Dynamic home base thickness. If the missile is punching the ERA forepart home base and hits the bed of high explosive charge this will be quickly initiated depending on different parametric quantities and on the type of high explosive charge. By the explosion force per unit area, the home base of the sandwich are instantly accelerated fly sheer to the surface with speeds matching to the ratio of sum of high explosive to the weight of home base ( Gurney equation ). The ephemeral clip of the jet is comparatively short. Therefore the ‘dynamic home base thickness ‘ is comparatively little and presents merely a little portion of the decrease consequence of the projectile public presentation.

Jet warp. A little part of the kinetic energy of the form charge jet is consumed by punching the home bases. An of import portion of the jet length will be deflected and sputtered. This consequence consumes merely a little sum of the winging plate stuff. A deflected jet does non hit the same crater hole, which means the incursion for such a disturbed molded charge jet is drastically reduced.

Shock burden and explosive merchandises. Explosion daze moving ridge and particularly the using merchandise of explosives with their force per unit area and speeds can besides present cross motion to the wining jet if they streaming out of the holes in the home base, largely non symmetrically built.

## 2.4.1 Gurney equations

Ronald Wilfred Gurney ( 1898, Cheltenham, England -1953, USA ) was a British theoretical physicist and research student of William Lawrence Bragg at the Victoria University of Manchester during the 1920s and 30s, Bristol University during the 1930s and subsequently in the USA where he died.

The Gurney equations are a set of mathematical expressions used in Explosives technology to associate how fast an explosive will speed up a environing bed of metal or other stuff when the explosive detonates. This determines how fast fragments are released by military explosives, how rapidly shaped charge explosives accelerate their line drives inwards, and in other computations such as explosive welding where explosives force two metal sheets together and bond them.

The equations were foremost developed in the 1940s by R.W. Gurney and have been expanded on and added to significantly since that clip.

## 2.4.2 Underliing natural philosophies

When an explosive surrounded by a metallic or other solid shell detonates, the outer shell is accelerated both by the initial explosion shockwave and by the enlargement of the explosion gas merchandises contained by the outer shell. Gurney modeled how energy was distributed between the metal shell and the explosion gases, and developed expressions that accurately describe the acceleration consequences.

Gurney made a simplifying premise that there would be a additive speed gradient in the explosive explosion merchandise gases. This has worked good for most constellations, but see the subdivision Anomalous anticipations below.

## 2.4.3 Definitions and units

The Gurney equations usage and link the undermentioned measures:

C – The mass of the explosive charge

M – The mass of the accelerated shell or sheet of stuff ( normally metal ) . The shell or sheet is frequently referred to as the circular, or circular home base.

V or Vm – Speed of accelerated circular after explosive explosion.

N – The mass of a tamping bar shell or sheet on the other side of the explosive charge, if present.

– The Gurney Constant for a given explosive. This is expressed in units of speed ( millimetres per microsecond, for illustration ) and compares the comparative circular speed produced by different explosives stuffs.

## 2.4.4 Valuess of and explosion speed for assorted explosives

As a simple approximative equation, the physical value of is normally really near to 1/3 of the explosion speed of the explosive stuff for standard explosives.

Gurney speed sqrt { 2E } for some common explosives

sqrt { 2E }

## Explosive

frac { g } { cm^3 }

frac { millimeter } { mu s }

frac { millimeter } { mu s }

1.72

7.92

2.70

1.60

7.63

2.68

1.754

8.25

2.79

1.835

8.83

2.80

1.89

9.11

2.97

1.81

8.48

2.80

1.84

8.80

2.90

1.885

7.67

2.377

1.76

8.26

2.93

1.77

8.70

2.83

1.62

7.57

2.50

1.63

6.86

2.44

## Tritonal

1.72

6.70

2.32

Note that is dimensionally equal to kilometres per second, a more familiar unit for many applications.

## 2.4.5 Fragmenting versus no break uping outer shells

The Gurney equations give a consequence which assumes that the circular home base remains integral throughout the acceleration procedure. For some constellations, this is true – explosives welding, for illustration, uses thin sheets of explosives to equally speed up level home bases of metal and clash them, and the home bases remain solid throughout. However, for many constellations where stuffs are being accelerated outwards the spread outing shell will fracture due to stretching as it expands. When it fractures, it will normally interrupt into many little fragments due to the combined effects of ongoing enlargement of the shell and emphasis alleviation moving ridges traveling into the stuff from break points.

For brickle metal shells, the fragment speeds are typically approximately 80 % of the value predicted by the Gurney expression.

## 2.4.6 Effective charge volume for little diameter charges

Effective charge mass for thin charges – a 60 grade cone

The basic Gurney equations for level sheets assume that the sheet of stuff is big diameter. Small explosive charges, where the explosives diameter is non significantly larger than its thickness, have reduced effectivity as gas and energy are lost to the sides.

This loss is through empirical observation modeled as cut downing the effectual explosive charge mass C to an effectual value Ceff which is the volume of explosives contained within a 60 grade cone with its base on the explosives/flyer boundary.

## 2.4.7 Anomalous anticipations

In 1996, Hirsch described a public presentation part, for comparatively little ratios of in which the Gurney equations misrepresent the existent physical behaviour.The scope of values for which the basic Gurney equations generated anomalous values is described by ( for level asymmetrical and open-faced sandwich constellations ) :

For an open-faced sandwich constellation ( see below ) , this corresponds to values of of 0.5 or less. For a sandwich with tamper mass equal to explosive charge mass ( ) a circular home base mass of 0.1 or less of the charge mass will be anomalous.

This mistake is due to the constellation transcending one of the underlying simplifying premises used in the Gurney equations – that there is a additive speed gradient in the explosive merchandise gases. For values of outside the anomalous part this is a really good premise. Hirsch demonstrated that as the entire energy divider between the circular home base and gases exceeds integrity, the premise breaks down, and the Gurney equations go less accurate as a consequence.

Complicating factors in the anomalous part include detailed gas behaviour of the explosive merchandises, including the reaction merchandises ‘ Heat capacity ratio or I? . Modern explosives technology utilizes computational analysis methods which avoid this job.

## Symmetrical sandwich equation

Symmetrical sandwich – level explosives bed of mass C and two circular home bases of mass M each

A level bed of explosive with two equal heavy level circular home bases on each side will speed up the home bases as described by:

Symmetrical sandwiches are used in some Reactive armour applications, on to a great extent armoured vehicles such as Main conflict armored combat vehicles. The inwards-firing circular will impact the vehicle chief armour, doing harm if the armour is non thick plenty, so these can merely be used on heavier armoured vehicles. Lighter vehicles use open-face sandwich reactive armour ( see below ) . However, the double moving home base method of operation of a symmetrical sandwich offers the best armour protection.

## Asymmetrical sandwich equation

Asymmetrical sandwich – level explosives bed of mass C, circular home bases of different multitudes M and N

A level bed of explosive with two different mass level circular home bases will speed up the home bases as described by:

Let:

## Boundlessly tamped sandwich equation

Boundlessly tamped sandwich – level explosives bed of mass C, flyer home base of mass M, and boundlessly heavy backup tamping bar

When a level bed of explosive is placed on a practically boundlessly thick back uping surface, and topped with a flyer home base of stuff, the circular home base will be accelerated as described by.

## Open-faced sandwich equation

Open-faced sandwich ( no tamping ) – level explosives bed of mass C and individual circular home base of mass M

A individual level sheet of explosives with a circular home base on one side, known as an “ Open-faced sandwich ” , is described by:

Since:

N = 0

Then:

Which gives:

Open-faced sandwich constellations are used in Explosion welding and some other metal organizing operations.

It is besides a constellation normally used in Reactive armor on lightly armoured vehicles, with the unfastened face down towards the vehicle ‘s chief armour home base. This minimizes the reactive armour units harm to the vehicle construction during fire.

## 2.4.9 Table of explosive explosion speeds

This is a list of the explosion speeds at specified ( typically, the highest practical ) denseness of assorted explosive compounds.The speed of explosion is an of import index for overall energy or power of explosion, and in peculiar for the brisance or shattering consequence of an explosive.

## Aromatic explosives

1,3,5-trinitrobenzene

TNB

7,450

1.6

1,3,5-Triazido-2,4,6-trinitrobenzene

TATNB

7,300

1.71

4,4′-Dinitro-3,3′-diazenofuroxan

DDF

10,000

2.02

Tnt

Trinitrotoluene

6,900

1.6

Trinitroaniline

TNA

7,300

1.72

Tetryl

7,570

1.71

Picric Acid

TNP

7,350

1.7

Dunnite

7,150

1.6

Methyl Picrate

6,800

1.57

Ethyl Picrate

6,500

1.55

Picryl Chloride

7,200

1.74

Trinitrocresol

6,850

1.62

5,200

2.9

Triaminotrinitrobenzene

TATB

7,350

1.80

## Aliphatic explosives

Methyl nitrate

8,000

1.21

Nitroglycol

EGDN

8,000

1.48

Nitroglycerin

Nanogram

7,700

1.59

Mannitol hexanitrate

MHN

8,260

1.73

Pentaerythritol Tetranitrate

PETN

8,400

1.7

Ethylenedinitramine

EDNA

7,570

1.65

Nitroguanidine

NQ

8,200

1.7

Cyclotrimethylenetrinitramine

RDX

8,750

1.76

Cyclotetramethylene Tetranitramine

HMX

9,100

1.91

Hexanitrohexaazaisowurtzitane

HNIW or CL-20

9,400

2.04

Tetranitroglycoluril

Sorguyl

9,150

1.95

Octanitrocubane

ONC

10,100

2.0

Nitrocellulose

North carolina

7,300

1.2

Urea nitrate

United nations

4,700

1.59

Acetone Peroxide

AP

5,300

1.18

## Inorganic explosives

Mercury Fulminate

4,250

3.0

4,630

3.0

Silver azide

4,000

4.0

Ammonium Nitrate

Associate in nursing

5,270

1.3