Chapter 6   Pipefitter Trade Math Section 6   Cord Length and Laying out Bolt Holes

A description of the problem as encountered in the field

Here is a situation which I encountered recently involving the layout of bolt holes.  

While working on a turnaround, along with some other workers I was assigned to make a cover-plate for the top of a reactor

to be temporarily installed when the spool piece was removed from the reactor.  

We were given the outside diameter of the flange, the diameter of the bolt circle, stud diameter, the number of bolt holes in the flange,

and the cord length between one bolt hole and the one next to it. We were advised that we only needed to cut 8 bolt holes due to the fact that this would not be

pressurized. We repeatedly tried to layout all 36 holes using the given cord length,

but always failed to end up back at our starting point thus completing the circle. My only explanation is that by rounding of to the nearest 16th we multiplied the inaccuracy by

36 holes by the time we completed the bolt circle thus ending up with too much slop.

 If we were off by 1/32 (0.03125) after that was multiplied by 36 we were now off by 1 & 1/8

inches. If we were off by 1/64 (0.015625) we would still be off by 9/16 in the end.

 To resolve the problem I decided to calculate the cord length for only the 8 holes we needed. At the time I did not know the correct formula and was merely lucky to eventually arrive at

something that was acceptable. Since then I have researched and tested to find and verify the correct formula.

Solutions

As usual there is more than one method we can employ to solve the problem. One of the simplest is to acquire a full-faced gasket and trace it, or create a template using a

blind flange. In the absence of such convinces we must resort to mathematical solutions.

 The Pipefitters Blue Book by WV Graves includes information for cord length but when I tried to

use it we encountered the problems described above (apparently as a result of rounding off the results).

Therefore I encourage you to chose a starting point and calculate each cord length from that point to minimize rounding errors.

 

There are also several formulas available for calculating cord-length. Each of these formulas requires certain information to be available in the beginning as well as

calling for varying levels of mathematical skill or knowledge.  

Below is a modified version of the formula I prefer, and an explanation follows.  

Cord length = Dia * the Sine of half of the angle  

   

 When Bolt circle diameter = 22 and the number of bolt holes = 8

 To calculate the length of Cord #1

cord length = diameter * the sine of 1/2 the angle cord length = 22 * sin(45/2) cord length = 22 * sin(22.5)

cord length = 22 * 0.38268 = 8.419  

To calculate the length of Cord #2 cord length = diameter * the sine of 1/2 the angle

cord length = 22 * sin( (45*2) / 2) cord length = 22 * sin(45)

cord length = 22 * 0.7071 = 15.556  

To calculate the length of Cord #3 cord length = diameter * the sine of 1/2 the angle

cord length = 22 * sin( (45*3) / 2) cord length = 22 * sin(67.5)

cord length = 22 * 0.92388 = 20.325  

The length of cord #4 is equal to the diameter of the bolt circle.