Easy Trig, or how to build an anvil stand

[SamT]

Having recently migrated back to windows, and lacking free CAD software, I used trigonometry to figure out the length needed for angled legs on a steel anvil stand I'm designing for my Mousehole. Really easier than I thought, figured I would post it here so anyone else who may ever need to do something similar can have have a reference if needed.

Ok, I want my face to be 32 1/2" off the floor, this is simple to figure out once parts are known anvil is 11 1/2, so that's 21 to top of stand. 1 1/4 plate for the top gets us down to 19 3/4, 1/4 for steel feet makes it 19 1/2, then 1 1/2 for 2x4 wood feet under those makes our final measurement for leg height 18"

(Notice, this is done in windows default calculator. go to view, and select "scientific. If you use any other scientific calculator, I imagine it's operation will be different, windows calc.exe isn't very intuitive with the trig functions)

Now for the trig. I want my legs splayed 20 degrees from vertical. Cosine is used to find the adjacent length. Since the leg itself will be the hypotenuse of a 20/70/90 triangle, and 18" is the adjacent leg, we have to work this in reverse. Normally trigonometric functions are solved with the hypotenuse given, and cosine is used to find the adjacent leg length by multiplying like this "A=cos20*H" where H is the hypotenuse, A is the adjacent, and 20 is the angle in degrees. Since we have the adjacent length instead (18") we simply change the formula to "H=A/cos20" so we enter into the calculator "18/" Here hit the "(" button, then type "20" and hit the "cos" button. now hit the ")" and finally "=" our result will be 19.155199904... It continues into absurdity, but since I'm using a chop saw, we'll call it 19 1/8" B) If we used the sine of 70* in this formula, the answer will be the same, it's all relative to what angle you input into the calculator.

Say I wanted to know just how far out from under the base the feet will be. This length will be the "opposite" let. The formula for finding the opposite is "O=sin20*H" Where O is the opposite, H is hypotenuse, and 20 is the angle in degrees. Into the calculator we punch "19.125/" then "(" and "20" then hit "sin" ")" The answer will come out 6.541135... Again continuing. We'll call this one 6 9/16 just because we can.

You can use these for any other triangles of course.

There is a .bmp image attached that puts this into more of a visual format, I had to see it to understand it, so I redrew it simpler than what I could find online.

Let me know if this helps anyone or if I made any mistakes! B)

SimpleTrig.bmp

[VaughnT]

That was easy? Shoot, I just built my stand using the same process of elimination you did and ended up drawing a full-scale "map" on the top of my table saw!

[GRiley904]

An easier method may be the use of the pythagorean therum , sorry if my spelling is off, this is used to determine the lengths of either the legs or hypotenuse of a right triangle, or a triangle with a 90 degree angle, the equation is "a squared + b squared = c squared" a and b being the legs and c being the hypotenuse. You could use this to determine your stands leg length if you know how wide you want the stance to be. This would be easier for me and equally effective.

Riley

[Glenn]

I like your explanation, easy to follow and detailed.

When I built my anvil stand, I welded a box from angle iron to hold the anvil and a piece of sheeting for cushion for the anvil. Next I used cribbing and brought the bottom of the box up to the correct height for the face of the anvil. Put the anvil in the box to check my measurements, then put the anvil back down on the top of the table top. No use having a 150 or so pounds floating in the air, looking for a reason to fall.

With a piece of angle iron as a guide, I eyeballed plum or straight down from the 4 corners of the box to the table. I drew the outline of the box on the table. Again using a piece of angle iron held against the box, one leg on either side of the box, and eyeballed the spread of the leg placement, then marked the table top. This was not off to one side of the box or off to the other, but off the corner like so * Y *. I off set the anvil box and drew a second box so the legs would match to the corners.

Next trim the bottom of the leg to fit flat against the table top and measure the common edge of the angle iron to fit against the middle of the box. WHOOPS, you need to adjust 1/4 inch for the piece of plate steel you use under the bottom on the leg as a foot. NOW weld things up.

The anvil box drawn on the table was a great help as I could now offset the box edges an equal amount and find the corners where the legs would contact the table top. Put the legs in their corners and where the top of the angle iron touches the anvil box is where you weld.

[Larry H]

I just found a stump....then put the anvil on top

sometimes a cigar is just a cigar (Sigmund Freud )

[matto]

i just took the difference off the legs from the stand design i was using to fit my anvil hight and the finish hight i wanted. someone already fixed the wheel i don't need to fix it again just make it work for me.

[Pug}{maN]

I just found a stump....then put the anvil on top

sometimes a cigar is just a cigar (Sigmund Freud )

"Amen, Brother"

[SmoothBore]

I'm sure that was the way my Great Grandfather did it, :rolleyes: :P ... and he earned his living for 60 years, as a Blacksmith, Tinsmith and Millwright.


But seriously, ... "back in the day", I was a stickler about always "doing the math", just to keep up those skills, ... but now, AutoCAD has made me lazy about doing those kind of formulas.

It's good to see someone keeping the "root" alive.

[SamT]

Well I was designing the stand during a slow night at work, so I couldn't use the real world way. My shop time is scarce these days so the more I can have definite measurements the better. Posted this for the formula in case anyone could use it on any triangles they needed to figure out. ;) GRiley, pythagorean theorum works if you know the length of any two legs of the triangle. I wanted the angle to be one of my constants since I'm using square tubing for legs, 20* seemed about right and easy to cut with the chop saw. If i had decided I wanted a specific height and a specific offset at the floor, then I would have ended up with a weird angle to cut.

[GRiley904]

There is more than one way to skin a cat. I suggested this method because it takes the guess work out of your finished product. Your way leaves the over all width of the stance to be determined upon completion or involves more math to double check (a 20 degree angle will give you about a 6 1/2 to 6 3/4 inch offset over 18 inches rise) no problems with that, your math is good and you seem good at it, but with my way you instead measure the finished product and work backwards, leaving you with what you want exactly. Being a carpenter this is important to me as in if you're not exact to the finished product you fail inspection. Call it force of habit but I want to know the dimensions of my end result and the angle can be tweaked with a grinder. I'm not saying that either way is better than the other, just that this is easier to me and wanted the info out there for others like me that aren't familiar with the teachings of Pythagoras

[Alec.S]

I would just like to add a little bit of information regarding anvil stands that you may find useful. Firstly. No matter how it is accomplished, an anvil needs to be mounted down to the ground, so that there is no energy lost due to vibration that does not transfer to the steel. So, let's think from the ground up. What is more solid: wood or steel? Obviously steel, so therefore less anergy will be lost if the feet are steel without wood underneath, as the wood will compress and spring with every hammer blow. The feet must have a mounting system of some sorts so that the stand can be mounted to the earth. Holes in each of the feet for bolts ( if you are in concrete ) and/or holes in each of the feet for stakes (if in dirt etc). The most solid backing for an anvil stand is a deep heavy mass of concrete either the floor or a separete 'pillar' of concrete in dirt so that the stand can be bolted down to so that as little energy is lost here. 1/2 inch anchor bolts are good for concrete. if you are staking into dirt, like me currently unfourtunaley, 5/8 or over stakes are best for the least energy loss. I currently have 2 foot long 5/8 stakes in each of my feet on my stand. the feet on my stand actually each have two holes - one 1/2 inch hole for bolting to concrete when i get my pillar poured and one 5/8 for dirt.
The legs. So, the least energy needs to be lost. Hypothesise this - you have two peices of square bar - one verical with the bottom resting on a solid base of some sorts, and one where the supports are only on either end of the bar. If you were to hit both in the middle of the plane that is upwards - which one would flex more? the one that is supported only at the ends. Obviously, this is an exageration of the way in which the support is on an avil stand with 20° angle. So, thiks is the point i am getting at. We want the most backing by the earth. the best backing, as we just found out is acheived when there is direct vertical support from the energy of the hammer blow. therefore, less energy will be lost if the legs are vertical and directly under the anvil. I know that the reason you wanted 20° leg angle is for 'tipping' support so it 'wont fall over' ( if not, please tell me what your reason it btw). But, if you mount your stand and anvil down the way it should be it is impossible allready for it to tip over because it is mounted down. also, remember that your blows from the hammer come straight down 99.99% of the time, not side to side!!... So, the ideal angle for the legs is 8° / 9° / 10° (max). This is for the maximum backing, while also with some extra 'tipping support' for when you are out of your shop with the anvil and it is not mounted perfectly! I also should point out, that your legs WILL snap off at 20° with heavy hammering. They have been known to snap off at 12° when we've been striking.
So, in conclusion, i would recomend not having wood blocks under the feet, and have less of an angle on the legs. Remeber to fasten the anvil to the stand, TIGHTLY! you will thank me when your anvil doesnt move at all! it makes forging so much easier! Dont believe me just by what i have said, go out and try it for yourself and you will see!
Most of this information is Brian Brazeal's findings with his experience. I have tried all of this, and there is only one reason I am saying this stuff to you - it works! :)

Hope that was useful!
Good luck!
We all wanna see picks of finnished stand btw! :)

alec

[SamT]

I can understand your way having it's merits too GRiley, if it works better for you then it's the better option. I just prefer having a comprehensive cut list. set the saw, cut three legs and weld them on. Thanks for this info Alec, I'll pull those legs in to 10^o or less and get rid of the wood feet. My reasoning for the wood feet was hoping to reduce ringing. That mousehole rings like a bell right now on the flimsy angle iron stand. Sheet of lead under the anvil will probably quiet it enough. Had planned for a 3"x4" foot with a 3/4 or so hole to peg it down into my dirt floor, so I had that part right at least. :P At the moment I'm thinking of popping two holes in that plate and putting 1" eye bolts with nuts underneath. Wrap the waiste of the anvil with a big chain and use the bolts and nuts like turnbuckles to cinch it down tight. May fill those 2" square legs with grinder swarf from work, its mostly steel with just a little alumina shed from the wheel. I'm sure the extra mass will help with vibrations, doubtful it will do much, but it's free.

So lets see, scrap the wood and that makes my vertical leg length 19 1/2". Now pull the angle in to 10^oso (19.5/cos10) = 19.8008" or right around 19 3/4". I don't think 50thou will make a difference!

I'm going to try and get that tube out and cut it this week then go to dad's shop and use his DC welder on it and a grinder pedestal with a truck (think kenworth, freightliner, etc) brake drum base. Just getting back into the shop from a few months where I've been wrapped up buying a piece of property and cleaning it up and this anvil stand is one thing I definately want. Right now my anvil is about midway between my wrist and elbow! :o very uncomfortable.

(edit) Will take pics too!

[Alec.S]

Good! i am glad that helped ! :D ...The quietest your anvil will get is if it is fastened down as tightly as possible - steel on steel. It will get quieter without the lead sheet!
For the legs, fill them with sand and a bit of oil. Or, the ideal thing would be to pour in lead! :P obviously, thats a demanding task though! The sand quietens the 'stand' down with extra mass and the oil stops it rusting from the inside out!
For fixing the anvil to the stand, that wont get it all the way clamped down, i have used anvils fastened down with chain, and it is not as good as an anvil - drilled and tapped on the underneath and bolted to the plate from the bottom into the anvil through the plate, angle iron with a hole on the top side, angle iron goes over feet, tighten bolts on both sides of the anvil. and other 'solid steel' mounting systems! :)

look forward to pics!

alec

[SamT]

OK, ditching the chain idea then. Probably find some heavy section angle and invert it over the feet, I like that idea. Wouldn't the steel swarf in the legs be heavier than the sand though? Filling the legs with molten lead wouldn't be that big of a problem for me. I already have a smelting pot and a little camp stove I use to reduce wheel weights into ingots. Could pour straight down into the leg.

[Alec.S]

it depends what type of swarf really... if it's fine and will settle much like sand with few air gaps between grains then good! if it like drilling swarf then i doubt it will be all that great! ... if you have the capabilities to pour it in through the hole on the plate you will have made for filling with whatever you fill it with... then! go for the lead! :)

[Alec.S]

I noticed you are in MS... If you really want to give your forging skills a boost and learn more than you could imagine, look up brian brazeal for a potential class. Have you been to any of the MFC meetings yet? Him and Lyle are often at these meetings!

alec

[SamT]

No, I haven't made it to a meeting yet, though I keep intending to join. With work and all the things I have going on with building a house and new shop time is stretched thin so for now I just go to the shop when I need some relaxation and beat on stuff. Not really all that good at forging, but I seem to be getting better. Learning every time I do it. The swarf is from grinders cutting the teeth in sawblades. it's very fine, finer than most sand I would imagine. But yes lead would fill better because this stuff tends to be fluffy once you break it out of the cakes that the filter makes with it, would be hard to pack.

[VaughnT]

Legs? Fill them with sand, and then back-fill that with oil. The oil fills the voids between the sand granules (haven't gotten to use the word "granules" in a loooong time) and prevents rust from the inside out.

The angle of the legs is, in my opinion, dependent upon the height of the anvil and the weight of the anvil. My 300lb anvil's stand is approximately 32" off the deck and the legs are only 8 degrees from vertical. This is plenty of spread to prevent a tip-over without getting in the way of my feet. A lighter anvil might require more spread because more umph is applied to the stand through the hammer.

You technique for determining the angle of the legs is solid, but you lost me at Paragraph 3 because I'm not a math guy and really don't understand anything about all that sign and cosign business. I drew a life-size drawing on my table saw's table that intentionally kept the legs inside a box that measured 2' on each side. Knowing that the legs would emerge from the top plate's edge, and the dimensions of said top plate, I only had to decipher the amount of divergence from plumb to stay within the boundaries required. That turned out to be between eight and ten degrees.

As for quieting the anvil, filling the tube legs with anything will certainly help... but the biggest issue is the anvil itself. I found that chaining the anvil down doesn't do anything to reduce decibel levels. A large magnet on the side also does nothing to help (at least until it's covered in scale, and then it's the scale that absorbs vibration!)

Placing two magnets, one under the heel and one under the horn, eliminate almost all vibration. Removing the magnets and seating the anvil in a bed of silicone caulk will silence the anvil even more. No chains needed!

[John McPherson]

As noted in another thread, I watched all the demonstrators, especially BB & the Young Smiths (sounds like a 60's cardigan band) at the ABANA conference this summer. EACH and EVERY stand that did not have a "Y" or "T" or similar bracing between the legs 'hopped' when struck, unless attached to the earth with huge spikes.

I don't care what the attachment angle is, or how strong the weld is, that sort of end-only leg attachment strategy is a recipe for eventual failure in this application. It turns the stand into a giant tuning fork. You need gussets, bands, braces, (or maybe 40 feet of logging chain like Brian) to spread the load and dampen the harmonic.

[SamT]

Where have I said I'm using an end-only leg attachment strategy?

[r smith]

I think he is just saying that watching anvils at the conference the stands without any additional support of the legs were flexing. Best to tie the legs together.

[SamT]

Understood. I already have a T shaped brace in the design. I originally made this post to show the trigonometric formulas in a way I thought was easier to understand than what I found online. The anvil stand was only meant as an example. I did get some new information that I will use, and I'm appreciative of that.

[Glenn]

Best thing I have found to stop the ring of an anvil is to bed it down in in say 3 inches of sand.

The only thing better is some 30 db or so ear plugs followed by quality ear muffs. It is interesting to hear the wind go into and out of your lungs, your heart beat, your joints creek and a whole lot of other sounds you do not hear otherwise. You then start to FEEL the metal move under the hammer.

[David Gaddis]

If you want to find out how much the noise reduction is you should try the sand and oil treatment installed in heavy wall tubing. I am the guy that made that striking anvil that the Youngsmiths used at ABANA. It was filled after the comparison was made. Brian used a striking anvil with chains, sand and oil. Upon demonstration of the quietness we drill, tapped, filled the new striking anvil with sunken pipe plugs. That is very easy to accomplish.

And Alec is very right about the rigidity of a good stand....for striking. Where we are we are lucky to see heavy striking very often. Most people never use an anvil to strike so intently as Brian, Lyle, or Alec, or many of the newer smiths. Not that some will not but lets face it, those striking anvils are just that. They are so greatly abused that they MUST be made with good geometry, and attachment. Heck the concrete better be good too.

Some people will sware by the mounting the anvil on a near 30 degree leg, measured from off vertical. For most or many that is a good formula. But a less vibrating way is with the legs 8, 9, or 10 degrees.

And most people will argue about the height of their anvil until the cows come home. It would seem to me that if you had a anvil mounted 30 something inches high one must be with very bad eye sight or 9 feet tall.

It is greatly rewarding to use an anvil that is attached to the concrete. It sure does reflect all the energy available back to the workpiece. The only other thing that could make it better is to own one of those monster sized anvils that could be freefloating on a bucket of sand.

Carry on

[Borntoolate]

All us "shop type build it yourself" types should learn some trig. The pic below is the basics. It looks greek (well maybe it is actually greek....). BUt once you learn 3 things it is just simple math.

1. This will only work if the angle at bottom right is 90 degrees!

2. Need to learn how to get the Sin, Cos, and Tan values for the Theta Angles. Theta is the name (greek) for the zero symbol with the line through it. So Sin is the value of the Sin (Sine) at the angle of .

Sin 90 degrees is 1.0
Sin 45 degrees is 0.707
Tan 22 degrees is 0.404

Punch in 45 and press the Sin button to get the value of 0.707.

You can get these values from windows calculator as described above. You can also get these values from many calculators or you can get them from look up tables in books.

These are pronounced Sin = Sign, Tan = Tangent and Cos = Cosign.
Spelling is Sine, Cosine and Tangent.

3. You always need two of the four things shown (A, B, C or ) in order to be able to calculate a 3rd one. This will require that you either get a list of all the various ways you can re-arrange these equations or learn how to do it yourself. You can get this from books, google etc... OR ask a high schools student with decent grades. THis is the hardest part. Don't give up.

So if you know one thing (height of anvil stand) and you want to cut a support bar to weld and you specify the angle to be 8 degrees then you just need to know the length to cut it to. You want to know the Hypotnuse length with side B = Anvil Height and angle 8 degrees from the vertical which is 82 degrees from the horizontal! So = 82 degrees not 8 degrees!!. Then "Hypotnuse = B (anvil height) / Sin 82 degrees" Sin 82 degrees = 0.99026. At 10 degrees or 80 degrees from horizontal sin 80 = .9848 I realize that at this small angle you could take anvil height plus a "lil bit "and you would be fine. BUt when the angles get to 70 degrees then what?

Learning some trig can be very useful.

I suggest a 4th step. When you calculate take a look at the answer and see if it makes sense. Make a simple drawing to work from don't just try to imagine it in your head. This can be just a sketch with wax pencil on the floor. If the calculated answer is wrong then YOU made a simple math error. Figure out the error and move on. You can get by without this but sometimes it is very very useful.