Formula for a Can of Soda

If she can't afford one, she could even pull one out of a dustbin somewhere.

Actually it will take more aluminum to make a soda can than what ends up in the final product. The extra sheet metal that did not get pressed into the can and any needed trimming. Fortunately this excess is not wasted but gets recycled back into the aluminum manufacturing materials.

unit (1 ea)
Grams / Ounces / Pounds / Units / Per Lb
12 oz can - 13.95 / 0.49207 / 0.03075 / 32.516
24 oz can - 25.55 / 0.90125 / 0.05633 / 17.753

you start with this....punch a disk about 4 inches in diameter then punch the can shape out.....send to paint...then to a bottling plant to be filled with liquid and the lid is crimped on by hydraulic press. I use to subcontract at Reynolds metal in Torrance Calif where they made the cans, VERY noisy place, warehouse after warehouse of empty cans

How many cans did they make in a day, and did they coat them with anything?

An average can weighs 14.9 grams.

You could have used a search engine for this.

Good luck.

I know but im looking for a mathematical formula that goes into it..if there is one..

Like the volume of a circle has formula..

Thanx.

there is a lot of geometry reinforcement in a aluminum can due to it's thin wall.

I do not believe there is a standard formula for what you are looking for.

The volume of a disc has a formula. As it is 2-dimensional, the volume of a circle is zero. Anyway, if you can work that out, then you can also work out the difference of volume of two concentric cylinders, the distance between them being the thickness of the aluminium. Formula? You're almost there on your own! Go for it.

A circle does not have a volume.

Therefore, there is no formula.

There may be a formula for the diameter of the circle needed to form the can, but without knowing the thickness of the raw material and the finished product there is not much hope for you.

I'd suggest a search,using a search engine, but know that would be a fruitless search for you.

Use a bottle.

You mean the volume of the disk has a formula, the same formula as a cylinder whose height is the thickness of the disk. Disks are circular, but they are not circles. Circles are two-dimensional objects having area only, whereas disks are three-dimensional objects having area and volume.

Volume of a circle??? I didn't know that a circle had volume. Area, yes...volume, no.

Sounds like another homework problem

I am not an educated person. but it seems that there are well known formulae for figuring out the volume of things. The limit is not whether there is a formula, it is do you have a design if the item is non-existent or the equipment and ability to measure a soda can if you are trying to make a knock off. Also, and I am not in manufacturing, but I would think there would be some production losses, and I would think those would be considered trade secrets by the manufacturers. (a ton of aluminium won't make a ton of soda cans) -- JHF

An empty can of FUZE iced tea weighs 15.1 grams. Just haled one out of my trash can and weighed it with my gram scale.

It really is amazing what a Google and a Wikipedia search can produce.

Laziness knows no bounds.

If you really have to have a formula, try this:

V = integral (A * dx) taken from bottom to top.

(Sorry, the available characters don't include the integral symbol.)

This would be much easier to calculate before the blank is drawn.

you mean this one

How'd you do that? But, yeah.

C4

or google.... I get those two mixed up sometimes.

Yes but the modern soda can is not a flat cylinder with a flat top and bottom, but has a tapered top side wall from the top to the straight side wall portion, and a bottom radiused side wall transition to the bottom so there are points of discontinuity and this will require at least four formulas to handle this, and then there is the top and bottom, which are not flat but concave or convex so we now have at least six formulas.

1. formula for increasing diameter

2. formula for radius area

3. formula as you have given for then standard diameter area

4. formula for bottom radius area

5. top formula

6. bottom formula

Basically, this is nearly impossible. Too much effort to put in here. Draw it in CAD and use the drawings to build it.

I think the OP is trying to calculate the diameter of the "blank" required to "draw" ( the metal stamping process of forming a 3d cup shape from a flat metal sheet) a soda can.

There are two methods, both of which can be done using most solid modeling programs.

1. Equal area: this method assumes that the sheet thickness is not changed by the drawing operation. This requires calculation of the surface area of the final shape, and then computing the diameter of the blank with equal surface area. This works for simple shapes from thin material
2. Equal volume: this method is far more accurate as it eliminates the assumptions about no change in thickness, and the area at the neutral axis.

The procedure is to divide the mass of the can by the density of Aluminum, about 0.1 lbs/ in3 (depending on specific alloy). Now given the original sheet thickness you can compute the required diameter of the blank. I'll leave the basic algebra up to you. Hint: be sure that your units are consistent.

But that's not what she asked. Weighing it will give the right answer.

No, in #5 she tells us a formula is desired.

A formula, just like figuring the volume of a circle, which is... uh... it's... ummm...

Let me see, pi and... no, that's not gonna do it.

Now, we're on to something!

As soon as someone can figure out the formula for the volume of a circle, we should hire them at LynDoor™Intergalactic Property Development, and make them Director of New Property Generation.

A typical soda can is made from two different aluminum alloys; mostly aluminum but the one used in making the can top typically contains additional magnesium. To further complicate things, the alloys used are often derived from recycled cans with the magnesium from the tops mixed in with the lot used to make the next generation's bodies. In other words, it's not straightforward at all and so by simply weighing empty cans, looking-up the density of pure aluminum and figuring the volume from these measurements alone will give incorrect results, even when we neglect interior coatings and paint.

The OP asked "how much aluminum?" The answer is: it varies. Continuously. Chances are and assuming a constant volume of metal, due to recycling two different cans are very likely to contain two different ratios of aluminum to other elements present.

What we have here, is failure to communicate.

All is not lost but, you're right, the question could be taken in one of several ways: The OP could mean 'aluminum' in the generic sense of

"How much metal is used to make a typical 'aluminum' soda can,"

or it could mean,

"How much space is occupied by the material used to make a typical 'aluminum' soda can; not the volume that the can encloses, but the volume of material used to make the can itself,"

or it could literally mean,

"How much of the specific element aluminum (all isotopes assumed present in their naturally-occurring ratios) is present in the total volume (or weight) of alloy used to make a typical soda can."

It's like when people order a 'coke' at restaurant:

"What would you like to drink?"

"I'll have a coke, please. Do you have Big Red?"

The vagaries of language, so let's ask the OP what it is he/she really wants to know? "What is your question, really, and what was it before?" - Humphrey Bogart, Casa Blanca

In my early days, it was a big deal to smash a beer can against your forehead. Today, they have lightweighted the cans so much that anyone can do it. Shucks!

Longnecks work. They're still glass.

Assuming the the OP meant the question exactly as written for the moment:-

Nobody seems to have fully addressed the fact that the sides and bottom of a modern can are sometimes a form of thin steel. I won a few bets many years ago by carrying a magnet in my pocket to prove it!! But a recent test here in Germany worked as well...

A magnet will stick to the sides of cans here, but not the top. Try it yourself. (I am talking about cans here in Europe!) Where you are may be different!!

Here the top appears to be Aluminium as far as I can tell and is not magnetic, neither is the pull tab magnetic either.

Furthermore, all internal surfaces are coated with a thin skin of plastic, what does that weigh?

What about the outside coating/product name/decals etc?

I just looked on the web and found a Wiki article which said:-

A beverage can is a metal container designed to hold a fixed portion of liquid such as a carbonated soft drinks, alcoholic beverages, fruit juices, teas, herbal teas, energy drinks, etc. Beverage cans are made of aluminium (75% of worldwide production)^[1] or tin-plated steel (25% worldwide production).

You carry a magnet in your pocket to prove that beverage cans contain steel? Good Lord. Got every contingency covered, ay, mate? (just don't carry big Nd magnets, one in each pocket, or you'll end up sounding like Mickey Mouse when they decide to kiss and make up).

Actually, the reason that I used to carry a magnet with me, just so you know, was to easily pick out pots and pans for using on an induction hob (you do know what a hob is I trust!) as they did not mark them as such around 10 years or so ago.....

The fun with cans was secondary.....almost accidental!!

Now, are you and your overt and obviously spiteful, aggressive character happy?

"No!" No surprise there!!!

By the way, were you the first one to discover not to "carry big Nd magnets, one in each pocket, or you'll end up sounding like Mickey Mouse when they decide to kiss and make up" ?

Are they still kissing? You sound "pained!" or something......

Have a great day in spite of the crushed "B******S"

(do you know that word? Its old!!)

Your mission, should you choose to accept it, involves you in trying to find out the meaning of both the words mentioned and posting them online here!!

As always, should any member of your team be caught or killed, the Secretary will disavow all knowledge of your actions. This message will self-destruct in five seconds.

No it won't, if you need to re-read it, it will still be here!!!

Lets see how you get on, it really cannot be difficult!

Here is a clue from the Oxford dictionary for the second word, the first one will be in any good online dictionary:-

[treated as singular] Nonsense; rubbish (used to express contempt or disagreement, or as an exclamation of annoyance). Origin mid 18th century.

Have fun!!

Exclamation marks. Are they paramagnetic?

It depends upon the ink used!

You what makes pushing your buttons so much fun, Andy, is that you offer so many choices. Just bumping into you I'm guaranteed to press a half-dozen at least. Nice rant, bro. Thank you.

No problem for me when you are the target!!

I pity you if you can't tell the difference between a steel can and an aluminum one by looking/feeling.

You are confusing the issue for no productive reason, again.

Yes, we all know using the taste test that aluminum is more saltier that steel when you lick it.

LOL!!!

Good answer.

He did not notice that the cans are coated internally, probably for that very reason!!!

Original Coke is a great cleaner of metals I found out years ago.....especially coins....maybe it would change the taste dramatically if it wasn't kept away from the metal!!

Even food cans are coated......inside!! Here in Europe anyway.....where you are, maybe not!

That salt taste test was a running joke with myself and the shop floor.

I was hiring an engineer at the time, and was interview a PE.

I gave him a tour of the shop and when walked pasted some stainless drops. and out of the blue, he said "Oh nice 316 stainless"

At that moment I didn't react.... and after a few steps I stop and asked him, "How can you tell?"

And he said 316 stainless is more shinier than 304. I could not believe this was coming from a PE and I took it as a bad joke, you know, like the ones here on CR4... Unfortunately, it was in ear shoot of the fabricators on the shop floor.

Anyways he was serious, I showed him (2) full sheets of stainless and asked him which they were. He said the 2B finish was 304 and the polished was 316.

Then I showed him the heat sheets (we were a ASME shop). They were both 304 SS.

Also unfortunately, this was also being observed from the shop floor personel.

Later they came to me and said I was wrong. You can tell the difference because 316 SS is more saltier than 304.

Original Coke is a great cleaner of metals I found out years ago

Also, its very corrosive on enamel.

Even food cans are coated......inside!!

Same here, you open it up, I believe its Teflon coated.

Actually, you obviously have never seen one (or maybe never checked one out with a magnet!), as the whole can "appears" to be made of Aluminium.....which is why I won some bets (which you may have forgotten about but I did mention before!!), because everyone takes a look and thinks its not steel, as it looks like Alu.........

Only the magnet proves them wrong.....they are commonly called Aluminium cans here.....

I was of the opinion that it might have been a "mixture" (not that I have a clue as to how steel and Alu could be mixed!!), but its apparently the tin coating that gives it an Aluminium "look".....strangely.....

Fools everyone, and I mean everyone!!

Not so. I drink juice from a steel can, with an Aluminum top, every day.

Even a blind man could tell the difference.

Can you furnish a picture of this "stealth" Al. can?

Here, the coating is visible if you open up the drink can, you can lift/scratch small pieces with a sharp blade or similar.

This coating prevents the drink being affected by the metal of the can.

It also prevent corrosion due to two dissimilar metals being immersed in a liquid, probably with some sort of acid in the liquid, as most soft (soda) drinks do.

Without that coating, I would guess that cans could develop corrosion leaks if stored for a long time (no idea what "long" is, bur the cans are really thin nowadays!!), maybe only a few weeks....

What would a picture do for you? I will get one if you REALLY need it but I don't see how that will help, inform me please how! They look just like normal drink cans.....

Steel beverage cans are stiffer and harder to crush. Plus they weigh more, empty, than a comparably-sized aluminum can. You don't need to carry around a little magnet in your pocket to 'prove people wrong' - what you live for, evidently, given how often your need to 'prove' others 'wrong' comes up in your posts.

So much so in fact that it would seem to be your primary objective regardless of the subject matter, yes? Hint: nobody cares one way or the other whether you are or not, so you can spare yourself the trouble - and the forum the noise - by putting the little magnet away and getting yourself a Real Life. The kind that other people have? The kind where you're secure enough in yourself that you don't need to continually prove to yourself (the real objective here, because everyone else here couldn't care less) that you're 'right' and they're 'wrong.' Maybe even believe your own 'proof' for a change? Your constant need for it suggests that perhaps, underneath it all, you're not quite convinced yourself? As in, "far from it."

Really, Andy, you're so much more transparent than you give yourself credit for, and do you reckon no one notices? Breaking news: most of us here might have been born yesterday in your estimation, but rest assured it wasn't late last night.

I will answer your post here:-

Steel beverage cans are stiffer and harder to crush. Plus they weigh more, empty, than a comparably-sized aluminum can.

Maybe you could measure a difference with proper equipment, but the steel is so thin, you will not really notice any differences "by hand!" I certainly don't. I have never weighed one as I do not have a similar sized alumnium only can to compare. Maybe as you have so much knowledge on the subject, you can provide us with that info, if you feel that it is a valid point.....this is not one of those heavy old fashioned beer cans of yesteryear....

You don't need to carry around a little magnet in your pocket to 'prove people wrong' - what you live for, evidently, given how often your need to 'prove' others 'wrong' comes up in your posts.

I am obviously communicating with someone who has never made a bet of any sort, if true, then I don't think you will ever understand. Have you ever made any sort of bet on something? Also, but you might have missed it, but I actually use it to test for induction cooking equipment, you may not understand why, but it is a simple and effective method that works 100% of the time....

So much so in fact that it would seem to be your primary objective regardless of the subject matter, yes? Hint: nobody cares one way or the other whether you are or not, so you can spare yourself the trouble - and the forum the noise - by putting the little magnet away and getting yourself a Real Life. The kind that other people have? The kind where you're secure enough in yourself that you don't need to continually prove to yourself (the real objective here, because everyone else here couldn't care less) that you're 'right' and they're 'wrong.' Maybe even believe your own 'proof' for a change? Your constant need for it suggests that perhaps, underneath it all, you're not quite convinced yourself? As in, "far from it."

I have noticed that people who they themselves have serious personality problems, think they see it in all other people they have contact with....this comment suggests to me that you have really serious hidden mental problems....sadly for those around you, if that is all you can do or say...

My mother was a similar damaged person. So I had first hand experience and spent many hours talking to her doctors....

But its water off a duck's back for me with you as you are a remote fleabite only, easily ignored if and when I have had enough of proving you wrong again and again!!!

Unlike you, I do not need to get my rocks off imagining such stupid and totally inaccurate attributes in someone else......

You should start taking the pills again!!!

Maybe you could measure a difference with proper equipment, but the steel is so thin, you will not really notice any differences "by hand!" I certainly don't.

Keep in mind there's a huge physical difference between the two. The Plasticity and ductility is the first that comes to mind.

Until you have got one in the hand, you will never believe just how easy the steel cans are to crush. A baby could easily damage one....when empty of course!!

About 20 years ago, I came home from the grocery store and was unpacking and putting the groceries away. I was going at a pretty go clip and was putting a 6pack away... I swung around to put in the refrigerator. And the 6 pack caught the corner of an opened cabinet door. Three cans ripped open and it was a mess. Needless to say in my grief, I killed the last 3.

I remember this like yesterday... Because of the loss.

LOL!!!

I have managed occasionally to damage 1 as the cans nowadays are almost fragile! But three must be a record!!

Luckily you had the other three to celebrate with!!!

I see your point.

I hope you're not telling us that his robe is open.

I think the OP really wanted something as simple as this:-

V_al = 2Πr²t + 2Πrht

Where t is the thickness of the aluminium metal.

And that funny character (Π) is the CR4 version of pi.

CR4 pi are square.

That's a big possibility. Although we know that the geometry of these cans has a lot of variations. So the proper answer I guess is "it depends on the geometry of a particular can"...

I think what the OP wanted was: For a certain volume of soda (liquid), he wanted to know how much aluminum he should use. If that is the case, it is not so easy, because that would depend on a lot of other variables and parameters. For example if he wanted to optimize or determine the least material that he could use, he probably would need to use differential calculus (maxima-minima). The thickness of the material need to be evaluated also against pressure (internal / external), corrosion, etc. So probably, a finite element analysis is needed. Those are not too easy.

The simplest is this, besides googling:

1. Get an empty soda can.

2. Get its weight.

3. If you want to just the volume of the material, divide that weight by the unit weight of the material.

4. Getting the thicknesses would probably get yourself hurt already... but can be done, have courage!

One the lighter side, there is a formula for the volume of a circle: pi (D)/4 x 0 (zero) thickness, which also gives a zero answer. However, not because there is a formula doesn't mean that there really is a volume of a circle unless I am missing something. :)

When I read some of the questions that get posted to this site I scratch my head and wonder.
How do they find it? Obviously they have no clue as to how search engine works so how did they end up here?
Do they really think you folks have nothing better to do than respond to *insert descriptor of choice* requests for solutions?
If they don't understand the initial problem do they really think they will understand the solution?
I mean, WTF?

Well I wonder what size soda can the OP is asking about? Maybe this one?