Jtam.dvi JOURNAL OF THEORETICAL AND APPLIED MECHANICS 45, 4, pp. 819-832, Warsaw 2007 THE TESTING OF OPERATING CHARACTERISTICS OF CLUSTER AIR WEAPONS Andrzej Żyluk Air Force Institute of Technology, Warsaw, Poland e-mail: andrzej.zyluk@itwl.pl In the paper, a general model for investigations of dynamical properties of cluster air weapons is presented. Flight tests were carried out in a research-development cycle. Results of simulation studies, preliminary tests in aerodynamical tunnel and in flight examination are presented. Themathematical model was verified through experimental flight tests. Key words: flight dynamics, cluster weapon, mathematical modelling, experimental verification 1. Introduction The practice of investigating air weapons has proved that the investigation process needs the following types of research work: • theoretical studies, with digital and computer-simulation generatedmo- dels engaged, and • experimental efforts, i.e. ground and flight tests using material models and real objects. Quite often, the practice of performing investigation work requires some different approach, usually a composite one. Most often, it happens while acquiring data for a simulation model, e.g. from aerodynamic wind-tunnel tests, while findingmass characteristics of a material model or a real object. The grounds for developing new and upgrading older designs of bombing- dedicated air weapons in the NATO countries derive from rich experience effected by hostilities inVietnam, theMiddle East, and theGulf. In the recent years, special attention has been paid to the design and construction of cluster 820 A. Żyluk air weapons to destroy armoured vehicles, runways, any hardware, and to suppress the hostile troops’ fast moving. The clusterweapon is a kindof air armament intended to affect the surface. This feature, being an advantage of great significance, enables more effective use of sub-munition to suppress widely dispersed objects. Depending on themission assigned, the cluster weapons can be filled with various sub-munitions, i.e. fragmentation, incendiary, anti-tank, anti-concrete, and with practice ones, e.g. aircraft-laid mines. 2. A mathematical model of a cluster bomb in 3D flight A general mathematical model for any of air munitions in 3D motion can be presented in the matrix form shown below M̃V̇ +KMV =Q+Uδ (2.1) where —modifiedmatrix of inertia M̃=M+M Ẇ (2.2) — acceleration vector V̇ = col[U̇, V̇ ,Ẇ,Ṗ,Q̇,Ṙ] (2.3) — velocity vector V = col[U,V,W,P,Q,R] (2.4) —matrix of external forces Q= [ F M ] = col[X,Y,Z,L,M,N] (2.5) with The testing of operating characteristics... 821 M Ẇ =      0 0 0 0 0 0 0 0 0 0 −M Ẇ 0 0 0 0 0      M=          m 0 0 0 Sz −Sy 0 m 0 −Sz 0 Sx 0 0 m Sy −Sx 0 0 −Sz Sy Ix −Ixy −Ixz Sz 0 −Sx −Iyx Iy −Iyz −Sy Sx 0 −Izx −Izy Iz          K=          0 −R Q 0 0 0 R 0 −P 0 0 0 −Q P 0 0 0 0 0 −W V 0 −R Q W 0 −U R 0 −P −V U 0 −Q P 0          (2.6) U=          XαzH XδH 0 XδV XδT 0 0 0 YδV YδT ZαzH ZδH 0 0 ZδT 0 0 LδL LδV LδT MαzH MδH 0 0 MδT 0 0 NδL NδV NδT          —control vector δ= col[αZH,δH,δL,δV ] (2.7) — kinematic relations can be shown in the following form ṙ= col[ẋ1, ẏ1, ż1, φ̇, θ̇, ψ̇] =F [U,V,W,P,Q,R,φ,θ,ψ] (2.8) This paper has been intended to show characteristic results of analysis of a mathmodel of a small-size bomb (bomblet) and an aircraft-laid mine. 3. Simulation-based and aerodynamic studies 3.1. Tests of a small-size aerial bomb (bomblet) Subject to tests was a small-size aerial bomb (bomblet) (Fig.1a). While studying the dynamics of bombs (Fig.1) with elastic braking-and- stabilising systems, deformations of fins have been taken into account in such a way that aerodynamic characteristics have been changed (Fig.2) depending on the angles of attack α and side-slip β, and the initial velocity V0. Real objects under investigation are featuredwith a decrease in drag coefficient Cx 822 A. Żyluk Fig. 1. (a) A small-size aerial bomb (bomblet): weight – 0.8kg, diameter – 70mm, length – 95mm; (b) a model of the small-size bomb (bomblet) as the flow velocity of themedium increases (Fig.2a). This happens due to fin deflections (decrease in the angle of fin opening), decrease in local angles of attack and changes in the effective face surface. Fig. 2. Change of the: drag coefficient Cx(α,Ma) (a), aerodynamic lift Cz(α,Ma) (b) and pitching-moment coefficient Cm(α,Ma) (c) Tests of a real-sizemodelwithin the rangeof operatingvelocities provideda reliable aerodynamic representation.While examining thedynamics of a bomb with elastic braking-and-stabilising systems, the effect of release velocity on the properties of bombmotion has been given consideration. The testing of operating characteristics... 823 The increase in the bomb’s initial velocity V0 results in: • extension of the range x1; however, the increments keep getting smaller and smaller, • lower loss of the altitude z1(t) (Fig.3a), • faster decrease in the total velocity V0 (Fig.3b), • slower increase in the angle of pitch Θ(t) at the initial stage of flight (Fig.4a), • increase in both frequency and amplitude of variations of the angle of attack α(t), • increase in the relative distance ∆l(t) between the bomb and the carrier (Fig.4b). Fig. 3. Change of the flight altitude z(t) for various velocities Vp (a) and total flight speed V0(t) (b) Fig. 4. Change in the angle of pitch Θ(t) (a) and relative distance between the carrier and the bomb (b) 824 A. Żyluk The initial rate of bomb release does not affect the time of reaching both the critical rate of descent Vcr (Fig.3b) and the angle of pitch Θ = 90 ◦ (Fig.4a). What occurs at the initial stage of flight is an increased variation in the angle of pitch Θ(t), and the bomb can instantaneously show a positive angle of pitch Θ. These are moments when collision of the carrier and the bomb is quite possible. The elastic control-and-braking system used to reduce the bomb’s rate of motion is featured with: • reduction of the drag coefficient Cx(Ma) as the speed of flight increases, • fast attainment of the critical rate of descent Vcr, independently of the initial (release) velocity V0, • strong attenuation of bomb oscillation. The initial stage of the bomb’s flight is themost important stage of bomb’s motion, since two things occurduring that time: decrease invelocity andflight- path curving. 3.2. Tests of a small-size aircraft-laid mine Subject to tests was a small-size aircraft-laid mine (Fig.5). Fig. 5. An aircraft-laid small-size mine: weight – 3.8kg, diameter – 116mm, length – 257mm While studying the dynamics of mines with rigid braking-and-stabilising systems, aerodynamic tests on real objects were carried out. Aerodynamic characteristics Cx(α,Ma), Cz(α,Ma), Cm(α,Ma) have been shown in Fig.6. The testing of operating characteristics... 825 Fig. 6. Change of the drag coefficient Cx(α,Ma) (a), aerodynamic lift Cz(α,Ma) and pitching-moment coefficient Cm(α,Ma) The testswere limited to a velocity of 136m/s, because at higher velocities of the flowofmediumtheplastic strain of thebraking systemappears (exceeds the limit of elasticity of fins). The analysis of simulation models of mines with rigid braking-and- stabilising systems has proved what follows: • the flight-path profile and the range of mine delivery depends first and foremost on the release velocity (Fig.6b) and the angle of fin opening, • mines experience decreasing variations in the angles of attack α and side-slip β (Fig.6c), • the critical velocity of amineandthetimeneededto reach itbothdepend on design parameters of the braking system and remain independent of the initial release velocity Vp (Fig.7). 826 A. Żyluk Fig. 7. Flight paths of the mine at various velocities Vp The following parameters of motion are of the greatest significance from the standpoint of functional quality: the critical velocity Vcr, the time to reach it, and the angle of fall Θk. The wind-tunnel and flight tests both prove that systems of that kind are very liable to deformation at higher flight speeds. Fig. 8. Change in the angle of attack α against the angle of side-slip β The testing of operating characteristics... 827 Fig. 9. Change of the total flight speed V0(t) for different initial velocities V0 4. Experimental examination (flight tests) of a cluster bomb A thorough R&D cycle to develop some new air weapon, cluster air weapon included, comprises the following stages: • studies and analyses, • preliminary design (foredesign), • engineering design, and • implementation. The analysis of the R&D cycle proves that in the course of subsequent stages of developing a product, i.e. foredesign, engineering design, and im- plementation, the testing work is carried out, including flight tests. It should be emphasised that the testing work at different stages is aimed at different objectives. At the stage of foredesign, amodel of the product is evaluated in terms of having reached functions assumed in the Specifications. In the course of preliminary and certification (State) tests, any prototype is subject to assessment in terms of whether the Specifications-defined requ- irements have been satisfied, and from the standpoint of safety of the product while transported and stored as well as in the course of combat applications and operational use. Although beyond the R&D cycle, the stage of implementation has been presented as a logical consequence of a creative process, since the testing of a pre-production batch should offer the assessment ofwhether themanufacturer iswell preparedandhasmastered theproductionofgoods thatmeet theabove- mentioned specifications, in particular, those dedicated to the procedures of the manufacture and acceptance of goods. 828 A. Żyluk Therefore, flight tests prove to be inherent in the investigative process, since the check-up of how the product performs under real conditions enables thorough assessment of the product under investigation/testing. The range-based flight tests are carried out using either dynamic models of cluster air weapons under development, or real combat objects. The tests include what follows: • evaluation of dynamic stability, • functional tests under real conditions, • determination of parameters of motion along the flight path and in the point of impact, • assessment of performance effectiveness, • investigation of how an obstacle affects the penetrating object. Another thing to be strongly emphasised is very specific nature of flight te- sts of any air weapons. The tests are very expensive, that is why development of an algorithm of the testing work and a suitable set of measuring equipment is very important. Unlike the aircraft, air weapons are single-use objects. Hen- ce, any set of information is a function of many variables, including a set of measuring equipment, organisation of test flights, flying skill’s and experience of a pilot, weapons launch (release) conditions, weather conditions, etc. Themeasuring equipment should provide capabilities to record: • carrier’s flight parameters at the moment of weapon launch/release, • the flight path and the point of impact of the weapon under testing, • how the object performs along the free-flight path. The recorders designed and developed at ITWL (Air Force Institute of Technology) and intended for investigation and tests of bombing weapons enable, among other things, the recording of: • overloads (excessive loads): – in the course of free flight, – during engagement of the braking system, – at the moment the bomb hits an obstacle, • transient responses (performance) of control systems, • technical data (parameters) of fuses (fuse systems), • parameters of aerodynamic heating, etc. Figures 10 and 11 show typical effects of overloads and bomb’s rotations while following the flight path. The testing of operating characteristics... 829 Fig. 10. The overload nx of a cluster bomb (weight 250kg) recorded at the moment of impact on the target (sandy soil) Fig. 11. Rotations of a cluster bomb (weight 250kg) while following the flight path 5. Conclusions Theabove-presentedmethodology of investigating/testing dynamic properties of airweapons enables analysis ofmotion of any systemof any structural confi- guration, and at the same time, it provides continuous delivery of information on changes in the flight-path parameters. The outcome of theoretical studies has been confirmed in the course of flight testing of real objects. General compliance of both calculation- and experiment-effected results verifies the generated model (algorithm) of the testing work. 830 A. Żyluk The presented investigating/testing method and results gained give good grounds for claiming that theoretical analyses of the object’s model should be used during both the research stage and that of preliminary design. The research/testing team keeps making efforts to apply new measuring methods to find and/or verify at least some of dynamic parameters. The above-specified issues would enable the team to formulate a possibly complete, generalisedmodel of an air weapon in terms of investigating/testing dynamic properties thereof. Acknowledgement The scientific work was founded from state science budget 2006-2009 as research project No. T00B00131/0017. References 1. Beecham L.J., 1971, A technique for the wind tunnel simulation of store release at high speeds, J. Aircraft, 8, 12 2. Gacek J., 1999, Balistyka zewnętrzna Cz. I, Modelowanie zjawisk balistyki zewnętrznej i dynamiki lotu,WydawnictwoWAT,Warszawa 3. Gacek J., Balistyka zewnętrzna Cz. II, Analiza dynamicznych właściwości obiektów w locie, WydawnictwoWAT,Warszawa 4. Loroch L., Kaźmierczak R., 1994,Metodyka oceny efektywności działania kasetowych odłamkowych środków bojowych, . Informator ITWL, Mrągowo, 143-152 5. Maryniak J., 1975,Dynamiczna teoria obiektów ruchomych,Mechanikanr 32, Prace naukowe PW,Warszawa 6. 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Umiejscowiono doświadczalne badania w locie w cyklu prac badawczo-rozwojowych. Zaprezentowano wyniki badań symulacyjnych, badań do- świadczalnych w tunelu aerodynamicznym i w locie. Model matematyczny zweryfi- kowano eksperymentalnymi badaniami w locie. Manuscript received September 13, 2006; accepted for print May 7, 2007