Ferrous Beuler

Mathematics in blacksmithing

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Way back in the olden days when I was in school I had a math teacher who said "mathematics is everything in all that we do". At the time I probably thought that was a bit of an overstatement but in hindsight I think he was right about that.
Today in "Problem solving" there is a post by smokeman about the math behind plotting a cone, important stuff if you want to get it right the first time, which he will thanks to replies from littlewolfsmithy and irnsrgn.
That got me to thinking that along with the existing topics/headings such as Blacksmithin', Problem solving, Power hammers, etc. there should be a heading just for mathematical formulas, how-tos, etc. so I did a search and found posts and threads on math scattered throughout the forums.

I feel math is important enough to have its own place here. Any thoughts? Dan:)

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TASMITH   

I would agree with you on that one Dan! I have several pages of notes on quick shop calculations for various types of work some of which are ;
Calculations for: Links, shackles, clams,hoop, coned hoop(top dia. smaller than bottom dia.), bevel clam,angle iron rings..etc. That is just a sample of some of the things I have quick calculations for as well as all the standard area, volume, capacity type calculations as well as the metric conversion charts for decimal, drill sizes, temperature and such. It could be a significant resource place.

Terry

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Glenn   

Dan as you say, mathematical formulas are everywhere. There are books written on the math used for very narrow subjects, the Golden Rectangle BP0026 Principles of Design, as well as layout and design, BP0005 Circle Division, being examples.

Collecting all these in one place could end up being a jumble of formulas which would have to be categorized in order to be found. The organization could be a nightmare as more and more formulas were added and they started to cross link across categories. The only way I can see it being done is through a search engine, but even then you would have to refine your search.

The next issue would be taking a formula, and providing a full explanation of how it is used with photos of the application, so the viewer could then understand and apply the information.

Dan, it is your idea, take a formula and set it up much like a blueprint, showing us the formula, the application in use, and photos. Send it to me and I will put it on the site. Second would be text only (or with drawings). A full explanation would still be useful to those that have problems with math in general.

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jimbob   

Glenn could it be done as a Sticky as we did with gas and coal forges?
as a side note it might be nice to develop some tables that could be printed and laminted to keep in your shop

Edited by jimbob

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Glenn   

The sticky idea uses the search engine and a little human intervention to get things started. As new material is added the sticky becomes more and more outdated. After a while the search engine is needed again to locate information. After a couple of revisions the sticky becomes lengthy and cumbersome and still does not cover the new information posted.

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Dan as you say, mathematical formulas are everywhere. There are books written on the math used for very narrow subjects, the Golden Rectangle BP0026 Principles of Design, as well as layout and design, BP0005 Circle Division, being examples.

Collecting all these in one place could end up being a jumble of formulas which would have to be categorized in order to be found. The organization could be a nightmare as more and more formulas were added and they started to cross link across categories. The only way I can see it being done is through a search engine, but even then you would have to refine your search.

The next issue would be taking a formula, and providing a full explanation of how it is used with photos of the application, so the viewer could then understand and apply the information.

Dan, it is your idea, take a formula and set it up much like a blueprint, showing us the formula, the application in use, and photos. Send it to me and I will put it on the site. Second would be text only (or with drawings). A full explanation would still be useful to those that have problems with math in general.

Wow! Looks like I opened a can of worms big enough to open a string of baitshops from Mille Lacs to Okeechobee!
As far as math goes I never considered myself in the running for the "student becomes the master" mentality, hence my hope a sap like me could have access to such a resource, I'm not the sort you want adding to it!:o

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The ever present math.

One of my big projects last year took more than three days total to do the math, and even then a number of calculations occurred on the fly during the creation process. From the most simple math to figure the length of stock needed for a hook, to much more advanced stuff for curved staircases and railings or intricate multi component structures we all need to be reminded how important this is.

Creating a simple source for these diverse and often difficult to locate formulas would be a big help to those who are math challenged. Good math takes the guess work out of forging, and for those who are contemplating a full time smithy, math is a very necessary evil.

I happen to really dig the technical and mathematical part of metal working. Obviously an artistic flair helps, but if you don't have or can't find or can't do the math, your gonna have problems.

Thanks in advance to those of you who have "volunteered" for this task.

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Seriously, I didn't use math very often, UNTIL I became a blacksmith. First I started using triangles to check square, then it was Pi for making rings. It was short step to using math to develop patterns for lighting.

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I'm the same as Gerald.
Not being what they call a 'gifted academic' at school, math was for the other guy.

Then blacksmithing... and boy did I have to scramble to catch up.

Good math skills allows me to forge with certainty. I don't have to constantly check or compare forgings.

It saves me a tremendous amount of time and perhaps the better thing is that because I don't have to check or compare, it actually cuts down the number of times a piece goes into the fire. This improves my quality of work.

I think an area of IFI dedicated to at least storing formulas or techniques where math or a geometric drawing is used to give a starting point to a problem (such as in tapered hoops - like rings for a barrel).

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irnsrgn   

drawn down tapers= 1/3 the total length to make a taper from shaft size to a point.

to determine what size flat a round shaft will make or vice-versa, measure the circumfrence or all the sides, they will be the same.

To find the diameter of a machine screw, multiply the size (number) by .013 and add .06 works in reverse too, diameter - .06 divided by .013 = machine screw size.

And don't forget trig, length of leg times tangent of angle gives the distance (tangent) at 90 degrees at the end, Cosine, is the same except it is the distance down to make a right angle at the bottom, Cosine and Tangent are the same distance just figured off differnt legs of an angle.

hypotenuse was the most used mathematical forumula in my work in the shop AB

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Lysdexik   

Hi Guys.
I have seen a lot of mentions of "Old Books" in a few posts lately, those old school books were realy good at explaining math and practical geometry for people who didn't have the luxury (or hinderance) of a calculator. Does anyone have a practical math and/or geometry book from the late18 early1900s, I use stuff I learned for my 11 plus every day, but, there was a pile of learning I was too green to see, I wouldn't mind a second shot at an education!!

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Lysdexik   

For Junior.
In the Lakota nation, there was a chief, who had three wives.
One wife sat on a buffalo skin, and she bore three sons.
Another wife sat on a horse skin, and she bore four sons.
And the final wife sat on a hippopotamus skin, and she bore five sons.
Which proves - WAIT FOR IT - that...
The squaw on the Hippopotamus, equals the sons of the squaws on the other two hides!!
Ta dah, thank you.
Paul.

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irnsrgn   

I have lots of old math books, algebra, geometry etc, The one old book I have that has the most understandable and easiest to comprehend math in it is, my 3rd edition of the American Machinists Handbook, not to be confused with Machinery's Handbook.

I also have an 1885 or 6 sheetiron and coppersmithing book.

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So going into more detail on the formula for checking square. For all you carpenters out there, this is old hat.

By using the math for a right angle triangle, we can check square on layout of a gate. Most of us know it as "3,4,5" Which means that if from a corner, I measure three feet on one side and then four feet on the other side, if the angle of the corner is 90 degrees, if I measure across, the length will be five feet. To make it more useful, let me put it in math terms: Actually Irnsrgn already did with AB

Edited by Gerald Boggs
grammer

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That Pethagerous feller, he was sharp...

I have something that I gleaned from an old book ( 1900 Practical Blacksmithing - Holdstrom ).

Ring size = diameter x 3 + 4 times the thickness. Used for tire length or other ring needs. Comes pretty close. I just tell 'em if you want it more accurate, hire a machinist.....

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one nice thing about 3,4,5 is that we can not always reach the diagonal, due to reach, height, blockages from other structure, power lines, etc. Its so nice to have options.

Thanks for the reminder.

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Hi Guys.
Does anyone have a practical math and/or geometry book from the late18 early1900s, I use stuff I learned for my 11 plus every day, but, there was a pile of learning I was too green to see, I wouldn't mind a second shot at an education!!


I don't have one from the 1800's, but it hasn't changed much.
I like 'Math on call"
ISBN13:978-0-669-50818-5 (Hardcover)
There is a soft cover version.

I find their explanations very easy to grasp. And lots of pictures-really!

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Ring size = diameter x 3 + 4 times the thickness. Used for tire length or other ring needs. Comes pretty close. I just tell 'em if you want it more accurate, hire a machinist.....


I just crunched some numbers using this formula. It is very close to being spot on.
And if you don't have a calculator at the side of the forge, easy math.
Thanks for this one. Very useful!

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