Pi and K factors: The mathematical beauty of sheet metal

I was never a math wiz, but I was blessed with good teachers. In high school, I remember sitting in Algebra II class and hearing one of my fellow students give a loud sigh before he raised his hand: “When will we ever use this?” My teacher shot back. “See the pencil you’re holding? The people who made it couldn’t have done it without the problems you’re working on right now.”

Sure, my classmates gave him the expected groans, but when I think back to that statement, I know we need more teachers like him. Even in this economy, manufacturers crave people who don’t get scared by adding and subtracting three or four places to the right of the decimal point. Operating a press brake, you basically work with a bunch of triangles (V die opening and bend angles) and degrees of a circle (bend radii). Algebra and (especially) geometry and trigonometry are everywhere.



A recent story on National Public Radio told how manufacturing jobs now require more math skills. I think it’s more accurate to say that the manufacturing jobs that are left happen to require a solid math background--and thousands of those jobs remain unfilled today, even in this economy. Also, it’s not as if metal fabrication jobs didn’t require math decades ago. In fact, you could argue those jobs actually required more math skill. Some shop leaders today have told me how they remember days (sometimes fondly) of manual flat layout, when they took out the slide rule and did it all by hand.

Today software and modern machine tools can automate much of the math, but I think the equations still matter. It’s really the grammar of metal fabrication. For decades, experienced press brake operators have known that a K factor, or bend deduction, is two times the outside setback (or X factor) minus the bend allowance. Some operators even knew that the bend allowance (length of the bend’s neutral axis) can be revealed by multiplying the complementary bend angle by several factors, including such cryptic numbers as 0.017453, which is pi divided by 180, essentially converting numbers to degrees around a circle.

Sure, even before modern software, operators looked at bend deduction charts and learned a lot by doing, paying attention to the experienced guys who knew the trade. But I feel that knowing the math really reveals the straightforward logic of sheet metal forming and fabricating. Material variables--be they varying grain directions or different heats--will always add a dash of unknowns.

But unlike so much in life, metal forming’s foundation is rooted in mathematical truths that, compared to the trials and tribulations of everyday life, are extremely predictable. Mix this scientific predictability with the wild ride of running a contract metal fabrication business, and you’ve got a thing of beauty that’s both chaotic and rational at the same time.