When it is necessary to measure tension using a sheave with a scale the tension must be calculated from the scale reading. This can be done efficiently using a table or by using the law of cosines to calculate the tension for the incoming cable. The method below assumes that the incoming tension equals the out going tension which is practical in most applications. This is particularly true if the cable has not yet arrived at the sheave. When larger cables pass through a sheave at ninety degrees 100 to 150 pounds of tension is added to the out going tension, but this is relatively a small number compared to the larger tension values. There are no data available on how many pounds of tension is added for varying degrees of deflection by sheaves, but certainly the amount of tension added to the out going cable would be a function of the stiffness of the cable and the number of degrees the cable is deflected by the sheave. Sheaves themselves are considered frictionless and no sheave produced tension is added in calculations as long as the sheaves are well lubricated, free wheeling, and properly maintained.
The table below was calculated using the Law of Cosines assuming a and b are equal.
Law of cosines:
C2 = a2 + b2 - 2 a b Cos (angle between adjacent vectors in solution triangle)
The angle between the vectors in the solution triangle as shown below is equal to 180 degrees minus the angle between the cables.
C = scale reading or sum of tension in and tension out
a and b represent the tension in and tension out - assumed to be equal.
The following equation was used:
Tension = SQRT (scale reading 2 / (2* (1 - COS (180 - angle between cables in and out))) )
The following calculator solves this problem:
The results for the given degrees between cables follows:
Multiply the scale reading by the multiplier to get the tension in or out.
Scale Angle Multiplier Between Cable to get in and out Tension in/out 175 11.463 170 5.737 160 2.879 150 1.932 140 1.462 130 1.183 120 1.000 110 0.872 100 0.778 90 0.707 80 0.653 70 0.610 60 0.577 50 0.552 40 0.532 30 0.518 20 0.508 10 0.502 0 0.500
Some applications follow:
For Straight Through Scale reads 0.
For Angle = 60 degrees:
For angle = 90 degrees:
For 120 degrees Scale reading = tension: