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Any Math & Physics Experts Around Here?

This pressure cooker lid at the Boston Bombing has me thinking.

What would the force have to be from a bomb so that the pressure cooker lid would end up 35 yards away and 6 stories up, landing on the roof of a building?

I don't know the math formula to figure this one out.

We have a pressure cooker, with the lid presumably locked to the main part of the device, inside a zipped backpack, and a bomb inside. The thing explodes, separating the lid from the main part of the device, and the lid ends up about 100 feet away and around 50-60 feet up (probably had to go 50-100 feet in the air) to land on a 6-story building's roof.

What would the force have to be? And then with that force, what sort of collateral damage SHOULD we see in the immediate area where the main part of the pressure cooker and whatever was inside of it went?

Can anybody around here do the math on that?

Here is information about where the lid was found:
http://www.dailymail.co.uk/news/article-2310200/Boston-Marat...



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That map does show

quite a distance the pressure cooker lid must have travelled. I'll leave it to the physicists below as to what kind of force that would take. (My only experience, from childhood, is one that merely blew across the kitchen, fortunately no one its path!) This clip at the Boston Globe shows *something* flying up, though not the lid. Wrong direction, to go by that map. http://www.bostonglobe.com/2013/04/15/gGfFH99UuwAcCjlSg5jE8M...

When we try to pick out anything by itself, we find it hitched to everything else in the Universe.
~ John Muir

I have an undergraduate

I have an undergraduate degree in physics and I would think that a blast would easily have enough pressure to launch the top of the container to where they found it. Trying to do the math would be relying on too many unknowns but there's no reason in my estimation to think that this is an unusual event for an explosive device to launch the lid that far.

Let's see.

The max operating pressure for a standard cooker is approx 1.8bar absolute. With estimated safety factor of 1.5times the cooker will explode at 2.7bar absolute. Pressure cookers are stainless steel and have a screw-on lid. At the 2.7bar the steel treads on the lid will shear or bend. The lid is going to fly a fucking long way (scientifically speaking) one way or another at this pressure. It would be hard to get the pressure much higher because the lid will blow off. So that's my WAG. Wild Ass Guess.

No, many are aluminum

and while the lid might begin to separate at the fail point, an explosion could put vastly more pressure behind the lid before it was gone.

New Hampshire and Ecuador.

The material is irrelavant if you have a maximum use pressure.

What would be the point of putting explosives in a sealed container? The whole point of the cooker is there is no need for large quantities of traditional explosives. All that is needed is a chemical reaction that causes expansion and shrapnel material. In that small confined space there does not need to be much expansion.

You're right,

material is irrelevant, but if you imply they're all stainless steel, what else are you wrong about? The main point is the fail pressure is not the maximum pressure. For proof, just look at the deformation of the pot.

New Hampshire and Ecuador.

You are right.

I did not claim all P-cookers were SS. I just said it 'cause mine have been. No big deal. I also did not claim that the fail pressure was the max cooking pressure. I stated the max cooking pressure (by virtue of a duckduckgo search) and gave a 'safety factor' of 1.5 (multiplied the max pressure by 1.5 - WAG - wild ass guess). That is where I came up with the point of PC (pressure cooker) failure. But you were right about the explosives. I have read since that a small amount of explosive material is used for the expansive effect. I guess a closed environment amplifies a tiny amount of explosives.

So we are both right! I love when that happens.

Lid Goes Farthest

I would assume the lid goes farthest because it is designed to separate and it is much more aerodynamic than the twisted other parts.

As soon as the pot underwent mechanical deformation I bet the lid separated cleanly and went off like a rocket.

I hate to get all dry and clinical during this terrible event.

This is a common thing in geology. They know the mass of a rock and how high it is so therefore you can reverse out the minimum speed the rock was going to get at that height such as after a land slide. It is simple physics with energy and velocity.

If you know the weight (mass) of the lid and its height above ground then you know the minimum velocity and energy at launch. Take that minimum number times 2 to get what the energy probably was.

Too many unknowns.

Mass of the lid?
Surface area of the lid?
Pressure of the closed lit on the pot? (Screws I assume.)
Explosives (assuming they're uniform) follow the inverse square law.
This means that the pressure of the explosives drops by a factor of 1/blast radius^2. I think it would be equally benefitial to look for known objects withing the blast area to see how far they were moved, or how much they were destroyed.
Sorry.

That's what I was thinking

It is simple physics. The sad part is I bet they have people at the FBI that looked at people that were close and how far the terrible shrapnel was embedded and they looked it up in a table they already had figured out.

They use pigs and cadavers to do this kind of research, this is why they can create ballistic gels with high accuracy to the real world.

Adam Smith was for separation of labor.

All solid economists agree. For our entertainment, we may dub in simple math formulas like Keynes did. However, rational people can only rely on their own rational faculty to integrate facts. Blindly relying on authority of others is not the way to knowledge. For example, it is not enough to agree with my post because Adam Smith or von Mises had said so, you must be able understand in your own mind (after reading their arguments) why it is so.

Separation of labor would let experts argue between themselves.

egapele's picture

Well said.

It's like listening to two doctors having a discussion about the physiology of the human body; great idea, however, not so good when the two doctors debating are a gynocologist and a podiatrist.

Pressure cookers

are designed to operate at a relatively low pressure and are made with a thick rubber seal and locking mechanism to keep the contents intact. There is a small relief valve on top that rocks and hisses while cooking to maintain constant pressure. I don't understand the concept for a bomb unless the whole lid locking mechanism allows sufficient pressure to build up from some sort of chemical reaction and then kaboom if and when the locking mechanism factor of safety is over come???

Most pressure cookers have a working pressure setting of 15 pounds per square inch (psi), sometimes expressed as "lb" or "lbs" (pounds), which equates to 103 kPa, 1.03 bar, or 1 kg per square centimetre (kg/cm2 or kgf/cm2) above atmospheric pressure. This standard was determined by the United States Department of Agriculture in 1917. At this pressure, water boils at 121 °C (250 °F). http://en.wikipedia.org/wiki/Pressure_cooking

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Maybe not enough to blow off

Maybe not enough to blow off limbs of people that close. I used to get dry ice at a grocery warehouse where I worked. Boca (vegan pansy burgers) would ship their stuff with dry ice on top with one of those big metallized mylar bubble-wrap sheets. I would take it home and put some in a 2 liter bottle, pour water into it, close it, and run. I put it under a 5 gallon mop bucket once. They are lighter than a drywall bucket. When it went off there was a portion of the bucket, about half, that went like 50 feet in the air. The rest was just broken pieces. Those "bombs" weren't that powerful.

Please come join my forum if you're not a trendy and agree with my points of view.

This is a fool's errand

There's no way to 'calculate' anything meaningful related to this. There are too many unknown factors and for what we know for sure (the range of the estimate), each has an error factor of at least two orders of magnitude.

Some examples: What was the source of the force? It could have been anything from steam to super nano thermite. Consider the speed at which the pressure built up and how that relates to the propulsion force on the lid once it was free.

What was the ultimate failure method of the container? Did the sides give first and offer the lock less resistance? Was one locking tab compromised by being dropped at some point? (even a well placed scratch could affect this.) Did one side let go before the other? So many questions.

What other projectiles 'helped' the lid to find it's ultimate path? With a very high velocity pressure build up (such as dynamite or C4), those projectiles would impact the lid, compromise it in some unpredictable way, and add to its acceleration.

How high did the lid go before stopping and returning to earth? Anything sending it higher than about 10' higher than the building is conceivable. Sure that may impart great sideways component to the landing compared to the vertical drop, but have you ever seen a football land at an oblique angle and bounce back in the reverse direction?

I don't really see the point in even pursuing this unless many other details are provided first.

A "fool's errand" is all in a

A "fool's errand" is all in a day's work here.

Ran a 3-DoF

I estimated aero using a tool I have. I assumed the lid weighed 2 lbs which may be too light. I applied about 13,000 lbf to it for 0.01 secs and set the initial flight path angle at 70 degrees (20 degs from vertical). The thing went about 31 meters down range (102 ft) and as much as 58 meters up (190 feet). Peak speed was just under Mach 0.4 so around 450 ft/sec. This accounts for gravity, but does not account for whatever force was needed to break the locks on the cooker lid.

Our family's journey from the Rocket City to the Redoubt: www.suburbiatosimplicity.com

Jefferson's picture

I'm

not a math wiz or an aero-engineer, but I do know a little about ballistic coefficients. It would seem that the drag on a deformed lid as opposed to a regularly shaped lid would be different.

It just seems like there are too many variables to get an accurate measure. But, I'm just a layman.

You're right

There are a lot of assumptions.

I did not do anything to account for deformed lid or even it tumbling which it probably did also.

Other have pointed out other assumptions that must be made.

However, contrary to what one poster seems to believe I suspect the government is doing detailed simulation and reconstruction analyses on the bomb event to determine stuff like how much explosive was used, how much inert mass was involved besides the cooker, etc. and then trying to match up those results with the video and photo evidence... or vice versa.

My cut was a 15 minute SWAG so take it for what that's worth.

Our family's journey from the Rocket City to the Redoubt: www.suburbiatosimplicity.com

This would be a tough one to determine

Since the lid could have flown several hundred feet in the air and landed on the roof on its way down. Since it is on the roof it must have been a parabolic so that the end of its trajectory had some kind of downward component. Since the lid landed on a roof close by, it had to have more of a vertical trajectory. This is because any mostly horizontal trajectories would travel large distances before dropping, or dropping to the ground initially without going up to roof level first.
Without knowing its path in more detail, but if you could characterize its path, calculating the exact force that launched it is easy, assuming you know its mass.

Another component possibly worth looking at is to determine the force required to rip the pressure cooker apart. This could be used to calculated a minimum explosives weight that it contained.

It would only be useful to determine what kind of explosives could have produced the blast we saw, given the limited volume of the pressure cooker. (Although I have a feeling that the list of explosives possible would be long, so not worth it). Or vice verse, knowing the type of explosive used, determine the space required to house it.

Okay I'm a class away from my BA in Mathematics

but I think sometimes your guys or people with all the truther stuff are a little bit too much for me. Sometimes I think you just need a bit more logic. Ben Swann did a good piece on if FBI knew as they always have. But to say that our own government is directly involve is a bit much. Overseas stuff are believable. thing is if you keep asking the same question, you must be looking for what is already in your head.

I'm a Mechanical Engineer, and

looking at how the vessel failed, the pressure inside had to be around 1000 psi to cause the actually pot itself to burst, assuming a 12 inch diameter, stainless steel construction and a 1/8" wall thickness.

1000 psi on a 12 diameter inch lid gives you 113,000 lbs of force, and assuming the 1 pound lid accelerates with this force over 1 foot, the lid would be traveling 260 meters per second, or around the speed of sound. Given the size of the expanding cloud, 1 foot is conservative.

Considering the thing is large, flat and lightweight, it will slow down very quickly, and the 100 foot range and 80 foot climb seems reasonable. Aerodynamic drag at high speed is tremendous, just think about how fast spitzer shaped bullets slow down. Translate that to a flat, spinning pressure cooker lid. Also, it could have climbed much higher than 80 feet to have landed on the roof. If it were found on the street, you wouldn't assume it only went one foot in the air.

260m/s is 850fps, like a black powder round, and is consistent with the type of collateral damage caused by the ball bearings.

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Would you expect such a blast ...

... to create a hole in the pavement?

My estimation would be no

My estimation would be no simply because upward and outward have less resistance the majority of the force would be directed in those directions and not into the ground.

This type of bomb was designed to throw shrapnel, not destroy structures.

This right here sounds

This right here sounds correct so go by this, not the basic stuff I posted.(been a few years since I did any physics stuff)

To climb the mountain, you must believe you can.

No one here is factoring

No one here is factoring gravity.

Gravity is 9.8m/s downward

Gravity is 9.8m/s downward pull. Yea, you could take it into account, but really unless you are looking for precision, it wont matter too much.

To climb the mountain, you must believe you can.

"Gravity is 9.8 m/s downward"

Odd, you gave a velocity unit, not acceleration. To get the acceleration of gravity, you need 9.8 Meters per second squared.

Ok, I accidently left off the

Ok, I accidently left off the ^2, simply overlooked the mistake.

To climb the mountain, you must believe you can.

Well, depends on what the

Well, depends on what the weight of the lid is.

Say it weighs 1kg and a single story is 4m x 6 stories means 24m lets just say 25m. Lets just say it took 1.5 seconds to get there.
This is all rough estimation, but should give a ballpark answer/idea of the force.

F=2md/t^2

so 2*1kg*25m/1.5s^2

This is about 22.2N of force. Roughly of course. A newton is about .225 lbs of force meaning it took about 5 pounds of force to blow it into the air that high.
Far from a precision calculation, but should give a ball park answer. Would of course depend greatly on how fast the thing traveled so say it could possibly be up to 4x the value I found or about 20lbs of force instead. If we say it only took a half second to get up there, than it could be 45 lbs of force. We can assume the lid blew almost vertically give or take a few degrees so whatever the overall height it went is, it wouldnt have landed too far away.

To climb the mountain, you must believe you can.