Actually, this node has so far entirely missed the reason that the bottoms of aluminum beverage cans are curved. It's simple:
Curved walls are stronger
This is true not only for cans, but for all sorts of structures and containers, it's a fundamental engineering principle. Here are some other examples of this principle in action:
- Automobiles. Notice that the hood of your car has few (or no) flat surfaces, it's all curves. Same is true for most of the rest of the surfaces (windshield is another good example - side windows don't have to be as strong, and they have to open, so they aren't curved).
- Corrugated boxes, roofs and so on. The corrugation makes for strength.
- Other containers, such as propane tanks, scuba tanks, all sorts of things. If they have to stack, then the bottom is either curved inward (which reduces the volume the container can hold), or a false bottom is placed around the real bottom to make them stackable.
Why is it this way? Because the strength of a cross-section goes by its cross-sectional moment of inertia. If this doesn't make sense to you, think about this:
Hold a flat sheet of paper in your hand. It's floppy and has no structural strength to speak of. This is because it has almost no moment of inertia around the bending axis (ie, all of its mass is on the bending axis). Now, roll the paper into a tube. Suddenly, the same sheet of paper has considerable stiffness. By rolling it into a tube, you increased its moment of inertia around the bending axis (by moving its mass away from the axis and out to the edge of the tube). This is also why I-beams have that "I" shape, but you're probably tired of this by now.
Keep an eye on the world around you. You will see this principle in action over and over again.
Nifty, eh?