© Donn Haven Lathrop 1996 
Safety is the primary, and the only, consideration in any work on a tower clock weight system. 

Always let a weight all the way down before releasing either end of the cable from its fastening, indeed, before doing any work on the cables or the pulleys.(Any time the weights are to be let downwhich puts all of the weight on the winding crankhave an assistant in the clock room to release the ratchet(s). Don't try to do it all alone. It is impossible [and not too smart to try] to stop a runaway winding crank. There is no way of stopping a runaway weight, since a clock winding barrel doesn't have a brake of any sortsomething that makes OSHA very nervous.^{12})  

(Any time the weights are let downwhich puts all of the weight on the winding crankhave an assistant with you in the clock room to release the ratchet[s]. Don't try to do it all alone. Too many things can go wrong.) 

(Any time the weights are let downwhich puts all of the weight on the winding crankhave an assistant with you in the clock room to release the ratchet[s]. Don't try to do it all alone. Too many things can go wrong.) 

Sould anyone find an error in any of these formulas, or a lack of clarity as to their intended use, please email me.
1. Weight Drop, Compounded:
C_{vd} = T_{vd} x (1/F) where:The reader must be reminded that the sheave(s) take up a finite amount of space above the weight, a space that must be taken into consideration in calculating the required weight drop.
C_{vd} is compounded drop, in feet;
T_{vd} is total weight drop required, in feet;
F is the number of falls.
2. Mechanical Advantage:
1. The accepted definition of a mechanical advantage is the ratio of effort to resistance, or, MA = R/E ; however, to compute a mechanical advantage ratio (really a disadvantage ratio, in that more weight is required with multiple falls), which is necessary to derive the total weight required in a compounded weight drive system, a permutation of the formula is required. Counting the number of falls at the weight and multiplying the design weight by the number of falls yields the same result.
(It must be remembered that this is a simple solution; no allowance is made for frictional losses and bending loads.)R = FE, where:
R is the total weight required, in pounds;
F is the number of falls;
E is the actual weight required to drive the clock, in pounds.
2. The mechanical advantage of a winding jack, wherein a smaller gear (pinion) drives a larger gear is;
MA = Dt/Pt , where;
Dt is the number of teeth on the driven gear, and;This is only the MA of the winding jack itself: the total mechanical advantage must also include the length of the winding handle, and the diameter of the winding barrel.
Pt is the number of teeth on the driving pinion (gear).
3. D/d ratio; which is the ratio of the sheave (or winding barrel) pitch diameter to the diameter of the rope;
D = (X d), where;
X is a manufacturer/federal specification constant for differing sizes and constructions of wire ropes, and;Pitch diameter is the pulley tread diameter plus one half the rope diameter.
d is the diameter of the rope in inches.
3A. How does one calculate the D/d ratio?
Add the diameter of the drum barrel to the diameter of the wire rope you want to use. Then divide by the diameter of the wire rope.
Example: When using ^{1}/_{2}" wire rope on a 10.75" drum barrel.
10.75 + .5 = 11.25. 11.25 divided by .5 = 22.5:1 D/d ratio. This meets the ANSI/ASME recommendation of 15:1 for pulling and 18:1 for lifting applications.
4. Bending stress: s_{b} = Ed_{w} /D, where:
s_{b} is in pounds;To calculate bending stress; s_{b}, in the outer wire(s), and the bending load; p_{b}, use these formulas:
E is the modulus of elasticity of the wire rope, which varies between 1 x 10^{7}, and 1.4 x 10^{7}.
1.2 x 10^{7} (12 ,000 ,000) is a frequently used average value;
d_{w} is the diameter of the component wire (for 6 x 19 rope, d_{w} is .063d);
D is the pitch diameter of the pulley in inches.
s_{b} = Ed_{w} /D, for bending stress; andE is the modulus of elasticity of the wire rope, which varies between 1 x 10^{7}, and 1.4 x 10^{7} . 1.2 x 10^{7}
p_{b} = s_{b}A; where A = d^{2}Q.
5. Bending load; p_{b} = s_{b} A; where A = d^{2}Q; where:
p_{b} is in pounds;
d is the rope diameter;
A is the metal crosssectional area of the rope; and
Q is a constant derived for a specific type of rope. For 6 x 19 wire rope with a fiber core, Q is .405.
N.B. In both 4. and 5. above, constants such as d_{w}, A, and Q, are provided by the rope manufacturer.
6. Radial pressure on a pulley or a barrel:
P = 2T / (D d) , where;
P is radial pressure in pounds per square inch;
T is rope tension in pounds;
D is tread diameter of barrel or pulley in inches;
d is rope diameter in inches.
7. Calculating weight of solid stone driving weights;
W = (h x d x w x 160) / 1728, where:
W is in pounds, and;
h, d, & w, are in inches;
1728 is cubic inches in a cubic foot;
160 (lbs) is an empirically derived constant (see text).
8. Fleeting pulley/sheave placement;
F_{sp} = barrel depth/2 x .035, or;
F_{sp} = barrel depth x 1.25 (ft.), where;
F_{sp} and barrel depth are in feet.
8. To compute the effort and resistance of a lever, as in a barrel/great wheel:
L_{ea} x Rwhere:
L_{ra } E
L_{ea} is the length of the effort arm;
L_{ra} is the length of the resistance arm;
R is the resistance (usually in pounds), and;
E is the effort (usually in pounds).
9. To compute frictional losses due to pulleys and wire bending loads:
P = W/r where
P is the force at the winding drum, W is the weight (in pounds) of the driving weight.
r (to compute frictional losses in rewinding the clock [lifting the weight] ) is;r (to compute frictional losses in driving the clock [weight falling] ) is;r = (1  µ) ^{m + 1} + (1  µ)^{ m + 2} +. . . + (1  µ) ^{m + n} : wherem is the number of 180° bends the rope makes at the weight;
n is the number of parts of line.
µ is the loss coefficient (friction due to pulley bushing[s]),
expressed as a percentage, e.g., with a 2% friction loss; µ = .02.
r =  ___1____  +  ___1___  +. . . +  ___1___ 
(1  µ) ^{m + 1}  (1  µ) ^{m + 2}  (1  µ) ^{m + n} 
An example: Assume a 50 pound weight is needed to drive a clock, requiring a triple fall (3 part) compound system:
Simple solution, disregarding r (no friction component): 50 x 3 = 150 + 10 (pulley weight) = 160 pounds; therefore 160/3 is 53.333 lbs. The weight itself must weigh 47 .666 pounds.
The complex solution:
Winding the clock: Let µ = .02, m = 1, and n = 3
1  µ = .98, therefore; r = .98^{2} + .98^{3} + .98^{4} (this is: .98 squared; plus .98 cubed, and so on.) therefore:
P = 160 / 2.82 = 56.74 lbs. (effective resistance to rewind effort)
Driving the clock:
r =  ___1____  +  ___1____  +. . . +  ___1 ___ 
(1  µ) ^{m + 1}  (1  µ) ^{m + 2}  (1  µ) ^{m + n} 
r =  ___1___  +  ___1___  +  ___1___  = 3.18 
.98^{2}  .98^{3}  .98^{4} 
P = 160 / 3.18 = 50 .32 lbs. (effective driving weight required)
These figures are ideal calculationsno real world modifiers such as a lack of lubrication, loading of the external hands, etc., are involved in the calculation. Still rather empirical, isn't it? We are, however, getting close to being able to determine the theoretical required weight to drive the hypothetical clock. Note, however, that it does take more effort to rewind a compound weight system.
10. To calculate the maximum length of rope (L) that can be wound on a winding barrel:
L = (A + D) x A x B x K, where:
A = nominal rope diameter,
D = diameter of barrel, inches,
B = width (or depth) of barrel, inches
K = appropriate factor from table below:
Rope Dia. (in) Factor 3/32 (.094) 23.4 1/8 (.125) 13.6 3/16 ).1875) 6.14 1/4 (.25) 3.29 5/16 (.3125) 2.21 3/8 (.375) 1.58 7/16 (.4375 1.19 1/2 (.5) .925
11. To calculate the theoretical maximum length of rope which can be wound on a barrel:
L = (D x pi) x (B/A) — 12, where:
D = barrel diameter, inches
pi = 3.141592654
B = width of barrel, inches,
A = nominal rope diameter
ANSI: The American National Standards Institute, from whose criteria the OSHA standards for safe operation of cranes and derricks and other systems using wire rope isntallations are derived.
birdcaging: An expansion of the strands laid into a rope; usually caused by twisting against the lay (q.v.).
block: A system of sheaves (q.v.) sharing a common frame, and (usually) a common axle.
compounding: A system of sheaves and weight lines designed to provide a shorter weight drop for (or a mechanical advantage in lifting or supporting) a weight. The decrease in weight fall is found by multiplying the total weight fall necessary by the inverse (1/number of falls) of the number of falls (q.v.). The mechanical advantage is computed by counting the number of falls going to and from the moveable sheave(s) attached to the weight.
core: The core material, either metallic or nonmetallic, around which the strands of the rope are helically laid. Cores are made of fiber (FC), a wire strand (WSC), or an independent wire rope (IWRC).
Crosby clip: A fastening device, also known as a Uclamp. A bolt in the shape of a U, used with a forged saddle to terminate a wire rope, usually in a loop. Strength of a clamped loop is 80% of wire rope rating.
fall: Any weight line which directly supports the driving weight. For a single fall, the weight line is attached to the winding barrel at one end and the weight at the other, without any compounding pulleys. Compounding requires at least one pulley, and results in multiple falls at the weight. Two lines at the weight is twofall compounding, three lines is threefall compounding, etc. Increasing the number of falls increases the compounding advantage, but also increases losses due to pulley bearing friction.
fiddle block: A block consisting of two pulleys in the same vertical plane held in place by their common cheek pieces.
Fist clip: A fastening device to be used in creating a loop in a wire rope. The clip has two forged saddles and two bolts to pull the saddles together. It doesn't tend to cut into or kink a wire rope. Strength of a clamped loop is 80% of wire rope rating.
fleet angle: The angle between the sheave/barrel centerline and the rope at its extreme deflection. The fleet angle should not be less than 1/2°, and should not exceed 2°.
fleeting pulley: A pivoted guide pulley whose pivot should be aligned with the centerline of the barrel and placed at a distance from the barrel determined by this formula: Dw x .5 / .035, where Dw is the depth (or width) of the barrel; multiplying by .5 takes half of the depth; .35 is a constant derived by trigonometrically solving for the adjacent by dividing the opposite by the tangent (.03492) of 2°. The rule of thumb is 1 .25 feet of separation between the barrel and the first, or main, pulley for each inch of barrel depth or width. The fleeting pulley must not be used as the lead sheave (q.v.)
fleeting sheave: A selfaligning sheave (grooved wheel or pulley) mounted on a horizontal shaft, which will allow the sheave to move from side to side as the rope winds on or off the barrel. See fleeting pulley for location and alignment data.
guard pin: A pin or bolt through the cheekpieces of a pulley, so placed as to prevent the wire rope from leaving the groove in the sheave (q.v.).
lay: (or laid) The lay is the direction of the helical path in which the strands making up the rope are laid. If the strands form a helix similar to the threads of a righthand screw, the lay is called right, or righthand; if the strands wind around to the left the lay is called left, or lefthand. In Lang lay rope the wires in the strands and the strands spiral in the same direction.
lead sheave: The first, or main sheave, or pulley for the rope as it comes off the winding barrel. See fleeting pulley for location and alignment data.
OSHA: Office of Safety and Health Administration. For information on safety requirements applicable to tower clocks, contact the local or regional Office.
overwound barrel: A winding barrel system in which the cable passes over the barrel as it is wound on. A right lay rope on an overwound barrel should start from the right hand flange, and a left lay rope from the left flange. See underwound barrel:
plow steel: Plow steels, made in grades ranging through plow, mild plow, improved plow to extra improved plow, are highcarbon (.45 to .80%) steels, used primarily in the manufacture of wire ropes.
pulley: The common, or layman's term for a grooved wheel. See Sheave.
reeving: A term used to describe the path of the wire rope through a system of blocks. A reeving diagram is a pictorial rendering of the desired path for the wire rope.
rock weights: Typical weights per cubic foot for various materials commonly used in tower clock weight systems: bricks; 125; cement, 137; granite, 168; gravel, 109; limestone, 162; marble, 168; sandstone, 143; slate, 175; soapstone, 168; sand (dry), 100.
sheave: A wheel with a grooved rim, mounted in a frame; a pulley wheel or any similarly grooved wheel, used to guide or change the direction of the rope or cable.
snag: A broken wire protruding from the body of the rope, indicating that the rope is probably stressed, either by excessive weight, or, more commonly, by bending around a sheave whose diameter is too small.
snatchblock: A block or pulley with one removable or pivoting cheekpiece, whereby the pulley can be located in the middle of a cable already solidly fastened at both ends.
soldering: Attaching a terminal to a wire rope with pure molten zinc. Strength rating is 100% of wire rope rating.
stop cable: A safety device attached to a weight to prevent its falling beyond the limits imposed by the length (and strength) of the stop cable.
strand: A wire rope strand is made up of wires; the strands are then laid (q.v.) into a wire rope.
swage: To fasten a termination to a wire rope by physically deforming the termination around the rope; as by hammering, or by hydraulic press. Strength is 100% of wire rope rating.
termination: Any of a number of devices and methods used to place a working terminal on a wire rope. Swaging (q.v.), soldering (q.v.), and Uclamps (q.v.) are common fastening methods.
thimble: A grooved metal reinforcement (in a teardrop shape) placed in a wire rope loop to prevent chafing and cutting.
Uclamp: A fastening device, also known as a Crosby clip. A bolt in the shape of a U, used with a forged saddle to terminate a wire rope, usually in a loop. Strength of a clamped loop is 80% of wire rope rating.
underwound barrel: A winding barrel system in which the cable passes underneath the barrel as it is wound on. Start a right lay rope from the left flange, and a left lay rope from the right flange. See overwound barrel:
Publications:
The catalog of ANSI standards may be ordered from:
The American National Standards Institute
11 West 42nd Street,
New York, New York 10036
Tel: (212) 6424900
Copies of each of the standards have to be ordered from the catalog, unless your local library happens to have copies.