If you imagine cutting out rectangles from sheet metal, you can completely tile the plane. Punching out circles, you'll use a maximum of roughly 91%. So I imagine the more of your material you use for the sides, the less scraps you'll end up with. I'm sure the problem is a lot more complicated than this though, with deburring, corrugation and whatnot.

One factor missed in other answers, mentioned in the letter, is that the ends are made from thicker stock than the cylinder, and increase in thickness as diameter increases. The scrap ratio of the ends doesn't change in area, but the volume of scrap per can does.

What's interesting is how the letter's scrap argument has aged - take a look at cans in common household sizes today. Most are only capped on one end. The cylinder and opposite end are a single deep drawn [0] unit. That can body will consume a round portion of material and definitely increases overall scrap ratio over old double-capped cans.

[0] https://en.wikipedia.org/wiki/Deep_drawing

I note that here in the UK, cans of soda tend to be deep drawn, capped at the top, and that most food/soup cans are of the traditional double capped variety. I wonder does this come down to the pressures of the contents or is there another reason involved.

I do a lot of manufacturing adjacent and overlapping work. The primary justification for cans (by a long shot) is going to be process steps and cycle time. Very roughly counting manufacturing operations, while surely overlooking tons of other handling and preparation common to either method:

A double capped can has 7 specific manufacturing tasks: 3 cutting steps (2 ends, 1 center), 1 roll forming step, 1 weld step to close the cylinder, and 2 end capping steps. Forming ribs into the cylinder and can should happen simultaneously when the cylinder is roll formed and when the ends are punched from sheet stock.

A single capped can has 4 specific manufacturing tasks: 2 cutting steps (1 blank for the can, 1 lid), 1 draw form step, and capping the end. Trimming the edges of the draw formed can should be combined with the forming operation.

Draw forming tools are expensive, the world is still full of cheap, perfectly functional, secondhand canning equipment. Either way, cans sell for cheap and at low margins. Takes a lot of volume to make ROI. Or... Aluminum! Aluminum is far more expensive than steel and is finicky to weld reliably. Draw forming soda cans eliminates any need for welding and allows manufacturing of thinner can walls, which reduces material consumption, and the bottom can be shaped to hold pressure with less material.

Thanks for sharing! I assume it's the dome shape on the bottom of a soda can that's specifically there for holding pressure in that case (a balance of accommodating the greatest strength per unit surface area measured against the cost of the forming process)

One explanation could be the following based on the supposition that one starts with rectangular pieces of metal. To minimize waste for a circle one begins with a square piece and cuts out the maximum circle contained therein. The waste is (area of square) - (area of circle). If the circle was to be 4 inches in diameter (2 inch radius) cut from a 4-by-4 square the waste is 4^2 - Pi2^2 = 3.43, whereas a 2 inch diameter circle cut from a 2-by-2 square has waste of 2^2 - Pi1^2 = 0.86. The cylindrical side needed to achieve a given volume is rectangular so has no waste in either case.

From a 4-by-4 inch square you can make 4 2-by-2 inch squares, therefore the loss from 4 small squares would be 0.86x4=3.44, same as one large square.

My first thought was for the ends, and for a similar reason that the smaller diameter cans pack more densely.

If you're punching circles out of sheet metal, you'll get more waste with larger circles.

> If you're punching circles out of sheet metal, you'll get more waste with larger circles.

I don't think you would. The design can be scaled up or down without impacting the proportion of the area which ends up being 'useful'.

The percentage waste per circle remains the same, but the absolute amount of waste per can goes up.

Edit: Disregard this. The other answers are better.

I guess it's because of the fat ends - if these have constant thickness, the volume will only increase as diameter changes.