Medium caliber HE blast values in CMBB

[Jim Boggs]

Originally posted by Mr. Tittles:

Actually was hoping JonS would come in and accuse me of being a propagandistical ogre.

But lets not let the thread 'bogg' down.

Actually it's been quite "tittillating".

Grog competitions are like that though.

[Michael Dorosh]

Originally posted by Mr. Tittles:

Heres an interesting passage from a German FO...

(13) On October 13, the Canadians were pounding us in preparations for their attack. Our observation house (10) was shot into rubble, leaving only the chimney. However, we stuck it out in the cellar. At dusk it was my turn to go up on watch. With a field telephone and binoculars, I climbed up the chimney and saw what seemed to be several officers looking over this bunker with binoculars and having maps before them. I called (whispered) for a single high velocity artillery round. (A straight shot that gives nobody time to duck). It was right on target and I saw a steel helmet flying like a Frisbee. A few minutes later a van came and men ran towards the bunker. It was getting dark and I couldn’t tell who they were, but I assumed they were medics and thus I refrained from further shelling of the area. - In the book 'Semper Paratus, The History of the Royal Hamilton Light Infantry', page 278, the author writes "On Friday the 13th, the Black Watch of the 5th Brigade went in, east of Woensdrecht, against the center of the isthmus. Joe Pigott watching through his binoculars from the RHLI positions near Hoogerheide, saw them cut to pieces by machine-gun fire (all four of their company commanders were killed) and their attack, too, failed." - I believe that my one 105-mm howitzer round killed these four officers.

Notice that the velocity of the 105mm shell, giving no warning, led to its effectiveness This is similar to direct fire from many weapons.

http://members.shaw.ca/calgaryhighlanders/knolle.htm

That is my website. Did someone want Herr Knolle's email address?

[Mr. Tittles]

Originally posted by Mr. Tittles:

Mave = 2 B^2 (to/di )^2(to + di)^3 (1+0.5 M/C) = average fragment mass (2)

where: C = mass of explosive charge

M = total mass of cylindrical section of case

B = a function of the explosive and the case material in equation (2), the

Gurney-Sarmousakis equation. As a rough approximation, for a mild steel

case, B = 338.1/PCJ, with the detonation pressure (PCJ) in kbar.

to = case thickness in inches

di = case internal diameter (i.e., explosive diameter), inches

Mave = 2 B^2 (to/di )^2(to + di)^3 (1+0.5 M/C) = average fragment mass

This is the Mott equation.

Lets take a brief overview of the mathematical implications.

The first term, B, is actually a numerator and a denominator. The numerator is a function of the metal of the shell. In simple terms, increase the strength of the metal, and you will increase the AVERAGE fragment size (all other terms staying the same).

The denominator is a function of the explosive. Its the detonation pressure. Increase this, and you will decrease the AVERAGE fragment size. The detonation pressure is also a formula.

DP=2.5*d*DV^2/100000

where:

d=density of HE (1.57 g/cm^3 for TNT)

DV=detonation velocity

Its 187 kbar for TNT.

Notice the relationship between to and di. For a given diametre shell SD, di =SD-2to

Mave = 2 B^2 (to/[sD-2to] )^2(SD-to)^3 (1+0.5 M/C)

So increasing to, case thickness in inches, for a given fixed SD, shell diameter, will increase average fragment size for the second squared term. Notice the third cubed term, (SD-to)^3, it will react opposite with increasing to. The last term, (1+0.5 M/C), is really a function of to. M will increase with to and C will decrease.

So whats the story here? Basically, for a given fixed B, 'to' case thickness is the major player. The relationship between the second and third terms needs to be analyzed.

Lets just plug and play before we start to do derivatives and integrals.

Lets take 75mm shells an example. One has a wall thickness of 15mm, the other 30mm. Please check my work but I get about a 15 times increase from just using the second and third terms. The last term would add to this also. So, roughly speaking, doubling the wall thickness has led to something like 16+ times increase in AVERAGE fragment size. edit: Since the density of steel (7.89 g/cm^3) is so much greater than the density of HE (1.57 g/cm^3), the last term (1+0.5 M/C) would also be significant. It would push the average fragment size up also!

In reality, a shell wall size of 30mm is too great for a HE shell. I just want to demonstrate how the equations parameters influence average fragment size.

But what does AVERAGE fragment size mean? Does it mean there is a bell curve about this size? That is, most of the metal is fragmented into masses that are very close to this value and the rest of the larger pieces and much smaller pieces are outliers?

[ November 15, 2003, 11:47 AM: Message edited by: Mr. Tittles ]

[Mr. Tittles]

Here is a pic of a british tank that has been struck what is most certainly either a 75mm or 88mm HE round (direct fire).

Its a fascinating picture. Notice the damage area , how it stops in a circle. This round, like a sherman 76mm HE round, is certainly a high velocity (500-700 M/s) strike. The fragments are 'blown forward'.

The energy of the event is telling by the bowed in armor and snapped off bolt. This is definetly not a HEAT round or an AP round hit.

The hole at the center of the hit probably was formed by the HE round penetrating the armor. As it detonated, it blew its sides out and forward, thereby stopping the penetration.

Imagine a brick wall getting clobbered by such an event. The round would probably make it in further before detonating.

[ November 15, 2003, 10:40 PM: Message edited by: Mr. Tittles ]

[Mr. Tittles]

The pretzel experiment.

Here's an experiment so you can get an idea of whats going on. Buy a bag of pretzels (get some beer too). Get the long rod type pretzels. The ones about 8-10 inches long and about a 1/2 inch thick. Take 21 of them. Bite off the ends. Its the best part and isnt needed for the experiment. Rub off the large salt pieces from the outside.

Drink a beer.

The pretzel rods, at this point, represent a HE shell that has 'minimally' fragmented. Cylindrical shells that break open during detonation will first split along the case so that every 15-18 degrees or so, there will be a saber (long fragment). A bursting type shell (smoke or WP) will take this shape. So if we took all 21 and arranged them around a cardboard tube such that they all touched, then you should get an idea of where we are.

Now, take one rod and break off 1/3 of it. Make sure you break the rods so that all the little pieces fall on the clean paper (you are working on a big piece of clean paper). The 2/3 piece represents an outlier of the largest fragment.

Take two more and break into halves.

Take four rods and break them into 1/3 pieces each.

Take 7 rods and break into 1/3 pieces. From each of these, take one piece and break into into a half (so its a 1/6). The piece should be held within two hands and snapped.

You are about 2/3 of the way through.

Notice the amount of fine splinters and micro-fragments being created.

Try to take the remaining 7 rods and break each one into 1/6 pieces. Try to break 7 of these 1/6 pieces generated into halves.

Notice the increasing amount of effort to break the smaller pieces. Use two plier devices if you have to.

Drink a beer.

Now put down the beer cause the president of the pretzel fragmentation research clinic has decided that 1/6 pieces are optimal. He demands that a HE be used so that more 1/6 pieces are to be generated. He is a scientifical man and his formulas show 1/6 are the best of the best!

Theres seventeen 1/3 pieces and obviously, that where the 1/6 pieces are going to come from. Maybe from the one big piece or the four halves also.

But heres the rub, if we start breaking those pieces again, we have to break our existing 1/6 pieces and also the smaller pieces too.

The real small flakes and crumbs are basically swarf. They lose their velocity so quickly. The big guys don't get all the velocity of the smaller guys but they are useful. Better than dust particles anyway..

So what do you do? Drink more beer?

[ November 16, 2003, 12:09 PM: Message edited by: Mr. Tittles ]

[JonS]

Originally posted by Andreas:

</font><blockquote>quote:</font><hr />Originally posted by JasonC:

105mm howitzer rounds are subsonic.

Speed of sound is 331.4m/s in air (temperature dependent). MV for the 10,5cm lFH18 is given as ~450m/s. </font>

[Mr. Tittles]

So, the point is that blithely quoting the highest possible MV for any given how, then thinking it applies in any and all cases is incorrect.

Muzzle velocity: 540 meters per second

Muzzle velocity: 469 meters per second

These are MV listed for a couple of German 105mm howitzers.

http://users.belgacom.net/artillery/artillerie/1810.html

I believe that the FO was quite clear that it was a high velocity shot. The target victims did not have time to duck. He was blithely explicit. Not that I would ever accuse you of not reading this very page of this thread (Mr. Dorosh referenced it). Would a round, fired at you, being barely supersonic or even subsonic give you any chance to take protective action?

My point is that it was similar to direct fire high velocity weapons. even though it was called in by a FO and 'indirect'.

[ November 16, 2003, 08:40 PM: Message edited by: Mr. Tittles ]

[Andreas]

Wouldn't trust that Belgian website.

Jon, thanks for the info.

[Leeo]

Tell us where The Queen is!

[Mr. Tittles]

The QuEEn? You mean? I dunno. belgians took 'er.

[c3k]

What I've learned from this thread: there's a whole lot of arcane stuff going on when HE hits something.

Also, it seems that better HE effects would be produced by shells made of pretzels.

Is this all correct so far?

Ken

[tar]

Oh yeah - speed of sound in air isn't even a constant. It varies with air-density, which is in turn affected by air temp and altitude.

Close. The speed of sound in air varies with the air temperature. Altitude only enters into this as it affects the temperature of the air.

Above the tropopause (roughly 36,000 feet, 11,000m), the air temperature becomes constant (at least tens of thousands of feet) and so does the speed of sound, even though the air density is still dropping with altitude.

[JonS]

Originally posted by tar:

</font><blockquote>quote:</font><hr />Oh yeah - speed of sound in air isn't even a constant. It varies with air-density, which is in turn affected by air temp and altitude.

Close. The speed of sound in air varies with the air temperature. Altitude only enters into this as it affects the temperature of the air.

Above the tropopause (roughly 36,000 feet, 11,000m), the air temperature becomes constant (at least tens of thousands of feet) and so does the speed of sound, even though the air density is still dropping with altitude. </font>

[Mr. Tittles]

Did you know that a minor point, if slowed down, can be a moot point?

[Industrializer]

I hadn't the time to read all articles in this interesting post by now but here is something that migh add some hard data, it's a page from the Pantherfiebel, the official manual for the Panther commander in WW2. It shows the saturation pattern and distribution of a 75mm HE shell.

every square represents 2m² and every dot one splinter considered lethal.

[Mr. Tittles]

Nice. Note the elongated forward spray area. This is an extension of the second zone of casualties. One of my main points about direct fire HE effectiveness is just this. The accuracy of the weapon is along the flight path of the projectile (unless on unusually flat terrain). The elongated path of lethality is ALSO along this path. In most higher angle indirect fire, this elongated path is shorter because of lower velocity and directed into the ground.

OV and MV must be SQ or Delay I pressume.

The other illustrations seems to show a ricochet shot and perhaps shooting into buildings with delay.

[ November 18, 2003, 09:51 AM: Message edited by: Mr. Tittles ]

[Mr. Tittles]

The pretzel experiment, hopefully, gave an idea of the dilemma of HE design.

A more rigerous explanation is that the distribution can be described as a log function. Imagine a X-Y graph with the function log running up the Y axis (represents number of fragments of a size) and fragment size running up the x axis. The graph of the distribution is a strait line. There will always be large fragments as well as a range of smaller fragments.

Its like a ladder against a wall. Where the ladder's legs touch the ground is the largest fragment (its number of fragments being 1 on the log y axis). If you push the ladder towards the wall (because you can not accept having such a large fragment(NOT EVEN ONE!)), then you will also be pushing up the number of smaller fragments (and NOT linearly). In other words, the area under the ladder always stays the same. Its the mass of the shell.

Ideally, you would want the shell to break up into an equal amount of optimally sized/shaped fragments. But thats 'perfectionistic' thinking and does not describe the natural fragmentation of a cylindrically shaped HE shell. A better approach is to optimize the maximum MASS of the shell into an acceptable RANGE. Accepting the small and large as being natural elements of the sitution.

The real heart of the matter is what is doing the shooting and what is being shot at. Theres basically three cases:

1. Indirect HE howitzer/gun fire

2. Mortar fire

3. HE direct fire

Case number 1, with its inherent dispersion of detonation points, is better served by smaller sized/quicker fragments. The forward spray is usually wasted. If forward effects are required, then delay fuze offers an option.

Case number 2, Mortar fire, with its inherent steep angle of descent, also requires smaller sized/quicker fragments. If the round comes earth ward too fast, and its fragments are too slow, then they will angle forward (actually downward) and spend themselves into the ground. Not ideal for most mortar work. It is, actually useful for trenches/lt. bunkers/dugout roofs. delay being used in that case. Most mortars have very low velocitys. They also have high HE content and non-cylindrical shape.

For case number 3, we are mostly interested in tanks/SPs firing at narrower targets. Things like antitank guns, MG nests, crewed weapons, targets behind walls/buildings, individual vehicles, bunkers, etc. The increased velocity and precision is augmented by having an elongated fragment effect. Indeed, the increased velocity gives it an increased forward fragment area. I would contend that a designer could trade size/high-velocity for more forward acting components IF they still had a size/velocity that was acceptably lethal. Indeed, for penetrating/destroying cover; size matters.

A note on Detonation Velocity:

In reality, for frag size, Detonation Velocity is actually to the fourth power! Examine the Mott equation. So if one were to double the Detonation Velocity, all other things being equal, then the size of the fragments would be 1/16th. They would also be blown out at greater velocity but ALSO towards the sides.

[ November 18, 2003, 01:12 PM: Message edited by: Mr. Tittles ]

[Mr. Tittles]

Originally posted by Industrializer:

every square represents 2m² and every dot one splinter considered lethal.

Notice the intial clover shape in the first zone of lethality (its marked with a 3 for some reason). If you count the squares from the center line, its actually longer than each of the wings is wider.

The ricochet shot seems to say that it jumps up to 10meters high and 50 meters forward.

[ November 19, 2003, 10:58 AM: Message edited by: Mr. Tittles ]

[Mr. Tittles]

Originally posted by Michael Dorosh:

</font><blockquote>quote:</font><hr />Originally posted by Mr. Tittles:

Heres an interesting passage from a German FO...

Notice that the velocity of the 105mm shell, giving no warning, led to its effectiveness This is similar to direct fire from many weapons.

http://members.shaw.ca/calgaryhighlanders/knolle.htm

That is my website. Did someone want Herr Knolle's email address? </font>

[Mr. Tittles]

Some thoughts on trajectory descent angle.

Lets take three cases, first is a shell landing perfectly on its nose. That is, its at 90 degrees. A mortar would be a close real world example.

Second case is a shell landing at 45 degrees. An artillery howitzer is a good example.

Third case is a high velocity flat trajectory weapon landing at 0 degrees. A panther HE round lets say.

The mortar round is probably ideal. Its ideal because the sides of the cylindrically shaped body, are 'pointing' (orthogonal) to the target area. Its distribution of fragments is circular about the point of impact. Its frontal spray is directly into the ground but this is a good trade off for the optimization of side spray.

The howitzer round landing at 45 degrees will spray the back side wall of the shell into the ground as well as its nose spray. The forward side wall will spray upward. The sides provide most of the lethality.

The tank round, as the pantherfiebel drawing shows, is another 'optimal' orientation of the shell. Its basically 'laying' on the grond when detonated. Its sides and part of the top provide a very good side spray. It also provides a very good (and long) frontal spray.

[Mr. Tittles]

http://www.geocities.com/Area51/Capsule/2930/pzpanther/lowres/pzpanther-charakter4.jpg

http://www.geocities.com/Area51/Capsule/2930/pzpanther/pzpanther-Charakteristics.html

Heres a side by side of Panther L70 rounds.

The German HE rounds I have seen seem to show very small fuzes. The US M48 75mm fuze appears to take up more of teh front of the shell.

[ November 24, 2003, 07:21 PM: Message edited by: Mr. Tittles ]

[Wol]

Mr Tittles can you email me please?

Wol

[Mr. Tittles]

Recently someone posted that if being attacked by tree-burst artillery, the best counter measure would be to lean up against a tree.

I have never heard of such a thing and recall the training specifying that IF we were to stick around during the attack, THEN balling up at the base of the largest available tree behind the incoming trajectory was as good as it was going to get. This is all coming about because no one has dug 4 foot deep fighting positions with overhead cover for you.

But what are the real dangers?

In the case of tank fire, it would probably be a good idea. The flat trajectory rounds that detonate in trees between you and the tank would throw fragments forward and at an angle and the tree would help you survive. Those rounds that detonate behind you would throw the fragments 'down range'.

In the case of mortars, I am not so sure tree bursts are THAT great. Since the round would throw much of its metal to the sides, it would be shredding the tops of the trees. Mortar airbursts that made it down to 2-10 feet off the ground before exploding, would be devastating. A round that penetrated the canopy and hit a lower branch lets say. The bulbous shape of most mortar rounds would throw metal downwards and in a more distributed shape than most arty shells so even high treebursts would be worthwhile I suppose. Using a delay might be an option.

The real threat, in my opinion, is the artillery shell coming in at an angle. Treebursts ahead of you and to the sides would rain down fragments from all angles. Treebursts behind you woould be worse! The lower side of the shell would blast fragments towards your exposed rear. Arty rounds and larger calibers with reaonable payload, would make secondary missiles from the trees themselves and the ricocheting of fragments off trunks is another possibility.

In reality, there would be no way on earth I would stay under such conditions for more than one round. I would high tail it to real cover.

I suppose defending a treeline is best done by having a trench/foxhole line forward of the actual trees, out in the 'open'. A fall back position could be further back in the trees (so the trees act as a buffer) and having decent dugouts/bunkers to get to.

[ November 25, 2003, 11:22 AM: Message edited by: Mr. Tittles ]

[Mr. Tittles]

http://www.fas.org/man/dod-101/navy/docs/es310/warheads/Warheads.htm

another good read

[Mr. Tittles]

http://www.europa1939.com/whermacht/artilleria/campana/sfh18.html

Here's a good site about 15 cm german howitzer. Its in Spanish. An interesting note is one shell had three options (my spanish is rusty but maybe someone can help us), large delay, small delay and zero delay (PD).