Put a pizza in a box, then put the box in a large space centrifuge such that the top of the pizza (and box) faces the gravitational force. How much force does it take to ruin the pizza?
This question was pretty much raised, but not answered, in Randall Monroe’s What If? blog, “Pizza Bird”.
ETA: I suppose it might be a question of time; that a pizza exposed to lower g-force for a long time would still be ruined.
~Max
I think you mean centrifugal force. If the force is applied evenly to the top of the pie, then it could probably withstand several gs since it is already basically flat. However, if the force is applied to the side, hardly any (less than 1g) would be necessary to accordion the whole thing into the side of the box.
No, the original situation called for tethering the pizza to an airplane. I was thinking more like, at what point does the box fall in and tear up the pizza? What happens to the cheese? To the dough?
ETA: Something happens when you press cheese too hard, right? Doesn’t the liquid come out?
~Max
That doesn’t take into account the differences between Chicago Deep Dish, New York, Cracker Crust or Stuffed Crust. And then there’s calzones.
Calzones, not being pizzas, are (in my opinion) irrelevant to this discussion.
Assuming, you mean that gravity is perpendicular to the plane of the pizza.
Assuming you mean, what speed does the pizza need to be rotated (spun) for it to ruin .
I do the calc with lots of caveats as to how a pizza is anisotropic. Consider the calcs to be order of magnitude, rather than exact. We engineers usually have to live with order of magnitude calcs.
1> Yield Strength of Pizza : This varies quite a bit based on if it is a fresh pizza or a refrigerated pizza, baking temperature and interior or crust. Lets pick a typical value of 6 kPa.
(Refer to tables 1 through 4, Page 21 - 24 at https://digitalcommons.wpi.edu/cgi/viewcontent.cgi?article=2817&context=iqp-all
2> Equations for Stress in a Rotating Disk can be found at : Rotating Bodies - Stress.
σz = ω2 r2 ρ / 3
= v2 ρ / 3
= ( 2 π n / 60)2 r2 ρ / 3 (1)
where
σz = stress (Pa, N/m2)
ω = angular velocity (rad/s)
r = radius of disc (m)
ρ = [density] (kg/m3)
π = 3.14…
n= revolutions per minute (rpm)
For our OP case :
Diameter = 300 mm or 0.3m (taken from the pizza publication mentioned above ), or r = 0.15 m
Density again varies, lets pick a typical density of ρ = 900 kg/m3 (Table 2, Page 171 https://www.tandfonline.com/doi/pdf/10.1081/JFP-120015599)
σz = 6kPa = 6000 Pa
So we have 
σz = ( 2 π n / 60)2 r2 ρ / 3
Solving for n,
n =(60 / 2πr )* sqrt (3σz/ρ)
n = (60/(2x3.14x0.15))xSQRT(3x6000/900) ( Final Equation)
Or n = 285 RPM
A typical 54 inch ceiling fan spins at about 300 RPM and thats about the RPM you will need to ruin the pizza. YMMV.
I am past the edit window, but I just realized that the new SDMB changes * into blank in an equation. I know this question belongs in ATMB but please reply if there is a better way to type equations on the new board.
Also to add that the number of g ‘s experienced on the periphery of the pizza is about 13.5g at 285 rpm. Is this what you mean by gravitational force ?
@am77494, that sounds like you’re spinning the pizza about an axis through its center, like a record on a record player. Picture instead a pizza sitting on a table, on an extremely high-gravity planet.
I think that the key to this question is going to be how we define “ruined”. I think that the first sign of failure will be cracks forming in the outer crust, but that won’t impact the eatability of the pizza at all. If you’ve got solid toppings like chunks of sausage, those will press down into the less-dense crust, but again, that’ll do very little harm from a culinary perspective. Once the cracks form in the crust, you’ll start getting sauce flowing out of them, which will certainly make a mess, and will impact the culinary properties of the pizza, but how much sauce people like is a matter of preference, and even if you like sauce, you might still be able to enjoy a pie with all of the sauce squeezed out, leaving just crust and cheese (i.e., it wouldn’t be “ruined”).
Thanks, am77494. Unfortunately though, the axis of revolution would be coplanar with the pizza’s face. If the pizza weren’t in a box, it would form a torus as the centrifuge spins.
~Max
You are right Chronos. I did assume a spinning pizza because the OP mentions a centrifuge.
That problem will be like a human falling into a black hole and being stretched like a rubber band ?
Thanks for the clarification. So essentially the pizza is spinning like people spin coins on a table. In that case, you can imagine the pizza to be made of strips i.e. there is no appreciable stress on the pizza in the direction of the axis. all stresses are perpendicular to the axis.
So, then the problem reduces to the longest strip (like a breadstick) which is the one with the full radius at the center.
You can treat this strip as a rod with a length L (equal to the diameter). In that case, the maximum stress is given by : (http://onlinemech.com/2018/12/stress-and-strain-part-2/)
σz = (ρ x ω^2 x (2r)^2 )/8
or ω = (1/2r) x SQRT( 8σz/ρ)
or ω = 24.34 rad/s
=> n = 60 ω / 2 π = 233 RPM. That’s about 9 g at the periphery.
Again, due to the variabilities pointed out earlier, this is an approximate answer.
The gotcha that tripped you up is that Discourse uses asterisks (and sometimes dollar signs, parens, brackets, and a few other symbols) as formatting codes. So it ate your asterisk(s) and turned the stuff between them into italic text. Oops.
Some of the formatting codes are real “smart” for example square brackets surrounding text that looks enough like a url will turn into a clickable url. The same sqaure brackets surrounding text that doesn’t look enough like a url won’t. ow much is “enough”? No way to know.
That “smartness” really amounts to inscrutability. You can’t trust a simple test to answer the question “Does Discourse’s formatter eat square brackets?”. The answer is always “maybe”.
When using those characters and you want them to display as the character they are, precede them with the “escape character” which is backslash \. And to display a backslash, you need to escape it too; the prior sentence was typed with two backslashes and a period.
So 3 * 4 * 5 = (12).
You can quote this post to see what I really typed.
Really looking at your work in the preview feature is invaluable when you’re trying to do anything other than plain prose.
Thanks LSLGuy. I tried and it works. Used the preview window on PC to check. Thanks again
I was picturing the center of the centrifuge being above the center of the pizza, probably much further above than the diameter of the pizza. I imagine the OP included a centrifuge because that’s the real-world practical way to subject something to high g forces.
I am imagining a rotating ship like in 2001: A Space Odyssey to provide artificial gravity.
I’ve tried to write this 3 times to get the tone right. Hope I succeeded.
We’re 16 posts in and I (we?) still don’t understand what orientation the OP means for his pizza versus the imposed forces. Nor whether he really means G-force or centripetal forces. Which difference matters hugely depending on where the axis of rotation is and how far away it is from the pizza itself.
Please @Max_S, some back and be explicit. Start from scratch, not from some assumption of what you already understand in your head. Or what you think some other poster (including me) understands.
We can do some good math & structural engineering here, but not while we don’t know what problem we’re solving.
My mom once told me not to play with my food. She likely had the OP in mind.
I think a lot of folks in this thread didn’t read the link in the OP.
The premise of the link is that a bird carries the pizza up to where an airplane can grab it. The airplane then hooks a line onto the pizza, and reels out this line so that the pizza isn’t immediately yanked at 500 mph. The pizza is accelerated slowly until it matches the speed of the plane, at which point the line is reeled in.
This completely ignores aerodynamics which would end up ripping the pizza box apart and the buffering in turbulent air that would turn the pizza into goo, but simplifies the question into how much g force can a pizza tolerate. So the question is basically ignoring all of the things that would actually affect the pizza and concentrating on one thing that would have a fairly marginal effect by comparison. And never mind the practicality of having a swallow (African or European?) link up in air to a drag line attached to an airliner, and coordinating the end of the drag line to match the speed of the bird.
The question (unrealistic as it is) reduces to the g-force applied to a pizza as if the pizza were a disk and the acceleration were along the normal vector to the pizza-disk’s surface.
In other words, if the pizza is lying flat in the X-Y plane, how much acceleration upwards in the Z direction can the pizza tolerate?
It’s not a question about rotation. The rotation simply comes from the idea of using a centrifuge to impart the forces onto the pizza in the same way that a pilot in a centrifuge is subjected to extreme g-forces.
Put them in a code block. Discourse has a math plugin, but it doesn’t seem to be installed on SDMB.
Code blocks can be any number of lines and are delimited with
[code][/code]
or
<code></code>
or
~~~
~~~
(I used zero width spaces between to display this,
as I used 3 ~ characters to delimit the whole block.)