MODELING AND SIMULATION FOR THE TIME CONSTRAINT DAMAGE EFFICIENCY OF MLRS

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1 MODELIG AD SIMULATIO FOR THE TIME COSTRAIT DAMAGE EFFICIECY OF MLRS 1 SOG WEI-DOG, 1, ZHAO CHEG-WAG, HUO JU-XIU 1 Pro., Shijiazhuang Mechanical Engineering College, Shijiazhuang ,China Assoc. Pro., Shijiazhuang Mechanical Engineering College, Shijiazhuang ,China 1 wsung@163.com, zhaochengwang1976@163.com ABSTRACT Aiming at the shortcomings o the present amage eiciency moel o multiple launch rocket system(mlrs) that ignores actors such as targets movement an viability while consiers actors like shooting accuracy, target characteristics, an amount o ammunition only, a time-constraint amage eiciency moel o MLRS was presente base on artillery irepower theory an irepower counterwork theory. The amage eiciency o MLRS in scenarios that containing time-constraint actors was compute base on the new moel. Simulation results show the eectiveness o the moel, an emonstrate that actors like targets maneuver an survival eman play an important role in amage eiciency o MLRS battalion an make the amage eiciency time sensitive. Keywors: Time-Constraint, Damage Eiciency, Shooting Accuracy, Ammunition Consumption, Target Maneuver 1. ITRODUCTIO The MLRS is a long-rang surace-suppressing weapon with ierce irepower an goo mobility. The amage eiciency o MLRS is etermine by actors such as shooting accuracy, targets characteristics, an amount o ammunition. Both military an civilian scholars have one a lot o ruitul work in amage eiciency, an presente some methos or calculating the amage eiciency uner ierent conitions [1-6], but the time-constraint cause by the target maneuver an survival nees, have not been pai enough attention an given in-epth stuying. With the avances o military technology, target characteristics have change ramatically, especially in the target imensionality, an the target istribution characteristics an target maneuver, which have a irect impact on the combat eectiveness o the weapon systems an tactical choices. In aition, with moern reconnaissance technology improving, the ability to get inormation is istinct rom the past. The increasing transparency o the moern battleiel brings convenience to the commaning an inormation transporting [7] o the MLRS while brings viability test too. Thereore, in orer to improve the viability o MLRS, the hostile counterattack spee [8,9] an irepower preparing time must be taken into account while computing the amage eiciency o MLRS. A new amage eiciency moel was set up base on use static moel in this paper. The new timeconstraint moel takes into account the change o target characteristics an ammunition consumption cause by time actor. The application to the classic scenarios shows the valiity o the time-constraint moel in amage eiciency calculation.. THE USED DAMAGE EFFICIECY MODEL OF MLRS [10,11] Each MLRS nees to be assigne its target when the MLRS battalion ires at the grouping targets, but in the amage eiciency calculating, the blast points are istribute evenly instea o actual blast points. The amage eiciency is: R = ϕ ( X, Z ) R ( x', z ' ) XZ (1) R '( x', z') is conitional amage probability, gaine by ormula below: R ( x', z') = 1 [1 P'( x', z' )] For blast points obey uniorm istribution, so: SM whenx' L an Z' L P'( x', z') = 4LL 0 otherwise The amage probability o any single target when shooting at gathering targets is: 404

2 S M ˆ L ( ) ˆ L 4 L L () R = Φ Φ ( )(1 e ) E ' E ' Which is equals to the amage probability o the group targets, so the amage eiciency can also be written as: ˆ L ( ) ˆ L M ( k ) = Φ Φ ( E ' E ' )(1 e S M 4 L L ) (3) In which, L, L is hal o the bombing point uniorm istribution in epth an ront; L L = = 3 B ρ 3 B ρ k 1 + h 4 n 1 + h 4 k, n is rear sight amount an irection number (gun number within a company) when iring. h, h is the grauation o the ajacent rear x z sight an the grauation in irection. E ', E ' is error on behal o intermeiate error when iring at group targets. x z E ' = E L E ' = E L ˆ L ( ) ˆ L Φ Φ ( E ' E ' z x ) is probability that error which obey the normal istribution alls in the evenly istribute blasting area( x ' L an z ' L ), actual, means the coverage probability o the units target in the area in which evenly istribute blast points evenly istribute. S M L L 1 e 4 is conitional amage probability. 3 THE TIME-COSTRAIT DAMAGE EFFICIECY MODEL OF MLRS 3.1 Time-Constraint Factors An Its Inluence On The Damage Eiciency Moel O Mlrs Being a surace suppressing weapon, the MLRS has many battle objects such as gathering eective, armore vehicles an sel-propelle artillery. In the changeul battleiel situation, both the ensity o targets an the coverage o blast points are subject to the target maneuver. Clearly, the change o target imensionality will cause amage eiciency to change. To the gathering targets maneuver, we iscuss the simple case in this paper. Assuming that the MLRS battalion commaner obtains the target inormation at moment t0 an organizes objectives to be assigne an ire at (the gathering target imensionality is rectangular an its size is L, the target group move away orm the L MLRS position at spee v at the moment t 0. The rocket arrives at the target area at moment t 1 ). The target imensionality at moment t 1 is change comparing with its initial state, as shown in ig. 1: Fig. 1 The Change O Gathering Targets Position 405

3 Area with horizontal lines an panes is the original imensionality at the moment t 0, ater some time t, the imensionality becomes to be the area with vertical lines an panes. Obviously, the area with panes is the area that belongs to both original imensionality an new imensionality. In the actual shooting, the commaner issues operational commans that shoul be mostly possible to make blast points evenly istribute in target imensionality, so it s clear that the blast points can t cover the imensionality entirely as shown in igure 1. Damage eiciency in this case, is lower compare to the conitions that group targets resting. By the ormula () or (3), the irst two items are the probability o blast point alling into the target imensionality, an the last item is the conitional probability o coverage an amage. In the illustrate case, it is clear that the gathering target maneuver has no impact on the conitional probability, while has inluence to the probability o coverage. From the physical sense, the change in probability o coverage o the target is equal to the change in probability o the burst points alling in the imensionality. As illustrate in the case o group target maneuver, to get the best amage eiciency, the blast points istribution shoul has the corresponing maneuver. The eective blast point istribution is the overlap zone in ig. 1. As shown in ig.1, L changes into L Vt / with the group targets maneuver, while parameters such as E', E' an L are the same as those when group targets in still conition. The probability unction φˆ is a approximate proportional unction, so it is reasonable to change the whole amage eiciency accoring to the change o eective blast points istribution area. So we can solve the amage eiciency o gathering target with maneuver characters as the ollowing ormula: S ' L' * L' R t ' = R = R S L * L S ' ( L ', L' )is the overlappe size o blast points istribution, the ierence compare with original S ( L, L ) emonstrates the inluence o the group targets maneuver on the eectiveness o blast points istribution. When the group targets move along other irections, the metho is the same as above, it is necessary to calculate the overlappe area size an multiply the original amage eiciency by the ratio o the overlappe area to the original blast points istribution area. 3. Time Constraints Cause By Oppose Factors An Its Inluence On Damage Eiciency The viability o MLRS aces serious test in moern warare with the use o a large number o high-tech reconnaissance means, an threats come rom aerial reconnaissance, moving target surveillance raar, emplacements raar an so on [8]. This paper iscusses only the change o amage eiciency cause by viability nee. One o the important mobile operations means o MLRS unit is receiving the mission an managing to ire in maneuver. The progress is maneuver-iremaneuver-ire. At the present time, the phase array emplacements raar equippe in oreign army has a 90 searching angle-range an 5km~50km reconnaissance istance against MLRS, an has the capacity o capturing multiple trajectory synchronously. This equipment can work about 5s once boot-strap, an etermine the coorinates o emission emplacements accoring to the rising arcs ballistics, an has higher positioning accuracy to position single artillery. Multi-gun salvo can introuce intererence an cause reuce positioning accuracy. Phase array emplacements raar has a high positioning accuracy to MLRS because o its big coniguring size an istance, especially in the case o multi-raar networking. Assume that or a MLRS, it nees ts to complete one single shoot, nees t total to complete one volley, nees t r to complete a iling, nees t c to change rom marching state to battling state. To the phase array emplacements raar, It nees T to capture the ballistic trajectory an complete positioning. To the irepower chain o comman an artillery units o enemy, it nees T to complete a shoot. Accoring to the current MLRS tactical an technical criterion, it is unrealistic to ill or the next wave o irepower ater completing a volley at one position. Obviously, The MLRS iring is subject to the time constraints as ollows because o survival consiering: t + t < T + T (4) ire The constraints in the ormula (4) etermines how much ammunition use o the MLRS, one shoot or multiple charge shooting. In other wors, the constraints etermine the in the coverage an amage probability. With the avance in military technology, such constraints will be more emaning in uture. Consiering the actual situation, the constraint is c p a a p 406

4 t t < T + T total + (5) c The MLRS unit can not be implemente a volley on the target without converting the position i the relationship exits in ormula (5), thereore the maxim ammunition a single MLRS unit can ire must be ecie beore calculating the amage eiciency, as shown in ormula (6) p Tp + Ta tc n = int[ ] (6) t I the MLRS battalion ire in time-constraint conition, the total ammunition can be obtaine by multiply the n by the number o vehicles in the battalion. In particular, the MLRS shoul, as ar as possible, arrange in a large area lan or security consierations. To gain the abrupt eect o irepower an improve the viability, the MLRS battalion shoul synchronize the emission to the greatest extent to orm multiple ballistic trajectories to avoi the accurate positioning o the phase array emplacements raar. 3.3 Damage Eiciency Moel With Time- Constraints Accoring to the analysis in 3.1 an 3., to solve the amage eiciency in actual battleiel environment, the inluence o group target maneuver on target coverage an the constraints o irepower ensity ue to viability nees shoul be consiere. So the amage eiciency o the MLRS battalion can be eine as ollows: max S M L' * L' ˆ L ( ) ˆ L 4 L L (7) R = ηr = Φ Φ( )(1 e ) T max L * L E' E' η is the covering coeicient, which equals the ratio o overlappe area to the original area when group target maneuver. is the maximum ammunition the MLRS can max launch in actual action. Without timeconstraint Target maneuver Conront conition With timeconstraint s a Interval in irection/m/ Tab. 1 4 SIMULATIO 4.1 Simulation Conitions A MLRS battalion carry out a suppress ire towars group armore vehicles that 0000m away rom the MLRS position. The battalion has three companies an inclues 18 MLRS units totally. The group target imensionality is 1000m 1000m an the estroy area o the armore vehicle is 80m. The battalion error is E = 60 m, E = 40 m, the sprea error is B = 60 m, B = 40m. The MLRS s conversion between ighting an marching consumes 10s, an the irst volley consumes 30s, single shoot consumes 0.5s, an one volley launches 60 rockets. The emplacements raar consumes 40s or capturing the ballistic trajectory an positioning. The group target moves apart rom the position or extra 100m. it nees 100s or the hostile irepower to complete the counterattack ater positioning. The shooting parameters obey the avorable irepower allocation metho. 4. Results An Discussions Accoring to the most avorable ire istribution calculation metho [1], the shooting parameters such as ire intervals, ierence in istance an amage eiciency was calculate without consiering the time-constraints irst. In timeconstraints conitions, the maximum ammunition a single MLRS can launch is 40 accoring to the ormula (6). The grauation o the ajacent rear sight an the grauation in irection nee to be etermine again with the new ammunition amount. Simulation results is shown in table 1 an ig.. Simulation Results Contrast Dierence in istance/m Ammunition amount/piece Damage eiciency/%

5 x/m z/m Fig. The Distribution O The Burst Point As can be seen rom ig.1, the actual target imensionality in portrait is between -600m-400m instea o -500m-500m, the rockets all in 400m- 500m istrict make no sense. This is coincient with ormula (7) in physical meaning. The blast point in t show the well-proportione istributing in ig. because o the ranomicity o istribution. As can be seen in tab.1, ajusting the shooting parameters is not necessary when consier the group target movement only, an the change o blast points coverage to target imensionality cause the amage eiciency ecline obviously. Uner the conition o consiering the survival eman, the limit o shooting time reuce the ammunition amount, an to gain the best amage eiciency, the shooting parameters must be ajuste, compare to the conition that not consiering time-constraints, there were obvious changes in the shooting parameters, o course the amage eiciency change obviously also. The eman o viability restricts the ammunition amount that the MLRS battalion can launch in a salvo, an the ammunition amount etermines the best irepower management inirectly. Furthermore, the change in gathering targets imension plays an important role to the change o amage eiciency. 5 COCLUSIOS The time-constraint amage eiciency moel was presente an applie to a scenarios, simulation results showe the rationality an availability o the moel. A conclusion can be rawn that the MLRS battalion commaner shoul consier not only the inormation o the target but also the inormation o the counterwork ability o hostile army to improve the amage eiciency an viability. To the change o amage eiciency cause by the target maneuver, only simple case was analyze in this paper. In actual battleiel, the change o target position cause by maneuver is more complex, an how to accurately measure changes o it worthy o urther in-epth stuy. REFRECES: [1] DAI Rong-rong, Xu Guang-wu, Yang Bozhong. Calculating an analysis or iring eiciency to uncover inantry o long range multiple rocket[j]. Journal o Moern Artillery. 007, 3(1),pp.5-7. (in Chinese) [] LI Tao, LI Xin. Fighting eiciency evaluation o rocket system base on clou theory[j]. Journal o Artillery Acaemy, 009(6),pp (in Chinese) [3] CHEG Hao, WAG Xue-qin, XIE Pengxiang. Moel o sea-base eectiveness analysis o the long istance rocket system[j]. Ship Electronic Engineering, 010, 30(1),pp (in Chinese) [4] TAG Ke, SU Lai-bin. Comparison o iring eiciency evaluation means o ual purpose cargo carrying projectile o long rang multiple 408

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