Fragmentation Modeling of Def Hgr 86

8/7/2019 Fragmentation Modeling of Def Hgr 86

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Fragmentation modeling and simulation of

Def Hgr 86

www.Medulla-soft.com

Fragmentation Modeling of Def Hgr 86



Introduction

A computer simulation model was developed to capture the effect of

fragmentation and dispersion of pellets upon the burst of a mini hand grenade Hgr86. thegrenade is made of polystol casing with approximately 2000 pellets made of iron,

measuring 2-2.5mm in diameter. The core detonation material is pentaerythritol

tetranitrate (PETN).Technical details such as the strength of explosive, ejecting velocity of the pellets, and

the curve of the density of pellets with distance is provided by the manufacturing and

testing body. The model will serve to demonstrate the effect for training purposes.

Underlying physical concept :

The detonation provides a large amount of energy which is used for the rupturing of the

outer casing, the ejection of pellets and to generate a shock wave which is a pressurewave traveling outwards form the centre of the detonation point.

The pellets are assumed to fly off normal to the protecting surface as plastic stress acts

normal to the surface of the material. After the initial launce the motion of the pellets are

guided by the laws of projectile motion. The trajectory of the pellets is not disturbed bythe shock wave as the velocity is very large(around 550m/s)

During the flight there are various forces that act on the pellets such as Air- drag, Coriolisforce, Magnus force, spin stabilization etc. In our case only air drag is the determining

force as the particles are extremely small and the rest of the forces can be neglected.

Also a ballistic model was found unnecessary as the particles are very small and do nottravel large distances. An important task is to capture the effect of the drag force as it is

not a constant force and varies from case to case.

The three dimensional equations of motion are formulated which are coupled, second

order non linear partial differential equation. These are solved by the standard Runge-

Kutta technique as they do not possess an analytical solution.





Position of pellets and flying angles:

The pellets are embedded in the inner surface of the casing which expands upon burst.

To get the position of the fragments as they leave the grenade, a graphical technique isadopted. A diagram of the grenade (to scale) is traced on a graph paper.(see diag). The

lower basal centre is taken as the origin and the coordinates of the various positions are

traced wrt this Cartesian system of coordinates.

The y axis is divided into sections of 2mm diameter each and the corresponding x

coordinate is marked. Each section corresponds to a ring of pellets with radius as the xcoordinate.

The position of all pellets in this ring can be traced as :

N=2*3.14*(x)mm)/2mm……………………..no of pellets in the ring.Theta(angle)= 2/x(mm)

(x,y,z)= [X(n) cos(theta), Y(n), X(n) sin(theta)]……………..for X= X(1), X(2)…..X(n)

A normal is drawn for each ring which is the direction of flying angles. This normal istraced back to meet the y axis and a second point is noted (p(2)).

With p(1) and p(2) as two points of a free vector in space, its angles with the x,y and z

axis can be easily found by applying standard 3D equations. These are the angles of bursthitherto incorporation of randomness. A certain amount of randomness in the form of

k(theta) is also added to the angles to replicate real life scenario, where k is a randomnumber.

The number of pellets rendered in this manner are greater than 2000, the actual amount of

pellets. For the simulation 2000 of these pellets are selected randomly for analysis.







The model has to be calibrated for the air drag and validated against real tests for it to be predictive.

Air drag varies with the velocity of the flying object. For our model the air drag ismodeled as:

C(d) = 0.98……………………...v<330m/s

C(d)=0.98/(M)^(0.5)…………….v>330m/s

M= v/330…..mach number.

The value of 0.98 was established with various tests run with a single projectile,comparing results with the maximum range of flight and maximum kill radius provided

by the testing body.

The ejecting velocities are distributed with a normal distribution curve with mean as

575m/s.

The tests conducted provided us with plywood frame of 2x1m in dimension placed at adistance of 2,3,4,5,10.15 meters and the no of pellets striking each frame. The frame is

divided into three segments to differentiate the impact at various levels. The number of

particles striking the lower section is larger than the middle which is larger than the upper

segment.

In the model, dummy targets are placed in the simulation and the number of particles

striking these targets is recorded and averaged for a number of runs. Also to get thedensity variation a target of size 5x4m is placed at various distances from the grenade and

the numbers of pellets striking are recorded. A curve is plotted and compared with the

original curve. The simulation records each observation in a excel sheet.

The model also has three dummy targets representing the standing, lying and crouched

position of the personnel and the particles striking the targets in these positions can beseen in a graphical user interface.

Results:

The pellets are lethal to human body above speeds of 300-350m/s. below these speeds

they are not considered as lethal. In the simulation the kill radius is established as 6+-6meters. The actual kill radius provided id 5+-6 meters.

The number of pellets that strike our targets placed at 2,3,4,5,10,15 meters match veryclosely to the field tests.(see results)

The density relation matches very closely to the provided data thus validating our

concerns.



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Fragmentation Modeling of Def Hgr 86