Missile System Research Articles

PLACEMENT OF ROBOTIC MISSILE DEFENSE COMPLEXES ON AN UNMANNED AIR VEHICLE

Objects of critical infrastructure of Ukraine need a multi-level anti-missile defense system, which should protect against various types of missiles with a flight range of several tens to several hundreds of kilometers. Timely detection of missiles allows for a number of measures aimed at interception and destruction of targets, the use of radio-electronic warfare, the installation of interfering and obstructing obstacles in various ranges of radio waves, as well as the inclusion of optical and thermal traps. The use of robotic complexes placed on aerostats increases the effectiveness of modern surface-to-air missile system (SAMS) many times over in the fight against low-flying targets with massed strikes of cruise missiles. The location of radar at an altitude of several kilometers ensures the detection range of low-flying targets several times greater than that of ground-based radar. This is of particular importance for SAMS when firing at targets beyond the radio horizon. The transfer of data about the location of the target from the radar of the air carrier to the air defense system and its illumination and guidance radar (at least the approximate location) provides the opportunity to bring the anti-missile to the point of inclusion of its homing head. It is proposed to modernize the radar with an active phased antenna array used on fighters to increase the range and installation on airships and balloons. This will ensure the effectiveness of defense against missile attacks, detection and tracking of up to 100 targets at distances of about 40...400 km. At the same time, the weight of the radar within the range of 200...500 kg and the dimensions of the antennas up to 1 meter are permissible for installation on large balloons. Countries for which attacks of various types of missiles are a real threat need a multi-level anti-missile system, in particular, using robotic complexes placed on air carriers. Keywords: anti-missile defense, radar station, balloon, airship.

FIRING EFFICIENCY OF ANTI-AIRCRAFT MISSILE COMPLEX “STRILA-10” IN TARGET DETECTION THROUGH THE OPTICAL VISOR AND AUTOMATED TARGET POINTER

When preparing for and conducting combat operations of the “SA-13 Gopher” anti-aircraft missile system, commanders and combat personnel of the system must know the missile firing efficiency indicators [1–4]. As an indicator of missile firing efficiency, the probability of hitting a target with one missile is usually used. Massive homing is carried out via the contrast channel or the infrared channel of the missile homing head. Under various conditions of use, it is necessary to evaluate the detection ranges that are realised and the probability of timely target detection, launch range and missile launch probability. It is also necessary to imagine the possible values of the inclined distances to the far edge of the kill zone of the complex. The probability of hitting a target with a single missile is affected by the geometric dimensions of the targets, their colour and contrast in the infrared wavelength range, the presence of target designation, meteorological range of visibility etc.
 The task of determining the firing efficiency of the “SA-13 Gopher” anti-aircraft missile system when detecting targets through the optical sight and automated targeting is therefore relevant and important.
 Research presented in the published [1–4; 12–13] do not allow determining the value of the probability of hitting different air targets in various conditions of the complex’s use. This literature provides only general approaches to solving this problem for typical conditions of use of an anti-aircraft missile system. A numerical modeling technique for determining the firing efficiency indicator in the form of values of the probability of hitting targets by a missile has been developed. The modeling took into account the speed of the targets, their plane in the shooting picture, their radiating capabilities and meteorological visibility range, the quality of the combat work of the operators of the combat vehicle, the sun exposure and the closing angles of the combat vehicle. Found possible detection ranges and detection probabilities of a typical target and a small unmanned aerial vehicle (UAV). A high probability of the operator of a combat vehicle missing a typical target at low and medium flight altitudes was noted. Considered launch ranges of missiles that are implemented and the probability of launching a missile when targets are captured in the contrast and infrared channels of the homing head. The largest inclined ranges to the far boundary of the zone of damage of the complex were calculated. The values of the probability of hitting a typical target and UAV in various firing conditions are determined. Sufficient firing efficiency has been proven when capturing and launching a missile in the contrast guidance channel and firing at a typical target. A comparison of the contrast and infrared channels of the homing missile head when firing at UAVs was carried out. Analytical expressions for the calculation of missile firing efficiency indicators and corresponding graphic material are presented.

Group-Fusion One-Dimensional Convolutional Neural Network for Ballistic Target High-Resolution Range Profile Recognition with Layer-Wise Auxiliary Classifiers

Ballistic missile defense systems require accurate target recognition technology. Effective feature extraction is crucial for this purpose. The deep convolutional neural network (CNN) has proven to be an effective method for recognizing high-resolution range profiles (HRRPs) of ballistic targets. It excels in perceiving local features and extracting robust features. However, the standard CNN's fully connected manner results in high computational complexity, which is unsuitable for deployment in real-time missile defense systems with stringent performance requirements. To address the issue of computational complexity in HRRP recognition based on the standard one-dimensional CNN (1DCNN), we propose a lightweight network called group-fusion 1DCNN with layer-wise auxiliary classifiers (GFAC-1DCNN). GFAC-1DCNN employs group convolution (G-Conv) instead of standard convolution to effectively reduce model complexity. Simply using G-Conv, however, may decrease model recognition accuracy due to the lack of information flow between feature maps generated by each G-Conv. To overcome this limitation, we introduce a linear fusion layer to combine the output features of G-Convs, thereby improving recognition accuracy. Additionally, besides the main classifier at the deepest layer, we construct layer-wise auxiliary classifiers for different hierarchical features. The results from all classifiers are then fused for comprehensive target recognition. Extensive experiments demonstrate that GFAC-1DCNN with such simple and effective techniques achieves higher overall testing accuracy than state-of-the-art ballistic target HRRP recognition models, while significantly reducing model complexity. It also exhibits a higher recall rate for warhead recognition compared to other methods. Based on these compelling results, we believe this work is valuable in reducing workload and enhancing missile interception rates in missile defense systems.

Improvement of methods of interception of enemy UAVs

The main result of this work is the creation of a methodology for determining the coordinates, velocities and trajectories of spatial movements of moving objects by means of kinematic design and the development of principle schemes for the optimal placement of radar search equipment for the successful detection of enemy UAVs. Its purpose is to increase the defense capability of military units, populated areas of Ukraine and their infrastructure by resisting attacks by attack and sabotage reconnaissance unmanned aerial vehicles (UAVs). The protection scheme is based on the determination of coordinates, movement speeds and trajectories of spatial movements of enemy aircraft by means of kinematic design. The established coordinates of enemy UAVs are reported to command posts equipped with liquidator drones (kamikaze) and small arms or to control points of anti-aircraft missile systems (SAMS), which eliminate these aircraft. The proposed improvement of the widespread method of radar search for moving objects is based on the introduction of additional search radar equipment and mathematical apparatus for precise calculations of coordinates and parameters of spatial movements of moving objects by means of kinematic design. Two paired radar search systems, equipped with modern high-speed computing equipment with appropriate software, are able to "screen out" false return electromagnetic signals. This makes it possible to clearly single out the wanted moving object and subsequently track its movement in space. Corresponding mathematical dependencies are proposed for calculating the distance of a moving object to radar stations, its coordinates in the introduced orthogonal coordinate system, speed and acceleration of movement, that is, instantaneous coordinates and parameters of spatial movements of moving objects. This makes it possible to increase the effectiveness of detecting enemy attack and sabotage-reconnaissance unmanned aerial vehicles, including Iranian-made drones of the Sahed-136 model.

Identification of Uncertain Parameter in Flight Vehicle Using Physics-Informed Deep Learning

This paper presents the estimation method for uncertain parameters in flight vehicles, especially missile systems, based on physics-informed neural networks (PINNs) augmented with a novel integration-based loss. The proposed method identifies four types of structured uncertainty: burnout time, rocket motor tilt angle, location of the center of pressure, and control fin bias, which significantly affect the missile performance. In the estimation framework, as neural networks (NNs) are updated, these uncertainties are also identified simultaneously because they are also included in the structure of NNs. After testing 100 simulation data, the average estimation errors are within 1% of the mean value for each type of uncertainty. The methodology is able to identify the parameters despite noise corruption in the time-series data. Compared with the conventional PINNs, adding the new loss based on the integration of differential equations yields a more reliable estimation performance for all types of uncertainty. This approach can be effective for complex systems and ill-posed inverse problems, which makes it applicable to other aerospace systems.

Three-dimensional trajectory tracking guidance against near-space maneuvering targets with multiple constraints under wind field

This paper presents a three-dimensional disturbance observer-based adaptive tracking guidance scheme for the trajectory tracking problem of a missile intercepting a hypersonic vehicle with the wind field, autopilot lag dynamics, and input saturation. Unlike most of the existing missile trajectory tracking guidance systems without velocity controllability and external wind field model, the wind field model is added to the dynamic model, and the velocity control channel is introduced into the three-dimensional trajectory tracking guidance problem to prevent impractical scenarios and increase tracking precision. The proposed tracking guidance methodology incorporates the sliding mode and adaptive control techniques, in which the sliding mode motion is finite time stable independently of the tracking guidance system's initial conditions. Also, the super twisting switch control law is added to cope with the chattering problem. In this context, external uncertainty disturbances and unmeasured states are lumped into lump disturbance and estimated using the backpropagation neural network extended state observer. To this end, numerical simulations demonstrate the tracking to reach zero between 3 s and 5 s against various uncertainties in engineering practical, and position tracking errors are within 0.15 m, superior to the existing tracking guidance methods.

Technical Effectiveness Considerations on the Replacement of Missiles with Interceptor UAVs

The large availability of low-cost, mass-produced drones has shaken the economic and production capabilities of most intermediate-range missile (IRM) systems. IRMs are capable of taking out mortars, rockets, unmanned aerial vehicles (UAVs) and missiles from 4 to 100[Formula: see text]km with a unitary cost of the “killer” unit of five figures. The preliminary design of these UAVs may benefit from existing jet models. This study evaluates the cost-effectiveness of these unmanned aerial vehicle interceptors (UAVIs) that can replace the IRMs with reusable small UAVs with booster rockets. This approach reduces the interception costs importantly.

A Preliminary Assessment of the Effectiveness of Training Using a Virtual Reality Simulator of the Anti-aircraft Missile Launcher

Training an anti-aircraft soldier is expensive, complicated, and time-consuming. As a result, many countries, weighing the cost-effectiveness, opt to introduce solutions aimed at minimizing this trend. One of them is incorporating modern training devices such as simulators and trainers into the training. However, to make this happen, it is worth analyzing the effectiveness of training with their use by comparing it to that conducted in a traditional way. With this in mind, the purpose of this article is to present the results of research on the effectiveness of using a Virtual Reality (VR) simulator developed at the Military University of Technology in teaching the construction and basic activities of combat work in the area of conducting a selected check of the functioning of the SA6 Gainful missile launcher system. The theoretical foundation for the empirical research was provided by a method of analyzing literary content. By using the method of comparison and generalization, knowledge was obtained about the general construction and use of training devices in the training of the anti-aircraft defense forces of the Polish Armed Forces, and the features of the VR simulator were described. As regards the empirical methods, a study was conducted using a research sample which was conducted using a parallel triangulation strategy scheme involving the simultaneous use of quantitative and qualitative methods. The synthesis served in formulating the final conclusions and in determining the relationships between theoretical and empirical studies. The results obtained in this way can provide valuable information about the effectiveness of using training devices in training anti-aircraft defense forces and serve as a basis for further work on their development and application.

Revisiting Presidential Nuclear Autonomy

The United States (US) Nuclear Command and Control (NC2) system is no longer appropriate for the current global security environment. The NC2 system lacks adequate hard checks and balances on the president’s use of nuclear weapons. Designed for decisiveness, there is no systemic barrier preventing the president from authorizing and ordering the launch of a nuclear weapon, regardless of the reason. As such, this memo proposes that Congress impose limits on the president’s nuclear first-strike authority. Congressional approval should be required before the president can launch a nuclear strike. In addition, the Department of Defense should reduce its reliance on silo-based missile systems and increase its reliance on submarine-launched ballistic missiles (SLBMs). The high vulnerability of silo-based intercontinental ballistic missiles (ICBMs) to enemy nuclear strikes creates a ‘use it or lose it’ scenario, where ICBMs must be launched before they are destroyed. This increases pressure on the president to launch these missiles before they are destroyed, increasing the chance of miscalculation or launch if there is a false alarm. SLBMs are not subject to the same vulnerabilities. As more survivable assets, SLBMs reduce pressure on the president to act hastily, eliminating the chance of a poorly informed nuclear launch.

Cavitating Venturi as a Mass Flow Controller in a Deep Throttling Liquid Rocket Engine

Abstract The most common solutions for rocket engines are the single operation point (thrust level) units. Oxidiser and fuel mass flow rates and the oxidiser-to-fuel mass flow rate ratio (OFR) are some of the determinants of the thrust level. Based on these, planetary ascent and descent; space rendezvous; orbital manoeuvring, including orientation and stabilisation in space; hovering, hazard avoidance during planetary landing; and ballistic missile trajectory control propulsion systems could use throttleable liquid engines. Several engine throttling methods, such as supply pressure variation and variable injector area, can be applied. Among others, a cavitating venturi propellant regulatory valve is one of the most promising throttling method. This type of valve can provide steady mass flow, despite the downstream pressure disturbance (i.e. from the combustion chamber), which sustains a stable engine thrust as the mass flow is kept. The article presents the valve sizing method, design and prototype test results of the cavitating venturi valve that has potential for utilisation in a deep throttling rocket engine. Mass flow stability and repeatability are presented for valve operating points in the 10%–110% nominal mass flow range. Valve design optimisation, based on CFD, to sustain cavitation for a higher downstream-to-upstream pressure ratio is shown.

GNSS denied navigation system for the manoeuvring flying objects

PurposeBefore designing a navigation system, it is necessary to analyse possible approaches in terms of expected accuracy, existing limitations and economic justification to select the most advantageous solution. This paper aims to collect possible navigation methods that can provide correction for inertial navigation and to evaluate their suitability for use on a manoeuvring tactical missile.Design/methodology/approachThe review of existing munitions was based on data collected from the literature and online databases. The data collected included dimensions, performance, applied navigation and guidance methods and their achievable accuracy. The requirements and limitations identified were confronted with the range of sensor parameters available on the market. Based on recent literature, navigation methods were reviewed and evaluated for applicability to inertial navigation system (INS) correction in global navigation satellite system-denied space.FindingsThe performance analysis of existing munition shows that small and relatively inexpensive micro-electro-mechanical system-type inertial sensors are required. A review of the parameters of existing devices of this type has shown that they are subject to measurement errors that do not allow them to achieve the delivery accuracy expected of precision missiles. The most promising navigation correction methods for manoeuvring flying objects have been identified.Originality/valueThe information presented in this paper is the result of the first phase of a project and presents the results of the requirements selection, initial sizing and preliminary design of the navigation system. This paper combines a review of the current state of the art in missile systems and an analysis of INS accuracy including the selection of sensor parameters.

Identification of KLHDC2 as an efficient proximity-induced degrader of K-RAS, STK33, β-catenin, and FoxP3

Targeted protein degradation (TPD), induced by enforcing target proximity to an E3 ubiquitin ligase using small molecules has become an important drug discovery approach for targeting previously undruggable disease-causing proteins. However, out of over 600 E3 ligases encoded by the human genome, just over 10 E3 ligases are currently utilized for TPD. Here, using the affinity-directed protein missile (AdPROM) system, in which an anti-GFP nanobody was linked to an E3 ligase, we screened over 30 E3 ligases for their ability to degrade 4 target proteins, K-RAS, STK33, β-catenin, and FoxP3, which were endogenously GFP-tagged. Several new E3 ligases, including CUL2 diGly receptor KLHDC2, emerged as effective degraders, suggesting that these E3 ligases can be taken forward for the development of small-molecule degraders, such as proteolysis targeting chimeras (PROTACs). As a proof of concept, we demonstrate that a KLHDC2-recruiting peptide-based PROTAC connected to chloroalkane is capable of degrading HALO-GFP protein in cells.

A High Watermark in Indian Missie Program

Development of tactical guided missiles is a very challenging task. There are many elements on ground for acquiring and tracking targets while there are equally complex subsystems onboard the missile. This paper brings out some of the critical issues solved by Defence Research and Development Organisation (DRDO) in case of three missile systems - TRISHUL, AKASH and NAG. Recently aLl these missiles have recorded excellent results in meeting all design requirements ending w ith s ucces sful tar get inte rcepts.

Integrated Controller for Divert Thruster Flight Propulsion Control Systems

Future generation missile calls for development of fast response propulsion based control systems to achieve hit-to-kill miss distance against highly manoeuvrable targets covering high-endo to exo-atmosphere regions. Control systems based on solid propulsion are developed connecting multiple pintle nozzles and control thrust vector is generated with distribution hot gasses in pitch/yaw directions. Differential distribution of hot gasses among multiple nozzles is complex due to time varying coupled non-linear chamber pressure dynamics with propellant combustion and nozzles’ flow phenomena and methods based on linear control may not ensure stability in wide operating conditions. There is need to develop "Unified Controller" based on non-linear formulation to ensure control stability in wide operating conditions of various mission applications, with advanced features for new generation missiles to counter various futuristic targets, and achieve hit-to-kill capabilities following integrated approach in order to improve the total system performance. Non-linear algorithms proposed in the recent literature do not exploit synergism between plant and actuation systems dynamics. Present paper presents novel non-linear feedback linearization technique, Dynamic Inversion, a relatively straightforward approach in Integrated Control Framework (ICF) implementing inherent time scale separation between solid motor plant and hot gas flow control valve actuation system. To ensure stability in various operating conditions and assure robust performance in the presence of parameter inaccuracies, controller is augmented with model-following neuro-adaptive design. Prototype systems: Thrust Controlled Motor (TCM) and Divert Thruster Flight Propulsion Control Systems (DTFPCS) are developed to demostrate/validate "Unified Controller" for missile control system. Closed loop control of chamber pressure is demonstrated with single pintle nozzle system and control thrust vector generation with multiple nozzle systems. Model update takes place adaptively online and unlike a typical indirect adaptive control approach, there is no need to update the individual parameters explicitly. Instead the inaccuracy in the system output dynamics is captured directly and then used in modifying the control. Based on present work, missilecontrol systems for various applications can be developed with limited controller changes and thereby minimizing number of developmental tests and cost.

DESIGN AND TECHNOLOGY SYSTEM FOR DEVELOPMENT AND OPERATION OF ULTRALIGHT SUBORBITAL ROCKET COMPLEXES

Abstract. Vehicles are called suborbital if they either move along a ballistic trajectory with a flight velocity sufficient to reach altitudes of up to 100 km or more, but insufficient for becoming an orbiter, or fly to altitudes of 100 km or more strictly vertically, but do not become artificial satellites of the planet, even if they reach sufficient velocity at some point. In both the first and second cases, this will be considered a space flight if its height exceeds 100 km (the Kármán line). Despite the active development of the suborbital rocket science in the world as a means of solving many scientific and technical problems in the space and defense industries, scientific research and engineering education, the development of suborbital rocket science in Ukraine has so far remained, at best, at the level of achievements of the 1960s and 1970s and has been supported by numerous amateurs. This article presents the results of the creation and development of a design and technological system for the development and operation of ultralight suborbital rocket systems as the basis for the creation of new models of domestic space rocket systems, rocket and missile weapons systems, the development of innovative technologies in the field of rocket science in general, practical training of highly qualified specialists for the space industry. This paper presents structural and layout diagrams of the developed suborbital rockets, design and technological solutions for the creation of on-board radio-electronic equipment and rocket engines, design modeling, bench and flight tests. The presented design and technological system is already used today at Oles Honchar Dnipro National University for comprehensive practical training of specialists in the field of creation and operation of rocket technology and missile and rocket weapons.

An iterative mass-to-drag ratio estimation method for ballistic targets

Ballistic target tracking and identification is a key task for missile defense systems. A vital problem in target track and recognition is how to estimate the target mass-to-drag ratio fast and accurately. Based on the constraints of energy conservation, this paper proposes an iterative mass-to-drag ratio estimation method. This algorithm first estimates the position and velocity of the target using unscented Kalman filter, and then estimates the mass-to-drag ratio of the target by using energy conservation. By iterating, the final value is outputted. The simulation results show that this method can estimate the mass-to-drag ratio of the target at a high altitude, which provides a precise way for mass-to-drag ratio estimation.

METHOD OF DATA IDENTIFICATION IN THE SYSTEM OF INFORMATION SUPPORT OF ANTI-AIRCRAFT MISSILE UNITS BASED ON THE INTERPOLATION METHOD

The issue of making timely decisions in the control system of anti-aircraft missile units in order to ensure the rapid detection of air targets and their timely firing at long distances requires constant attention from military specialists of the leading countries of the world. The article presents the results of developing a methodology for identifying data in the information support system of anti-aircraft missile units based on the interpolation method. The object of research is the process of data identification in the information support system of anti-aircraft missile units. The subject of research is data interpolation methods. The purpose of the research is to develop a methodology for identifying data in the information support system of anti-aircraft missile units based on the interpolation method. Conclusions. An algorithm has been developed that implements a methodology for identifying the targeting data of the air defense missile control center, obtained from data from radio engineering troops, with the data of the unit's own or attached reconnaissance and targeting station and allows to increase the accuracy of combat information. To determine that the marks from the target received from the reconnaissance and targeting station and from the control center of the air defense missile unit are marks of the same target, an interpolation procedure is performed, provided that the data received from both sources is secondary information of the target observation vector. The interpolation procedure itself involves the formation of a spatial identification strobe and a comparison of the target trajectory obtained from the trace data of the own (supporting) reconnaissance and targeting station and the interpolated data of the target's movement relative to the latest external targeting data in the opposite direction. This algorithm can be used to implement the relevant tasks in the complex of automation tools for the control center of military units of air defense missile forces, automated workstations of commanders of air defense missile forces, which will reduce the time for searching and detecting air targets by the missile guidance station of the air defense missile system and directly increase the firepower of these units.

JUSTIFICATION OF MODERNIZATION PATHS FOR SHORT-RANGE AIR DEFENSE MISSILE SYSTEMS OF LAND FORCES

Modern air defense systems of large, medium, short, and close range are among the most complex types of military equipment. The ability of a country to independently produce modern air defense systems is an indicator of the level of development of its defense industry. Therefore, the development, serial production, and modernization of these systems require a high level of scientific and technological advancement, as well as significant investment in research and development.
 During the full-scale invasion of Ukraine by the russian federation, both manned and unmanned aerial attack means were employed by the air and space forces. From the initial moments of the invasion, all components of the air defense encountered the need for the modernization of the existing air defense systems.
 The need for the modernization of existing air defense systems in Ukraine is justified by a comparative assessment of their tactical and technical characteristics with similar systems provided by Western partner countries within the framework of material and technical assistance. The modernization of air defense missile systems covering mechanized units will enhance the capability to detect and track targets, thereby increasing the effectiveness of the system in modern combat conditions.
 The issue of air defense system modernization has been the subject of numerous publications. These works discuss prospective directions for the development of short-range air defense systems, including the description of new technologies and materials that can be utilized to enhance the functionality and reliability of such systems. The publications focus on various methodological approaches to evaluate options for upgrading weapons and military equipment.

Adaptive reinforcement learning control for a class of missiles with aerodynamic uncertainties and unmodeled dynamics

AbstractIn this paper, a super-twisting disturbance observer (STDO)-based adaptive reinforcement learning control scheme is proposed for the straight air compound missile system with aerodynamic uncertainties and unmodeled dynamics. Firstly, neural network (NN)-based adaptive reinforcement learning control scheme with actor-critic design is investigated to deal with the tracking problems for the straight gas compound system. The actor NN and the critic NN are utilised to cope with the unmodeled dynamics and approximate the cost function that are related to control input and tracking error, respectively. In other words, the actor NN is used to perform the tracking control behaviours, and the critic NN aims to evaluate the tracking performance and give feedback to actor NN. Moreover, with the aid of the STDO disturbance observer, the problem of the control signal fluctuation caused by the mismatched disturbance can be solved well. Based on the proposed adaptive law and the Lyapunov direct method, the eventually consistent boundedness of the straight gas compound system is proved. Finally, numerical simulations are carried out to demonstrate the feasibility and superiority of the proposed reinforcement learning-based STDO control algorithm.

Experimental characterization of unidirectional carbon – Carbon composite laminate

Advanced polymeric Composites have wide applications in various industrial sectors of Missile System, Automobile, and Space Structures have been sound prominent and endlessly receiving the wide awareness for many industries. The structural engineer desires to be eminent with the belongings of the composite material structures. The performance of fiber reinforced polymeric composite material beneath dynamic load plays a crucial task in designing such structures. In the recent work, an attempt is made to determine optimum fiber angle and the behavior of the advanced polymeric composite material, i.e., Carbon – Carbon Composites under Tensile and Compressive loads. Mechanical properties, viz., Compressive and Tensile strength are determined by using experimentation method. Hand layup technique is used for fabricating the laminates. FE Analysis (Ansys) is carried out on various fiber angles likely be [0°-90°], [30°], [45°], [60°] to validate the results which is obtained from experimentation.