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Calculate Rate of Disintegration of Projectile

by Skyler0114
Tags: calculus, friction, iron, meteor, projectile
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Skyler0114
#1
Jan20-13, 05:35 PM
P: 24
I was thinking about meteorioids and how upon their entry into the atmosphere the large amount of disintegration they experience so i wanted to try running through a calculation of something similar to see if i could i understand it better. I'm going to outline a general thought process I've come up with then ask a specific case.
Ignoring gravity or the existance of a floor for now because of the complications that would cause.

General:
Lets say we have a [insert size and mass/density here] [insert shape name here] of [insert material here] [falls apart/does not fall apart] and we fire it at [insert velocity here].
Question:
How [long or far] will it travel before the object fully disintegrates?
OR
How [much mass/volume] is lost before the object stops disintegrating.

Example:
Lets say we have a 1 meter radius sphere of iron (density 7.874 gcm−3) in 1 atm air. We assume it does not fall apart or explode in it's transit. We fire it at 100 km/s, how much mass does the object lose in its transit.
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SteamKing
#2
Jan20-13, 05:44 PM
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Not a simple problem. The interactions between the projectile and the air as it is traveling at hypervelocity do not lend themselves, IMO, to analysis by a couple of simple formulas.
Skyler0114
#3
Jan20-13, 05:50 PM
P: 24
Quote Quote by SteamKing View Post
Not a simple problem. The interactions between the projectile and the air as it is traveling at hypervelocity do not lend themselves, IMO, to analysis by a couple of simple formulas.
Im not really interested in a simple formula as much as trying to piece together information to come up with more information and more formulas. I'm interested in the journey for this calculation, not so much the end product.

As more variables are introduced I want to see what you have to consider and what doesnt matter.

Nugatory
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Jan20-13, 08:52 PM
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Calculate Rate of Disintegration of Projectile

Quote Quote by Skyler0114 View Post
Im not really interested in a simple formula as much as trying to piece together information to come up with more information and more formulas. I'm interested in the journey for this calculation, not so much the end product.

As more variables are introduced I want to see what you have to consider and what doesnt matter.
If you're thinking about meteorites hitting the earth....
You could start by assuming that the entire kinetic energy of the projectile is converted into heat. That's a pretty good approximation for the total energy released.
Skyler0114
#5
Jan20-13, 11:06 PM
P: 24
Quote Quote by Nugatory View Post
If you're thinking about meteorites hitting the earth....
You could start by assuming that the entire kinetic energy of the projectile is converted into heat. That's a pretty good approximation for the total energy released.
I was more interested in learning about the rate of disintegration, distances traveled, heats experienced, and just about different factors that need to be considered and how each of them would likely be playing out as per the relevant formulas .
haruspex
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Jan21-13, 12:01 AM
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What fates may befall the material? Combustion, evaporation, thermal cracking, explosion... Rate of heating will matter, since rapid external heating would create greater stresses. Conductivity. Spin?
Skyler0114
#7
Jan21-13, 01:28 AM
P: 24
Quote Quote by haruspex View Post
What fates may befall the material? Combustion, evaporation, thermal cracking, explosion... Rate of heating will matter, since rapid external heating would create greater stresses. Conductivity. Spin?
For now lets assume the particle does not fracture into macroscopic fragments. Should a fate like that befall it then instead the methodology we create here can instead be reapplied for the fragments in question (with a lot of new variables that is).

How would one be able to determine the heat gained from air friction?

Also how would one be able to determine the transfer of heat into the "cooler" center of the sphere?

Obviously thermal conductivity comes to play a very large role here but even if the conductivity high is would it effect disintegration in the first (maybe few) second(s) at some non-negligible amount?


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