Modeling, simulation, and evaluation of HE ammunition for counter ...

Modeling, simulation, and evaluation of HE ammunition for counter-RAM systems Markus Graswald and Hendrik Rothe Helmut-Schmidt-University / University of the Federal Armed Forces Hamburg Institute of Automation Engineering Holstenhofweg 85, D-22043 Hamburg, Germany ABSTRACT Military camps in out-of-area missions are permanently threatened by rockets, artillery projectiles, and mortar grenades (RAM) launched by terrorists. A good portion of these attacks are undertaken by mortars due to their specific advantages for the warfare of irregular forces and their worldwide distribution. The military installations can be protected by counter-RAM systems consisting of several artillery weapons, radar and electro-optical sensors, C2 and fire control computers. A system analysis has shown that the precision of the sensors is vital for defending the camp with low ammunition consumptions. Furthermore, the type of ammunition is also of great impact: 35 mm Ahead ammunition is hardly suited for this application due to its small hit density and low kinetic energy of the sub-projectiles, especially in the case of mortar grenades. Therefore, 155 mm high-explosive (HE) ammunition is investigated using experimentally determined fragment data. Russian mortar projectiles are considered as worst-case RAM targets and their ballistics are mathematically modeled by an air drag function that is also used for computing firing tables. Due to uncertainties of the target positions that are given by an elliptic cylinder for specific sensor parameters, simulations are conducted in order to determine the ammunition consumption. Penetration and detonation criteria for the terminal impact are also considered and the resulting thresholds are displayed in a 3D fragment map. The results show that HE ammunition is superior to low-caliber ammunition because of their high numbers of effective fragments reducing the number of rounds significantly from hundreds to less than ten. Keywords: rockets artillery mortar (RAM), modeling and simulation, terminal ballistics, probability calculation, error propagation, ammunition consumption, radar sensor

1. INTRODUCTION Especially in Afghanistan, unguided rockets, artillery, and mortar projectiles (RAM) are a severe and dangerous threat for stationary military installations of the Western alliance. Potential targets of the irregular forces are field camps and air bases providing a high media coverage after attacks. In the recent past, successful engagements with mortar projectiles produced heavy damages. For a number of good reasons, the focus of the paper lies on mortar projectiles as RAM threat: firstly, mortars were produced in large quantities by several countries of the former Eastern block and emerging markets providing easy access to potential attackers. Secondly, they are well suited for the asymmetric warfare. And thirdly, mortar projectiles are hard to combat due to their small size (and radar cross section), short firing distances and flight times, and thick cases made of steel or cast-iron. From the authors point of view, they are rated as a worst-case target due to the aspects of detection and destruction. The following applications have been investigated in detail facing the RAM threat adequately, see.1 On the one hand, there is a passive early warning system alerting soldiers dependent on the predicted hit point. This system also allows classification of mortar projectiles and determination of the firing location that can be combatted afterwards. On the other hand, there is an active counter-RAM (C-RAM) system detecting, tracking, intercepting, and destructing (or deflecting) approaching RAM targets. The mathematical models introduced can Further author information: (Send correspondence to Markus Graswald) E-mail: [email protected], Telephone: +49 40 6541-3351 Modeling and Simulation for Military Operations III, edited by Dawn A. Trevisani Proc. of SPIE Vol. 6965, 69650G, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.777054

Proc. of SPIE Vol. 6965 69650G-1 2008 SPIE Digital Library -- Subscriber Archive Copy

be used to evaluate sensors or ammunition appointed for these systems, while low-caliber intercept ammunition was explicitly examined as an example. This paper concentrates on C-RAM systems using high-caliber HE ammunition as intercept projectiles and therefore extends the model given in.1 Section 2 introduces theoretical models of the intercept projectile’s motion and the dynamic fragment cone. The error budget of the system is examined in the next section with focus on the range errors of the radar sensor and the most germane errors depending on the effector or intercept ammunition. The theoretical part is succeeded by Sec. 4 providing simulation results of the ammunition consumption as well as the warhead mechanisms of fragment impact and blast. The conclusion in Sec. 5 and the simulation scenario in App. A finishes this paper.

2. THEORETICAL MODELING 2.1 Equations of Motion The mortar projectiles considered are arrow-stabilized and fired on short distances up to approximately 8 km. Therefore, the 2-DOF equations of motion treat the projectile as point mass with gravitation and air drag as external forces. Consequentially, the system of differential equations in a path-dependent form for a right-handed frame of reference is as follows1 dvx = −c2 (M a) v(x) , dx g dp =− , p
= dx vx (x)2 dy y
= = p(x) , dx 1 dt = , t
= dx vx (x)

vx
=

(1a) (1b) (1c) (1d)


where p = tan θ = vy /vx , v = vx 1 + p2 , vx is the x-component of velocity vector, vy is the y-component of velocity vector, g is the acceleration due to gravity, t is the computed time of flight, θ is the quadrant elevation, c2 (M a) is the coefficient of air drag depending on Mach’s number. The drag coefficient c2 consists of a velocity depending part modeled by an experimentally determined reference function (that is also used for computing Russian firing tables), a part depending on the atmosphere considered as constant, and a term that depends on the projectile itself called ballistic coefficient.

2.2 Fragment Cone This section describes the fragment cone model that uses fragment data experimentally determined by arena tests. At detonation time, the center of mass of the intercept projectile is located in the center of the space-fixed (inertial) reference system as shown in Fig. 1. The model relies on the following assumptions: • The fragment source is punctiform. • Due to the projectile symmetry, fragment numbers and masses are distributed isotropically in the radial direction within a strip of the departure angle. • The fragment shape is neglected.

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YI

. ...... . ........................................ .... .... ........... . . . ........ ... .... . ....... . . ...... ... ... . ... . . ..... . . . . . . . ... . . .. .. ... ... . . ................. dθ . . .................... . ... . .... ... .. .. ... .................................... ... ... .............. . . dϕ ..... ........ . . . . ... . . ............. ... ........ ........ .. .. ..... dΩ ... . ..... ............................. .... ........ .... ....................... .... ..... ............................ .... ... . .......... .. ............. . .. .. ... ................................... . ... v f,dyn .. ................... ....... ......................................... ... . ... . . . . . . . . . . . . . ... .. . . . . . . . . ................... .......... ...... ... ..... . ...... ..................... ................... .... ......... .. . . . . . . r ... ... . ...ϕ .. ...... ... . .. ......................................... ... . . .. . .......... .................... .. . . ....... . .... ... ......................................................................................................................−θ . ........................................................... XI ................................. . .... .. . . . .. .. c.m. v G ... .... ... ... ... .... .... . . . . . . . .... . . . . . . .. .. . ... ..... ... .. ....... ...... .. .. .. . . . .... . .. ...... .. . .............. ... . .. ........... ... ......... ... .... ............. . . . . . . . . . . . . . . ................. ................................................................ ........ ZI Figure 1. Geometry of the fragment cone with the intercept projectile at time of detonation.

2.2.1 Static Distribution of Fragments The matrix for the fragment numbers is given by ⎤ ⎡ nf12 · · · nf1l ⎢ .. ⎥ , i = 1..N , l = 2..N , .. nf = ⎣ ... θ m . . ⎦ nfi2 · · · nfil

(2)

where i indicates the strip of the angle of departure in the horizontal plane θ and l indexes the mass class m (the mass class consisting of fragment grit only is not considered). Representative fragments representing all fragments of a certain departure angle strip and mass class are characterized by an average angle of departure and an average mass 1 θ¯i = θi + (θi − θi−1 ) ∧ 2 < i < 17∗ , 2 mfi,l . m ¯ fi,l = nfi,l

(3) (4)

The initial fragment velocities at detonation time are calculated by measured mean maximum fragment velocities of their according strips2 eCi,l − 1 vf,stati,l = v¯Pi , (5) Ci,l where 1 ρL cD Afl ri , Ci,l = 2 1000 m ¯ fi,l (1+b)

¯ fi,l Afl = a m

,

and v¯Pi is the average maximum velocity of a representative fragment, ri is the fragment’s flight distance, m ¯ is the average fragment mass ([m] = g), ρL is the air density, cD is the drag coefficient of natural fragments (dependent on Mach number), Afl is the (virtual) projected frontal area of the fragment (dependent on the material; [A] = mm2 ), a, b are constant values for calculating (virtual) projected frontal area. ∗¯ θ1

= 0◦ , θ¯18 = 180◦ .

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2.2.2 Dynamic Distribution Dynamic fragment data for every departure angle (strip) and mass class is determined by static data, the relative velocity of the intercept projectile and mortar target, and air drag. Considering only air drag as an external force, the fragment trajectories are given by straight lines. The fragment cone opened in the direction of projectile motion depends on the relative velocity vrel , the initial fragment velocity vf,stat and the angle of departure θ. Assuming that the projectile moves in the positive direction of XI , the velocity vector of a fragment in the XI -ZI -plane is given by ⎤ ⎡ ⎤ ⎡ cos θi vrel ⎦, 0 (6) v f,dyni,l = ⎣ 0 ⎦ + vf,stati,l ⎣ 0 − sin θi and its absolute value |v f,dyni,l | =

 2 + v2 vrel f,stati,l + 2 vrel vf,stati,l cos θi ,

where vrel = vG +vM : vG is the velocity of the intercept projectile and vM is the velocity of the mortar projectile. Furthermore, the angle of departure changes in the dynamic case (vrel = 0)

−vf,stati,l sin θi . (7) θdyni,l = arctan vrel + vf,stati,l cos θi The maximum (half the amount of the) opening angle of the fragment cone βmax is calculated as βmax = max(θ dyn ) .

(8)

The (absolute amount of the) fragment velocity is reduced with increasing flight distances due to drag2 vri,l =

1 Ci,l (tE − t0 ) +

,

(9)

log vri,l − log |v f,dyni,l | . Ci,l

(10)

1 |v f,dyni,l |

This leads to the flight distance in the interval [t0 , tE ] rfi,l = −

2.3 Ammunition Consumption The normally distributed hit probability of a single fragment is both calculated in the plane of the mortar projectile’s symmetric axis and the plane normal to this axis. The destruction probability pK|H is calculated by an exponential function of a fraction consisting of a minimum energy and the internal energy provided through a rigid body impact of a fragment with the target. Finally, the kill probability of a single fragment pK is the product of these three probabilities. Calculating the kill probability of Nw effective fragments hitting the target area, it is assumed that the base area of the fragment cone equals the area of the radar’s circular error probability (CEP) at the target location. This leads to the multi-shot kill probability and the desired number of rounds NS to destroy the target at a given confidence level P 1  1 NS (P ) = . (11) 1 − (1 − pK )Nw (P ) Despite determining the number of effective fragments by empirical equations providing penetration and detonation thresholds (see Section 4.2), the destruction probability is still applied. This leads to a more conservative estimation of the ammunition consumption.

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Overall system

Dependent on effec- Sensor tor or ammunition dependent

Variations

Result

• Azimuth • Elevation • Range (time) • Time for developing the shot • Muzzle velocity • Ballistic dispersion • Detonation time • Time for developing the fragment cone

Number of rounds (C. L.)

Figure 2. Overview of relevant parts of the error budget.

3. ERROR BUDGET Figure 2 shows the relevant components of the error budget of a C-RAM system consisting of an artillery weapon (e.g., Tank Howitzer 2000 (PzH 2000) or Artillery Gun Module (AGM)) and the radar sensor. All relevant statistical spreads are given influencing the kill probabilities and the ammunition consumption of the overall system. Since the main focus lies on comparing different C-RAM systems, other major error sources affecting the hit probability like the firing position, propellant temperatures, air density, and wind are not considered. For convenience, errors are divided depending on their source: the sensor or effector and ammunition respectively. The requirements on the errors of the azimuth and elevation measurements are already given in.1 Therefore, this section concentrates on the deviations of the range measurements and on the effector and ammunition dependent deviations. Stating the statistical significance of the estimated ammunition consumption, the confidence level (C. L.) is given. With an increased confidence level the probability of errors is reduced presuming the assumptions are correct and the mathematical model reproduces the reality with sufficient accuracy.

3.1 Range Measuring This section determines how accurate the range measurements have to be for achieving a certain ammunition consumption. 3.1.1 Estimation of fragment numbers Considering the probable location of a RAM target given by radar measurements, the number of fragments is determined geometrically by best-case and worst-case considerations. Therefore, given a probability P it is assumed that the RAM target is located in an elliptic cylinder with length 2 u1−α/2 σR and elliptical base areas with semi-major axis u1−α/2 σαR and semi-minor axis u1−α/2 σεR † , see Fig. 3. Assuming σα = σε , the probable target location is limited by a circular cylinder. Assuming that the intercept projectile is fired in direction of the radar beam‡ , the height of the fragment cone and hence the virtual detonation point§ is determined by the forward base area Av . In the following, the fragment density and the number of effective fragments against the target area AT are determined as best-case values. However, the target can be located on the other side of the cylinder (in area Ah ) leading to worst-case values for the fragment density and number of effective fragments. These assumptions are made for the following calculations: †

The radar range R is used to convert the angular errors of azimuth and elevation in range errors. Symbols with index l. § Basically, the virtual and real detonation point differ by the fragment cone developing time being primarily a function of the detonation velocity and the projectile geometry. ‡

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Y

AT

bmax usR X

use usa

Virtual detonation point

Ah Av

Radar beam

Z

Figure 3. Geometry of the fragment cone with an elliptic cylinder (dashed line) marking the limits of the probable radar location of the RAM target.

• The RAM target is located within a circular cylinder, i.e., standard deviations of azimuth and elevation are equal (σα = σε ). • The effective fragments located in area Av are effective in area Ah as well. • The projected area of the target AT is given by the circular caliber area. By geometry, the forward and rear area of the cylinder Av and Ah are given by¶ Avl = π (u σαR )2 ,

(12a) 2

Ahl = π (hK,hl tan βmax ) ,

(12b)

where βmax is (half of) the fragment cone angle and the height is u σαR hK,vl = , tan βmax hK,hl = hK,vl + 2 u σR . The desired numbers of effective fragments hitting the target area AT =

N

(13a) (13b) π 4

d2M

is

Nw,vl = ρf,vl AT ,

(14a)

Nw,hl = ρf,hl AT ,

(14b)

N

where fragment densities ρf,vl = Avf and ρf,hl = Ahf are determined by the number of effective fragments Nf l l and Eq. (12). The ratio of rear to forward area being also true for the fragment densities is given by Zl =

Ahl ρf,vl = . Avl ρf,hl

(15)

Below, the case of combatting the RAM target by an intercept projectile fired transverse to the radar beam and thus the symmetric axis of the cylinder is considered under the same assumptions . Substituting σαR with the ¶ 

Quantiles of the normal distribution u1−α/2 are abbreviated by u. Symbols with index q.

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standard deviation of the range σR and vice versa, Eq. (12) and (13) can be easily adapted Avq = π (u σR )2 ,

(16a) 2

Ahq = π (hK,hq tan βmax ) ,

(16b)

and u σR , tan βmax = hK,vq + 2 u σαR .

hK,vq =

(17a)

hK,hq

(17b)

The number of effective fragments Nw,vq and Nw,hq as well as the ratio Zq can be calculated by applying Eq. (14) and (15) with Eq. (16) accordingly. 3.1.2 Estimation of the radar range error The section aims at determining the order of magnitude of the standard deviation of the range measurements σR in order to provide an adequate fragment density valid in the entire fragment cone, i.e., especially in the rear area of the target cylinder. Combatting the target in the direction of the radar beam, the according equations of the previous section are introduced in Eq. (17b) and resolved for σR  N f AT 1 tan βmax Nw,hl π − hK,vl . (18) σRl = 2u In the case of firing transverse to the beam direction, σR is determined by Eq. (16a) resolved for the desired parameter

Nf AT 1 . (19) σRq = u Nw,vq π Furthermore, the number of effective fragments hitting the rear cylinder area is of interest. It is calculated by equations given in the second part of the previous section Nw,hq =



Nf AT

πu2 σRq + 2σα tan βmax

2 .

(20)

3.1.3 Examples HE ammunition of 155 mm caliber and an arbitrary fire-control radar is used to combat a Russian 82 mm mortar projectile (Nf = 8000, βmax = 79◦ , σα(R=1000 m) = 0.5 m, σR = 8.2 m). The confidence level being the probability that the target is located within the circular cylinder is given with P = 50% (u = 0.6745). The results of Tab. 1 clearly show for pK = 1.57% = constant (in reality, pK is reduced with increasing distance due to the air drag) that a destruction is practically impossible if the target is located on the rear side of the cylinder in the case of firing in the beam direction (NS > 15, 000). In the other case, 0.44 effective fragments are even on the forward area too little resulting in an unacceptable ammunition consumption of 145 rounds. Therefore, the standard deviation in range is too large and the following calculations shall provide thresholds for this error so that the ammunition consumption is acceptable. Determining the desired standard deviation σR , the calculations use the same data that has been already given, while parameter Nw is varied. The results are compiled in Tab. 2 (firing in direction of beam) and Tab. 3 (firing transverse to beam) respectively. The evaluation leads to the following conclusions: • Realizing ammunition consumptions NS  50, the range error of the radar sensor must be at least in the order of magnitude of the azimuth error (at 1000 m radar distance). Ideally, it is essential: σR  σα(R=1000 m) .

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Table 1. Estimation results for the numbers of effective fragments. in beam direction transverse to b. d. index v index h index v index h 2 A in m 0.36 10,295.15 96.10 254.55 Z 28,805.7 2.6 hK in m 0.07 11.13 1.08 1.75 ρf in 1/m2 22,389.1 0.8 83.2 31.4 Nw 118.24 0.004 0.44 0.17 NS 2 15,421 145 382 Table 2. Range error depending on the number of fragments in Ahl . Nw,hl σRl in m pK,hl in % ∗∗ NS,hl ∗∗ 1 0.48 7.9 13 5 0.19 8.1 3 10 0.12 8.2 2 50 0.03 8.2 2 100 0.004 8.2 2

• For standard deviations of σR < 12 cm, two rounds are only necessary for combatting a target located somewhere in the circular cylinder (firing in beam direction). • Firing transverse to the radar beam direction, an one-digit ammunition consumption is not realistic due to Nw,hq  1. Therefore, the angle between radar beam and firing direction is supposed to be small, i.e., the radar is placed near by the effector.

3.2 Errors Depending on Effector or Ammunition The standard deviations that are dependent on the effector or ammunition are arranged in temporal order of their occurrence. The ballistic dispersion affect the accuracy of fire in the plane normal to the firing direction, while the other errors move the detonation point along the trajectory. In the case of a programmable fuze, the deviations of the time for developing the shot and the muzzle velocity can be neglected by using a muzzle velocity radar and programming the fuze afterwards. In detail, these errors are considered: 1. Time for developing the shot: This time consists of the time span between the discharge impulse and the time the projectile exits the barrel and should be determined experimentally. Since it influences the detonation point, its deviation should be small and constant. 2. Muzzle velocity: Determining the impact of the muzzle velocity variation on the detonation point on a temporal basis, its standard deviation is used to calculate N = 1000 trajectories. Their times of flight at a combat distance of 1000 m give the desired standard deviation. 3. Ballistic dispersion: The standard deviation of the ballistic dispersion results from manufacturingrelated tolerances of the weapon and the ammunition and also consists of the weapon’s aiming accuracy. These variations affect the accuracy of fire. ∗∗

Determined by a statistical approach introduced in.1 Table 3. Range error and number of fragments firing transverse to the radar beam. Nw,vq σRq in m pK in % ∗∗ NS,vq ∗∗ Nw,hq NS,hq ∗∗ 1 5.44 2.3 44 0.26 162 5 2.43 4.5 5 0.52 43 10 1.72 5.6 3 0.63 29 50 0.77 7.4 2 0.85 16 100 0.54 7.8 2 0.91 15 500 0.24 8.1 1 1.02 13

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50 50% C. L. 90% C. L. 99% C. L.

14

50% C. L. 90% C. L. 99% C. L.

12

40 35 90° attack 30 0° attack 25 20 15

Number of rounds

Single-shot kill probability in %

45

10 8 6 4

10 2

5 0

1500

2000

2500

1500

2000

2500

Intercept range in m

Intercept range in m

Figure 4. Kill probabilities (left) and ammunition consumptions (0◦ attack, right) combatting an 82 mm mortar projectile O-832 with 155 mm HE.

4. Detonation time: The deviation of the detonation time is caused by the fuze and depends on the measuring system and the initiation law. 5. Time for developing the fragment cone: This time is defined as a period between the time of fuze initiation and the time that first fragments reach the forward area of the elliptic cylinder containing the RAM target with probability P (see Fig. 3). Assuming a steady-state detonation, it is a function of the length of the energetic material, the detonation velocity, and the fragment characteristics for a certain probability P . The standard velocity is estimated as a portion of this period.

4. SIMULATION RESULTS This sections discusses results of ammunition consumptions and fragment response plots for Russian 82 mm mortar projectiles intercepted by HE ammunition of 155 mm caliber. The setting can be found in App. A.

4.1 Ammunition Consumption The results of this subsection are derived for the setting of the field camp taking the complete error budget of the effector, intercept projectile, and radar sensor into consideration as discussed in Sec. 3. Aiming at quite conservative results, the target velocity vM is neglected and the fragment cone consists of Nw = 7, 857 effective fragments and an opening angle of βmax = 80◦ . Figure 4 (left) shows kill probabilities of single intercept shots for different intercept ranges, attack directions, and three confident levels. The kill probabilities are declined for increasing intercept ranges due to the lower fragment hit densities and the number of effective fragments. This is also true for the attack directions, since the flight distances are longer in the 0◦ -case reducing the velocity of the projectile at intercept and hence the impact velocities of the fragments. The ammunition consumption is determined by the kill probabilities and valid throughout the entire target cylinder. This worst-case value is calculated with a mortar projectile located at the rear base area of the cylinder, see Fig. 4. In the best case (mortar projectile at forward area), the maximum ammunition consumption is two shots through 99% C. L. Therefore, the objective is to significantly reduce the parts of the error budget contributing to the variation of the detonation position (time for developing the shot, muzzle velocity, detonation time), e.g., by using programmable fuzes. This may also lower the uncertainties of the target trajectory prediction.

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Table 4. Effectiveness of fragments dependent on the initial relative velocity vrel at time of detonation and the fragment’s time of flight tE − t0 |rfmax | Ndet Ndet vrel in m in A.U. tE in ms (de > dcr ) (de < dcr ) Npen Nni βmax in ◦ 0.32 1.0 23 3313 6402 14314 2.2 77 3.0 23 3255 3215 17558 6.2 77 0.36 1.0 24 3328 6415 14284 2.2 73 3.0 23 3254 3463 17310 6.4 73 0.40 1.0 26 3762 7427 12836 2.2 71 3.0 26 3326 3396 17303 6.5 71

4.2 Fragment Impact and Blast This section discusses simulation results of the fragment impact and blast effect as the most significant warhead mechanisms of HE projectiles. The theory applied here to obtain the following results is presented extensively in.3 Supplementing the data of the intercept and target ammunition in App. A, the fragment impact is determined for a given relative velocity (incorporating the velocities of the intercept and target projectile and fragments) and flight time of the fragments. The impact angle is assumed to be 0◦ (NATO). Examples of the results are displayed in Fig. 5 and Tab. 4. 4.2.1 Hazard Assessment Plot The fragment map shows fragments with their impact velocity (= vrel at detonation time) and logarithmically scaled average masses. The diameter of the circle represents fragment numbers. The lines of the response plot stand for different thresholds: the penetration threshold usually called ballistic limit (B. L.) marks velocity-mass-combinations for penetration, i.e., fragments above this line can penetrate the projectile shell with a probability of 50%. The other lines represent the detonation threshold: fragments exceeding it may cause a prompt detonation. The second detonation criterion consists of the special case of small but fast fragments resulting in high numbers of effective fragments. In future, the theoretical thresholds require experimental verification, especially the special detonation threshold. 4.2.2 Areas of the response plot The following areas result from the threshold lines containing fragments with different impacts against the mortar projectile: 1. Low impact: Nni fragments located below B. L. have supposably no impact when hitting the target. 2. BVR: In the Burn-to-Violent Reactions (BVR) area, Npen + Ndet (de > dcr ) fragments are able to penetrate the shell. Consecutive reactions are very hard to predict due to the multitude of factors influencing them. They can range from perforation to combustion or deflagration. 3. Detonation: In the part of the response plot laying above the detonation thresholds, the impact of a fragment onto the case leads to a shock wave attenuated by the case. If the pressure and diameter of the shock wave are sufficient, the energetic material is activated and the mortar projectile detonates. The standard criterion (supplementary diameter of fragment hitting the shell de exceeds the critical diameter of the explosive dcr ) provides only a few appropriate fragments Ndet , while the special case (de > dcr ) some thousands. These fragments are located in the BVR zone (see Fig. 5). 4.2.3 Blast Effect The effect of blast waves always occurring with detonations is investigated by empirical equations and applied to the intercept of mortar with HE projectiles. The results show a threshold of approx. 60 cm to deflect an 82 mm mortar projectile from its current trajectory at an angle of 20◦ . Hence, the blast effect can positively result in a deflection so that the threat is not dangerous for the attacked installation anymore. A negative result of the blast is that target trajectory data becomes obsolete delaying further intercepts planned.

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1 B. L. SDT: de < dcr

1000

SDT: d > d e

500 100 10

cr

0.01

i

m in A.U.

0.1

0.001

0.0001 0

0.2

0.4

0.6

0.8

1

V in A.U. i

Figure 5. Classified fragment response plot for tE = 1.0 ms , vrel = 0.36 A.U.

5. CONCLUSION The paper introduces a method for evaluating sensor, effector, and ammunition requirements for counter-RAM systems focussing at mortar projectiles as asymmetric threat. The C-RAM system is intended to enhance the safety of military installations in an active and sustained way. The model combines physical methods with a statistical approach and aims at determining the number of rounds at a given confidence level. This ammunition consumption is considered as the key parameter in comparing the performance of different C-RAM systems. Dynamic fragment data is generated by static arena test data and superposed with the intercept and mortar projectile velocities. The system’s error budget with the most relevant components is considered to determine the kill probabilities and ammunition consumptions indicating system limits and decisive parameters for performance improvements. The sensor precision for estimating the target’s trajectory as input for the fire control solution and the intercept ammunition with high fragment densities and impact against a target are key elements. Furthermore, the hazard assessment plot of 155 mm HE ammunition confirms these statements in terms of the assumed fragment numbers and their impact. Besides other investigations in this field, live firings in order to verify the terminal ballistics of HE intercept ammunition against hard targets as well as a general proof of concept are planned for the future.

APPENDIX A. EXAMPLE DATA This section contains the setting for the simulations according to Fig. 6. • The field camp’s size constitutes to 2000 x 1000 m with the coordinates of the edges given in the figure. • The radar sensor is placed at the camps’s center (= origin of the coordinate system) fulfilling the requirement for small angles between radar beam and firing direction, see Subsection 3.1.

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yF (1000, 500)

0° Attack xF

(0, 0)

90° Attack

(-1000, -500)

(1000, -500)

I

Intercept ranges 1500 m 2000 m 2500 m

Figure 6. Field camp with sensor, effectors, and attack directions.

• Tank Howitzers (PzH 2000) or AGM’s as effectors are deployed in the edges of the field camp preferably avoiding engagements with firings over the installation. The maximum propellant charge of 155 mm caliber projectiles is used. Arena tests yield approx. 24,000 natural steel fragments modeled as cylinders with L/D = 1. • Russian 82 mm mortar projectiles (O-832, No. 6) serve as RAM threat attacking the camp in a 0◦ and 90◦ direction. The projectiles are fired with the maximum propellant charge available and their point of impact is in the camp’s center. • The points of intercept result from the trajectories of the mortar projectiles for intercept distances of 1500 m, 2000 m, and 2500 m (measured from center of origin). The real distance of flight for the HE projectiles is determined by the trajectory data and the battle field geometry.

REFERENCES [1] Graswald, M., Shaydurov, I., and Rothe, H., “Analysis of Weapon Systems Protecting Military Camps against Mortar Fire,” in [Computational Ballistics III], Brebbia, C. and Motta, A. A., eds., WIT Press., Ashurst (2007). [2] N., N., [STANAG 4589: Static Testing of High-Explosive Munitions for Obtaining Fragment Spatial Distribution ], 1 ed. (2000). Final Draft. [3] Graswald, M. and Rothe, H., “Terminal Ballistics of Intercept Ammunition against Mortar Targets,” in [Proceedings of the Military Modeling and Simulation Symposium, Part of Spring Simulation Multiconference], The Society for Modeling and Simulation International (SCS), Ottawa, Canada (April 14 – 17 2008). to be published.

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