Principal And Phenomenology Of Era Biology Essay

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Dynamic plate thickness. If the projectile is perforating the ERA front plate and hits the layer of high explosive charge this will be promptly initiated depending on different parameters and on the type of high explosive charge. By the detonation pressure, the plate of the sandwich are immediately accelerated fly perpendicularly to the surface with velocities corresponding to the ratio of amount of high explosive to the weight of plate (Gurney equation) [1] . The passing time of the jet is relatively short. Therefore the 'dynamic plate thickness' is relatively small and presents only a small part of the reduction effect of the projectile performance.

Jet deflection. A small portion of the kinetic energy of the shape charge jet is consumed by perforating the plates. An important part of the jet length will be deflected and sputtered. This effect consumes only a small amount of the flying plate material. A deflected jet does not hit the same crater hole, which means the penetration for such a disturbed shaped charge jet is drastically reduced.

Shock load and explosive products. Detonation shock wave and especially the expending product of explosives with their pressure and velocities can also introduce transverse movement to the succeeding jet if they streaming out of the holes in the plate, mostly not symmetrically built.

2.4.1 Gurney equations

Ronald Wilfred Gurney (1898, Cheltenham , England -1953, USA) was a British theoretical physicist and research pupil of William Lawrence Bragg at the Victoria University of Manchester during the 1920s and 30s, Bristol University during the 1930s and later in the USA where he died. [2] 

The Gurney equations are a set of mathematical formulas used in Explosives engineering to relate how fast an explosive will accelerate a surrounding layer of metal or other material when the explosive detonates. This determines how fast fragments are released by military explosives, how quickly shaped charge explosives accelerate their liners inwards, and in other calculations such as explosive welding where explosives force two metal sheets together and bond them. [3] 

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

2.4.2 Underlying physics

When an explosive surrounded by a metallic or other solid shell detonates, the outer shell is accelerated both by the initial detonation shockwave and by the expansion of the detonation gas products contained by the outer shell. Gurney modeled how energy was distributed between the metal shell and the detonation gases, and developed formulas that accurately describe the acceleration results.

Gurney made a simplifying assumption that there would be a linear velocity gradient in the explosive detonation product gases. This has worked well for most configurations, but see the section Anomalous predictions below.

2.4.3 Definitions and units

The Gurney equations use and connect the following quantities:

C - The mass of the explosive charge

M - The mass of the accelerated shell or sheet of material (usually metal). The shell or sheet is often referred to as the flyer, or flyer plate.

V or Vm - Velocity of accelerated flyer after explosive detonation.

N - The mass of a tamper 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 velocity (millimeters per microsecond, for example) and compares the relative flyer velocity produced by different explosives materials.

2.4.4 Values of and detonation velocity for various explosives

As a simple approximate equation, the physical value of is usually very close to 1/3 of the detonation velocity of the explosive material for standard explosives.

Gurney velocity \sqrt{2E}for some common explosives

Density

Detonation Velocity

\sqrt{2E}

Explosive

\frac{g}{cm^3}

\frac{mm}{\mu s}

\frac{mm}{\mu s}

Composition B

1.72

7.92

2.70

Composition C-3

1.60

7.63

2.68

Cyclotol 75/25

1.754

8.25

2.79

HMX

1.835

8.83

2.80

LX-14

1.89

9.11

2.97

Octol 75/25

1.81

8.48

2.80

PBX 9404

1.84

8.80

2.90

PBX 9502

1.885

7.67

2.377

PETN

1.76

8.26

2.93

RDX

1.77

8.70

2.83

Tetryl

1.62

7.57

2.50

TNT

1.63

6.86

2.44

Tritonal

1.72

6.70

2.32

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

2.4.5 Fragmenting versus no fragmenting outer shells

The Gurney equations give a result which assumes that the flyer plate remains intact throughout the acceleration process. For some configurations, this is true - explosives welding, for example, uses thin sheets of explosives to evenly accelerate flat plates of metal and collide them, and the plates remain solid throughout. However, for many configurations where materials are being accelerated outwards the expanding shell will fracture due to stretching as it expands. When it fractures, it will usually break into many small fragments due to the combined effects of ongoing expansion of the shell and stress relief waves moving into the material from fracture points.

For brittle metal shells, the fragment velocities are typically about 80% of the value predicted by the Gurney formulas.

2.4.6 Effective charge volume for small diameter charges

http://upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Gurney-Effective-Volume.png/100px-Gurney-Effective-Volume.png

Effective charge mass for thin charges - a 60 degree cone

The basic Gurney equations for flat sheets assume that the sheet of material is large diameter. Small explosive charges, where the explosives diameter is not significantly larger than its thickness, have reduced effectiveness as gas and energy are lost to the sides.

This loss is empirically modeled as reducing the effective explosive charge mass C to an effective value Ceff which is the volume of explosives contained within a 60 degree cone with its base on the explosives/flyer boundary.

2.4.7 Anomalous predictions

In 1996, Hirsch described a performance region, for relatively small ratios of in which the Gurney equations misrepresent the actual physical behavior. [4] The range of values for which the basic Gurney equations generated anomalous values is described by (for flat asymmetrical and open-faced sandwich configurations):

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

This error is due to the configuration exceeding one of the underlying simplifying assumptions used in the Gurney equations - that there is a linear velocity gradient in the explosive product gases. For values of outside the anomalous region this is a very good assumption. Hirsch demonstrated that as the total energy partition between the flyer plate and gases exceeds unity, the assumption breaks down, and the Gurney equations become less accurate as a result.

Complicating factors in the anomalous region include detailed gas behavior of the explosive products, including the reaction products' Heat capacity ratio or γ. Modern explosives engineering utilizes computational analysis methods which avoid this problem.

2.4.8 The equations

Symmetrical sandwich equation

http://upload.wikimedia.org/wikipedia/commons/thumb/7/71/Gurney-Symmetrical-Sandwich.png/300px-Gurney-Symmetrical-Sandwich.png

Symmetrical sandwich - flat explosives layer of mass C and two flyer plates of mass M each

A flat layer of explosive with two equal heavy flat flyer plates on each side will accelerate the plates as described by:

Symmetrical sandwiches are used in some Reactive armor applications, on heavily armored vehicles such as Main battle tanks. The inwards-firing flyer will impact the vehicle main armor, causing damage if the armor is not thick enough, so these can only be used on heavier armored vehicles. Lighter vehicles use open-face sandwich reactive armor (see below). However, the dual moving plate method of operation of a symmetrical sandwich offers the best armor protection.

Asymmetrical sandwich equation

http://upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Gurney-Asymmetrical-Sandwich.png/300px-Gurney-Asymmetrical-Sandwich.png

Asymmetrical sandwich - flat explosives layer of mass C, flyer plates of different masses M and N

A flat layer of explosive with two different mass flat flyer plates will accelerate the plates as described by: [5] 

Let:

Infinitely tamped sandwich equation

http://upload.wikimedia.org/wikipedia/commons/thumb/5/55/Gurney-Infinitely-Tamped-Sandwich.png/300px-Gurney-Infinitely-Tamped-Sandwich.png

Infinitely tamped sandwich - flat explosives layer of mass C, flyer plate of mass M, and infinitely heavy backing tamper

When a flat layer of explosive is placed on a practically infinitely thick supporting surface, and topped with a flyer plate of material, the flyer plate will be accelerated as described by.

Open-faced sandwich equation

http://upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Gurney-Open-Faced-Sandwich.png/300px-Gurney-Open-Faced-Sandwich.png

Open-faced sandwich (no tamping) - flat explosives layer of mass C and single flyer plate of mass M

A single flat sheet of explosives with a flyer plate on one side, known as an "Open-faced sandwich", is described by:

Since:

N = 0

Then:

Which gives:

Open-faced sandwich configurations are used in Explosion welding and some other metal forming operations.

It is also a configuration commonly used in Reactive armour on lightly armored vehicles, with the open face down towards the vehicle's main armor plate. This minimizes the reactive armor units damage to the vehicle structure during firing.

2.4.9 Table of explosive detonation velocities

This is a list of the detonation velocities at specified (typically, the highest practical) density of various explosive compounds. [i] The velocity of detonation is an important indicator for overall energy or power of detonation, and in particular for the brisance or shattering effect of an explosive.

Table of Explosive Detonation Velocities

Explosive Name↓

Abbreviation↓

Detonation

Velocity (m/s)↓

Density

(g/cm³)↓

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

Trinitrotoluene

TNT

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

Lead styphnate

5,200

2.9

Triaminotrinitrobenzene

TATB

7,350

1.80

Aliphatic explosives

Methyl nitrate

8,000

1.21

Nitroglycol

EGDN

8,000

1.48

Nitroglycerine

NG

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

NC

7,300

1.2

Urea nitrate

UN

4,700

1.59

Organic Explosives

Acetone Peroxide

AP

5,300

1.18

Inorganic explosives

Mercury Fulminate

4,250

3.0

Lead azide

4,630

3.0

Silver azide

4,000

4.0

Ammonium Nitrate

AN

5,270

1.3

Explosive Name

Abbreviation

Detonation

Velocity (m/s)

Density

(g/cm³)

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