A more precise formula
A more precise formula
thanks for the lead this could come in handy,anything for 360 degrees ? big tanks
The formulas in the books and in the web calculator I linked are approximations and do not account for chord length but assumes the bend is circular.
Using the more exact method with chords, for any angle the distance between bends is given by: 2 * inner_radius * tan[angle/(2*#bends)].
For example, to get a circle with an inner radius of 10" and 8 bends:
2*10*tan[360?/(2*8)] = 20*tan(22.5?) = 20*0.4142136 = 8.2843" between bends. The developed length = 8 * 8.2843 = 66.2742".
Another example: to get a 90? bend with an inner radius of 10" and 3 bends: 2*10*tan[90?/(2*3)] = 20*tan(15?) = 20*0.2679492 = 5.3590" between bends. The developed length = 3 * 5.3590 = 16.0770". Compare to the book approximation using a segment length of 5.23" and developed length of 15.7".
As the number of bends increases, the approximate method approaches the chord method. This is because we are getting closer to a circular shape:
For example, to get a 90? bend with an inner radius of 10" and 30 bends:
2*10*tan[90?/(2*30)] = 20*tan(1.5?) = 20*0.02618592 = 0.5237" between bends. The developed length = 30 * 0.5237 = 15.7116". Compare to the book approximation using a segment length of 0.52" and developed length of 15.7".
Keep in mind that even the more precise calc using chord lengths will not exactly match the field results because the field bends not sharp angles between chords but mini-arcs. The chord method should give better results but you need a calculator with a tan function.