Ferrous Beuler

Mathematics in blacksmithing

48 posts in this topic

Thanks for the ISBN Mark, makes ordering real easy, I had never seen the (DX3) + (4XT) before, but I like those old "ready reconer" solutions. I love working with computer jockeys who have to run back to their office to find out how high is up. Sorry but it's my pet peave! I was teaching an engineer to make a windsor chair, he was trying to use a calliper to make his measurements, the seasonal changes in his elm plank seat amount to three sixteenths, why bother with five decimal places - AGAIN Sorry! but it's my axe and I'm gonna grind it - LOL.
Paul

Share this post


Link to post
Share on other sites

Pushing the envelope here to the furthest limits of my abilities... I would like to contribute what I can to help this out.

If I had an apple and Suzy came along and gave me another apple (drumroll...) I would have TWO apples.

Ran through that one twice to be sure. Dan ;)

Share this post


Link to post
Share on other sites

Ah, but you have to be careful there.
If 'A' beats 'B' and 'B' beats 'C' you might think that 'A' would beat 'C'

....not in scissors, paper & rock,!

Share this post


Link to post
Share on other sites

Developing patterns for pyramids or here's a second place we can use 345

Ok, here we go. Bear with me as I try to get this written in a manner that's understandable. This if I remember correctly, was my first math problem beyond checking square and left me wishing I had spent a bit more time in school. The shop I first worked at (Stokes of England) suddenly started getting lighting orders. This particular order was pretty straight forward except for figuring out the tops. The order was for thirty lanterns, ranging in size from 12 inches high to 32 inches. They were all the same design. The old four-sided straight sides with a pyramid top. The math problem was: how to make all the tops look the same in proportion. When looking at the drawing, the top is ten inches high and ten inches wide, what then size to make the pattern of each side?

First off, if you look at a pyramid from the side, it's a equidistant triangle. In this case a triangle with a base of ten inches and a height of ten inches. An equidistant triangle can always be divided into two right angle triangles of equal size. So I now have a right angle triangle with a base of 5 and a height of 10. To get the hypotenuse,* I simply apply 345. So 5 squared is 25** and 10 squared is 100, giving me 125. The square root*** of 125 is 11.18 inches or in fractions 11 3/16 inches. What I now have is the height of one side of the pyramid, 11 3/16, Remember the sides of the pyramid was a equidistant triangle with a base of ten inches. Now all that remains is to make a pattern 11 3/16 high by 10 inches wide and you have one side of the pyramid. Lay it out four times side by side and you have your pattern.

*that's the long side of a triangle.
**Squared is simply multiplying a number by itself. 2 times 2 is four
*** The square root is going back the other way. The square root of 4 is 2, for a 25 it's 5 and for a 100, it's 10 etc...

Does this make any sense, or am I rambling incoherently?

Here's a photo of some lights I did using the math above.

10885.attach

Share this post


Link to post
Share on other sites

Management rule 1 "If you can't convince 'em confuse 'em"

Sorry, you lost me, but I am sure (Ithink) you're right.

Share this post


Link to post
Share on other sites

Does this help?

10900.attach

Edited by Gerald Boggs

Share this post


Link to post
Share on other sites
Management rule 1 "If you can't convince 'em confuse 'em"

Sorry, you lost me, but I am sure (Ithink) you're right.


Promote that man!

Share this post


Link to post
Share on other sites

Hi All,

I have a 13 year old son on the autism spectrum who is very interested in blacksmithing and has been so for several years. He is very high functioning, extremely creative, but has an  aversion to math. I'd love to be able to bring some practical application into our homeschool environment to teach him the basic math skills to help him be successful in blacksmithing and life. Ace is an out of the box kids who currently has no desire to go to college and that's totally okay with me. I know his hands on approach to life is how he best learns and to force too much on him at once is detrimental.

Tonight he is taking his very first blacksmithing class at The Crucible in Oakland, California. Any helpful advice, especially concerning math, would be greatly appreciated.

Thanks so much!

Teri 

Share this post


Link to post
Share on other sites

Well one classic example is calculating layers in a pattern welded billet.  Others are How much steel do you need to make a circle of diameter X or a Square or a triangle for a dinner gong or ...  Lots of stock calculations that can be done---how much stock do you need to buy to make X of an item?  What's the percentage of wastage that you need to cover if you were selling them? How would that change the price.  (Have him keep a log on how long it takes to make things so you know in the future how much to charge...)

Share this post


Link to post
Share on other sites

The math of the blacksmith is geometry, some easy some not so. Linear quantities is probably the most common thing we need to know. How much do I need to do x x x? Making a railing or grill shape is probably the easiest, simple addition. Scrolls and other curvy things is trickier and CAN involve math far beyond my meager skills. I use a piece of wire to trace the forms and measure the wire.

Circumferences is a LITTLE harder but it's simple multiplication, give him a large button calculator and tell him to suck it up life is about doing things we don't like. No help with that one.

The toughest calculations I know of is how much stock to start with for tapers. The longer and more narrow you draw stock out the farther it will go on the same stock. Confusing? You betcha.

For example making a pointed leaf without a drip end. Draw one end a piece of 3/8" sq. to a short point say 1/2" long. How far back on the stock do you start the taper? NOT 1/2" back! That would make a taper about 1" long or more. I don't try to figure out how much to start with, I just make the short taper as short as possible, it's easy to make them longer. The trick is in hammer control, you MUST deliver strikes to the tapered face, NOT wander all over the end of the stock.

A method I use to estimate starting quantity to duplicate, repair, restore, etc. a piece is weight. I weigh the original and add for scale loss. Estimating scale loss before starting a project is pure experience you have to be able to estimate how many times the project has to go to the fire. HOT steel in air scales, the hotter the faster and the more is lost. Folk who claim a wastage % are referring to their skills, equipment and practices. There really is no set % scale wastage as a rule of thumb. The faster you get with skill the less wastage.

Some of these things are very visceral, by feel, ear and sight so your boy may become very successful. I've taught a couple aspberger boys and they picked things up quickly. Be straight and to the point, frustration comes from not knowing what a person is talking about. The biggest problem I had with the boys was getting them to ask questions when they didn't know what I was talking about, I had to come up with a comic book punishment to threaten them with if they didn't. We all laughed and things got moving well after that. 

Frosty The Lucky.

Share this post


Link to post
Share on other sites

There is A LOT of mathematics behind blacksmithing, but people who are creative and know little math can exell at some things that non-creative but highly learned people will have trouble with. I've worked with people that can't do ANYTHING without formulas and measurements. It would benefit him to learn some basic metallurgy, (not nearly as "mathy" as it seems) as that would open the door to making blades, but there are a lot of options out there that people like that can really do well. 

Share this post


Link to post
Share on other sites

With my own high-functioning autistic son who likes blacksmithing, I will often go the route of "Look at this: isn't it cool? Let's do it! Hey, you know how we were talking about [geometry problem XYZ] -- well, this is the kind of thing that uses that. Let's review what we did and think about how that formula helps us." 

In other words, use the smithing as a way to introduce concepts and practice their application, as well as using something that he likes doing (e.g., striking) as a reward for getting something right.

Share this post


Link to post
Share on other sites
5 hours ago, Frosty said:

give him a large button calculator and tell him to suck it up life is about doing things we don't like.

Amen.

The guy who does the state inspection on my truck was telling me a similar story about his son.

Typically, the boy's argument was along the lines of "I'll never need to know this stuff in the real world".

And my response was, ... "The guy who can't do the math, will ALWAYS end up working for the guy who can".

Share this post


Link to post
Share on other sites

I recommend the book, "The Value of Science in the Smithy and Forge" by W H Cathcart as the book has formulas that I have not seen anywhere   else.  Available free on Google Books and elsewhere........ or in hard copy as a reprint. 

Share this post


Link to post
Share on other sites

Mathematics can have a number of definitions, even to the point of bordering on the ethereal. Los Alamos is not too far from me, me being in Santa Fe. Los Alamos is full of PhD's, and I had one as a student who was a professional mathematician. In that particular class, I went to the chalk board and was working on diameter and circumference: Pi times the mean diameter equaling circumference. I said that even blacksmiths needed to do some math. My student piped up and said, "Frank, that's not math; that's arithmetic." I kind of knew what he was inferring, and I asked him to elaborate. He told me that he could not explain it very well, but that professional mathematicians get so embroiled in some of the concepts, that they sometimes just have to go fishing (literally).

Share this post


Link to post
Share on other sites

Frosty's point about weight is very instructional.  There are a lot of finished pieces that have curved or twisted tapers which are difficult to measure for starting stock. 

Building on his point, I think ratio's are very helpful to allow scale mock-ups, especially with  easier-to-change mediums like clay.

Calculating volume from weight is helpful when it fits on a scale.  We can also use water displacement to calculate volumes and densities.

 

Share this post


Link to post
Share on other sites
On 2/13/2017 at 1:20 PM, ThomasPowers said:

 Have him keep a log ...

That would be a common log, naturally...:)

Share this post


Link to post
Share on other sites

eeeeeee it might

Share this post


Link to post
Share on other sites

If his daily record shows the same problems repeating in a regular pattern, that would be his log rhythm. 

Share this post


Link to post
Share on other sites

A great many math problems in the smithing world can be solved using graphical layout, no arithmetic or numbers needed.  Dividers, ruler/scale, compass, string, plumb bob, drawing implements, understanding of geometry.  Just a suggestion for a different but entirely valid approach to problem solving.  

Share this post


Link to post
Share on other sites
On 2/14/2017 at 5:59 PM, Judson Yaggy said:

A great many math problems in the smithing world can be solved using graphical layout, no arithmetic or numbers needed.  Dividers, ruler/scale, compass, string, plumb bob, drawing implements, understanding of geometry.  Just a suggestion for a different but entirely valid approach to problem solving.  

That's true.  Superposition is a very accurate way to get things to fit together perfectly.  It's often faster and more accurate to find the middle of a uniform bar section by balancing it on a cutting edge.  For the purposes of forging identical parts out of bar stock, equal mass correlates to equal length.

An old carpenters trick for dividing lengths evenly is to take a ruler or tape measure and pull it at an angle across a table.  You're looking to get the point where the rule crosses the edge of the table to a number that easily divides by whatever you need.  For example, let's say you wanted to divide a 40-1/2" wide piece of plywood into three even sections.  For the sake of argument, let's say that the width sides are parallel, but the ends aren't square.  Dividing fractional inches involves more math, so we're going to do this an easier way.  Putting the corner of the tape measure on one corner, you'd pull the tape diagonally until it crosses at the 45" mark.  Since 45 divided by 3 is 15, we mark the plywood at the 15" and the 30" spots on the rule. 

Those marks will be precisely 13.5" apart albeit at an angle.  You can repeat the exercise with the tape angled in the opposite direction to generate two more points  which line up to divide the piece into three equal sections. 

It takes longer to explain than to execute. 

Another quick tip is to know that an equilateral triangle has angles of 60 degrees.  Using a compass set to the length of one side, you sweep an arc.  Switch the pivot to any point on that arc and sweep another arc that intersects the first arc.  The two pivots, and the intersection define your equilateral triangle every time.  If you need 30 degrees, you mark half the length of one side and connect it to the opposite angle to divide 60 degrees into 30.

Again, it's faster to do it than it is to explain it. 

Share this post


Link to post
Share on other sites

I like laying out hot flat rings with dividers to locate where holes for feet should be places.  Got some old hand forged ones that just seem the right tool for the job.

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!


Register a new account

Sign in

Already have an account? Sign in here.


Sign In Now