Calculate Shrink with Offsets
- Thread starter EEC
- Start date
- Status
im not sure on the calculator. But i can tell you your amount of shrink varies with each degree you bend.
per inch of offset subtract
10 degrees would be 1/16" per inch of bend
15 degrees is 1/8"
22.5 degrees is 3/16"
30 degrees is 1/4"
45 degrees is 3/8"
60 degrees is 1/2"
if your bending an odd degree like a 36 you can get close enough by estimating 5/16
per inch of offset subtract
10 degrees would be 1/16" per inch of bend
15 degrees is 1/8"
22.5 degrees is 3/16"
30 degrees is 1/4"
45 degrees is 3/8"
60 degrees is 1/2"
if your bending an odd degree like a 36 you can get close enough by estimating 5/16
The mathematical approach to determine shrink per inch of offset is...
[(1 ? cos θ) – 1] ? sin θ
...where θ is the bend angle.
The above calculation does not account for the gain of the bend, which is why the result will be slightly greater than the amounts posted by nunu161. However, the difference will become noticeable on large offsets.
Many scientific calculators have different entry process. The following is for a basic one such as the one included with MS Vista Ultimate OS on my computer.
For example, an offset of 6" using 30? bends...
[3] > 3
[0] > 30
[cos] > 0.866...
[1/x] > 1.154...
[–] > 1.154...
[1] > 1
[=] > 0.154...
[/] > 0.154...
[3] > 3
[0] > 30
[sin] > 0.5
[=] > 0.309...
[*] > 0.309...
[6] > 6
[=] > 1.856...
The value after " > " is what is shown on the display.
***
Accounting for gain per bend with a shoe radius of say 4 1/2"...
0.0126 ? 4.5" = 0.0567
2 ? 0.0567 = 0.1134
Subtract one-times your gain from the basic bend to bend distance...
6 ? 2 (multiplier for 30? offset) = 12
12 – 0.0567 = 11.943 or 11-15/16" for bend-to bend marks
Subtract two-times your gain from basic math shrink...
1.856 – 0.113 = 1.743 or 1-3/4" total shrink.
If 30 degree offset has 1/4" shrink per inch of bend. The table for shink for 6 inch offset, will be 1 1/2 inches of shrink. From this [(1 ? cos θ) – 1] ? sin θ
you came up with 1.856
But now you are taking gain into account. I do not understand why you do this. I guess your'e saying that the raduis of be bends has a effect on the shrink calculation
you came up with 1.856
But now you are taking gain into account. I do not understand why you do this. I guess your'e saying that the raduis of be bends has a effect on the shrink calculation
The values posted by nunu161 are approximate shrink per inch of offset. They will serve the purpose in many if not most instances, especially those where you can fudge the angle a little, and/or cut the tail to length after bending.
And yes, the radius of the bends have an effect on shrink... and it actually has an affect on bend to bend distance also. Most reference materials only account for straight line measurement. A bend in the "corners" will always shortcut that distance a little. It is called gain, and is more notably discussed for 90? bends in reference material. However, all bends have some gain... varying in length from negligible to inescapable (i.e. where pre-bend accuracy is required).
Do yourself a favor and get one of these...
http://www.howtowireahouse.com/Greenlee_38405.html
Check your supply house to see if they have it for free... but usually when they get them they disappear real fast, and usually on the who-buys-the-most buddy system
The method for calculating shrink in this hanbook is, IIRC, to find the cosecant of the bend angle and subtract the secant. I believe the result is the same as the formula I gave you (cosecant and secant are just inverted trigonometric functions). It also has a table of gain mulitpliers, amongst a bevy of other info... some related directly to their bending equipment, some not.
No, the gain in the first bend makes up for it.
After drawing it out in CAD I discovered the formula I posted earlier is in error. The correct formula is...
(1 ? sin θ) ? (1 ? tan θ)
which is the same as
csc θ ? cot θ
The calculator entry for a 30? offset in Windows Calculator would be
[3] > 3
[0] > 30
[sin] > 0.5
[1/x] > 2
[?] > 2
[3] > 3
[0] > 30
[tan] > 0.577...
[1/x] > 1.732...
[+] > 0.267...
multiply for 6" offset
[*] > 0.267...
[6] > 6
[=] > 1.607...
***
Subtract two-times your gain from basic math shrink...
1.608 ? 0.113 = 1.495 or 1-1/2" total shrink, which is the same as 1/4 inch shrink per inch of offset.
- Status