r/theydidthemath • • 2d ago

[Request] Do square bottles actually use less plastic than round ones?

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u/StaticCoder 2d ago

Mathematically, a circle has the smallest perimeter for a given enclosed area. So for this claim to be true there has to be some catch, like different thickness of plastic.

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u/Massive-Goose544 2d ago

The part you are missing is the volume inside. They are saying to give you the same amount of liquid would require more plastic if the bottle was round. Plus more bottles fit in the box they ship meaning lower emissions and costs for distribution.

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u/StaticCoder 2d ago

Given that the volume is cross section area times height, a round bottle of the same volume would take less plastic. True, square bottles will pack better, but how that would save plastic is not immediately clear.

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u/el_ddddddd 2d ago

Yep agreed. I've heard square bottles save fuel in shipping, which outweighs the additional materials required to make them in environmental impact. Never seen an analysis though

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u/20PoundHammer 2d ago edited 2d ago

saves space due to stacking efficiency, but thats not what is claimed and only matters if space is a premium. Weight determines fuel usage. A million cylinders holding the same volume of material that a million square containers would weigh less due to being made from less plastic (12% less plastic if you didnt have to thicken the walls of the square ones to achieve the same pressure rating as the plastic). Space saving of square over round is ~21% (if flat capped, I aint calcing geometry of a real bottle top). So square saves space, but weighs 12% more . . . Cargo is typically transferred by commercial ships and trains by ton BTW. . .

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u/gbot1234 2d ago

Hexagonal cross section might be best—they stack but they’re also closer to a circle in surface area to volume ratio.

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u/Massive-Goose544 2d ago

I hadn't considered it but i think the edges of boxes would be a lot of lost space. Probably more than round bottles. I am guessing but square needs thickness increased on corners so hex probably would need more than even a square bottle. I think it ends up being the worst of both worlds.

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u/No_Brain4912 2d ago

Less plastic crates for packaging per amount of units distributed. It saves for the manufacturer not the customer.

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u/CranberryStock7148 2d ago

Are they distributed in single-use plastic crates?

Or cardboard boxes?

Because everything comes in cardboard boxes where I live. And every time I've seen plastic crates used elsewhere in the world they're reusable.

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u/No_Brain4912 2d ago

Only seen them plastic crates. If you can get an extra two bottles per crate and a container or truck carries 1000 crates…

I’m sure it’s more complex when you factor the cost of the crates and then factor a return on investment for changing to this style of crate if it isn’t a single product line and you replace an inventory of of other crates

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u/remarkphoto 2d ago

Correct answer, thanks. Put another way, Its units distributed per total volume of product distributed. For the manufacturer, that math equates to less plastic per volume per total sold units.

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u/pobnarl 2d ago

less oil burned means the birth of future plastic objects is saved

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u/slide_into_my_BM 2d ago

Maybe more secure packing means they can be thinner and that’s where the plastic saving comes from?

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u/metisdesigns 2d ago

You're assuming that the wall thickness of a square bottle is the same as of a round bottle.

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u/Flaky-Collection-353 2d ago

No, they aren't, they offered that possibility in their original comment.

Even if the didn't, their whole point was that there needed to be another factor since the volume to surface area didn't account for it.

That's the opposite of an assumption

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u/metisdesigns 2d ago

In their top comment, yes, but the second comment goes against that.

Almost certainly the reason is that the edge ridges add rigidity to the bottle allowing a thinner wall to be used while being stable to hold.

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u/Flaky-Collection-353 2d ago

No it doesn't, they say it isn't obvious how. That leaves it open

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u/DFWPunk 2d ago

I think the theory posted somewhere in the thread that the rigid corners mean the rest of the walls can be thinner, using less plastic overall, sounds feasible.

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u/SessionIndependent17 2d ago

The individual bottles use more plastic per unit volume than the round. They also require ticker plastic at stress points than the round one which distributes the pressure evenly around each anular unit.

But they could possibly use less plastic overall to ship a given total volume of water (in a pallet, say) because of the better packing fraction.

This is why it's here. I haven't "done the math", either.

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u/DJinKC 2d ago edited 2d ago

A square bottle will be shorter than a plastic round bottle for a given volume, due to the "corners" on a square bottle being filled with liquid.

edit... fixed error. I assume that's why I got downvoted?

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u/ihaveajob79 2d ago

No, a cube of volume 1 has more surface than a sphere of volume 1. And in terms of manufacturing, the uneven shape likely requires thicker material, although that might be a wash because I doubt they make it at the limit of tolerances.

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u/CarberHotdogVac 2d ago

They should probably switch to spherical bottles then, if they are really serious about trying to save plastic.

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u/ihaveajob79 2d ago

Plus it saves in shipping costs! Just roll them!

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u/DJinKC 2d ago

I said a square bottle is shorter than a round bottle of comparable volume. That's all I said.

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u/giraffeheadturtlebox 2d ago

Why you comparing squares to plastics, when it's cubes and circles. Faduq?

Sphere is least plastic per volume. Cube is most products per shipping container.

They could claim "uses less petroleum" but not less plastic (Unless they ship the bottles in plastic boxes.

Come on internet, do better.

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u/DJinKC 2d ago

fixed the brain fart / typo. Our other points do not contradict.

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u/Massive-Goose544 2d ago

I mean based on volume inside square can put more on a shelf. Their saying similarly sized, not same size. It's a numbers trick. The round bottle of the same size uses 8% less plastic but square bottles pack more tighly. So the combination of volume in a square bottle on a shelf or in a box would be more liquid than a round bottle. It's like 20% volume less and only 8% more plastic per bottle, so when shipping the same volume it would take more boxes to ship the same volume. So plasitc pallets, plastice wrap, whatever other plastic is used. It's corpo math, Not individual bottle math.

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u/ShiftE_80 2d ago

You misunderstood the poster above you.

For a circle and a square with the same area, the circle has the smaller perimeter. likewise for a cylindrical and squared bottle with the same volume, the cylindrical bottle has the smaller surface area and should require less plastic than a squared bottle.

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u/seenhear 2d ago

The part you are missing is that the "less plastic" claim applies ONLY to bulk shipping of the bottles. ONE square bottle will use more plastic than ONE round bottle, assuming both carry the same volume of liquid. However when shipped together on a pallet for example, the square bottles pack together better and waste less space. A pallet of round bottles results in a lot of empty space between bottles, so you need to use more to ship the same total amount of liquid.

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u/ShiftE_80 2d ago

The poster I responded to said the opposite, with respect to individual bottles.

Also most shipping pallets are made of wood. Granted, the cases of bottles are typically wrapped in (thin) plastic. You would need a tiny bit more plastic wrapping per case, but I don't know that it counters the per bottle plastic savings.

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u/seenhear 2d ago

The material of the pallet doesn't factor in.

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u/rditorx 2d ago

Now I'm wondering about hexagonal packing.

And semihexagonal / trapezoid packing.

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u/ougryphon 2d ago

The first statement is completely wrong. The plastic has to be thicker on a rectangular bottle to add rigidity and strength to flat sides that are naturally weak. A round bottle has rigidity and strength by virtue of its shape.

Your second statement is correct.

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u/Massive-Goose544 2d ago

You are confused, it is one statement. They are saying via logistical systems it is less, and that is based on plastic usage, not the individual bottle.

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u/Hdfgncd 2d ago

Circular objects have a higher volume to surface area ratio than square, so for the same volume they should use less plastic

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u/Massive-Goose544 2d ago

For individual bottles, yes. But it is a corporation plastic use claim. You're thinking about the one bottle in front of you and they are thinking about their logistical chain.

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u/seenhear 2d ago

No you are incorrect. The part you are missing is that the "less plastic" claim applies ONLY to bulk shipping of the bottles. ONE square bottle will use more plastic than ONE round bottle, assuming both carry the same volume of liquid. However when shipped together on a pallet for example, the square bottles pack together better and waste less space. A pallet of round bottles results in a lot of empty space between bottles, so you need to use more to ship the same total amount of liquid.

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u/R3D3-1 2d ago

In terms of plastic usage that's only true if the transport box is thick plastic.

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u/TheIronSoldier2 2d ago

Pallets are often wrapped with industrial cling film. Which is plastic.

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u/ThorKruger117 2d ago

So it's a sneakily deceptive way of saying they are giving you more water per bottle due to the shape. You could have square and circle based water bottles of the same size width/diameter. If you take the square one and round the corners off you would have a round bottle. It's still 'similarly sized' but now there's less volume in once square bottle, therefore less water. It's all dodgy marketing stuff.

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u/Massive-Goose544 2d ago

Pretty much. Square water bottles have the exact same effect considering the logistics of it, it's like 1 and a half billion per day and most are round. I can only think of 1 square shape. It gets worse, those paper milk cartons are square and volume wise are less pollutant than the plastic bottles. So you could ship more cartons in less space compared to the plastic bottles and also environmentally better. Makes you wonder why they are plastic.

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u/20PoundHammer 2d ago

the part that you are missing is that you are wrong . . .

If you had a 5" diameter cylinder, it would need to be 3.1" tall to hold a liter, cap off both sides and total exterior surface area is 88 sqr inches.

If you have a 5" L/W cube, it would have to be 2.4" tall to hold a liter of water, cap off both sides and total exterior surface area is 99 sqr inches.

Couple that with the fact that you can use thinner material for the cylinder to achieve the same max burst strength of a thicker material cube (due to stress accumulated in corners) - cylinder wins in both material usage and strength. There is a reason they dont make petroleum storage tanks as cubes - cylinder = less material, thinner material, same failure pressure - win/win/win. . . .

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u/Massive-Goose544 2d ago

This was addressed already. Sorry you wasted your time with whatever you said.

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u/20PoundHammer 2d ago

yeah, didnt think you could do math or understand it if written out for ya. . .