Drawing Out Math

[Ridgewayforge]

Hi all,

I was wondering if there is a formula that can be used to determine how much stock you need if you are going to be drawing out to a certain length.

For example, If I were making tongs out of 3/4" round stock, what length of bar would I need to draw out the reins to a given length and a given diameter?

I'd greatly appreciate some help with this matter, I'd like to better be able to predict how my metal will move.

 

Thanks,

RidgewayForge

[Steve Sells]

if you know finished size,  calculate the  volume and start with that plus a little more to compensate for losses to scale.

[Glenn]

You are changing shape not volume. 

 

Like Steve said, always add a little for any loss, or imperfections in the new shape. 

 If in doubt use modeling clay to check your math.

[Jack Evers]

Good advise, doesn't matter how much you hit it, the volume won't change. A true cone has a volume 1/3 the base area times the height, while a cylinder volume is the base times the height so a rod drawn into a true cone would be three times as long. I suspect your next question would concern curves. The neutral axis (center) doesn't change length. I want a 6' circle from 3/4 ' wide stock, the center of the stock forms a 5-1/4 inch circle so the stock length would be 16.5 inches (Pi times 5-3/4).

[LastRonin]

Basic geometry. L x W x H = (n) for square and rectangular, and Pi x R² x L = (n) for round. (n) is the resulting answer. These are the formula's to determine the volume, use the numbers for the end result you want, then take the (n) and use it along with the dimensions of the starting stock in these formulas: (n)/W/H=L for square or rectangular stock, and (n)/Pi/R²=L

 

Pi is a very long number but 3.14 should be accurate enough.

 

And like Steve and Glenn both said, add a little for loss and imperfections.

 

@Glenn- Definitely a good idea about using the clay. Question on this... I would guess you start by making the desired finished shape and then mash it into the starting stock's dimensions to get the length?

[Francis Trez Cole]

this might help even though it is a promotion video

http://www.youtube.com/watch?v=lp274DW9dIc

[Pault17]

Ronin, I do the clay thing alot.  many times I use it to practice/plan hammer strokes on a particular element.  it always works to help figure starting amounts, again, adding a little for loss and confusion.

 

Ridgeway, the math is solid (funny how in school I used to wonder when I would use this stuff), if you're the figuring kind.  After a while you will develop a level of ability to visually guesstimate the amounts and not be far off (for things like tongs and tooling). 

[Rich Hale]

The neutral axis (center) doesn't change length. I want a 6' circle from 3/4 ' wide stock, the center of the stock forms a 5-1/4 inch circle so the stock length would be 16.5 inches (Pi times 5-3/4"

Jack I have not tested your formula. However I  have made a lot of horseshoes. I can take a piece of 5/16" x 3/4" that is 11 inches long and turn a shoe that will grow on the outside curve almost two inches in length. 
As I change it from straight to curved it thins along the outside and thickens along the inside. A shoe needs to be mor flat than that and in fact hs to be thinner in some parts that others. that requires more forging,,,if the shoe is fullered it gains leength and punching nail holes also causes it to grow.

I know it grows even if not fullereed or holes punched.

My message here is not about shoes or formulas..simply that as you work steel and change shapes metal moves. How much or where is dependant on the smith and that is somewot dependant on skill level. If yoiu can change the shape in a minimum of heats with a minimum og work it will change less.

If you are going to do a run of pieces the same size you can find a starting point with math. But then a test p;iece will let yoiu know how close you are. As you repeat that piece and get the moves down yoiu may find a difference in first to last ones. If you are improving and use fewer heats you will also lose less to scale. Shop notes help this a lot.

[swedefiddle]

Happy New Year!!

 

Use Play-Doh or Plasticene. Make a piece of play-doh into what you want to make. Roll it up and make it into the size of stock that you have. Add a little bit for scale loss. K.I.S.S.

 

Neil

[Jack Evers]

The neutral axis (center) doesn't change length. I want a 6' circle from 3/4 ' wide stock, the center of the stock forms a 5-1/4 inch circle so the stock length would be 16.5 inches (Pi times 5-3/4"
Jack I have not tested your formula. However I  have made a lot of horseshoes. I can take a piece of 5/16" x 3/4" that is 11 inches long and turn a shoe that will grow on the outside curve almost two inches in length. 
As I change it from straight to curved it thins along the outside and thickens along the inside. A shoe needs to be mor flat than that and in fact hs to be thinner in some parts that others. that requires more forging,,,if the shoe is fullered it gains leength and punching nail holes also causes it to grow.

I know it grows even if not fullereed or holes punched.

My message here is not about shoes or formulas..simply that as you work steel and change shapes metal moves. How much or where is dependant on the smith and that is somewot dependant on skill level. If yoiu can change the shape in a minimum of heats with a minimum og work it will change less.

If you are going to do a run of pieces the same size you can find a starting point with math. But then a test p;iece will let yoiu know how close you are. As you repeat that piece and get the moves down yoiu may find a difference in first to last ones. If you are improving and use fewer heats you will also lose less to scale. Shop notes help this a lot.

 

 

Actually, Rich you have tested my formula. My formula would suggest that the perimeter of a full circle using 3/4 inch stock would be Pi*0.75 longer than the original stock or 2.3 inches longer. Since a shoe is about 3/4 of a circle, you might expect 0.75* 2.3 = 1.7 inches longer for the perimeter, but we bevel the heel more on the inner edge (heel check) than the outer and we push a little steel to the outside and get the 2 inches you mentioned. I also get about 2 " for a plain stamped shoe, about 2-1/4 for a creased shoe (when I don't bump extra into the toe). And as you say - that's the starting point. Your own forging habits will modify it. Pencil the heel, emphasize sole relief, etc.

 

An interesting experiment that I did was to form a half circle  (180 degree bend, both ends of the 3/4 inch bar are pointing the same direction) and a mushroom, (both ends of the bar pointing the same direction, but quite a few contortions in between). The stretch on the perimeter was the same for both cases. The extra length gained in doing the mushroom head, was nullified by the reverse bends into the stem. 

[Frank Turley]

Volume is one thing, weight another. I formerly forged finished weight, 16 ounce toe-weighted horseshoes, I didn't have much help calculating, so I turned to a weight chart for mild steel which told me that a one foot length of 3/8 x 1" weighed 1.275 pounds. Dividing by 12" inches, I found that each inch of that size weighed .10625 pounds. From that, I found that 9.5 inches of that stock would weigh 1.009375 pounds. This got me in the ball park of the 16 ounces that I needed for the completed shoe. I could vary the length of the shoe from one horse to another by forging each heel/quarter to the length I wanted. For non horseshoers, the toe-weight shoe was intended to give the front leg more fold and lift in order to look showier to the judge in the show ring. Pictured is an "Early Turley" toe-weight.

 

Another route to go in terms of volume is to do the actual forging of a test piece on scrap stock and measure. This is assuming your work is of a managable size and you can waste a little stock. For example, you want a 5" long, straight sided pointed cone on 3/4" round MS.The length you start with is arbitrary, so long as it is longer than 5" and perhaps a handling length. Let's say that your beginning piece is 3/4 x 19". Measure it before you start forging the cone. Forge the cone pointy end first and working back until you get your 5". Now, subtract the untouched length from 19" and that tells you how much length of native material it took to forge the cone.

[Tim S.]

I almost replied yesterday to the question about trade secrets. This sort of ties back into that topic. The general answer is the math works. In the days when I had to make a lot of one off stuff in industry, I always started with the math. Then I planned out accordingly but always doing my best to leave myself a way out or a plan B. Sometimes that just isn't possible. These were the times when I got nervous. The worst was when it was some expensive material that the customer had supplied… Most of what has been said above is true. The efficiency with which you can reach the finished size will effect the degree to which you can expect to see losses along the way and therefore will need to add in a little material. In other words if you have a 500lb hammer and can shape the item in two heats, it will be much more exacting than if you take 5 heats in a 50lb hammer. This is where knowing your equipment is key. In the shop where I used to work there were two blacksmith from different parts of Germany that didn’t get along. One had a formal apprenticeship and one had learned along the way just by doing. One day the guy with the informal training asked the other how to calculate the volume of a crane hook. The only answer he got was “You are a blacksmith, you should know that.” We worked to the numbers as much as possible because test pieces took time and money. This was  a big part of what I enjoyed in that job. Being able to plan a job from a blueprint to a finished part and make it all come out in tolerance gives a feeling of real accomplishment.

[metalmangeler]

 One thing that is obviuos when you think about it but not if you don't is that in drawing say 3/4 stock to 3/8 riengs is that it will grow 4X I noramly do not use exact calculations, especially if I am just making tools for myself. but your example the calculation would go, depending to the tong type, say a farrier tong, 1 inch for the jaw, 1inch for the boss, 3 inches for the 12 inch reigns, 1/2-1 inch for the miscalculation if you want  to paly it safe though I would not bother on this project. Write down what you started with then on the next one you might want to adjust.  

[Bruce Beamish]

I was taught to calculate the volume of the forging divide it by the cross sectional area of the bar being used and add 5 % for wastage (scaling etc)

Over the years I have found this to be a good method. It certainly gives you a good starting point.

[Alan Evans]

Hi all,
I was wondering if there is a formula that can be used to determine how much stock you need if you are going to be drawing out to a certain length.
For example, If I were making tongs out of 3/4" round stock, what length of bar would I need to draw out the reins to a given length and a given diameter?
I'd greatly appreciate some help with this matter, I'd like to better be able to predict how my metal will move.

Thanks,
RidgewayForge

I always calculate the volume of the finished piece and divide that by the cross sectional area of the parent bar like most of those above.

There are fudges and nuances of course.

I find that the 5% allowance for scale can often be compensated for by just running the hammer along the arris to create a chamfer.

If I am towards the limit of my hammer capacity I will allow a bit more to compensate for the extra number of heats.

When forging tapers I calculate for a straight line taper using a formula for calculating the frustrum of a cone or pyramid and then make an allowance either way if I want a full sided (cigar shaped) or hollow sided taper. I rarely forge tapers to a point so this formula calculates for a frustrum (flat topped/truncated) rather than a full cone or pyramid. It also usefully works on hexagonal, octagonal, rectangular or any other polygon that you can calculate the top and base area of and even gives a great starting point on combination tapers. Start square run into octagon for instance. I just enter the top and base surface areas and the length and it gives the base bar length.

I tried to upload my Excel Frustrum volume calculator spreadsheet to iforgeiron.com a few months ago but the system only allowed for image files. You should be able to do a search for the thread and see the images. Let me know if you can't find it and I will email it to you.
This is the operative cell equation:-

=B3*(B1+SQRT(B1*B2)+B2)/3

B1 = top area
B2 = base area
B3 = height

I have this formula in all my digital devices though nowadays in the forge it is mainly used from my mobile phone. You can probably find a similar on online.

While on the subject, I have also found it useful to remember the basics when dealing with volumes:-

Halving the linear measurement will quadruple the length, true for round or square.

In your example above for instance if you wanted the reins to be 3/8 diameter you would use a quarter their final length of 3/4 diameter.

There are four 1/2 inch bars contained in a 1 inch bar!

Alan

[Alan Evans]

Yippee! With the latest forum software update I see the restriction on file formats has been removed and we can now upload excel files as well as the image files of yore.

Herewith the Excel file for calculating the frustum of a cone (standard blunt ended taper) that I was unable to share back in 2013…I hope it is useful for somebody...

 

Alan

ALAN EVANS FRUSTRUM.xls

[SmoothBore]

The Geometry is very interesting, and informative, ... but has little relevance to "real world" conditions.

In one of my "former lives",   I worked as a Manufacturing Engineer in a Company that forged Automotive Valves.

It was an interesting exercise, to calculate the exact volume of a part to be forged, and from that, determine the diameter and length of the "slug" needed to produce that part.

But it was essentially, a waste of time, ... that served primarily to quell the nerves of the Bean Counters.

For a variety of reasons, ... it was necessary to add about 10% to the "slug", to insure consistent results throughout the 19 to 27 additional steps, in the Manufacturing Process.

The cost of that 10% additional material, amounted to less than 2% of the cost of the finished part, ... while a "scraped" part, cost over 6%.

Much ado about nothing .....

[Alan Evans]

Call it how you see it why don't you, don't hold back!

I am sorry you don't see a use for it...I use it all the time. And I was working in my "real world" last time I looked. All my projects are one off, rather than production runs. There are sometimes a few hundred repeat elements but I have to calculate the first one for every project for cutting.  I don't want to end up a couple of inches short after a day's forging for two men....maybe your customers could afford that wasteage in your industry.

If I am calculating a taper say to end up two meters long of octagonal section starting from a 60mm AF down to 30mm AF from a 60mm square  section which in turn was forged from an 80mm square parent bar.... being able to calculate out the various volumes of the 80mm base bar for each length of the various cross sections I can work in one heat is vital.

As I would have thought you would know given your previous experience, you have to work the centre areas of a long bar on the hammer first so that you don't have too much leverage / weight on the far side of the anvil. 

Of course there is fudge factor as I mentioned in the January 2013 post above, but being able to get an accurate starting length and to dot mark where the various cross section start and stop on the parent bar make it possible for me.

Alan

On 2/24/2015 at 10:55 AM, SmoothBore said:

The Geometry is very interesting, and informative, ... but has little relevance to "real world" conditions.

In one of my "former lives",   I worked as a Manufacturing Engineer in a Company that forged Automotive Valves.

It was an interesting exercise, to calculate the exact volume of a part to be forged, and from that, determine the diameter and length of the "slug" needed to produce that part.

But it was essentially, a waste of time, ... that served primarily to quell the nerves of the Bean Counters.

For a variety of reasons, ... it was necessary to add about 10% to the "slug", to insure consistent results throughout the 19 to 27 additional steps, in the Manufacturing Process.

The cost of that 10% additional material, amounted to less than 2% of the cost of the finished part, ... while a "scraped" part, cost over 6%.

Much ado about nothing .....

 

[ianinsa]

I think the value in the calculation is one of perspective especially when using expensive material you need to know if your starting point is "OPM. or MBM."

OPM=other peoples money

MBM=my bit of money

 

[ianinsa]

Sorry double post

 

Edited February 25, 2015 by ianinsa

[SHVTZHOT]

On 1/1/2013 at 1:11 PM, swedefiddle said:

Use Play-Doh or Plasticene. Make a piece of play-doh into what you want to make. Roll it up and make it into the size of stock that you have. Add a little bit for scale loss. K.I.S.S.

I have read another idea about using modeler's clay too. What a fantastic idea you have! I can borrow some of this from my 4 year old.