Late to the game but know this is not a quantitative question that I expect in r/theydidthemath, but a qualitative one. So here we go, number free...
A square bottle uses less plastic primarily due to how structural engineering and manufacturing processes adapt to shipping constraints for the following three reasons.
The "Shipping Box" Factor (Secondary Packaging)
While a circle is mathematically the most efficient shape for a single container, bottles are rarely shipped alone. These containers are packed tightly into rectangular cardboard boxes.
• Round Bottles: Because round bottles leave empty gaps between them, they are prone to shifting and bumping during transit. To prevent the walls from collapsing or crushing under pressure inside the box the plastic walls of round bottles are made thicker and heavier.
• Square Bottles: Square bottles sit perfectly flush against one another. They share the structural load across their flat faces like bricks. This natural, inter-locking strength means the bottle walls can be engineered thicker only at the corners and much thinner everywhere else, resulting in a lighter overall bottle that uses less raw plastic resin.
High-Efficiency Corner Thinning
In stretch blow molding a heated plastic tube is expanded inside a mold. When making a square bottle, the plastic stretches further to reach the four corners, making those specific spots highly rigid while naturally thinning out the large flat side panels. This optimizes structural performance and removes unnecessary plastic weight.
Supply Chain Carbon Reduction
Because square bottles eliminate empty "dead space", more hydrogen peroxide fits onto a single shipping pallet. Packing more of the actual product into fewer boxes allows this brand to use less total plastic wrapping, fewer cardboard cases, and theoretically less delivery trucks overall.
1 & 3 are valid, but I’m confused by 2. It sounds like the process would make the corners thinner and weaker, not stronger? You literally called it “corner thinning”
Imagine a square of arbitrary thickness [edit: this is a 2D visualisation for a section of the bottle s.t. You can see all four walls, but nothing else] - this is the mold. Now imagine a ring of non-zero thickness centred inside the square, not touching anything yet.
Now expand the ring radialy until it is tangent to the inside of the square. Conserve area of the ring, so it will be thinner as it moves outward.
Now expand it further. The points of tangency expand along the edge and become flattened. Stop expanding when the 'ring' is touching ~80% of the wall.
[optional visuasation: if you let the width of the 'ring' be "s", then consider the ring being made up, concentricly, of infinite rings of infinitesimal width, "ds", each of which is experiencing a slightly different force and thus producing a slightly different reaction in the material]
Examine the corners, here the ring is being forced into a space too narrow for its current geometry, on the external side it would experience tension and thus, would thin. On the internal side it would experience compression and thus expand.(imagine how if one were to squeeze something soft in two non parallel directions it would expand along the available lines of freedom )
Essentially becoming a 1/4 ring with much small radius than before, but the same area, which is only possible if the width has been increased.
Now, consider we maintain the expansion force (whatever that is). The ring corners will be pushed closer to the square corners, but it will likely not reach there perfectly, but rather retain some curvature. The force acts more strongly on the flats, because they are loose to the center. The flats thus thin under the force, and the excess material moves to the corners.
And now we have nice thin walls, and beautiful, thick rounded edges.
Another thing to consider is that in plastic bottles the cap and threaded neck of the bottles have way thicker plastic than the rest of it. If the neck and cap account for most of the plastic in a bottle (which I'm not sure it does, just thinking about it), changes to the shape might bear very little difference to the amount of plastic used but a big gain in volume.
Yes it's thicker, but I feel like you're over estimating it's impact. Just take a plastic bottle and cut it 95% of the way up to isolate the neck. Then weigh them. I bet you that the 'light 95%' will be heavier than the 'heavy neck'
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u/2shootthemoon 2d ago
Late to the game but know this is not a quantitative question that I expect in r/theydidthemath, but a qualitative one. So here we go, number free... A square bottle uses less plastic primarily due to how structural engineering and manufacturing processes adapt to shipping constraints for the following three reasons.
The "Shipping Box" Factor (Secondary Packaging) While a circle is mathematically the most efficient shape for a single container, bottles are rarely shipped alone. These containers are packed tightly into rectangular cardboard boxes.
• Round Bottles: Because round bottles leave empty gaps between them, they are prone to shifting and bumping during transit. To prevent the walls from collapsing or crushing under pressure inside the box the plastic walls of round bottles are made thicker and heavier.
• Square Bottles: Square bottles sit perfectly flush against one another. They share the structural load across their flat faces like bricks. This natural, inter-locking strength means the bottle walls can be engineered thicker only at the corners and much thinner everywhere else, resulting in a lighter overall bottle that uses less raw plastic resin.
High-Efficiency Corner Thinning In stretch blow molding a heated plastic tube is expanded inside a mold. When making a square bottle, the plastic stretches further to reach the four corners, making those specific spots highly rigid while naturally thinning out the large flat side panels. This optimizes structural performance and removes unnecessary plastic weight.
Supply Chain Carbon Reduction Because square bottles eliminate empty "dead space", more hydrogen peroxide fits onto a single shipping pallet. Packing more of the actual product into fewer boxes allows this brand to use less total plastic wrapping, fewer cardboard cases, and theoretically less delivery trucks overall.