Edit: of course if he no longer is, my condolences, but please tell us what you can remember.
I had always wondered what the key innovation was that allowed aluminum cans to be made so thin. Based on a TV episode of "How It's Made", I think the key idea was to develop machinery that could delicately stretch and extrude aluminum without tearing it.
Amusingly, there seems to be 3 versions of the same video with different voices saying the same words:
 http://www.youtube.com/watch?v=L4EzU8792e0 Original female Canadian narrator
 http://www.youtube.com/watch?v=V7Y0zAzoggY Male American narrator
 http://www.youtube.com/watch?v=V4TVDSWuR5E Male British narrator
My father sold tooling for making cans and there were many small but important innovations that came along. It wasn't as if someone sat down and designed the finished thing, innovations came along and the likes of your grandpa and my father made things happen. Sometimes it would be a slither of steel that would be saved per can, other times it would be innovations that would go nowhere - anyone remember transparent pet-plastic cans? No...!
In introducing a change, an incremental change there is no way that the whole production line is going to be upgraded/altered, as in everything else connected to a conveyor belt.
The modern ring-pull tops were obviously a huge part of this story of innovation, as was being able to extrude the base and sides of a can out of a disk. However, the real innovation behind these processes is to have some type of press and tooling that can make these wonderful and intricate shapes in as few steps as possible. That is when you have a business case, and that technology - real technology - is a long way from the 'easy' stuff presented in this article.
Related to alcohol beverages is the story of the Guinness widget:
The Wikipedia article just explains a little bit, however the small bit of plastic in beer cans took decades to get right and the investment level was considerable, even for a brewer the size of Guinness. Combined with the technology that goes into the can, a beer can is quite a technical wonder.
The bottoms of the cans are coated with a varnish to make them slide easily on conveyor belts and in vending machines. It's the varnish that glows.
Maybe not the most useful thing I learned in Calc 1, but the thing I remember best.
Also, you won't be able to use a can opener if the diameter is too small, since can openers work in a straight line, if the diameter is too small it won't fit in the curvature
(couldn't resist ;)
"Aesthetically, a slightly taller can looks nicer. The Golden ratio is approx 1.6, so a can with a height of approx 1.6x it's diameter (3.2x the radius) would be very appealing."
However, it is a myth that the Golden Ratio is the most appealing ratio. Many things, from the Parthenon to paper sizes, don't have a golden ratio and that doesn't make them less attractive.
Also, the supermarket in my neighbourhood sells soup in a variety of containers (cans, tetrabriks, plastic bags) and if only the standard soup can would sell well, I wouldn't see the other packages.
"Perhaps the best known pseudoscientific claim about the golden ratio is that the Greek Parthenon, the famous columned temple atop the Acropolis in Athens, is designed around this ratio. Many are the amateurs who have superimposed golden rectangles all over images of the Parthenon, claiming to have found a match. But if you've ever studied such images, you've seen that it never quite fits, at least not any better than any other rectangle you might try. That's because there's no credible historical or documentary evidence that the Parthenon's designers, who worked more than a century before Euclid was even born, ever used the golden ratio in any way, or even knew of its existence."
2ndly, theres a difference between not having golden ratios and not being based off the golden ratios.
It has a bunch of interesting properties, but aesthetics is not one of them.
In terms of dimensions there's several factors to consider: label size, stacking efficiency and directional integrity. If you want a nice big color photo of your product, a taller, slimmer container will allow for a large color background and plenty of text for both the front and rear labels. Depending on if it's skinny or wide will determine how other products can be stacked around or on top/below it. And some foods (like tuna) keep their shape/consistency better when laid horizontally to prevent from breaking up while being transported. Similar foods hold together better when the pieces are larger, so larger portions of canned fish have the typical vertical orientation. And of course there's only so much horizontal space that can be allocated per unit before the shelves burst at the seams.
For sealable cuboid containers, more and more containers are being modified with grippable edges to make it easier to handle, since the customer doesn't use the entirety of the product at once (http://ecx.images-amazon.com/images/I/81W3JCB8tHL._SL1500_.j...). Resealable bagged containers are also becoming more popular, as they reduce the amount of air in the container, pack more efficiently, save weight, and are easier recycled. (http://www.gofoodindustry.com/uploads/members/comp-1509/file...)
The shape is a compromise for volumetric efficiency, stackability, ease of manufacture, and field-toughness.
Spheres are highly impractical on all dimensions.
Caulk and pepesi (pardon my pun) don't come in spheres, squares, or rectangles either...probably for similar reasons.
The only real reason the article gives against using cuboids is that "the edges would be stress points", but it goes on to imply that this is mostly solved with "filleted (rounded) edges to reduce stress concentrations and to make them easier to manufacture."
I enjoyed the rest of the article relating to the optimal dimensions of the cylinder, but I still don't really understand why more products don't use cuboids (with or without filleted edges). Surely the space savings for shipping and shelving would be pretty significant, no?
Metal likes to be formed by rolling, and it's relatively easy to image how cans are cut to length, passed through a die and seam welded. Obviously that's a lot of capital for one can size so round dies are easily swapped for various size cans on the same line. Forming stamped and bent edges would be much more intensive for changeovers.
Lids would require directional placement:
Round shapes fit in all directions, pretty clear here that any other shape would require it to be directionally correct.
Can liners are sprayed:
The inside of your cans are coated to protect the food, corners are harder to maintain an even sprayed coating
There are plenty of others I'm sure and this is a rambling post but maybe it gives a little more insight into the world of cans.
However, part of me thinks that given some time and ingenuity, we'd come up with techniques that are better suited for the efficient production of cuboids. In other words, most of the things you mention are conceivably solvable by the right tooling (i.e. fixed costs). If that were the case, I'd have a hard time believing that marginal/per-unit costs would be significantly higher, and I think it would be interesting to look at the savings in shelf and transportation space compared to any of those increased production costs.
I would guess that cardboard is less expensive to source and work, so they can afford to take the extra effort to make it a box.
I think the bottom of a cylindrical can might be doable but rolling the lid seam on a filled can would be tough.
That salt will impart flavour on the food.
So you can argue it both ways. Even just a little bit of a metallic taste in most food is quite unpleasant.
I'm not sure if it's used more or less than cylinders, but I see more cuboids than cylinders on my local shelves.
Edit: an interesting link to irregular can sizes (also plenty of cuboids)
I'm not sure what their motives are, but articles like that scares me.
See for example the comments from the Recology Recycling Program Manager on this page:
Plenty do, when they are small enough that they can have sufficient strength and still have a pull-top opening (lots of sardine/anchovy cans are this way.) When they are bigger, they don't, because can openers.
Though I'm starting to see more "canned" vegetables/etc. that use lined cardboard cuboids rather than metal cans, so there's that.
Optimal cylindrical can (h=2R): V=2piR^3, S=6piR^2
Cube with the same volume: V=x^3->x=((2pi)^(1/3))R, hence S=6x^2=6((2pi)^(2/3))*R^2
That's ~8.4% more sheet metal. If you don't mind contents swirling inside the can cylinders are the way to go.
Space saving matters a lot during shipping, on shelves not so much. The first job I ever had was stacking shelves in a supermarket as a teenager and I was so bored I would pass the time by calculating the volumes that fit on palette, on display and so on :) 25 years later not much has changed - most supermarkets still stack products 2 high and 2 deep or 1 high and 3 deep (depending on how stackable the product is), not least to limit the potential for mess. Smaller volumes usually have higher margins, so what's economically efficient for the supermarket isn't necessarily what's efficient in terms of volume.
I agree, but if cuboids were the norm, I'm sure we'd come up with a better tool for them.
Expense may very well be a factor, but if that's the case, I'd expect an article like this to mention it.
Cylindrical cans are a natural fit for a fairly simple tool; I doubt there is anything really comparable for a cuboid.
(There's a practical use of math for you.)
On cuboids the label alignment is beyond critical (even just randomly off center 1/4 inch on the shelf would look awful) and the capital cost to align the cubioids perfectly in their box and on the shelf are expensive.
(edited to add, I'm not saying our economic system would collapse if the cost of cuboid soup cans went up three cents a piece, but it would be an incredibly difficult corporate sell to convince one mfgr of many that he should accept a 1/3 of a million dollar loss compared to his round competitors on ten million units sold just to make them cube-ish, for, uh, fun)
Also wear in the box. Cuboids would tend to wear off entire faces of the label while being tossed around the warehouse but cylinders at worst will end up with a vertical streak.
Finally having worked retail as a starving student a quarter century ago there is a huge installed base of semi-standardized grocery store shelving that was never designed for the peculiar spacing cubiods would require. Or rephrased, cylindrical cans and rectangular prism boxes have evolved over decades to fit certain semi-standard discrete shelf configurations... If you want it on an American supermarket shelf, then a grid pattern of X by Y (preferably one shipping crate) will take up a certain discrete space. Not a quarter inch too big necessitating reconfiguration of the whole section, etc.
Nothing exhibits the Second Law of Thermodynamics quite like grocery store shelves.
Besides being cooked in the can (as egypturnash points out), a can of tuna contains two sandwiches of tuna. A jar of tomato sauce contains two servings of tomato sauce. A can of soup contains two servings of soup.
Yes, you have to be able to hold it in your hand, and stack it on a shelf. But you can't make a smaller can because that would be "less soup". No one wants to buy smaller cans of soup, and the manufacturers certainly don't want to sell less soup per purchase either.
Economics trumps material efficiency.
Pop, chip, candy makers used to label their products as multiple servings when it was normally used as a single portion and have since been forced to stop.
Forced to stop? As far as I've ever heard, serving size for all of those things has always been set by law. It's a little weird to say you're "forcing [someone] to stop" doing something you were forcing them to do in the first place.
You can see the Code of Federal Regulations defining the serving size of chips as 30 grams here: http://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfcfr/CFRS... . For "pop" (ok, carbonated beverages), a serving is defined as 8 fluid ounces. Unsurprisingly, a 20-ounce bottle usually contains 2.5 servings of carbonated beverage. How is that the pop, chip, and candy makers' fault?
Searching for images I came across this very relevant article on irregular can types:
Example of tuna cans in some spanish-speaking countries:
When I look for tuna at the grocery store, I looked for the can shape, rather than the tuna section or tuna labels. If tomorrow I went to the grocery store, and all the cans of tuna were a different shape (or a different package) I would end up having to ask someone.
Absolutely not. The purpose is to maximize profit.
The can improves profit via sales (being appealing on the shelf and in the kitchen cabinet; perhaps a familiar shape sells better), marketing (the image of the brand and the product, including environmental issues), distribution (the obvious costs and the value of being appealing to the sales channel (e.g., oversized products might be unappealing to the supermarket)), manufacturing costs, functionality for the consumer (food stays fresh, fits standard can-openers, etc.) etc etc.
You aren't designing the cans.
Not that it negates your point. Just struck me as interesting that tinned tuna would be seen as expensive in some places in the world. I guess it depends on the quality of the tuna.
Think of how a can opener would work with a cube, hexagonal, or other shaped can.
Cool article, but seems it builds a lot of assumptions into its analysis.
Joking aside. DataGenetics is the consultancy company I set up when I was doing that line of work. It was all about spotting trends/patterns/explanations in data (sort of like the DNA), and the term described the work I did. A lot of the work I did was related to video games, and what the characteristics (chromosomes) were about games and how they performed. When selecting a business name, you can chose to attempt to describe your business function in the name "GreatPokerHands", "DataGenetics", "CheapTickets" or you can try an obscure reference "Amazon", "King", "Zynga" and then spend additional money educating people on that brand and what it represents. (Amazon sell things online, and has nothing to do with the river. If we listen to Jeff, he says the name was selected because it started with the letter "A", so will appear first on lists).
I continue to blog under DataGenetics as I own the domain, and have followers there. It's a hobby. Not every post is about data, either, it's just a place I put my thoughts. It's my hobby.
The name you chose is not obscure or esoteric, but rather uses two words associated to information and relies on the reader to make the connection that your business has something to do with information. The problem, however, is that 'Genetics' refers to a specific domain of information -- this leads the reader to believe that the 'Data' (an ambiguous term for unordered knowledge) refers to datums regarding 'Genetics' (the specific form of data which biology/inheritance are so concerned).
The first thing that popped into my mind when reading the name was "Must be a biotech/bioinformatics group.".
I don't want to sound critical; i'm not trying to. I've been linked a few articles on that blog and enjoy the content -- just trying to give you some (probably) useless data on how John Q. Public may encounter the site.
Your articles remind me how much calculus/math I have forgotten since leaving school and, sadly, how little use there is everyday to use calculus :(