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:
