The OREO Project

One Christmas, I received an Oreo mug as a gift. The mug has bits of Oreo trivia, including a question on how many Oreos it would require to build a pile as tall as the St. Louis Arch. A civil engineer friend of mine, now living in Saint Louis, laughed at the prospect of building a tower of Oreos that high. He claimed that the Oreos would never hold up to the loads required.

Obviously, a free-standing structure would be impossible. The tower would be inherently unstable, and would topple in the wind, or by vibrations induced by adding cookies. Therefore, a stabilized tube-structure would be required to provide lateral support. The remaining question is would an Oreo cookie be able to withstand the immense load placed upon it by the cookies above it in the tower.

Having faith in the mother of all sandwich cookies, I did some searching online to see if there was any information about the strength of an Oreo. Googling "oreo st. louis arch," I found a few Oreo trivia sites, such as: http://www.classwebsite.org/oreoproject2002.htm

Googling "oreo saint louis arch" shouldn’t be done at work. Weird.

We start by determining the weight of a test cookie. A sample of 4 cookies were taken from a box of Oreos, bought at a local bulk-foods store (I eat a lot of Oreos).

I weighed each cookie on a gunpowder scale, accurate to 1/10^{th}
of a grain (1/70,000^{th} of a pound). There are 7000 grains in a pound. After tareing
the scale, I obtained the following weights:

weight (gr) | weight (lb) | |

Oreo 1 | 167.2 | 0.023886 |

Oreo 2 | 169.2 | 0.024171 |

Oreo 3 | 169.4 | 0.0242 |

Oreo 4 | 168.7 | 0.0241 |

Thus, our average cookie weight is .024lbs. According to the mug, it takes 15,120 cookies to reach the top of the arch. That brings the weight of the tower of Oreos to: 364.23 pounds. Thus, the bottom Oreo must sustain a weight of 364.206 pounds.

We know the area of a circle to be Pi * r^{2}. Using a micrometer
to measure the diameter of our Oreos gives us the following:

width 1 | width 2 | |

Oreo 1 | 1.792 | 1.752 |

Oreo 2 | 1.805 | 1.775 |

Oreo 3 | 1.79 | 1.76 |

Oreo 4 | 1.805 | 1.775 |

According to our measurements, Oreos are actually ovid! Wider than they are tall. For simplicity’s sake, we will assume that they are round, with an average diameter of 1.78". This gives a surface area of 2.49 square inches. Thus, the bottom Oreo must sustain a pressure of 146.071 psi.

I brought the cookies to a local fitness store, where a friend of mine works. They had lots of free weights, which we could use to test the cookies. The first test involved an Oreo at room temperature. The Oreo was placed between two small weight blocks, to provide a smooth surface and ensure even weight distribution over the surface of the Oreo. Weights were then applied until the Oreo was so flat it could no longer support the stack. The room temperature Oreo failed at 257.5 pounds.

I also tested a cooled Oreo. The summer in St. Louis is normally hot and muggy.This can adversely affect the strength of the Oreo by causing it to go stale. What would happen if we cooled the Oreo to common St. Louis winter temperatures, as if we built our tower in the winter? Average daily highs from December to February are about 25°F. Our Oreo was stored overnight in a freezer, then placed in an insulated container and surrounded by ice. Unfortunately, I did not have an accurate thermometer to test the temperature of the Oreo, but I would expect it to be about 35°F or lower. Weights were then applied to the cookie. It failed at 282.5 pounds.

Conclusion:

The Oreos started to show failure after about 180 pounds. Therefore, a single tower of Oreos 630 feet tall using only 15,120 Oreos would not be possible. However, if we distributed the weight among 2 or more Oreos at the base, the cookies would provide an adequate foundation for the rest of the structure. At the very least, crushing Oreos under 200 pounds of force is an excellent way to make crumbly dessert topping. Not even the white filling is able to keep its structural integrity.