Flapjack follows function
As a structural engineer and zealous pancake man, I was alarmed to learn that Extra Crispy recently attempted to break the Guinness Record for tallest pancake stack without requesting my advice. In their hubris and naïvety, Extra Crispy failed, leaving the record in the possession of British resort Center Parcs Sherwood Forest. The stack of 101.8 cm was built by a team of chefs (no engineers) to mark Shrove Tuesday, better known as Mardi Gras. While I congratulate them on being the first to break the one meter barrier, it is my contention that the design of world’s tallest pancake stack is a challenge that belongs not to the chef, but to the engineer.
To begin my design process, I consulted the parameters set by Guinness World Records, which is the de facto building code for this project. According to their rules, each pancake must have a diameter of between 12.5 cm and 25 cm and a thickness of less than one cm. (This is rather thin, but the rule presumably exists prohibit maniacs like me from breaking the record with one megalithic pancake.) The pancakes must be edible and must be distributed for consumption, ensuring that no food is wasted in the pursuit of world records. The batter recipe has no restrictions, but must be disclosed to the record keepers at Guinness. And based on the widely accepted spirit of the challenge, there are to be no guy cables, buttresses, tuned mass dampers, or other structural tricks.
To engineer a better pancake stack, we must first engineer a better pancake. The task at hand requires us to evolve beyond the fluffy, carefree flapjacks of our youth. Instead, we must optimize the pancake’s structural characteristics, even if that means sacrificing all palatability. Remember: nobody ever asks how A992 steel tastes.
When a tall building is subject to a lateral load (due to wind or earthquakes) it resists that load through its strength in bending. In a structural system undergoing bending, one side will see a tensile stress, while the opposite side will see a compressive stress. Real world structures in steel, wood, concrete, or masonry can be designed to resist these bending moments because of their ability to resist both compression and tension.
But in a pancake stack, a given pancake has no mechanical bond to the pancake directly above or below. (We’re not welding or grouting these pancakes into one solid column.) While compressive stress can certainly be transmitted from pancake to pancake through bearing, tensile stress has no means of transmission at the pancake interface. They can peel right apart. In practice, a pancake stack actually can resist some amount of tensile stress simply because the tension is counteracted by the weight of all the pancakes above. But if, at any point, the tensile stress due to bending is greater than the compressive stress due the weight of the upper pancakes, the pancake stack will be unable to resist the bending moment and will topple. Call this Weinberg’s First Pancake Law.
Thankfully, we can assume that the erection of our pancake stack will not occur during a wind storm or earthquake. But as pancakes are added to the stack, any slant or out-of-plumbness will induce a similar bending moment. This appears to be the failure mechanism for the overwhelming majority of pancake stacks. To avoid this hazard, we must ensure that our individual pancakes are as flat as possible and that our stack remains perfectly plumb at all stages of construction.
The mechanical properties of a typical pancake also pose a challenge to stack construction. Pancakes, like all linearly elastic solids, shrink when compressed and stretch when pulled. The ratio of the force applied (stress, in pascals) to the resultant deflection (strain, in millimeters per millimeter) is called the Young's modulus (in pascals). In simple terms, a material with a higher Young's modulus will be stiffer and will shrink less when compressed.
Since the editors at Extra Crispy repeatedly denied my request for a $380,000 piece of testing equipment to perform an empirical study on the elastic properties of pancakes, we have to rely on existing literature. Studies have shown that typical non-load bearing cakes have a very low Young’s modulus, somewhere on the order of 50 kilopascals. (Steel, by comparison, is 4 million times stiffer.) This squishiness means that as the pancakes are stacked, the applied compressive stress will cause them to become even thinner than they were initially.
Every pancake in the stack will flatten by an amount proportional to the weight of the pancakes above it. If we assume that our stack of pancakes has a diameter of 25cm and a weight of about 30kg, then the bottommost pancake will lose 12% of its thickness. This flattening will require us to add more pancakes to the stack to reach our target height, thereby amplifying the risk of imbalance. The solution is to make a stiffer pancake that will deflect less under loading.
First, we should use a custom pan with an internal diameter of 25cm (the maximum allowable size) with an upturned rim to ensure that each pancake is perfectly circular. Although the pancake serves as the idiomatic paragon of flatness, most non-structural pancakes actually have a slightly domed contour. As more and more of these convex pancakes are stacked, this shape can compound itself and become a source of disequilibrium. To prevent the dome from forming and to ensure maximum flatness, the batter must be distributed evenly across the entire cooking surface. Ideally, the pan would have some kind of heated lid (like a tortilla press) to ensure that both of sides of our pancake are seared flat.
Just as the contents in a concrete mix are tightly controlled in order to achieve the behavior sought by the engineer, our pancake batter can be designed to achieve the desired stiffness. The flour must be tough but not too heavy—perhaps some kind of buckwheat. The rigidity of a cake generally decreases as sugar content increases, meaning that our batter should just omit sugar entirely. I would also suggest using the baking additive potassium bromate, which improves the structural properties of cake-like foods (and probably causes cancer).
After production, each finished pancake should be visually inspected and tested for flatness. Practical experience and empirical studies have shown that cakes become stale and therefore more structurally sound when the they are left out, so our pancakes should be prepared a set number of hours (or days) prior to construction.
The construction surface should be level, stable, and maybe even placed on vibration isolators. Our stackers should have steady hands and steely nerves. As stacking proceeds, the builders should check the tower’s flatness and plumbness by using a level and plumb bob at regular intervals. (I would not rule out the use of a theodolite.) Once the stack has topped out, it must remain upright and unsupported for five seconds to qualify for the Guinness record. The stack can then be disassembled, and the cold, rigid, carcinogenic food discs can be distributed for joyless consumption.
Victory is not always sweet.