A Scientific Breakdown of Cinderella’s Glass Slippers

Let’s talk (not too seriously) for a minute about Cinderella Shoes.

We do not really know the exact size and shape of the slippers that Cinderella wore, but we can assume they look something like the image to the left. cinderella-shoes

Let’s focus on comfort and failure, not about Cinderella’s failure to keep on her shoe, but about mechanical stress.

Keep in mind that every time we design something we perform multiple tests to ensure the product is strong enough and ready for production. Let’s apply these concepts to Cinderella’s heels, pretending they are made of glass (even though we know that they were probably not made of glass, but fur).

First test is about the compressive stress done by Cinderella’s weight. We can assume her weight is about 110 LBS. Will the shoes break under that pressure?

cinderella-shoes-forcesA rough estimate of her foot size and her foot area comes to be about A=0.015m2

And if we apply 110 lbs of weight uniformly on the area, the compressive stress developed in the material would be σ=F/A =mg/A ≈ 33KPa

Normal glass stress support is approximately 50MPa , which is way above what Cinderella weight will enforce on the shoes. In summar, this tells us that Cinderella’s shoes will not break under the stress of her weight. We can assume they are safe, but what about dancing and walking? That would put the shoes under different stress.

Let’s make some simplifying assumptions. Let’s assume her heels diameter is ϕ=2cm and a length of l=6.

We can model the heel as a simple cantilever beam of circular cross section.

For her to be safe dancing and walking, we need to take at least a safety factor of 2, and also assume the bending stress can go up to 75MPa. In simpler words her shoes must have a strength of at least 150MP.

cinderella-shoes-heel

Safety glass has a yield strength around 200MPa, that means she is safe if her glass slippers are made of safety glass.

And when she runs?, we can expect the impact force to be 3-5 times the impact of regular walk, but we should assume that Cinderella’s dress won’t let the take long strides, her running won’t be too fast and the impact force won’t be too high.

We can conclude that Cinderella’s shoes could be made of safety glass without breaking and causing major damage to her feet.

Comfort, on the other hand, is a different story. Girl was crazy for wearing stiff, glass shoes.:)

 

cinderella-and-prince-dancing