More on the Offset Bend math and calculator

I updated the offset calculator and article again. I was curious about finding if the method to find the distance between bends by multiplying the height of the offset by the cosecant of the angle was correct. This is where those multipliers of 6 for 10 degrees, 2.6 for 22.5 degrees, 2.0 for 30 degrees, 1.4 for 45 degrees, and 1.2 for 60 degrees come from. This method is an approximation and is not mathematically correct. For most offsets of up to 45 degrees, there is little difference in using this method or using the correct mathematical calculation. However, again for steep angles and large pipe these multipliers will give you errors that require recutting the pipe and/or altering the bend angles. I have placed the correct calculation in the offset calculator and added a conversion for decimal to the nearest 16th of an inch in fractions.
I purchased Jack Benfield's Benfield Conduit Bending Manual from Amazon.com. I read in this book that has sold over 2 million copies that there is no need to use complex trigonometry and that the tables and methods in this book can be used for any size pipe. I differ with Jack on this because I have used his famous zip tables in the field for large rigid pipe and had nothing but curse words for whoever invented these inaccurate tables. Jack Benfield wrote the book based on his experiences starting back in the 1930's. Perhaps from the 1930's to the 1960's using precise mathematical calculations was a bit of a task. However, today, with a desktop computer in every job shack, I think the time has come to quit being simple and inaccurate. Jack's book is, in my opinion, outdated. Today's electricians are computer literate. The IBEW apprenticeship school in Fairbanks, Alaska even has a computer lab to teach journeymen and apprentices how to use a computer. I believe that using computers for bending pipe has come of age.