"Once you pop, the fun don't stop", is the slogan of the popular American chip brand Pringles. But if you're an engineer, you might be interested in Pringles for more than just their addictive crunch and taste.
In fact, Pringles have been designed in the shape of a hyperbolic paraboloid.
So, what is so special about the shape of a Pringle?
Well, the shape helps to prevent the Pringles on the bottom of the can from cracking under the pressure of all the Pringles on top of them. But the shape also helps give Pringles their characteristic crunch.
Allow us to explain why this unique geometry is fascinating.
What is a hyperbolic paraboloid?
But before we get into the "nitty-gritty" of Pringles chips, it might be useful to find out just what a hyperbolic paraboloid is. In the wonderful world of geometry, this shape is a quadratic surface and a doubly-ruled surface that has exactly one axis of symmetry, and no center of symmetry.
Often referred to as "saddles" (for obvious reasons), their name comes from the fact that their vertical cross-sections are parabolas. This shape's horizontal cross-section, on the other hand, are hyperbolas -- hence the name.
This shape has many useful applications in the physical world, aside from tasty potato-based snacks. As hyperbolic paraboloids are doubly-ruled, they are relatively easy to construct using a series of straight structural elements, making them useful as impressive structural elements in architecture.
For this reason, you will often find them used to construct thin "shell" type roofs. These can be formed using either timber or steel sections that are then clad, or they can be constructed using concrete.
"The use of hyperbolic paraboloids as a form of thin shell construction was pioneered in the post-war era, as a hybrid of modern architecture and structural engineering. Being both lightweight and efficient, the form was used as a means of minimizing materials and increasing structural performance while also creating impressive and seemingly complex designs," states Design Buildings.
In architecture, hyperbolic paraboloids derive their structural integrity from their shape rather than their mass (like many conventional roofing methods). The shape's curvature also helps to reduce its tendency to buckle under compression, giving it exceptional stiffness.
The shape also aids materials and structures in withstanding unequal loading from both dead loads and live loads (like wind).
The geometrical sturdiness of a hyperbolic paraboloid is widely exploited in architecture and engineering, especially in structural roof construction. The London Velodrome, the Scotiabank Saddledome in Canada, and the Scandinavium in Sweden are some of the more sophisticated structural examples of a hyperbolic paraboloid in real life.
How are pringles made?
And now on to something a bit more palatable, as a matter of fact, delicious. How, exactly, are Pringles made?
Pringles, unlike more traditional potato chips (or crisps if you are from Blighty) are not made just out of potatoes. In fact, the life of a Pringle starts out as a slurry of rice, wheat, corn, and potato flakes - along with a number of additives.
This Pringle "dough" is then pressed and rolled into an ultra-thin sheet before being cut into chip-sized pieces. These cuts are then separated from the remains of the sheet by a specially-designed machine.
These chips then move forward on a conveyor belt and are pressed onto molds to give them their iconic shape. These molded chips then move through boiling oil and are fried for a few seconds.
The chips are then blown dry, sprayed with powdered flavoring, and finally flipped onto a slower-moving conveyor belt that allows them to stack. Once complete, the chip stacks are then transported to their cans, foil sealed, and shipped out to their eagerly awaiting customers.
What is so special about Pringle's hyperbolic paraboloid geometry?
Perfectly executed geometric shapes are always pleasant to look at, as their proportions are quite eye-catching. Just like how a nearly perfectly symmetrical human face that is naturally proportioned to conform to the golden ratio tends to be deemed beautiful. In the case of a Pringles chip, the intersecting curves form a sturdy structure as well as an attractive geometry.
This special geometry is referred to as the hyperbolic paraboloid in the world of mathematics, as we have mentioned above.
What is interesting about a hyperbolic paraboloid is the point where the maximum and the minimum of the two principal curvatures meet each other at a zero point. This is known as the saddle point or the minimax point.
The hyperbolic paraboloid's intersecting double curvature prevents a line of stress from forming, which doesn't encourage a crack to naturally propagate. That's why Pringles have that extra crunch in them when you either bite a piece off or when you put a whole Pringle in your mouth.
If you frequently eat Pringles you would know that they never break off symmetrically, but instead, they crack in different directions and produce flakes with varying shapes. It's all due to the hyperbolic paraboloid geometry of each chip.
Moreover, the two opposing curves perform well together under tension and compression, which gives each Pringle some structural strength despite their relatively thin shape.
The concave U-shaped part is stretched in tension while the convex arch-shaped part is squeezed in compression. Through this double curvature, the shape strikes a delicate balance between push and pull forces, allowing it to remain thin yet surprisingly strong.
The practicality of hyperbolic paraboloid chips
It's obvious to anyone that the shape of Pringles also makes stacking the chips advantageously easy. Again, this is due to their saddle shape, which allows the chips to be smoothly placed on top of each other.
And as for the Pringle that is placed at the very bottom of the tube, it's able to retain its shape without breaking because the net weight of the chips doesn't usually exceed 150 grams. Plus the hard body of the tube, made possible because of the hyperbolic paraboloid geometry of the chips, minimizes the chance of breaking the chips when they are being transported.
From potato chips to structural roofs, this unique geometrical wonder is truly fascinating.