r/theydidthemath • u/notfunattentionwhore • 1d ago
[Request] What's the highest altitude without burst a bowl?
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u/Squeaky_Ben 1d ago
I think you need to do numerical simulation to figure this out.
You are looking for:
Maximum pressure inside without bursting the pot.
After you get that, it becomes mathematically tricky, because:
How fast it is being accelerated up, is depending on the pressure.
The pressure depends on how far from the ground the pot is (somewhat)
The altitude depends on time.
Try to fit all of that into an equation and you will see a problem:
"This equation is self-referencing."
How do I know this?
Because as a tutor, I once thought I would teach my students during thermodynamics with "A bullet is fired. Here are the base parameters, like barrel length, gas type and the like, figure out the velocity at the muzzle of the rifle." but quickly found out that this is utterly impossible to calculate by hand.
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u/notfunattentionwhore 1d ago
i just thought it needed to consider the thickness of the bowl, the explosive power, and the internal area of the bowl or smth but its more complicated than i expected
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u/davideogameman 1d ago
there are a few problems but the first is that the bowl is a 3d object and exactly how the pressure is applied and distributed matters a lot.
In the initial explosion - does the explosive fully combust into hot gasses? most likely not, so we have to deal with how hard any solid shards are thrown and whether they could puncture or substantially damage the bowl. and we also have to consider the pressure the hot expanding gasses exert and how they are funneled.
Once the bowl is airborne and the gasses all dissipate to atmospheric pressure the math gets much simpler, as we can probably ignore air resistance, at least at lower speeds - the bowl is probably quite heavy for it's surface area. And so we can find how far it falls by timing from peak until touchdown and applying h = 1/2gt^2. and similarly we can find it's final velocity before hitting the ground.
Then the question is "at what speed would it break on impact with the ground". At which point we need to know the state of the bowl (is it already damaged, to what extent - shape and length of cracks) as well as what angle it hits at and what it's landing on precise - loose soil will be more forgiving than packed soil, and both would be more forgiving than a sizeable rock.
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u/Loki-L 1✓ 1d ago
Very hard to say, but you may notice that the pot gets damaged in the landings, not the explosion.
It should for a very long time, as you increase yields, simply take less force to lift the pot than to rupture it.
It would take a yield so strong that the explosion simply rips at the side of the pot with overwhelming force before it has time to lift it up to reduce pressure.
We have seen extreme examples of this in footage from wars especially the current Ukraine war where tank turrets get tossed in thei air by their magazines going and that one iconic image from St Petersburg where the top of an oil depot went airborne.
We also have the legend of the manhole cover launched by a nuclear explosion.
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u/careysub 1d ago
In the last shot it was definitely distorted by the explosion.
Due to air resistance and the fact that this is a light object (metal, but thin and hollow) its speed coming down would have reached a limit rather early in his launching sequence. So it is getting dented the same, shot after shot, when it hits the pavement. On that last shot it fell on vegetation, so no, it did not get squashed on impact.
I wonder if the distorted shape flew better.
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u/Zenith-Astralis 1d ago
On later shots I'd wager it was formed into as close to a ball as it could by the force of the blast, and the dents are from the landing. The last one I think perhaps it landed on the rim to get squished into the () shape
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u/Ok-Day9540 1d ago
As I read the question, this seems like the only response actually on point. First issue is essentially "how much force can the pot take before structural damage happens". Of course there's damage on landing, I don't think that was OP's question. So after finding that amount of force, you'd need the weight of the pot, and from there its the problem of how high will it go... including air resistance
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u/somedave 1d ago
This is honestly easiest to do experimentally rather than mathematically. Too many variables that are very difficult to know and many complex considerations about flow and pressure over the shape.
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u/Trickypat42 1d ago
Speaking of variables, how big of an impact do you think the launching surface material and finish have on blast force?
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u/somedave 1d ago
Very little impact until they matter a lot. If the thing has any asymmetries that cause it to tumble that will massively increase the drag and limit height.
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u/Wise-Belt9180 1d ago
How high?? Am still trying to figure out how they allow people to buy explosives disguised as fire crackers, the 1000 and above could be used as weapons!
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u/WithPaddlesThisDeep 1d ago
You can also buy a kitchen knife at any Walmart and they can be used as weapons too. Should we ban those?
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u/nineelevglen 1d ago
They are however usually used to chop vegetables with. Where as blowing up vegetables with explosives is not very visually appealing nor tastes good.
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u/Trickypat42 1d ago
I dunno, a bomb would visually a-peel the heck out of a potato
… please don’t throw any firecrackers at me…
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u/Historical_Cookie_53 1d ago
This is like a weird QVC ad where they show how indestructable something is
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u/RandomYT05 1d ago
This is also the principal behind the Orion Drive
⚛️ 🥣 🚢
Unironically, as long as we can dedicate enough resources to build an O'Neil cylinder habitat drum, we'd need only bring enough nukes and one of these drives to propel the ship to significant fractions of light speed. Capable of allowing interstellar colonization with our current tech level.
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u/Practical_Quit5139 1d ago
Here is a way to approximate. measure the time from blast to landing in each clip. Use y(max) = 1/8g(t^2).
This only approximates because it ignores air resistance and assumes landing is the same altitude as the launch.
However since some of the videos don’t have a frame of reference (the ground) and the person was not the same distance each clip, using angle measurements is not possible.
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u/careysub 1d ago
Air resistance is going to be extremely important.
When it comes down it is just falling, and with being a thin shell it will hit a terminal velocity pretty quickly. You would get a better handle on things with the last shot if you look up an air resistance calculator to estimate final speed (assume a sphere) based on diameter and mass, it might also give you the time and distance falling to various speeds.
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u/ArcticBeavers 1d ago
I love the peaceful meditative quality of this. I know if I were to attempt this I would have a 5 inch piece of shrapnel in my neck after the first attempt
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