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Weird and Wacky Engineering

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sudo

10/20/2012 1:43 AM EDT

As for the inflexibility of the sole, the Dutch and the Swedes have clogs and ...

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sudo

10/20/2012 1:38 AM EDT

That's where you need material woven out of textile-grade fiberglass. Higly ...

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# Engineer solves Cinderella glass slipper dilemma

## 10/12/2012 2:36 PM EDT

Once upon a time, there lived a mechanical engineer who pondered a question that has bothered intelligent, curious children for years. Namely, what qualities would the glass in Cinderella’s slippers need to have in order for her to walk and dance comfortably (and hold her weight)?

Yes, that was a question answered by one Antariksh Bothale, a BTech and MTech in Mechanical Engineering, on question and answer site Quora this week.

“It is delightful to have my masters degree in Mechanical Engineering put to use in resolving age old engineering problems,” wrote Bothale before giving a thorough mathematical breakdown of the problem.

The question made me smile because it’s one I used to ask my parents all the time. After all… the risks seemed huge! What if the glass broke and sliced through her feet? It seemed like such a ridiculous choice of footwear. “They were MAGIC glass slipers” my mother used to say, exasperated by my relentless story hole poking. But that just didn’t cut it for me. Bothale’s answer, however, does.

“Whenever we design  something that needs to bear force, we test for various possible modes  of failure and try to ensure that our object is strong against all of  them,” he writes before undertaking an analysis of the compressive stress on the slippers arising from Cinderella's weight which he estimates at around 50kgs.

“I  mean, her cousins were fat and ugly, so we have to leave them some room  on the top, right?” he jokes.
Bothale starts by assuming Cinderella’s weight can be applied uniformly  across her shoe, and roughly estimates her foot size and overall foot area at A = 0.015m squared.

If 50 kgs of weight were to be applied uniformly across this area, Bothale calculates that the compressive stress developed in the material would be:

Turns out it’s good news for Cinderella and fairy tale purists alike then, because Bothale writes that the Yield strength  of ordinary glass for compressive stress is approximately, which is three orders of  magnitude more than what Cinderella's weight can produce.

Perfect. Or maybe not quite yet, because Cinderella doesn’t just stand there looking pretty in her glass slippers, she actually has to walk around and dance, and that, points out Bothale, could lead to more compressive  stress due to the bending moment applied to her heel every time she  walks.

For simplicity’s sake, Bothale makes a couple of assumptions. He gives Cinderella’s heel a diameter of 2cm and a length of 6cm from the tip to the point where it joins the rest of the shoe. He then assumes her stepping angle to be about 30°, which would mean that only half of her weight would act in the normal direction to the heel. Plugging those numbers into his equation, Bothale calculates the maximum  bending stress in the heel to a max of 19MPa, which he says is “dangerously close” to the critical stress level of 50MPa.

“Even if we make a few more allowances by making the heel  thicker or the stepping angle smaller, we cannot let our little princess  veer so dangerously close to disaster,” he writes.

And so, Bothale recommends using thermal toughened safety glass, with its yield strength of 200MPa and a higher Young’s Modulus.

Even when the clock strikes midnight and Cinderella has to hightail it to her pumpkin carriage in those glass heels, increasing the impact force three to five times that of regular walking, Bothale calculates her dress would likely prevent her from making long strides, keeping her stepping angle within safe limits and ensuring the shoes don’t shatter. Though he does say the princess to be would be “well-advised to develop a toe-first foot strike, which would totally solve the problem.”

I don’t know about happily ever after, but Bothale’s attempt at solving the glass slipper conundrum certainly made my day.

What theoretical fairy tale problems would you like to see solved through engineering? Let us know in the comments section below.

michaela.lassig

10/12/2012 2:59 PM EDT

1. That is AWESOME! This provides a whole other dimension to finding the rightful owner of the glass slipper.
2. I think there should be a whole series of engineering fairy tales!
3. You should start with the 3 little pigs (how much force it takes to knock down the various houses or something)

Eduardo.Viramontes

10/12/2012 4:00 PM EDT

Flying carpets anyone?

ElPopularVale

10/12/2012 4:09 PM EDT

Cool, let's move to Rapunzel's hair, that's a baffling one.

RTewell

10/13/2012 10:23 AM EDT

How about "The Goose That Laid the Golden Eggs" (gotta love that Aesop). A little biology mixed with heavy duty alchemy? To boot, isn't this story what Silicon Valley is all about - ok maybe I'm being a little cynical.

Love the 3 little pigs idea - sounds like great fodder for MythBusters!

Frank Eory

10/15/2012 5:28 PM EDT

Agreed, the 3 little pigs idea would make a great MythBusters episode!

BrandX

10/17/2012 12:25 AM EDT

Actually, this has been kind of done...

agk

10/15/2012 8:25 AM EDT

Is some one is going to manufacture this item based on these information?

ReneCardenas

10/15/2012 6:12 PM EDT

What about Jack and the beanstalk, what kind of genetic engineering and mechanical engineering is required to have a plant grow as long as to reach the sky?

Not to metioned the speed and materials required to make it grow over night!

SylvieBarak

10/15/2012 11:59 PM EDT

But no matter how tall it was, Rene, I bet Felix Baumgartner would have skydived off it :)

BrandX

10/17/2012 12:29 AM EDT

Talking about something similar, have you heard of the concept of Space elevator?

http://en.wikipedia.org/wiki/Space_elevator

Arthur C. Clarke introduced it to the general public in "The Fountains of Paradise", although it is an idea from a Russian scientist...

ReneCardenas

10/16/2012 11:31 AM EDT

LoL, yea there is always some loony that seeks the adrenalin rush.

But in a second thought, that would be a cool amusement park! ;-)

10/16/2012 11:26 PM EDT

and How will they make the glass shoe flexibility to suit for soft feet when walk or even run?

sudo

10/20/2012 1:38 AM EDT

That's where you need material woven out of textile-grade fiberglass. Higly recommended for the show upper, to increase comfort.

sudo

10/20/2012 1:43 AM EDT

As for the inflexibility of the sole, the Dutch and the Swedes have clogs and can still dance. :-)

ACCAR

10/18/2012 4:49 AM EDT

The engineering analysis was tremendously fun. However, the explanation for the appearance of the glass slipper, is that it was never in the original story, which was french, and in that the shoe was made of vair, or grey squirrel fur, and vair sounds like verre, which is, of course, glass (http://www.iletaitunehistoire.com/genres/contes-legendes/lire/cendrillon-biblidcon_029).

BrandX

10/18/2012 1:36 PM EDT

Actually, no.

The original publication by Perrault refers clearly to the word "verre". There is a controversy in French because author Balzac, 150 years later, proposed it could be a typo and should read "vair"... But it most likely is not the case.

http://fr.wikipedia.org/wiki/Controverse_sur_la_composition_des_pantoufles_de_Cendrillon