What if an egg was...

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derpcube
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What if an egg was...

Postby derpcube » Tue Jun 04, 2019 10:51 am UTC

How fast would you have to spin an egg for it to crack due to the centrifugal force exerted onto the shell by the yolk and whites?

commodorejohn
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Re: What if an egg was...

Postby commodorejohn » Tue Jun 04, 2019 1:26 pm UTC

I wonder if you even could, since the yolk is a free-floating denser mass inside a volume of much thinner, rather slippery liquid.
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p1t1o
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Re: What if an egg was...

Postby p1t1o » Tue Jun 04, 2019 1:52 pm UTC

Lets see, well outward pressure would manifest as tension spread evenly thoughout the "equator" of the plane the egg is spinning in. Other parts will experience different forces but my gut says the forces will be greatest at the equator.

So the rate of rotation is limited by the tensile strength of eggshell, a form of calcium carbonate called calcite. Basically chalk.

Things will be complicated by the structures within the egg, and by the different fluids, but assuming it is filled with homogenous fluid of even density will give us a pretty close answer.

I am also assuming it is being spun on its long axis, the rotationally symetric one, as the calculations otherwise would be much more involved.

Here: https://phys.org/news/2017-01-strong-egg.html it is explained how when you crush an egg end-to-end, the failure is also dependent on radial tension, and eggs are very hard to break this way (a chicken egg can support over 100lbs axially, under good conditions).

So now all you need is the mass of egg contents and the tensile strength of eggshell to find the answer.


Lets focus on a 1cm strip centered on the equator, to simplify and get a ballpark figure. I think this is where maximum tension will be reached.

Eggshell is roughly 0.3mm thick

One source (https://link.springer.com/article/10.1007/s12666-009-0027-8) measured the tensile strength of different Calcium Carbonate fillers an got answers in the region of ~600MPa or 600N/mm2

So at 10mm * 0.3mm we have a 3mm2 cross section so an 1800N breaking force.

Wall tension = Internal pressure * Radius

So internal pressure = Tension / Radius

So relative internal pressure required to rupture = 1800 / 0.02m (average) = 90kPa (or about 0.9atm)




So there are some numbers that should give you an idea of the magnitude of the answer, however I have been unable in a short time, to figure out how to calculate a rotation rate related to that outwards pressure required to rupture the shell. I think theres gonna be a horrid integral or something to get a proper answer.

Plus, obviously, I've made a lot of quite broad assumptions in order to more easily arrive at an estimate.



Hang on, lemme see if I can break this down more....

So you can simulate this by sectioning off a "column" of the whole circular business.

Column of fluid 2cm tall, 1cm2 cross section
2cm3 volume
Estimated at 2g mass
floored with calcium carbonate
Simulate mass of fluid with a point mass at height 1cm (0.5*radius - point mass averages out difference in force from top to bottom of column)
What acceleration must be applied to the point mass to exert 90k / 10,000 Newtons = 9N (to get force on 1cm2 generated by 90kPa pressure) ?

to make 2g exert 9N, it must be accelerated at about 450g

Which using this calculator - https://www.omnicalculator.com/physics/ ... ugal-force - which is doing the angular momentum calculations for me:

gives a tangential velocity of about 6m/s and an rpm of about 6400rpm or about 106Hz


106Hz - thats pretty fast, but not like, crazy fast, and since eggs are known to be surprisingly strong, I reckon thats in the right ballpark.


Unless I made any glaring errors, which has about a 30% propability.

p1t1o
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Re: What if an egg was...

Postby p1t1o » Thu Jun 06, 2019 2:29 pm UTC

lol so I was looking for any possible data online for this, because the problem has stuck in my head...

...I didnt find any data that helped, mostly just "kitchen hacks" to make funky eggs by mixing them within the shell before cooking...

(apparently if you spin them fast enough, the yolk and white "swap" places)

...including this:

https://www.vat19.com/item/the-golden-g ... -scrambler

I love the internet

solune
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Re: What if an egg was...

Postby solune » Fri Jun 07, 2019 2:58 pm UTC

I'm way too lazy to do as much math as you did, but I have a couple of thoughts:

I'm pretty sure that the egg will spin on it's side no matter how hard you try. In free fall, an asteroid will do that to minimize it's rotational energy. Add to that, that the egg center is lower when it's on its side.

When it starts rotating, the egg will try to become a disk. Thus the egg shell will want to increase its curvature on the sides and decrease its curvature on the top and bottom.
The shell will crack more easily from a decrease of the curvature than from an increase (my own opinion). However the curvature effect is stronger on the sides than on the top/bottom, so I expect the break to come from there.

So I think we need to know the folding strength and folding breakpoint of a calcium carbonate plate.

p1t1o
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Re: What if an egg was...

Postby p1t1o » Fri Jun 07, 2019 3:18 pm UTC

solune wrote:I'm way too lazy to do as much math as you did, but I have a couple of thoughts:

I'm pretty sure that the egg will spin on it's side no matter how hard you try. In free fall, an asteroid will do that to minimize it's rotational energy. Add to that, that the egg center is lower when it's on its side.


Not just eggs, any body with one dimension longer than the other.

solune wrote:When it starts rotating, the egg will try to become a disk. Thus the egg shell will want to increase its curvature on the sides and decrease its curvature on the top and bottom.
The shell will crack more easily from a decrease of the curvature than from an increase (my own opinion). However the curvature effect is stronger on the sides than on the top/bottom, so I expect the break to come from there.

So I think we need to know the folding strength and folding breakpoint of a calcium carbonate plate.



I think that outwards pressure will be much larger force than bending caused by said outward pressure, and it is known that an egg in axial compression (long axis) is tension-limited.

I am also skeptical that liquids want to form discs, I can only imagine discs forming in this way with substances that have some structural integrity, here, most of the mass is a fluid, which just wants to go sideways. But Im stretching my experience in that matter.

However, I did indeed massively simplify the problem as if we were to accurately assess the strength of a doubly-curved asymmetric egg-body, rotating around the short/side axis, things would get extremely complex very quickly!




PS: is your name a reference to "The Incal"?

solune
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Re: What if an egg was...

Postby solune » Fri Jun 07, 2019 4:49 pm UTC

p1t1o wrote:I am also skeptical that liquids want to form discs, I can only imagine discs forming in this way with substances that have some structural integrity, here, most of the mass is a fluid, which just wants to go sideways.

Small liquids will try to form discs but remain together thanks to surface tension. But I was actually thinking about the Earth as an oblate spheroid, and treating the egg as a solid object.
I think my reasoning would work for an empty eggshell, but you're right for the filled egg.

p1t1o wrote:PS: is your name a reference to "The Incal"?

Yes! You're the first one who's picked up on that :D

p1t1o
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Re: What if an egg was...

Postby p1t1o » Mon Jun 10, 2019 11:11 am UTC

solune wrote:
p1t1o wrote:I am also skeptical that liquids want to form discs, I can only imagine discs forming in this way with substances that have some structural integrity, here, most of the mass is a fluid, which just wants to go sideways.

Small liquids will try to form discs but remain together thanks to surface tension. But I was actually thinking about the Earth as an oblate spheroid, and treating the egg as a solid object.
I think my reasoning would work for an empty eggshell, but you're right for the filled egg.


Yes, that all seems to make sense, at least in relation to my assumptions.



solune wrote:Yes! You're the first one who's picked up on that :D


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