Combat stiffness of the launcher platform Текст научной статьи по специальности «Строительство и архитектура»

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COMBAT STIFFNESS

OF THE LAUNCHER PLATFORM

o Milos S. Lazarevic

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University of Kragujevac, Faculty of Engineering, Kragujevac,

5 Republic of Serbia,

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- e-mail: laky_boy_kg@hotmail.com,

yj ORCIDiD: http://orcid.org/0000-0002-5441-4482 a.

g http://dx.doi.org/10.5937/vojtehg65-14716 CO

FIELD: Mechanical Engineering ARTICLE TYPE: Original Scient ARTICLE LANGUAGE: English

o ARTICLE TYPE: Original Scientific Paper

I

m Summary:

Possible loads on a multiple rocket launcher have been systemized and ^ analyzed. Based on the analysis of loads, a mathematical-mechanical

model has been made to describe the stability of a MLR hit by a high explosive-fragmentation projectile (HE-FRAG) in a close range. The results give the dependency of the launcher stability on explosion SN proximity, its typeand the explosive charge mass. The stability limit is

LA determined by the force that can turn over the laucher and compromise

^ the stability of projectiles inside. To simplify the given model, the kinetic

energy is calculated for a projectile fragment that hits the launcher.

Key words: load, explosion effect, surface explosion, above ground EH explosion, conditions, critical pressure, critical distance, overturn

OT stability, kinetic energy.

Introduction

In order to meet stringent tactical-technical requirements regarding mobility, efficiency, range, up-to-date targets and stiffness,a multiple launching rocket system construction needs to be specific in comparison to other assets of support (Kari, 2007, p.9). Looking at it generally, a multiple launching rocket system is under the following loads (MilinoviC, 2002, p.155):

Static loads (mechanical):

- the effects of the vehicle weight and the launcher type.

Thermic loads:

- the effects from the combustion products during the launch on the launcher box;

- the detonation products effects when a projectile explodes in the vicinity of the launcher.

Dynamic loads:

- dynamic loads during above ground and surface explosions in the close proximity;

- dynamic loads from the gases during a rocket launch;

- transport loads;

- wind blasts.

From all these loads, the most critical are the dynamic loads during above ground or surface explosions in the close proximity, so we will only take this group for a further analysis.

Determining the maximum pressure of the blast wave on the launcher

As a model for the blast wave pressure, we have accepted a cylindrical coordinate system with independent variables 9 and 6 as shown in Figure!

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Figure 1 - Physical model for the directional effect of the blast wave on the launcher

(Lazarevic, 2017, p.11) Рис. 1 - Физическое воздействие ударной волны на РСЗО (Lazarevic, 2017, p.11) Слика 1 - Физички модел детства ударног таласа на лансер (Lazarevic, 2017, p.11)

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Figure 2 represents the basis of the mechanical-mathematical model of the stability of the launcher hit by the blast wave from an explosion. The end result is the maximum pressure of the blast wave during which the stability of the launcher will not be compromised.

Figure 2 - Balance force of the launcher (Lazarevic, 2017, p.20) Рис. 2 - Равновесие сил РСЗО (Lazarevic, 2017, p..20) Слика 2 - Равнотежа сила самоходное лансера (Lazarevic, 2017, p.20)

S F = о Z F = о; Z MA =0

p-(t + r2 = о) f (Q + g ) = t + r2

(i)

where:

Px = Ap sin (p cos в ■ Al = cx

2.5 ■App

Ap + 709205

sin p cos в ■ Al

- the

resulting force caused by the explosion from the left side of the vehicle onto the side surface of the launcher AL;

Pz = bp ■ Ag - the force of overpressure from the blast wave from

the upper side of the vehicle on the upper surface of the launcher AG;

f - adherence coefficient of the self propelled launcher when it is static or when it is on the move.

The average values of the coefficient are given in Table 1.

2

Based on the balance (equation 1), it follows (Kari & Milinovic, 2008, p.36):

2.5 ■bp.

bp + 709205

sin ç cos Q ■ Al = f ■ Ag + g)

(2)

Table 1 - The average values for the adherence cofficient (Simic, 1988, p.104) Таблица 1 - Средние значения коэффициента сцепления (Simic, 1988, p.104) Табела 1 - Просечне вредности коефицц'ента прц'а^а^а (Simic, 1988, p.104)

Types and conditions of the road Adherence coefficient

Dry Wet

Concrete 2 years old 5 years old, dirty 0.74 0.68 0.71 0.64

Asphalt new old, dirty 0.7-0.8 0.5-0.6 0.25-0.45

Woodblocks 0.6-0.8 0.3-0.5

Fired bricks sand filling asphalt filling 0.7-0.8 0.82-0.89 0.4-0.5 0.60-0.65

Gravel or macadam 0.6-0.7 0.3-0.5

Slag 0.5-0.6 -

Dirt road 0.50-0.65 0.3-0.4

Lawn25—30%on the wet ground 0.20-0.30 -

Snow powder packed 0.20-0.40 0.30-0.50

Ice, flat, glazed (temperature below 0° C) 0.05-0.10

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On the basis of the moment equation (2), we get the condition for the overturning of the launcher onto its side surface during an above ground or surface explosion (Kari & Milinovic, 2008, p.37):

2.5 ■

bp + 709205

sin ç cos Q ■ Al

■Hg-(bPç-AG + G )) = 0 (3)

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The condition of a critical explosion distance that would impair the stability of the rocket inside the launch tube from the side is:

1.2 •■

2.5 • bp„

App +709205

sin p cos 9 • Al - 3gT = 0

(4)

The approximate surfaces for the silhouette of the launcher (Figures 3 and 4), are calculatedfor the BM-21 Grad launcher on the basis of the dimensions given in the tactical-technical characteristics (Jovancic, 2014, pp.80-81). Based on them, the surface on which the overpressure of the blast wave acts has been determined.

Figure 3 - The left side surface of the rocket launcher (Lazarevic, 2017, p.22)

Рис. 3 - РСЗО вид с боку (Lazarevic, 2017, p.22) Слика 3 - Површина бочне стране лансера ракета (Lazarevic, 2017, p.22)

Figure 4 - The surface on the upper side of the rocket launcher (Lazarevic, 2017, p.22) Рис. 4 - РСЗО вид с верху (Lazarevic, 2017, p.22) Слика 4 - Површина горъе стране лансера ракета (Lazarevic, 2017, p.22)

2

The obtained input data are shown in Table 2.

Table 2 - Dimensional characteristics of the vehicle (Lazarevic, 2017, p.23)

Таблица 2 - Размерные характеристики транспортного средства (Lazarevic, 2017,

p.23)

Табела 2 - Димензионе карактеристике возила (Lazarevic, 2017, p.23)

Weight of vehicle T 13700 kq

The explosion effect angle Ф 20°-90°

The explosion effect angle 0 -180°-180°

The side surface of the vehicle Al 13.6 m2

The upper surface of the vehicle Ag 16.8 m2

The rear surface of the vehicle Az 10.1 m2

The height of the action of the pressure center Hq 1.58 m

Vehicle center height ht 1.2 m

Vehicle width B 2 m

Tire width b 0.3 m

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Since this is a squared equation, there are two solutions, out of which one is negative, so during our calculations we will only use the positive values of the blast wave pressure acting on the rocket launcher.

Determining the explosion critical distance

Most of the equations for the calculation of the blast wave and the impulse are based on the TNT equation. Thus, for explosives which are not TNT, it is preferable to know their equivalent mass.

The equivalent mass is calculated with the following equation (Mihelic, 2013, p.18):

E,

M.

J deksp

TNTe

E

M

eksp

(5)

dTNT

where:

MTNTe - equivalent TNT mass [kg];

Edeksp - the energy from the explosive detonation [J/kg];

EdTNT - the energy from the TNT detonation [J/kg];

Meksp - explosive mass [kg].

The calculation of the TNT equivalent is commonly based on the energy released during an explosion. The energy can be determined in many ways. Commonly used methods are based on the hydrodynamic or thermodynamic parameters.

In Table 3, the calculated TNT equivalents are shown for secondary explosives. The results are precise enough to be used for the calculation of the critical distance (Mihelic, 2013, pp.18-19).

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Table 3 - TNT equivalent for secondary explosives (Mihelic, 2013, p.20) Таблица 3 - ТНТэквивалент бризантных снарядов (Mihelic, 2013, p.20) Табела 3 - TNT еквивалент за бризантне експлозиве (Mihelic, 2013, p.20)

TNT equivalent For the range of pressures(MPa)

Pressure Impulse

CompositionB 1.11 0.98 0.035-0.350

Composition C3 1.08 1.01 0.035-0.350

Composition C4 1.37 1.19 0.070-0.700

Octol 72/25 1.06 1.06 -

PETN 1.27 - 0.035-0.700

RDX 1.14 1.09 -

RDX/TNT 60/40 1.14 1.09 0.035-0.350

Tetryl 1.07 - 0.021-0.140

TNT 1.00 1.00 Standard

Tritonal 1.07 0.96 0.035-0.700

In order to make the calculation of equivalent explosive mass in ammunition easier, armies in the world maintain data bases with all necessary data on the amounts of explosives. Such a book is usually called "the yellow book".

The necessary data for the explosive mass equivalent to a 155 mm fragmentation shell is shown in Table 4.

Table 4 - Equivalent mass of explosive for the 155 mm HE shell (Lazarevic, 2016, p.9)

Таблица 4 - Эквивалентная масса взрывчатых веществ фугасного снаряда, калибра 155 мм (Lazarevic, 2016, p.9)

Табела 4 - Еквивалентна маса експлозива за ТФ гранату калибра 155 mm

(Lazarevic, 2016, p.9)

TNT-RDX ТХ

Mass of explosive charge Meksp 8.25 kg

TNT Equivalent Edeksp/EdTNT 1.14

Equivalent mass of explosive MTNTe 9.405 kg

The main characteristics of the blast wave are the overpressure on its front and the time duration of the impulse whose value depends on the type of explosive used, the mass of the explosive and the distance from the explosion. On the basis of the experimental results for spherical blast waves resulting from the detonation of a certain amount of TNT, Sadovsky has suggested an empirical equation for the calculation of the blast wave overpressure in the wave front in the following form (Jeremic, 2002, p.369):

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Ap = k,^- + k2^- + k3^ [or] (6)

r r r

Type Above ground explosion Surface explosion

k1 0.85 1.1

k2 3 4.3

k3 8 14

ф

where: Ë

me - explosive charge mass in kg; г - distance from the center of the explosion in m; к1, k2, k3 - empirical coefficients which depend on the explosive chargetype.

For TNT explosive and other types of medium-strength explosives, ^ empirical coefficients for above ground explosions can be taken from Table 5:

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Table 5 - Coefficients ki, кг кз depending on the type of explosion (Lazarevic, 2017, p. 13) Таблица 5 - Коэффициенты ki, кг кз в зависимости от типа взрыве (Lazarevic, 2017, p.13)

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Табела 5 - Коефицу^енти к1, к2, к3 у зависности од типа експлозще (Lazarevic, 2017, p.13) -q

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In the case of a surface explosion, the blast wave in the air spreads in the form of a half sphere (the volume is cut in half), so the overpressure in this case is bigger. That is when double mass (of the explosive charge mass) is usually used in equation (6).

Since during a surface explosion there is also a deformation of the ground, it is necessary to introduce the coefficient n which depends on the type of ground, so the calculation of the explosive mass in equation (6) is equal to (Kari & Milinovic, 2008, p.33):

mp = 2^me (7)

By introducing the k1y k2, and k3 coefficients of the equivalent explosive mass, the overturn pressure limit and the pressure which can compromise the stability of the launcher into equation 6, it is possible to determine the critical distance for above ground explosions and surface explosions.

The solution of equation (6) is obtained by transforming it into the following form (http://forum.matemanija.com/viewtopic.php?f=2&t=186, 2017):

y3 + py + cx + d = 0 (8)

Where p and q have the following equality:

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p =--v'A 2 (9)

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q =--^-3—^--^ (10)

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W 2 3

=5 D =q- + P- (11)

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With the help of the Cardan equation, we get the solutions which go by y.

' q , m , 3

G yi = 3j - 2+4D+3l-2-4D (12)

LU

So we can get the solution for the third level equation with the oc following form:

k1m3 ,„m

^ = y — tA (13)

3APV

Critical distance in the function of mass

Under the assumption of the launcher overturning onto its side with the help of equation 3, we get the maximum pressure of Apv = 314654 Pa. On the basis of that pressure, the diagram which shows the dependence between the o critical distance and the explosive charge mass is made. The explosive mass is > from 1 to 25 kg. The obtained results are shown in Figure 5.

The influence of fragmentation effects on the launcher

During an explosion of a fragmentation projectile, besides the blast wave effect on the launcher, there is also the fragmentation effect. The fragmentation effect can affect the operation of the launcher system. The fragmentation effect is defined with the kinetic energy of a fragment, because of which a short calculationwill be given further on in the text.

The following fragmentation effect factorsdepend on the HE projectile construction (Stamatovic, 1995, p.152).

- the number, individual weight and shape of fragments;

- the look and direction of the fragmentation dispersion form;

- the range and kinetic energy of fragments.

- Overground explosion

-Surface explosion

1.50 2J00 2.SO 3.00 3S0 4.00 4.50 5-00 550 6.ОС

Critical distance r [mi

Figure 5 - The correlaction between the critical distance and the explosive chargemass

for an above ground and surface explosion (Lazarevic, 2017, p.30) Рис. 5 - Зависимость критического расстояния от массы взрывного заряда, при воздушном и наземном взрыве (Lazarevic, 2017, p.30) Слика 5 - Зависност критичног растоjаша од масе експлозивног пушена, при надземноj и површинсщ експлозир (Lazarevic, 2017, p.30)

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The number, individual mass and shape of fragments

It is usual to evaluate the effect of a projectile on the basis of the following constructional parameters (Stamatovic, 1995, p. 152):

- relative projectile mass given in the following form kp = m/d3;

- relative mass of the explosive charge given in the following form

ke = me/d3;

- charge coefficient k = me/m100 (%);

- projectile shell thickness 5 given in calibers.

If the parameters ke, k and 5 change while caliber stays the same, we will prove that there are optimal values for these parameters with which we get the biggest number of fragments for the given explosive and projectile

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mass within the boundaries set beforehand (Table 6) (Stamatovic, 1995, p.152).

Table 6 - The fragment mass for the 150 mm HE projectile (Stamatovic, 1995, p.156) Таблица 6 - Масса фрагментов осколочно-фугасного снаряда 155 мм (Stamatovic, 1995, p.156) Табела 6 - Маса парчади тренутнофугасног проjектила 155 mm (Stamatovic, 1995, p.156)

Explosive and mass (kg) Number of fragments

Case production up to 5 g from 1.5 to 100 g over 100 g total

Warm forging TX/8.25 185 251 14 327

Casting TX/8.25 1969 1596 1 2263

The look and direction of the fragmentation dispersion form

The usual shape of the inside of a projectile case (Figure 6) produces three beams during an explosion and the case destruction (Stamatovic, 1995, pp.159-161):

- the beam formed from the front, oval part (around 10%);

- the side beam of the case cylinder part (around 70%);

- the rear beam formed from the case bottom (20%).

Figure 6 - The directions of fragment dispersion (Stamatovic, 1995, p.161) Рис. 6 - Направления разлета осколков снаряда (Stamatovic, 1995, p.161) Слика 6 - Правци разлеташа парчади (Stamatovic, 1995, p.161)

The kinetic energy of fragments

The velocity of fragments on the path x decrease under the effect of wind resistance, which can be shown with the following equation (Stamatovic, 1995, pp.169-172):

1 2

Fw = - CxSpwVp (14)

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We can also adopt that with an explosion in the close proximity of the launcher there are only side beams, i.e. only 70% of the total number ^ of fragments. Also, projectile fragments lighter than 5 grams donot have a significant effect on the launcher, thus they will not be taken into consideration.

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where: i

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Cx - the coefficient of the aerodynamic resistance of the fragment of o a mass of mp;

S - the biggest fragment cross section normal to the direction of movement;

pw- air density; jg

Vp - fragmentation velocityat the end of the pathx.

As mpVpdVp = F„dx, it is obtained:

1 S

dVp =- Cx——Vpdx (15)

p 2 x mp p

By adopting that the aerodynamic resistance coefficients = constfor supersonic speeds (for subsonic and transsonic speedsCxisnot constant) and with the integration of the last equation, we get:

2"Cx— Pwx

Vp = Vp0e2 mp (16)

where:

V^ - resulting initial velocity of the fragment; Vp - the velocity of a fragment at the end of the pathx. The fragment with the mass mp possesses kinetic energy, if, when hitting the target, it has the velocity Vpmin obtained from the following relation:

a> m V

= E (17)

2

8 The kinetic energy of the fragment with the mass mp is obtained if we

° put equation (17) into equation (16):

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E = —^-J— . (18)

2

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1 on the launcher. uj This model is a rough approximation of the real system. For more >- reliable models, we need to do experimental testing inside a ditch or

depression and to de radar, which is costly.

Overview of the results

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« The condition for the overturn of the launcher

Under the assumption that the equivalent explosive mass during an above ground detonation is constant, i.e. 9.405 kg (equation 5), the critical distances for overturning are calculated for the independent variables y and Q, which are between 20 - 90 and -180 to 180,

9 respectively. The obtained results are shown in Figure 7.

2

Figure 7 - Critical distance of launcher overturn in the function of p and 9 for an above ground explosion (Lazarevic, 2017, p.37)

Рис. 7 - Критическое расстояние опрокидывания РСЗО в функции ри 9 при воздушных взрывах (Lazarevic, 2017, p.37)

Слика 7 - Критично расто]а^е преврта^а лансера у функции ф и 9 при надземноj експлозии (Lazarevic, 2017, p.37)

Having in mind that the equivalent explosive mass during a surface explosion is two times bigger because of the half spherical spread of the blast wave, multiplied with the coefficient of the ground, we get an explosive mass of 14.108 kg (equation 7). On the basis of the mass and critical distance of overturn (equations 3 and 7), the critical distances of overturn have been calculated for the independent variables ф and 9, which are in the range between 90-20 and -70 to 70, respectively. The obtained results are shown in Figure 8.

Figure 8 - Critical distance of launcher overturn in the function of qp and 9 for a surface explosion (Lazarevic, 2017, p.38) Рис. 8 - Критическое расстояние опрокидывания РСЗО в функции qp

и 9 при наземных взрывах (Lazarevic, 2017, p.38) Слика 8 - Критично pacmoja^e преврта^а лансера у функции ф и 9 при површинсщ експлозии (Lazarevic, 20l 7, p.38)

The condition forcompromising the stability of the projectile inside the launcher tube

With a process similar to the one for overturning during an above ground explosion, we calculated the critical distance of compromising the stability of a projectile inside the launcher. With equations (4) and (5), we

Figure 9 - Critical distance of compromising the projectile stability in the function of p and 9 for an above ground explosion (Lazarevic, 2017, p.39) Рис. 9 - Критическое расстояние нарушения надежного удержания ракеты в

функции ри 9 при воздушных взрывах (Lazarevic, 2017, p.39) Слика 9 - Критично расто]аше нарушаваша поузданог држаша ракете у функци]и ф и 9 при надземноj експлозии (Lazarevic, 2017, p.39)

Having in mind that the equivalent explosive mass during a suface explosion is two times bigger because of the spread of the blast wave multiplied with the ground coefficient, we get an explosive mass of 14.108 kg (equation 7).

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For a surface explosion, the critical distances for compromising the projectile stability inside the launcher are calculated. With equations (4) and (7), we get the critical distances for the independent variables q> and Q, which are in the range from 90-20 and -80 to 80, respectively. The obtained results are shown in Figure 10.

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Figure 10 - Critical distance of compromising the projectile stability in the function of ф and 9 for a surface explosion (Lazarevic, 2017, p.40) Рис. 10 - Критическое расстояние нарушения надежного удержания ракеты в функции фи 9при наземных взрывах (Lazarevic, 2017, p.40) Слика 10 - Критично расто^аъе нарушаваша поузданог држаша ракете у функци]и ф и 9 при површинсщ експлозии (Lazarevic, 2017, p.40)

Conclusion

This mathematical model is a rough approximation of the real situation. To further develop the model, it is required to take into account the launcher suspensionand the launcher oscillations.

The analysis of the results has shown that during an above ground explosion the minimum distance to avoid the overturning of the BM21 Grad launcher iz 3.6 meters and it is 4.71 meters for a surface explosion (Figures 7 and 8).

As an addendum to the paper, the critical distance of the explosion during which the projectile stability would be compromised inside the launcher tube is also calculated. The stability of the projectile inside the launcher tube is defined with a maximum force of 3g.

The analysis of the results has shown that, in an above ground explosion, the minimum distance at which the projectile stability inside the launch tube would not be compromised is 6.42 meters and it is 8.41 meters when an explosion is a surface one (Figures 9 and 10).

A rough approximation of the fragmentation effect of the projectile on the launcher was done.

In order to get reliable data, it is necessary to carry out a series of tests run on a testing field on the given launcher.

References

http://forum.matemanija.com/viewtopic.php?f=2&t=186. Accessed: 07.06.2017.

Jeremic, R., 2002. Eksplozivni procesi. Belgrade: GS VJ, Uprava za SiO VA (in Serbian).

Jovancic, S., 2014. Samohodna visecevna raketna artiljerija. Belgrade: Vojnotehnicki institut (in Serbian).

Kari, A. & Milinovic, M., 2008. Borbeno opterecenje visecevnog lansera usled dejstva udarnog talasa.Vojnotehnicki glasnik/Military Technical Courier, 56(1), pp.3141. Available at: http://dx.doi.org/10.5937/vojtehg0801031 K (in Serbian).

Kari, A., 2007. Poboljsanje performansi lansiranja i gadanja kod samohodnih visecevnih bacaca raketa upotrebom posebnih mehanizama oslanjanja, Master thesis, University of Belgrade, Faculty of Mechanical Engineering (in Serbian).

Lazarevic, M., 2016. Odredivanje konstrukcionih parametara projektila 155 mm RM15P5, Seminar work, University of Kragujevac, Faculty of Engineering (in Serbian).

Lazarevic, M., 2017. Borbena zilavost lansirnog sistema, Master Thesis, University of Kragujevac, Faculty of Engineering (in Serbian).

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ф Mihelic, B., 2013. Prilog formulama koje se koriste u upravljanju municijom.

Kragujevac (in Serbian).

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E БОЕВАЯ УСТОЙЧИВОСТЬ РСЗО

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0 Милош С. Лазаревич Университет в г.Крагуевац, Факультет инженерных наук, г. Крагуевац,

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1 ОБЛАСТЬ: машиностроение ш ВИД СТАТЬИ: оригинальная научная статья ^ ЯЗЫК СТАТЬИ: английский о:

¡5 Резюме:

В данной работе приведены систематизация и анализ предельной нагрузки многоствольной ракетной пусковой установки. Исходя из анализа нагрузки, разработана механико-математическая модель w устойчивости РСЗО, пораженной ОФ снарядом. На основании

С W

_i полученных результатов выявлена зависимость устойчивости

^ пусковой установки от диапазона взрыва, типа взрыва и массы

>о взрывного заряда. Главным условием боевой устойчивости РСЗО

является разработка мер по предотвращению опрокидывания ш РСЗО и нарушения надежного держания ракеты в пусковой трубе.

¡5 В целях упрощения данной модели произведен расчет

кинетической энергии воздействия осколков на ракетную пусковую о установку.

Ключевые слова: нагрузка, действие взрыва, наземные взрывы, воздушные взрывы, условия, критическое давление, критическое расстояние, опрокидывание, устойчивость, кинетическая энергия.

БОРБЕНА ЖИЛАВОСТ ЛАНСИРНОГ СИСТЕМА

Милош С. Лазаревич

Универзитет у Крагу]евцу, Факултет инженерских наука, Крагу]евац, Република Срби]а

ОБЛАСТ: машинство

ВРСТА ЧЛАНКА: оригинални научни чланак JЕЗИК ЧЛАНКА: енглески

со CM CD

О CD

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Сажетак:

У оквиру овог рада извршена je систематизац^а и анализа могучих оптереЯеъа вишецевних лансера ракета. На основу анализе оптереЯеъа изранен je математичко-механички модел ^ стабилности вишецевног лансера ракета пого/еног у нeпосрeдноj [= близини тренутно-фугасним проjeктилом. Доб^ени резултати ,р указу/у на зависност стабилности лансера од удаъености експлоз^е, типа експлози'е и масе експлозивног пуъеъа. Као гранични услов борбене жилавости лансера усвоjeн je услов ^ почетног превртаъа лансера и нарушаваъа поузданог држаъа Ц ракете у лансирноj цеви. Ради упрошЯаваъа приказаног модела извршен je прорачун кинетичке енерг^е ефикасног парчета ще делу/е на лансер.

Къучне речи: оптереЯеъе, дejство експлоз^е, површинска експлоз^а, надземна експлоз^а, услови, критичан притисак, критично растоjаfoe, превртаъе, стабилност, кинетичка т енерг^а.

о О

Paper received on / Дата получения работы / Датум приема чланка: 02.08.2017. Manuscript corrections submitted on / Дата получения исправленной версии работы / Датум достав^а^а исправки рукописа: 12.08.2017. ^

Paper accepted for publishingon / Дата окончательного согласования работы / Датум £ коначног прихвата^а чланка за об]ав^ива^е: 14.08.2017. n

a

© 2017 The Author. Published by Vojnotehnicki glasnik / Military Technical Courier (www.vtg.mod.gov.rs, втг.мо.упр.срб). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/rs/).

© 2017 Автор. Опубликовано в «Военно-технический вестник / Vojnotehnickiglasnik / Military Technical Courier» (www.vtg.mod.gov.rs, втг.мо.упр.срб). Данная статья в открытом доступе и распространяется в соответствии с лицензией «CreativeCommons» (http://creativecommons.org/licenses/by/3.0/rs/).

© 2017 Аутор. Обjавио Воjнотехнички гласник / Vojnotehnicki glasnik / Military Technical Courier (www.vtg.mod.gov.rs, втг.мо.упр.срб). Ово jе чланак отвореног приступа и дистрибуира се у складу са Creative Commons лиценцом (http://creativecommons.org/licenses/by/3.0/rs/).

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