 12 by 10, whichgives you 120. This you divide by 10 plus 6 (numberof sheaves in a threefold purchase), or 16. The answeris 7 1/2 tons safe working load.Lifting a Given WeightTo find the size of fiber line required to lift agiven load, use this formula:C in the formula is the circumference, in inches,of the line that is safe to use. The number 15 is theconversion factor. P is the weight of the given loadexpressed in tons. The radical sign, or symbol, over15 x P indicates that you are to find the square root ofthat product.To square a number means to multiply thatnumber by itself. Finding the square root of a numbersimply means finding the number that, multiplied byitself, gives the number whose square root you areseeking. Most pocket calculators today have thesquare root function. Now, let’s determine what sizefiber line you need to hoist a 5-ton load. First,circumference equals 15 times five, or C = 15 x 5, or75. Next, the number that multiplied by itself comesnearest to 75 is 8.6, Therefore, a fiber line 8 1/2inches in circumference will do the job.The formula for finding the size of wire roperequired to lift a given load is: C (in inches) = 2.5 xP (tons). You work this formula in the same mannerexplained above for fiber line. One point you shouldbe careful not to overlook is that these formulas callfor the circumference of the wire. You are used totalking about wire rope in terms of its diameter, soremember that circumference is about three times thediameter, roughly speaking. You can also determinecircumference by the following formula, which ismore accurate than the rule of thumb: circumferenceequals diameter times pi In using this formula,remember that equals approximately 3.14.Size of Line to Use in a TackleTo find the size of line to use in a tackle for agiven load, add one-tenth (10 percent for friction) ofits value to the weight to be hoisted for every sheavein the system.Divide the result you get by thenumber of parts of the fall at the movable block, anduse this result as P in the formulaFor example, let’s say you are trying to find thesize of fiber line to reeve in a threefold block to lift 10tons. There are six sheaves in a threefold block. Tentons plus one-tenth for each of the six sheaves (a totalof 6 tons) gives you a theoretical weight of 16 tons tobe lifted. Divide 16 tons by 6 (number of parts on themovable block in a threefold block), and you getabout 2 2/3. Using this as P in the formula you getThe square root of 40 is about 6.3, so it will take aline of about 6 1/2 inches in this purchase to hoist 10tons safely. As you seldom find three-sheave blocksthat will take a line as large as 6 1/2 inches, you willprobably have to rig two threefold blocks with acontinuous fall, as shown in figure 4-33. Each ofFigure 4-33.—Rigging two tackles with continuous fall.4-19

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