figuring

[fat pete]

I just searched "math and arithmetic" i didnt see a post that just discussed different math or arithmetic used in smithing...i realize the inventory, the pricing ect...but how many of yas actually sit down and actually figure out how much metal to use to draw a taper for instance ... what, or maybe i should ask when or even, do you sit down to figure before you light the fire?

[Doug C]

Just do a search on formula here are a few results...Maybe we should collect all of these and put themm in the Alchemy and Formula forum.

When Blueprints are back go here for drift size info: I Forge Iron - BP1051 Punch Calculations

Rivet length to width ratio(thanks Glenn): 1-1/2 times the stock diameter is a good place to start.

Scroll Collars

Calculating radii

Chimney Diameter

Proper Anvil Height

[fat pete]

Thanks...I didnt think to use formula...lol the power of key words!
I aggree...that would be a good idea to have a section of typical simple math solutions to different shop math problems...fortunately i am aware and actually pretty good with math..i blame it on learning the times tables..somehow i guess they dont teach the kids the times tables any more...some new stuff...but for the guy who int nessasarily realy good at 'rithmatic...or when to apply it I thought a little thread would open some new views for beginners and the experienced as well...its usually mentioned in the classes I have had and in most of the books.

[Dave Hammer]

You guys take this way too seriously..... Whatever happened to just using eyesight and your thumb???????

[BIGGUNDOCTOR]

1; By gosh,and by golly

2; eye

3; experience

4; go with the flow till it looks good

:rolleyes:

[jake pogrebinsky]

Mensuration was always essencial,even(or maybe especially)before the industrial revolution,when the blacksmith became the machinist.

Traveller,inside and outside caliper,and a lead or leather strip to take down curves were the tools ALWAYS at hand,in constant usage all day.

Repeatability,to name only one of the concepts,was paramount.(We're talking stub-axles for a wagon or a cart,vs.some goofy plain-twist on a candlestick).

I've seen an old(early 20th century)textbook for blacksmithing tradeschool,in England.The FIRST exercise there was calculating the measurements and shape of a quadrefoil,so that the last lobe that has a weld in it will come out even.The precision was high.The students in the photos looked about 11-years old...(Wish that i was there).For those whose remarks above advocate random eye-balling:How many quatrefoils have you done?What if there's a number of them collared together?Or how about the pitch of the elements decending down a stairwell?(Curving/compound...?).

As it is,doing serious work randomly is reinventing it all,one needs it,it did not come about as an accident.And for those serious about learning,please don't overlook that most important skill.

[Don A]

Repeatability,to name only one of the concepts,was paramount.

Until I got serious about blacksmithing, I never had a great deal of respect for gothic architecture and other styles that contain numerous duplictes and repeats.

In the early days, "make one of these" wasn't too bad, but when I got to the point of "we need 14 just alike", well, thats where accurate calculation started to matter.

I probably overkill it a bit (I work in AutoCAD for my day job), but I enjoy the challenge of trying to make my stuff come out the way it looked on paper and/or in my head.

I still keep a spool of lead wire close at hand at all times.

Don't get me wrong though; I still enjoy design on the fly, from time to time. Knife blades happen that way on occasion.

Don

[jeremy k]

Pete - I use formulas sometimes. For instance, I needed 3 pcs that have a 1" ball on each end and 1/2" round between them ( basically a long dumbell shape 20" in total lentgh each ). I started out with 1" round stock - swaged a ball on each end and drew out the middle down to 1/2" round. This required figuring the total volume needed of the finished piece and then starting with a known stock size ( the 1" round ) and cutting that to length so it has the same volume ( just under 6" of 1" round )as what the finished piece does. After all the forging is done, and the metal is moved into the right places - you have your finished piece at the finished pre-determined sizes. Yes it does take a little bit of time to do the numbers but - it works and it's fun to see it take shape and end "in the right shape". - This is a time I wished I had taken more math in school. - JK

[Mainely,Bob]

I suppose there are actually 3 different approaches.
1-do the math
2-use jigs,patterns and layout tools
3-trust your eye/experience and just wing it

I agree that it would be extremely handy to have these formulas in one place here.
It would free me from having to remember where I last put my pipe fitting,tin knocking and machinery handbooks. :)

[jake pogrebinsky]

Very well put,Don,thank you.Yes,once one is comfortable working deliberately,then the sky's the limit as far as creativity goes.Before that,i guess it all depends on one's "talent",innate ability.And for many of us winging it ends up looking sub-par.

Jeremy,good for you.I wouldn't know how to compute by volume(booted out of 7th grade...).I usually do the most primitive kind of figuring:Measure and mark from the unworked end of stock,to at least know how much it took to forge a sample of what i need.Done at several stages it can provide somewhat of an idea.Experimenting like this is not the most economical way,coal/time/stock-wise,math is cheaper!
But then again,the original stock is not always regular(been working much anchor chain lately),and so winging it is always present in any case,so it's all a balance.Yet another reason to cover all bases,if possible.

[dablacksmith]

most of my math is to get close for forming circle (pie) i dont try for a exact number but somwhere close add a couple inches and go.. also figureing how many product you can get out of a leingth of steel ... that kinda thing havnt used much in formulas but can understand useing one if it helps....nevered figured volume tho way to much thinkin fer me!

[primtechsmith]

This has got me thinking...

1. Sometimes I do measure for tapers etc. but it is measure the bar before and after the taper and subtract the two numbers for a rough taper length.

2. Maybe I should make my measurements nd math more accurate and stick to that. I think that within itself would become a great excercise to make me better at the anvil. I find myself not at all pleased with my projects and I think it is mainly due to my lack of sticking to the original design and measurements. I always find myself saying it is close but not exactly what I had drawn/thought up.


...I think it would also help if my tape did not have the first 3 inches wasn't burnt up and hard to read due to me and a hot bar....

Peyton

[clinton]

Brian Brazeal gives some really good info on math for scrolls in this thread
on the second page he explains how c scrolls fit inside a circle its just math

[D-ski]

There is a time and a place for both "eyeballing" and for doing the math. I do a lot with constant volume forging. If I am taking 5/8" square down to 5/16" round, how much 5/8" do I need to start with to get 5" of the 5/16"? I have charts that tell me the number of cubic inches of steel in 1 inch of the various stocks that I routinely use. I also keep a small calculator in the shop to help with these calculations.

You can also work with weight. If you know the weight of the final object, you can divide that by the weight of a cubic inch of steel. Once you know that figure, you can translate it into how many inches of stock you need. True you could get the same answer through trial and error, but using math gets you inside the right ball park a lot quicker.

If you have been reading the Mark Aspery books, you will notice that he uses a lot of math to help figure things out.

A good example of needing math came up this past weekend at the Gichner Memorial Hammer-In. If you are going to submit a ring to the upcoming ABANA CONFERENCE, the ring needs to be made from 1/4" by 1" and the diameter needs to be 10", how much stock do you need to start with??

Formulas and a calculator are just another tool in the toolbox.

[thingmaker3]

If you are going to submit a ring to the upcoming ABANA CONFERENCE, the ring needs to be made from 1/4" by 1" and the diameter needs to be 10", how much stock do you need to start with??

Easy! Use 2.224 pounds. B)

[pkrankow]

If using volume or weight of the finished part (or any other estimation method for that matter), don't forget to account for scale loss from the necessary number of heats. In one of the books listed in the (still missing) blueprints the author recommends as much as 10% loss of material depending on the number of operations, thickness of stock, and skill level of the smith. The 10% loss was used for the student lessons that were presented.

Obviously a skilled smith with a power hammer or skilled strikers will have less loss than a new smith with a hand hammer. Less obvious is that thicker sections will have less loss of material per heat than thinner sections. Likewise taking one or two heats to make something will loose less material than taking 10 or 20 heats for the same set of operations.

Phil

[Dragons lair]

This has got me thinking...

1. Sometimes I do measure for tapers etc. but it is measure the bar before and after the taper and subtract the two numbers for a rough taper length.

2. Maybe I should make my measurements nd math more accurate and stick to that. I think that within itself would become a great excercise to make me better at the anvil. I find myself not at all pleased with my projects and I think it is mainly due to my lack of sticking to the original design and measurements. I always find myself saying it is close but not exactly what I had drawn/thought up.


...I think it would also help if my tape did not have the first 3 inches wasn't burnt up and hard to read due to me and a hot bar....

Peyton

Now it's got me thinking. I take a 9" bar taper measure and subtract both from what?
May just be the oldtimers acting up.
Ken

[Nakedanvil - Grant Sarver]

Well PK, yes and no! A number of low heats will scale off very little compared to a couple of blistering heats.

I still have a steel weight slide rule. Set the bar size and read the weight opposite the length. Then set to the bar size you'll be starting with and read the length of that opposite the weight.

Volume of a sphere is diameter cubed times .524 times that by .283 to get the weight.

I usually calculate and then do a trial piece.

[Sukellos]

I can fail a simple math test in 6 languages!

[pkrankow]

I can fail a simple math test in 6 languages!

Yes, but you can use a computer, so just Google the "volume of a ..." that you need, and work form there. There are a bunch of free web tools for that. Google also acts like a calculator and conversion tool, but I'm sure that you computer has a decent calculator on it too.

Phil

Grant,
You are right, making a sparkler out of steel can take inches off 1/2 inch steel quite quickly.
Phil