Optimal size for a soda can

At Cutting Edge they had in the bin of drinks some skinny soda cans. I checked the volume, and it was the same, 12 ounces, or 355 ml., as the conventional size can. This bothered me, because there must be some optimal dimensions of a can to enclose 355 milliliters. At least one of these cans had to be off of the optimal dimensions, and I suspected it was the tall skinny one.

Let me preface the following by saying that I know that a soda can is not a perfect cylinder. It is tapered at the ends and the bottom is concave. However, for the take of simplicity, let's ignore that. I think these factors are minor compared to the big picture of minimizing surface area.

Let me also make all do apologies to my fellow Yanks by doing this whole discussion in the metric system. To heck with that, I don't apologize and am all in favor of converting to it.

That said, I show the following height, radium, volume, and surface areas of both cans. All measurements in centimeters.

Measurement	short	long
height	11.316	15.275
radius	3.160	2.720
volume	354.991	355.033
surface area	287.419	307.539

In other words, the tall can is using 7% more aluminum than the short can. This bothers me as I find it very wasteful.

Doing some calculus, I find the optimal can size to be even shorter and thicker than the current can, by a significant degree. To be specific, the optimal size can should be 68% the height of the conventional can. Let's call that the Wizard size.

Measurement	Short	Long	Optimal
height	11.316	15.275	7.674
radius	3.160	2.720	3.837
volume	354.991	355.033	355.000
surface area	287.419	307.539	277.545

Note that my Wizard size can uses 3.4% less aluminum than the standard size to enclose the same 355 milliliters.

The question for the poll is what size can do you think we should use?


I'm in Australia.

The tall skinny cans are a psychological marketing thing, believe it or not they sell better than the traditional shorter fat can.

So my answer to the poll is other - I think beverage companies should use the size and shape of can that makes them the most money.

Also, this is a surprisingly interesting video on the history of Aluminum can design. It answers your question about the bevels as well.

https://youtu.be/hUhisi2FBuw

Well, the optimum can size for saving aluminium would be a sphere. But that would be too impractical to manufacture. It looks like Wiz's calculus points to the most "sphere-like" cylinder -- one where the diameter is equal to the height.

One other thing to consider is that the skinny cans are more optimal for cooling the can. The larger surface area and the lower radius will allow the beverage in the skinny can to cool down to the desired temperature faster than the standard or "optimum" cans.

As for the "wasted" aluminum, don't most aluminum cans get recycled these days? Or am I just dreaming?

There could be any number of reasons that the skinny can is in use. Maybe some marketing genius decided that it's got better visual appeal Maybe it's merely easier to handle. Maybe it retains carbonation better.

Whatever the reason, 7% more aluminum seems like a LOT. There better be a REALLY good reason to justify it.

I'd also like to remind everyone that a spherical container has the highest volume to surface area ratio, but is the worst in regard to wasted space when packed in a sipping container. Could the skinny can save enough shipping space to make it worth it?

But the skinny can (as well as the Wiz optimal can) has too many hurdles to overcome. Mostly that can/cup holders and coozies, etc, are designed for the standard can.

After all, there's a reason that the 16oz beer can is taller but the same diameter as the 12oz can. Also note that you can purchase soda in 8oz cans that are shorter but same diameter as 12oz cans.

By the way, I believe the dent in the can bottom is because of the pressure. I.E. It if was a flat bottom, by the time it got to the consumer, the pressure would cause a bulge. Of course, that doesn't explain the similar dent in the bottom of glass beer bottles or the crazy deep dent in glass wine bottles....

I remember doing the calculations in a calculus class many moons ago. I'm not going to double check your math though. :)


IIRC, a few reasons why the "not-optimal" size is used:
1. More aluminum (thank God you didn't write "aluminium" like a dirty Brit) is used on the top/bottom than what you're assuming, since you assumed a perfect cylinder.
2. Ergonomics - Holding a can in your hand fits rather well. The short one is I reckon like 16% bigger than the tall one (width) while the "optimal" one is 20% wider than the short.
3. 100% optimization isn't necessary and optimizing (minimizing) the amount of aluminum used isn't necessarily the #1 goal. For instance, soda cans are generally purchased in either 6, 12, or 24 packs -- and it could be that the size of multiple cans (6, 12, or 24) is more optimal for transport given the current size rather than the "wizard optimal" sized cans. It could be more efficient to use the 'regular' size cans than the 'wizard optimal' size cans due to something in the manufacturing/ process (not that I can even guess at what it may be, if it even exists).

Or perhaps it's just so ingrained in the business, it's not worth it to make a switch to use 3.4% less aluminum. I believe the can manufacturers aren't necessarily the same as the bottling company (like Pepsi or Coca Cola), which would make it even more difficult to make the switch -- because the can manufacturer would have to make new machines to make the new optimal cans which would cost money for their one client just to save 3.4%...but would (IMO) potentially cost the client more than what they're saving.

sometimes you smart people take the long way around something. To determine if you are getting the same liquid, take 2 cans and pour them into 2 different glasses that are the same type of glass. See which one has more.

To see which one has more aluminum, take the empty cans and weigh them. If you really want to be precise rinse out the cans with water and then use a dryer to evaporate all of the water.

To answer the optimal can size it would be dependent on what you are doing with it and how you are storing it. My portable cooler works best with the shorter cans because they fit better. My larger cooler the taller ones would be best because it is easier to pack other stuff with them.

I think the real question should be what is the optimum ounces. They make 8 ounce cans, 12 ounce cans, 16 ounce bottles, and 24 ounce bottles. In a bottle I prefer 16 ounces. In a can I would actually like them to drop it to 10 ounces. 8 ounce is too little and quite often I waste a little bit in the 12 ounce ones.

Quote: Joeman

One other thing to consider is that the skinny cans are more optimal for cooling the can.

Good point. To be specific, the rate of heat transfer is proportional to the surface area, conductivity of the metal, and difference between the outside and inside temperature.

Quote:

As for the "wasted" aluminum, don't most aluminum cans get recycled these days? Or am I just dreaming?

That's getting off topic a bit, but I will say I knew someone who worked for Republic Services, who pick up the trash and recycling in Las Vegas. She said, despite getting free material to recycle, the only thing they turn a profit on is cardboard. I think it could be said that recycling requires more energy than making a fresh can. I'd be interested to see an unbiased study of the pros and cons of recycling, but for now I'm trying to keep the topic at hand simple at optimizing the can shape to enclose 355 milliliters. Also, the larger the volume, the more squat the can size will be.

Quote: DJTeddyBear

....By the way, I believe the dent in the can bottom is because of the pressure. I.E. It if was a flat bottom, by the time it got to the consumer, the pressure would cause a bulge. Of course, that doesn't explain the similar dent in the bottom of glass beer bottles or the crazy deep dent in glass wine bottles....

IIRC, the indentation on glass bottles is or was due to some process in the glassblowing process way back in the day and it's easier to make a "flat" bottom as opposed to a bumpy one if it's just a hollow circle. Nowadays I think it's due to tradition (it's always been done that way, so still make them that way now).


Source: I've watched hours of "pointless" YouTube videos. Check out Practical Engineering, Wendover Productions, Half As Interesting, and other channels like them because they interesting AF. Oh yeah, also VSauce and his channels as well as Numberphile.

Quote: RS

.... the indentation on glass bottles is or was due to some process in the glassblowing process way back in the day and it's easier to make a "flat" bottom as opposed to a bumpy one if it's just a hollow circle. Nowadays I think it's due to tradition (it's always been done that way, so still make them that way now).

The video gamefreak posted, starting around the 2:50 point, said the reason for the dome in an aluminum can is because it distributes the pressure from the weight of the beverage more efficiently on the bottom of the can, requiring less material.

Maybe the same is true of wine bottles.

If a can is faster to cool, it will be faster to warm, also.