Impact model for spheres

[Ssnake]

Most kinetic energy penetration models deal with roughly cylindrical projectiles, not the least because of their favorable aerodynamic shape that helps to preserve most of the momentum at longer ranges.

 

Yet there's a proud history of the embodiment of perfection (at least according to Mr. Plato from Greece) - spheres. There is a wide range of calibers in history (up to about 50cm), a wide range of materials (iron, lead, tungsten), a wide range of impact velocities (1410m/s down to a few dozen).

 

Is there a "grand unified theory" for spherical impactors?

 

Or at least one that can be applied to the latest application of their use, the M1028 canister shot? In this case we have pellets of tungsten, of approximate spherical shape, about 10mm in diameter, and with an impact speed of up to 1410m/s (but rapidly decelerating).

What is a reasonable expectation of these tungsten pellets as far as RHA is concerned - relevant, because lightly armored vehicles might be engaged by 120mm super shotguns. When are they "safe" against the monster buckshot?

 

How would a BTR fare against the iron balls of HMS Surprise, were "lucky Jack" to engage them in a decidedly tradition-breaking 22nd novel?

[jwduquette1]

There yah go -- you need to hire somebody to do some finite element modeling.

 

Speaking of musket balls and such, the little round ball is from buck & ball shot used by smooth bore muskets during the American Civil War. Sort of the infantrymen’s mini-canister round. The buck & ball cartridge consisted of a 0.65-caliber musket ball and three of these 9.4 to 9.5mm buck shot balls. These are a little smaller than the M1028 canister shrapnel balls -- and lead rather than tungsten. But it gives you a perspective on just how small these things really are. That's why I am doubtful they are going to do better than say 30-cal M2 AP or the like in terms of steel or aluminum armor penetration. The bullet next door is standard NATO 7.62mm ball.

 

The large ugly stump under it all is my hand. My hand is copyrighted material.

 

[gewing]

There yah go -- you need to hire somebody to do some finite element modeling.

 

Speaking of musket balls and such, the little round ball is from buck & ball shot used by smooth bore muskets during the American Civil War.  Sort of the infantrymen’s mini-canister round.  The buck & ball cartridge consisted of a 0.65-caliber musket ball and three of these 9.4 to 9.5mm buck shot balls.  These are a little smaller than the M1028 canister shrapnel balls -- and lead rather than tungsten.  But it gives you a perspective on just how small these things really are.  That's why I am doubtful they are going to do better than say 30-cal M2 AP or the like in terms of steel or aluminum armor penetration.  The bullet next door is standard NATO 7.62mm ball. 

 

The large ugly stump under it all is my hand.  My hand is copyrighted material.

 

404856[/snapback]

 

 

This thread reminds me of an old question of mine.

 

What would the penetration capability be of a standard steel BB at 8-10k fps???

 

Ok, so it might only penetrate a little more than its diameter as it ablates (?) into the target.

 

It would still be interesting, imo!

 

And what it would do in gelatin...

[arcweasel]

Most kinetic energy penetration models deal with roughly cylindrical projectiles, not the least because of their favorable aerodynamic shape that helps to preserve most of the momentum at longer ranges.

 

Yet there's a proud history of the embodiment of perfection (at least according to Mr. Plato from Greece) - spheres. There is a wide range of calibers in history (up to about 50cm), a wide range of materials (iron, lead, tungsten), a wide range of impact velocities (1410m/s down to a few dozen).

 

Is there a "grand unified theory" for spherical impactors?

 

Or at least one that can be applied to the latest application of their use, the M1028 canister shot? In this case we have pellets of tungsten, of approximate spherical shape, about 10mm in diameter, and with an impact speed of up to 1410m/s (but rapidly decelerating).

What is a reasonable expectation of these tungsten pellets as far as RHA is concerned - relevant, because lightly armored vehicles might be engaged by 120mm super shotguns. When are they "safe" against the monster buckshot?

 

How would a BTR fare against the iron balls of HMS Surprise, were "lucky Jack" to engage them in a decidedly tradition-breaking 22nd novel?

404055[/snapback]

 

You might try the literature for artillery fragments instead of more typical projectiles.

 

For example I have the following equation for velocity:

 

=B4*EXP(-(B8*B6*B5*B9)/(2*B7))

 

B4 = Initial Velocity (mps)

B8 = Air Density (~1.2kg/m^3)

B6 = Drag Coefficient (0.8(NATO Frag), 0.5(sphere))

B5 = Fragment Area (m^2) (I think that this is presented area not total surface area)

B9 = Distance From Initial Velocity (m)

B7 = Mass of Fragment (kg)

 

Regards,

 

Jay

[jwduquette1]

You might try the literature for artillery fragments instead of more typical projectiles.

 

For example I have the following equation for velocity:

 

=B4*EXP(-(B8*B6*B5*B9)/(2*B7))

 

B4 = Initial Velocity (mps)

B8 = Air Density (~1.2kg/m^3)

B6 = Drag Coefficient (0.8(NATO Frag), 0.5(sphere))

B5 = Fragment Area (m^2) (I think that this is presented area not total surface area)

B9 = Distance From Initial Velocity (m)

B7 = Mass of Fragment (kg)

 

Regards,

 

Jay

405015[/snapback]

 

Determining down range velocity of the shrapnel balls isn't an really issue.

 

Penetration of sphere into various forms of armor is.

[jwduquette1]

This is from a paper by Hohler & Stilp on very low aspect ratio rod penetration and perforation ability. The original figure is steel L/D=1 rods vs. Roll hardened armor. I have added predicted values for tungesten heavy alloy rods -- also L/D=1 -- based upon Andersens empirical relationship for rod penetration as a function of L/d effects.

 

The lower red curve is semi-infinite penetration by WHA L/D=1 rods into RHA. The Yellow curve is my guesstimate for perforation. I estimate backsurface effects of L/D=1 tungsten rods is about 0.8D to 1.2D.

 

I have also added normalized perforation data for 30-caliber M2 AP ammunition (the blue stars) as a gut check. The M2 projectile uses a hardened steel core penetrator with L/D a bit over five. So in theory it should be a less efficient penetrator than an L/D=1 steel rod. This is pretty much what the figure shows. Moreover the stars plot slightly below the L/D=1 curve for steel rods.

 

 

I'd guess WHA spheres might perforate about P/L=1.75 to P/L=2.25 at the velocities of most interest for the M1028. So an individual sphere might perforate 18mm to 23mm of RHA at 0-degrees and point blank range.

 

It would be of interest to conduct an additional gut check via addition of normalized perforation for say tungsten carbide cored bullets. Don’t the Russians use tungsten carbide cores in some of their 12.7mm or 14.5mm AP & API cartridges? Or are these all hardened steel cores?

Edited December 16, 2006 by jwduquette1

[jwduquette1]

This thread reminds me of an old question of mine. 

 

What would the penetration capability be of a standard steel BB at 8-10k fps???

 

Ok, so it might only penetrate a little more than its diameter as it ablates (?) into the target.

 

It would still be interesting, imo! 

 

And what it would do in gelatin...

404886[/snapback]

 

 

Sure -- it's always interesting. Normalized penetration and perforation will sort of approach an asymptotical value for max-perforation. If you look at the figure I posted above, I have extrapolated the sort of a range of where I would expect P/L to be for steel L/D=1 rods vs. steel armor. Assuming your BB is steel and its zipping along at 8Km/s it might slice thru P/L = 2.9 to maybe 3.25. I don’t remember the diameters of the BBs I used to shot with my old Crossman -- maybe 4mm or some such thing? So perforation might be about 11mm to 13mm or armor at 8Km/s.

Edited December 16, 2006 by jwduquette1

[arcweasel]

Determining down range velocity of the shrapnel balls isn't an really issue. 

 

Penetration of sphere into various forms of armor is.

405021[/snapback]

Sorry I was digging for the specific papers to cover the 2nd bit which is the penetration.

 

I was just sudgesting that the fragment literature may be a better place to look than conventional ballistics. Papers such as:

Target Interaction: Penetration of Thin Targets by Fragments - Recht, R.F.

 

I've attached a bit of interest:

 

Regards,

 

Jay

[gewing]

Sure -- it's always interesting.  Normalized penetration and perforation will sort of approach an asymptotical value for max-perforation.  If you look at the figure I posted above, I have extrapolated the sort of a range of where I would expect P/L to be for steel L/D=1 rods vs. steel armor.  Assuming your BB is steel and its zipping along at 8Km/s it might slice thru P/L = 2.9 to maybe 3.25.  I don’t remember the diameters of the BBs I used to shot with my old Crossman -- maybe 4mm or some such thing?  So perforation might be about 11mm to 13mm or armor at 8Km/s.

405034[/snapback]

 

 

 

iirc 4.77mm.

 

I wrote up a scifi weapon once that was a portable coil gun. though the standard ammo was basically a flechette, it could also be used to fire BBs, for antipersonnel work, or in an emergency.

 

actually, as I suspect a coil gun could self center the projectile in the "bore", my initial idea could fire a 10mm mini grenade too.

 

It would probably suffer dramatically in accuracy though.

[jwduquette1]

Sorry I was digging for the specific papers to cover the 2nd bit which is the penetration.

 

I was just sudgesting that the fragment literature may be a better place to look than conventional ballistics.  Papers such as:

Target Interaction: Penetration of Thin Targets by Fragments - Recht, R.F.

 

I've attached a bit of interest:

 

Regards,

 

Jay

405047[/snapback]

 

I agree -- I suggested this to Nils in another forum. FSP testing.

[jwduquette1]

Sorry I was digging for the specific papers to cover the 2nd bit which is the penetration.

 

I was just sudgesting that the fragment literature may be a better place to look than conventional ballistics.  Papers such as:

Target Interaction: Penetration of Thin Targets by Fragments - Recht, R.F.

 

I've attached a bit of interest:

 

Regards,

 

Jay

405047[/snapback]

 

regarding the attachment -- do you have something similar for tungsten heavy alloy projectiles?

[arcweasel]

regarding the attachment -- do you have something similar for tungsten heavy alloy projectiles?

405097[/snapback]

 

That was what I was actually looking for but I don't think so or at least I can't find it at the moment.

 

Regards,

 

Jay

[jwduquette1]

That was what I was actually looking for but I don't think so or at least I can't find it at the moment.

 

Regards,

 

Jay

405111[/snapback]

 

Okee dokee. Thanks anyway.

 

That was sort of the chief reason I turned to low aspect rod penetration models. Usually fragmentation penetration models are dealing with lower initial velocities than close range M1028 shrapnel pellets. In addition, while some fairly modern fragmentation projectiles are using tungsten carbide or WHA shrapnel pellets, the majority of information floating around out there in the public domain deals with steel fragments vs. steel armor, or steel fragments vs. aluminum armor, or steel fragments vs. ceramic armor, etc.

 

Regards

Jeff

[Ssnake]

Thanks a lot, guys. I think this is sufficient for my purposes.

[arcweasel]

Okee dokee.  Thanks anyway. 

 

That was sort of the chief reason I turned to low aspect rod penetration models.  Usually fragmentation penetration models are dealing with lower initial velocities than close range M1028 shrapnel pellets.  In addition, while some fairly modern fragmentation projectiles are using tungsten carbide or WHA shrapnel pellets, the majority of information floating around out there in the public domain deals with steel fragments vs. steel armor, or steel fragments vs. aluminum armor, or steel fragments vs. ceramic armor, etc.

 

Regards

Jeff

405229[/snapback]

 

Hello Jeff,

 

I was certain that I had seen a paper discussing the effects of tungsten cubes similar to what was used in AGM-88 HARM. Can't seem to find it now.

Does it ring any bells?

 

Even any data on how the HARM cubes penetrate may allow us to draw some inferences. Does anyone have any info?

 

Regards,

 

Jay

[jwduquette1]

Hello Jeff,

 

I was certain that I had seen a paper discussing the effects of tungsten cubes similar to what was used in AGM-88 HARM.  Can't seem to find it now.

Does it ring any bells?

 

Even any data on how the HARM cubes penetrate may allow us to draw some inferences.  Does anyone have any info?

 

Regards,

 

Jay

405403[/snapback]

 

No, I haven't seen the paper. If you find it, I would be interested in reading it. I am aware that various modern warheads use tungsten shrapnel or tungsten cube fragmentation.

 

There are numerous studies floating about on low aspect ratio rod penetration as well as spherical projectile penetration. The velocity ranges are useful in that many are running around 1 to 2Km/s. These were what I relied upon to generate the penetration & perforation curves on the figure I posted above. Backsurface effects could use a bit more attention.

 

Regards

Jeff

[C.G.Erickson]

No, I haven't seen the paper. If you find it, I would be interested in reading it. I am aware that various modern warheads use tungsten shrapnel or tungsten cube fragmentation.

 

There are numerous studies floating about on low aspect ratio rod penetration as well as spherical projectile penetration. The velocity ranges are useful in that many are running around 1 to 2Km/s. These were what I relied upon to generate the penetration & perforation curves on the figure I posted above. Backsurface effects could use a bit more attention.

 

Regards

Jeff

Guys,

 

I suggest raiding the Franklin Arsenal test evaluations for projectiles. They tested spheres, cubes, long rods...etc

 

C.G.

[Ssnake]

I suggest raiding the Franklin Arsenal test evaluations for projectiles. They tested spheres, cubes, long rods...etc

Is there a web site?

 

Pardon my ignorance, but Google didn't turn up too much useful stuff, and if it can only be found in libraries, I'm not sure if I'll have much luck in Hannover...

[C.G.Erickson]

Is there a web site?

 

Pardon my ignorance, but Google didn't turn up too much useful stuff, and if it can only be found in libraries, I'm not sure if I'll have much luck in Hannover...

 

 

The Franklin Arsenal test results can be found in the Philadelphia Branch of the National Archives. Tests as far as cubes and spheres were shrapnel tests for Artillery rounds versus APC's. This is where I found the preliminary tests of Depleted Uranium penetration tests, First done by the Canadians in 1968.

 

Fascinating reads.

 

C.G.

[jwduquette1]

I managed to track down several references dealing more specifically with tungsten heavy alloy fragment perforation. This allowed me to get a better estimate of backsurface contribution to perforation. My original semi-infinite estimates are pretty good, but backsurface contribution is much less than I initially estimated. It's more like 0.2D to 0.3D for a 10mm sphere vs. RHA at 0-degree obliquity. Penetration to Perforation is than more like:

 

semi-infinite + ~0.2D = perforation

 

Where semi-infinite is modeled as a L/D=1 WHA rod.

 

The adjusted normalized V50 perforation for a 10mm WHA sphere vs RHA would look more like the yellow curve in the figure below.