Rigging Math

(Made Simple)

A Primer by

Delbert L. Hall, Ph.D.

ETCP Certified Rigger

ETCP Recognized Trainer

Lesson 12: Fleet Angles

       In an ideal world, when a cable runs over the sheave in a loft block (or any other type of block or pulley) the cable should be perfectly perpendicular to the axle.  If this were true, then the cable would align perfectly with the groove in the sheave, and its fleet angle would be zero.   We do not live in a perfect world, and when a cable runs between the head block and a loft block (for example), the cable might not be perfectly aligned with the groove in one or both sheaves.  If this is the case, the cable can cause the groove to wear, since the cable is harder than the sheave.  The further out of align (a fleet angle greater than zero) the more (and faster) the sheave will wear.  Stage rigging manufacturers specify that the blocks or pulleys used in stage rigging should be installed so that the fleet angle of the cable is no greater than 1.5 degrees.  This raises the question, “How can you tell if the fleet angle is 1.5 degrees or less?”  That is the subject of this lesson.

       To start, we need to establish a line with a zero fleet angle to the groove of the sheave.   Once this is done, we compare the “Offset” to the “Distance” from the sheave to the point of the zero fleet angle line from when we measured the “Offset.”  

A good rule of thumb (one that is easy to remember) is that you are allowed 1 unit of “Offset” for every 40 units of “Distance.”    A slightly better equation is Maximum Allowable Offset = Distance * .026 (which is the Tangent of 1.5 degrees).  This will not tell you the fleet angle of the cable, just if it exceeds 1.5 degrees.   Using this equation, let’s work though a sample problem.

Example:  What is the maximum allowable offset of a cable at 25 feet?

The equation for solving this problem is:  Maximum Allowable Offset = 25 * .026

[ON/C] 25 [X] .026 [=]         (.65) feet

By multiplying .65 [X] 12, you can convert feet to inches, which would give you a measurement that might be a little easier to understand. 

Maximum Allowable Offset = 7.8 inches. 

Computing the actual fleet angle

If you want to know the actual fleet angle (in degrees), you must know both the Offset distance and the measurement Distance.  Then, plug these numbers into the following equation:

Angle = Arctangent of (Offset / Distance)

If the Offset is 6” (.5 feet) and the Distance is 25 feet, the fleet angle is:

Angle = Arctangent of (.5 / 25)         or

Angle = Arctangent of .02                or

Angle = 1.145 degrees

Worksheet

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