How did the 330 ml beverage can get its typical shape?

If  the dimensions which a 330 ml cyclindrical can must have in order to achieve a minimum surface were determined in a mathematical calculation, then 2.2% less material would be used compared to that required for the 330 ml can currently available on the market. 

This material saving related to the annual ouptut of 330 ml cans would lead to a significant cost reduction.  How were the dimensions used today actually arrived at?

If one were to carry out a purely mathematical calculation to obtain a can with optimal volume and minimum surface area, then the basic container would have to have a flat end and a flat surface. This yields a volume of 350 ml.  The current volume of a 0.33-litre beverage can is approx. 342 ml. 

Volume optimisation is, however, not the sole criterion guaranteeing optimal material use. When using the present production process for empty cans (wall-ironing of the can metal), the current can shape with a concave base and a slightly convex top end has proved extremely expedient. The mathematically calculated cylindrical can body would require significantly thicker plates to guarantee the same stability as that provided by the currently used can shape and consequently a greater amount of material would be used. A Ball Packaging Europe beverage can is designed to withstand an internal pressure of up to 6.2 bar. This is made possible by the concave base and the slightly convex top end.  These features are necessary in order to compensate pressure fluctuations which would otherwise damage the can.   

Another significant aspect is the optimal loading of the pallets used for distribution. In this respect it is important to mention, that for logisitics reasons (transport, storage, costs etc.) the retail trade does not permit any extreme shortfalls in pallet loading and under no circumstances products projecting beyond the pallet edges. That means that it is essential for the 1200 mm x 800 mm pallet area (Euro pallet) to be optimally loaded. Taking into account the cardboard packaging (trays) used, this can be guaranteed with the current can shape.  Each pallet layer can accommodate 216 cans.

With the mathermatically optimised can, it is only possible to accommodate approx. 150 cans per pallet layer.  And the pallet would not be optimally loaded.