Grenade throwing - how far?

[Muerrisch]

I Quote:

undesirably wide radius of lethality, because the 'm' bit of its kinetic energy - 1/2 mv2 - was too great.

I take it this is 1/2 m vsquared in which case it is difficult to say which of larger m, or squaring the v, was to blame for lethality.

I think.

[themonsstar]

This is from Notes on Training

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[themonsstar]

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[Jack Sheldon]

Grumpy

The mass of the individual fragments is what caused the problem. Once accelerated, they flew a long way. The same was true of the fragmentation patterns of the shells of the period, which tended to break into large chunks. As I stated, modern grenades split into tiny fragments, whose energy is swiftly dissipated. Lethality of +/- 10 metres (and often less, as with 40mm grenade launcher ammunition) is what is needed.

Jack

[Muerrisch]

So are you saying that v is more-or-less the same, regardless of m, at usual ranges?

I ask this becausing doubling m only doubles KE, but doubling v quadruples it.

And what is the trade-off between the initial v immediately after bang, and the likely m?

Does a grenade that breaks in 4 pieces impart the same initial v [averaged over the pieces] as a grenade that breaks into 8, for example?

And if not, why not.

My Physics did not extend beyond an A level, 58 years ago.

Not straightforward to a layman.

[Jack Sheldon]

Grumpy

I am afraid I cannot answer your precise question. However, given equal initial velocity, mass is the main determinant of the ultimate distance. In other words heavier fragments travel further because they have greater carrying power. I suspect that smaller fragments are more susceptible to air resistance, though I cannot give you chapter and verse.

Jack

[salesie]

And let's not forget that the lethal range is not a precise calculation by any means - the softer the ground the shorter the killing field, the harder the ground giving the opposite effect, of course (a touch of Newton's 3rd law at work?). Giving any mathematical calculations an extremely high level of tolerance at the sharp end (not to mention any undulations creating "dead-ground", or "not so-dead-groud" in this instance).

Cheers-salesie.

[Gareth Davies]

Compared to warheads, which propagate their lethal effect in the form of a shock wave, fragmentation warheads are generally cheaper and have a greater lethal range. Principally, this is because the energy of the fragments dissipates more slowly than the energy of a shock wave. There are two major criteria for fragmentation warhead design: will the individual fragments have sufficient energy to damage the target and whether or not there is a high probability that a fragment will actually hit the target.

The kinetic energy of an individual fragment at some distance from the explosion will depend on two factors: the initial velocity, and the reduction in speed due to wind resistance.

The fragments will be thrown outward at a velocity which depends on the nature of the explosive material (how energetic the explosion is) and the configuration of the warhead (the mass of the explosive charge, the amount of material available for fragments and the physical arrangement). A theoretical analysis that predicted the initial velocities of the fragments was done by R.W. Gurney in 1943. The velocity is a function of three factors:

1. The heat of explosion per unit mass of the explosive material, DE, in J/kg. To convert from kJ/mol, you must multiply by 10⁶ and divide by the molecular weight. For example DE = 616.4 kJ/mol of TNT. Since TNT has a molecular weight of 227 g/mol

DE = (616.4 kJ/mol)(1 mol/227 g)(10³ J/kJ)(10³ g/kg)

DE = 2.715 x 10⁶ J/kg = 2.715 x 10⁶ m²/s²

2. The configuration. Most warheads will fall into one of three simple shapes: a flat plate, a cylinder and a sphere. For example, a land mine is a flat plate, a 2000 lb. Bomb is a cylinder and a hand-grenade is a sphere.

3. The ratio of explosive charge to fragmenting metal, C/M. This is also known as the charge-to-metal ratio.

Here is the theoretical result:

where the value of K depends on the configuration. For a sphere: K = 3/5

The lead term, , is known as the Gurney constant for the explosive material. The DE term is the heat of explosion in J/kg. The Gurney constant has units of velocity [m/s]. It is a rough measure of the speed of the explosion. For example, the Gurney constant for TNT is 2328 m/s. The expression after the Gurney constant generally is in the range of 0.5 to 2.0.

Reduction in Velocity with Range: As soon as the fragments are thrown outward from the casing, their velocity will begin to drop due to wind resistance (drag). The drag force is given by:

Drag = ½ rv² C_d A

where: r = The density of air. Normally 1.2 Kg/m³.

V = The fragment velocity.

C_d = The coefficient of drag. Depends on the shape of the fragment and to some extent, the velocity.

A = The cross-sectional area of the fragment.

One can solve the equations of motion for the projectile and get the fragment's velocity as a function of the distance traveled:

where s = the range, and v₀ is the initial fragment velocity.

Simples!

[auchonvillerssomme]

That whistling sound was the last post going right over my head, hopefully just like a piece of shrapnel.

[Muerrisch]

Gareth: I followed almost all of that and will revisit it this evening.

It does make "given equal velocity" look a bit simplistic!

[Gareth Davies]

A rather poor copy of Gurney's work can be found here:

http://www.dtic.mil/dtic/tr/fulltext/u2/a800105.pdf

[Jack Sheldon]

Mr Simplistic - that's me. Mind you I was raking back into the dim and distant past when I was dozing through a lecture on ballistics at Sandhurst - and I still stick to my main point.

Jack

[squirrel]

Homeguard Manual 1941 states this regarding the Mills 36 HE grenade :

(ii) Characterisitcs:

Is a weapon for short range.

Comaratively heavy (can be thrown 25 to 35 yards).

Danger area about 20 yards. May wound up to 100 yards.

Dangerous on stony ground.

Thrower mus be protected.

Useful in trenches, street fighting etc.

Dangerous to be on the receiving end on any type of ground IMHO!

[Muerrisch]

Mr Simplistic - that's me. Mind you I was raking back into the dim and distant past when I was dozing through a lecture on ballistics at Sandhurst - and I still stick to my main point.

Jack

It was one of those topics that suddenly intrigued me.

However, unlike musing on the very wobbly equations regarding Military Mining a la Great war, and the massive bang at RAF Fauld in the Second, it will NOT trigger a learned article!

The conclusion re. Mining is that, to be sure of a bl$$dy great hole, you need a bl$$dy big bang, and you might just overdo the bang. Ideal for RE officers, Mad, Methodist, Married as someone said.

PS from internet:

“The officer Corps had the sobriquet of 'mad, married or Methodist'," adds RE Museum Director Richard Dunn. “In the days of bought commissions here were guys who could only enter by dint of their intellect, so they must be mad and quite eccentric. They also tended to be older and many were Low Church families and Methodist. There’s a touch of social reform to this part of this army.”

[Mark Hone]

On a slight tangent, I shall post some photos of the said 17th Manchester Bombers when I scan the scrapbook of Captain Thomas Cartman (see the thread on him). He was the battalion bombing officer in 1916/17

[8055Bell]

Mark,

The photos would be very welcome. My grandad will be included from A Company III Platoon.

Tim

[Muerrisch]

On a slight tangent, I shall post some photos of the said 17th Manchester Bombers when I scan the scrapbook of Captain Thomas Cartman (see the thread on him). He was the battalion bombing officer in 1916/17

Yes please!

[squirrel]

It was one of those topics that suddenly intrigued me.

However, unlike musing on the very wobbly equations regarding Military Mining a la Great war, and the massive bang at RAF Fauld in the Second, it will NOT trigger a learned article!

The conclusion re. Mining is that, to be sure of a bl$$dy great hole, you need a bl$$dy big bang, and you might just overdo the bang. Ideal for RE officers, Mad, Methodist, Married as someone said.

PS from internet:

“The officer Corps had the sobriquet of 'mad, married or Methodist'," adds RE Museum Director Richard Dunn. “In the days of bought commissions here were guys who could only enter by dint of their intellect, so they must be mad and quite eccentric. They also tended to be older and many were Low Church families and Methodist. There’s a touch of social reform to this part of this army.”

Kipling "Sappers":

We build 'em nice barracks -they swear they are bad,

That our Colonels are Methodist, married or mad.'

Insulting Her Majesty's Roayl Engineers

With the rank and pay of a Sapper!

[Lancashire Fusilier]

My WW1 No.23 Mk.II Mills Bomb/Grenade weighs about 1.65 lbs., so throwing it any real distance is not that easy, particularly when using the ' official ' overarm throw or lobbing action.

LF

[Guest]

At school I was average at throwing a cricket ball, but there were a couple of lads who were exceptional. One could throw 3 times further than anyone, quite amazing. He was a great all round sportsman. Another, even when 7 years old, could throw a stone right over the river Tay at Kenmore (70 yards +), the speed of his throw was incredible. I'm not sure if a fast arm was the key to being a good bomb thrower though?

Mike

[squirrel]

IMHO technique is the key as much as strength. As well as cricketers, those who played racket sports using overhead shots would also be able to throw reasonably well.

[SteveMarsdin]

Which was the easier shape and design to throw: the German stick-grenades (potato-masher) or the Mills bomb type ?

[JMB1943]

On 02/01/2013 at 13:57, Gareth Davies said:

3. The ratio of explosive charge to fragmenting metal, C/M. This is also known as the charge-to-metal ratio.

Here is the theoretical result:

where the value of K depends on the configuration. For a sphere: K = 3/5

The lead term, , is known as the Gurney constant for the explosive material. The DE term is the heat of explosion in J/kg. The Gurney constant has units of velocity [m/s]. It is a rough measure of the speed of the explosion. For example, the Gurney constant for TNT is 2328 m/s. The expression after the Gurney constant generally is in the range of 0.5 to 2.0.

where s = the range, and v₀ is the initial fragment velocity.

 

Gareth,

for the sake of completeness, could you repost the expressions for,

IMG00007.GIF / IMG00008.GIF / IMG00009.GIF.

I have looked at RW Gurney's original paper on-line, but can only find very poor copies and the clarity of the text leaves a lot to be desired.

Regards,

JMB

 

[Gareth Davies]

Blimey. I posted that 10 years ago. I have no idea where I saved the information, sorry.

[JMB1943]

Gareth,

I thought that might be the case.

Regards,

JMB