Showing papers on "Trajectory of a projectile published in 2013"

Equations of motion of a spin-stabilized projectile for flight stability testing

Abstract: The paper presents a mathematical model of motion of a balanced spin-stabilized projectile considered as a rigid body with 6 degrees of freedom. The modeling uses coordinate systems conforming to Polish and International Standard ISO 1151. The design of kinematic equations describing motion around the center of mass uses the system of Tait-Bryan angles or Euler parameters. The total angle of attack and aerodynamic roll angle express aerodynamic forces and moments.

Method and accessory device to improve performances of ballistic throwers

Abstract: An accessory device for a ballistic thrower/launcher that can be handgun or a gun or other object throwing or launching device that is meant to improve the quality of the action, the comfort and safety of the operator. It is made of accessory devices that stabilize the operation of the throwing device aligning the recoil with the projectile trajectory making the process reproducible, predictable and controllable. It adds environment monitoring electronics, cameras and actuators, for accurately launching after aiming, considering all the major process perturbations, as movements, wind, humidity, atmospheric pressure, target movement, shooting post movement, etc. The device adds other features of safety for the operator, as stealth action, dimming process noise, recoil shock, flames and heat signature being suitable for remote operation.

Effect of the mathematical model and integration step on the accuracy of the results of computation of artillery projectile flight parameters

Abstract: Abstract. In the paper the three different mathematical models of motion of a spin-stabilized, conventional artillery projectile, possessing at least trigonal symmetry, have been introduced. The vector six-degrees-of-freedom (6-DOF) differential equations of motion are an updated edition of those published by Lieske and McCoy and are consistent with STANAG 4355 (Ed. 3). The mathematical models have been used to developing software for simulating the flight of the Denel 155mm Assegai M2000 series artillery projectile and to conduct comprehensive research of the influence of the applied model and integration step on the accuracy and time of computation of projectile trajectory.

Acoustic shockwave-based bearing estimation

Abstract: The paper presents a smartphone-based shooter localization system. As muzzle blasts are difficult to detect at longer distances and consequently present higher false detection rates, the system relies on shockwaves only. Each sensor uses four microphones to detect the Angle of Arrival and the length of the shockwave. This information, along with the sensor's own GPS coordinates, are shared among nearby smartphones. Assuming a known weapon type, it then proceeds to estimate the two possible projectile trajectory candidates for each sensor that are consistent with the observations in the horizontal plane of the sensors. A simple clustering algorithm identifies the correct projectile trajectory relying on as few as two sensors. The trajectory is then used to estimate the bearing to the shooter relative to each sensor. The paper presents the overall system architecture, the design of the sensor node that interfaces with the smartphone, the trajectory and bearing estimation algorithms, and the evaluation of the system based on a field experiment.

Launch Dynamics of Supersonic Projectiles

Abstract: The aerodynamics of projectiles launched from barrels of various devices is quite complicated due to their interactions with the unsteady flowfield around them. A computational study using a moving grid method is performed here to analyze various fluid dynamic phenomena in the near field of a gun, such as the projectile–shock wave interactions and interactions between the flow structures and the aerodynamic characteristics of the projectile when it passes through various flow interfaces. Cylindrical and conical projectiles have been employed to study such interactions and the fluid dynamics of the flowfields. The aerodynamic characteristics of the projectile are hardly affected by the projectile configuration during the process of the projectile overtaking the primary blast wave for small Mach numbers. However, it is noticed that the projectile configurations do affect the unsteady flow structures before overtaking and hence, the unsteady drag coefficient for the conical projectile shows considerable vari...

Feasibility analysis of the modified point mass trajectory model for the need of ground artillery fire control systems

Abstract: The work shows computational results of the effect of a simplified mathematical model of the flight dynamics of a spin-stabilized projectile on the accuracy and speed of calculation parameters for the projectile trajectory (in the entire range of operating quadrant elevation of the barrel and possible perturbations of the conditions firing) to determine an appropriate mathematical model for the automated fire control systems of ground artillery.

Projectile Impact Point Prediction Based on Self-Propelled Artillery Dynamics and Doppler Radar Measurements

Abstract: Any trajectory calculation method has three primary sources of errors, which are model error, parameter error, and initial state error. In this paper, based on initial projectile flight trajectory data measured using Doppler radar system; a new iterative method is developed to estimate the projectile attitude and the corresponding impact point to improve the second shot hit probability. In order to estimate the projectile initial state, the launch dynamics model of practical 155 mm self-propelled artillery is defined, and hence, the vibration characteristics of the self-propelled artillery is obtained using the transfer matrix method of linear multibody system MSTMM. A discrete time transfer matrix DTTM-4DOF is developed using the modified point mass equations of motion to compute the projectile trajectory and set a direct algebraic relation between any two successive radar data. During iterations, adjustments to the repose angle are made until an agreement with acceptable tolerance occurs between the Dop...

Ballistic Fire Control Computer (FCC) For Main Battle Tank (MBT)

Abstract: Fire Control Systems (FCSs) plays a critical role in the battle effectiveness of a Main Battle Tank (MBT) whether it is high first-round-hit-probability, ballistic solution computation for projectile trajectory, or moving target engagement. FCS comprises of Fire Control Computer (FCC), sensors, and gun controller. Fire control computer computes the elevation and azimuth (pitch and yaw axis) angles, based on the ballistic algorithm. A 32-Bit ARM processor based FCC for 125mm smoothbore gun MBT has been designed, developed and tested. The development is a migration from traditional 8-Bit or 16-Bit controllers to a 32-Bit ARM processor, making the solution more efficient and effective. The developed solution is cost-effective and easily configurable to wide variety of Armoured Fighting Vehicles (AFVs). The ARM Cortex-M4 processor provides over 100 ballistic computational updates per second. FCC computes the ballistic solution for static and moving targets. The FCC was fitted on a MBT and was rigorously field tested by firing armoured piercing (AP) shells at a range of 2000 meters. The accuracy for the ballistic computations by the fire control computer was within allowed error range. This paper presents the complete development cycle of fire control computer, implementation of ballistic algorithm, and testing of developed system.

Extension of application field of analytical formulas for the computation of projectile motion in midair

Abstract: The classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account with the drag factor assumed to be constant. An analytical approach is used for the investigation. Application field of the previously obtained approximate analytical formulas has been expanded both in the upward launch angle and in the direction of increase of the initial speed of the projectile. The motion of a baseball is presented as an example. It is shown that in a sufficiently wide ranges of initial velocity and launch angle the relative error in calculating the distance of the ball does not exceed 1%.

Horizontal projectile motion demonstration device

Abstract: The utility model discloses a horizontal projectile motion demonstration device. The horizontal projectile motion demonstration device comprises a panel, a second guide rail and a third electromagnet which are disposed on the panel, and further comprises a vertical guide structure which is disposed on the panel and is used for guiding the second guide rail to vertically move up and down, a fixing device for fixing the second guide rail onto the vertical guide structure, and a horizontal guide structure which is disposed on the panel and is sued for guiding the third electromagnet to move horizontally. According to the provided horizontal projectile motion demonstration device, any point on the horizontal projectile trajectory of a first ball is selected as a drop point, the second guide rail and the third electromagnet are adjusted positions corresponding to the drop point and are fixed; through the demonstration, an observer can see that the first ball will collide with a second ball and a third ball at any point, thereby proving that motions of the three balls have isochronisms at any point on the horizontal projectile trajectory of the first ball and further convincingly proving that horizontal projectile is the resultant motion of horizontal uniform rectilinear motion and vertical free-fall motion.

A Study on Optimizing Design of Trajectory for Glide Extended-Range Projectile

Abstract: An optimizing design of sliding extended-range is researched. The gliding extended range projectile model is established. The whole ballistic include ballistic period and sliding period. Different methods are used to optimize paragraphs ballistic. The whole ballistic achieves the optimal. Taking someone glide extended-range projectile as study object,the design of trajectory is achieved maximum extendedrange. The conclusion of this study is conducive to the design of gliding extended-range projectiles in future.

A Synopsis of Yaw-Induction Techniques Used During Projectile Free-Flight Aerodynamics Experiments

Abstract: : Projectile free-flight motion measurement from yaw cards, spark ranges, and instrumented projectiles and accompanying analyses have become integral components of weapon system development. The projectile's aerodynamics can be extracted from these free-flight motion data by fitting to the 6-degree-of-freedom equations of motion. Because many of these aerodynamic coefficients vary as a function of angle of attack, generating a sufficiently large angle of attack and/or a variety of angles of attack is necessary for complete aerodynamic characterization. Achieving this often requires special attention. Over the years, numerous yaw-induction techniques have been developed to deliberately increase the angular disturbances experienced by the projectile during launch. Yaw-induction during free-flight experiments is often necessary for two main reasons: (1) to produce angular motion large enough to diminish the effect of measurement and modeling errors, thereby increasing the accuracy of the fitted data, and (2) to produce a set of shots at varying yaw levels to characterize the nonlinear behavior of aerodynamic coefficients with respect to yaw. This report describes a variety of techniques that have been used to induce free-flight projectile angle of attack during the launch phase, and provides insight pertaining to their implementation and success based upon some quantitative results.

The Influence of Projectile Trajectory Angle on the Simulated Impact Response of a Shuttle Leading Edge Wing Panel

Abstract: In support of recommendations by the Columbia Accident Investigation Board, a team has been studying the effect of debris impacting the reinforced carbon-carbon panels of the shuttle leading edge. The objective of this study was to examine the effect of varying parameters of the debris trajectory on the damage tolerance. Impacts at the upper and lower surface and the apex of the leading edge were examined. For each location, trajectory variances included both the alpha and beta directions. The results of the analysis indicated in all cases the beta sweep decreased the amount of damage to the panel. The increases in alpha resulted in a significant increase in damage to the RCC panel. In particular, for the lower surface, where the alpha can increase by 10 degrees, there was a nearly 40% increase in the impulse. As a result, it is recommended that for future analyses, a 10 degree offset in alpha from the nominal trajectory is included for impacts on the lower surface. It is also recommended to assume a straight aft, or zero beta, trajectory for a more conservative analysis.

The DF-21D antiship ballistic missile

Abstract: The People’s Republic of China is reportedly developing an antiship version of its DF-21 ballistic missile, intended against aircraft carriers in particular. This missile, known as the DF-21D, follows a ballistic trajectory towards the approximate target coordinates. During re-entry, its maneuverable re-entry vehicle (MaRV) can be steered towards the target using control fins, guided by an on-board radar. If effective, this weapon may cause a shift in the naval power balance in the Pacific. The performance of the DF-21D is analyzed based on technical information from open sources and assuming that the MaRV is similar to the U.S. Pershing II MaRV. It is sufficiently maneuverable to ensure that, during the flight of the missile, the aircraft carrier cannot travel far enough to escape. If the ballistic trajectory is aimed to overshoot the aircraft carrier, the MaRV pitches down during the guided phase. In theory, the lateral acceleration can peak at almost 50 g and the MaRV approaches the target at a high speed (Ma ≈ 6) from almost directly overhead, which will make intercepting it extremely difficult.

Simple analytical description of projectile motion in a medium with quadratic drag force

Abstract: It is a review of the classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon with allowance for the resistance of the medium. Drag force is accepted as a quadratic function of speed. A full description of the problem is ensured by the simple approximate analytical formulae. This description includes the determining of the basic parameters of the projectile motion. The motions of a baseball is presented as examples.

Numerical Investigations on the Drag and Aerodynamic Characteristics of a Hollow Projectile

Abstract: With the purpose of obtaining the minimum drag coefficient of a normal hollow projectile,based on RANS governing equations and 2nd-order AUSM scheme,the two-dimensional flow fields and aerodynamic forces of different shapes of hollow projectiles have been simulated numerically,both the external and internal flow features of hollow projectiles with different shapes are obtained,as well as the drag variation curves and the aerodynamic shape of the hollow projectile with the minimum drag coefficient.Moreover,the projectile with minimum drag coefficient and normal projectile with ultrasonic sound flow fields are simulated respectively,the flow characteristics of them are discussed and compared,and the minimum drag effect of the obtained projectile is validated,our numerical results can provide important guidance for relative investigations.

Simulation of Dynamic Echoes Sequence of Missiles and Its Translational Motion Compensation

Abstract: By analyzing the motion characteristics of ballistic target,this paper proposes a simulation method that combines with such three factors as ballistic trajectory,target micro-motion,and radar observations,where,the radar’s dynamic echo sequence of ballistic missile is generated by the target attitude angle observed by radar in the background of flight trajectory computed by simulation,and by combining with the static data of ballistic target.By using the simulation results of typical processional motion warhead,the influences of translational motion of ballistic targets on micro-Doppler are analyzed,and the influences of radial acceleration on micro-Doppler analysis can be eliminated effectively by the translational compensation method with minimum entropy.Simulation results show that this proposed method can compensate effectively the effect of translational motion.

Optimization of Projectile Trajectory: A Review and Improvement to the Techniques

Abstract: This paper is a review, reproduction and improvement to the techniques of optimization found in literature. The problem is to optimize an angle of launch so that the projectile may hit a fixed target in plane in minimum time. The prob- lem is formulated as Augmented Lagrange (AL) equation and is solved numerically by Conjugate Gradient (CG) method. Golden Section Search (GSS) method is used for line search. An improvement of 23% to the computational efficiency is achieved by implementing improved algorithm of GSS i.e., Golden Mean algorithm. By computing iterative values of La- grange multiplier more efficiently an overall improvement of 38% is achieved.

A method of trajectory inverse estimation for space targets and performance analysis

Abstract: Discrimination of the decoys and warhead is one of the key problems in the ballistic missile defense system. As the ground-based radars hardly observe the decoy release, it is of profound significance to investigate the ballistic trajectory inverse technology of space target. In this paper, a method of inverse technology based on two-object movement theory of midcourse ballistic trajectory is presented firstly. An Extended Kalman filter algorithm is then proposed to preprocess the data of the ballistic trajectory. The new algorithm shows a better performance comparing to the traditional least squares filter algorithm. Finally, some simulations are carried out to analyze the estimation error, considering some factors such as radar measurement error and radar parameters.

Study on the Trajectory Simulation of the Ballistic Missile

Abstract: Based on the geocentric coordinate system, the object coordinate system as well as the theory of elliptic trajectory, it makes research and analysis of the ballistic-parameter-based trajectory generation method of the ballistic missile and, meanwhile, verifies the effectiveness and rationality of this method. It, under the assumed condition of elliptic trajectory, also researches the solution process of the ballistic parameters in the midcourse of the ballistic missile and, meanwhile, makes the simulation verification on the midcourse trajectory of the ballistic missile according to the radar sights variation relation in the object coordinate system during the motion process.

Variable Combat Weapons Systems External Ballistics Solver

Abstract: The kinetic energy of the projectile in the air during exercise is very complex, approximation belongs to the rigid body of the general movement,due to the shape of the projectile structure than standard ammunition,bore rifling,projectiles flying around the bomb axis of rotation movement does not produce,conducted projectile the external ballistics research when in fact only the translational motion of the projectile analytical calculations and research.In this paper,flight distance x independent variable natural coordinate system, the center of mass movement equations,by introducing false speed and Sciacca alternative to understand the operator of the kinetic energy Exterior Ballistic reverse calculated constant kinetic energy to combat different distances animate target the muzzle velocity corresponding to the kinetic energy of the projectile ideal.

Ballistic Resistance of Aluminium Foam by Ogive-Nosed and Conical-Nosed Projectiles Impact

Abstract: The paper investigates oblique penetration and perforation of low density aluminium foam with ogive-nosed and conical-nosed projectiles. Based on dynamic spherical cavity-expansion approximation, the simplified analytical penetration model has been reformulated to calculate ballistic penetration resistance of aluminium foam. In oblique penetration and perforation process, the axial and lateral force, and rotative moment of the projectile can be calculated accurately; the variation of velocity, deceleration and energy dissipation can be obtained. Ballistic trajectory and attitude of the projectile are the more important parameters to describe its motion state; ballistic trajectories of the nose and rear depict the effects of angle of incidence, angle of attack and initial strike velocity. This paper provides an analytical method which can obtain accurate and fast calculations of oblique penetration and perforation.

A Precise Trajectory Prediction Method for Target Designation Based on Cueing Data in Lower Tier Missile Defense Systems

Abstract: A recent air defense missile system is required to have a capability to intercept short-range super-high speed targets such as tactical ballistic missile(TBMs) by performing engagement control efficiently. Since flight time and distance of TBM are very short, the missile defense system should be ready to engage a TBM as soon as it takes an indication of the TBM launch. As a result, it has to predict TBM trajectory accurately with cueing information received from an early warning system, and designate search direction and volume for own radar to detect/track TBM as fast as it can, and also generate necessary engagement information. In addition, it is needed to engage TBM accurately via transmitting tracked TBM position and velocity data to the corresponding intercept missiles. In this paper, we proposed a method to estimate TBM trajectory based on the Kepler's law for the missile system to detect and track TBM using the cueing information received before the TBM arrives the apogee of the ballistic trajectory, and analyzed the bias of prediction error in terms of the transmission period of cueing data between the missile system and the early warning system.Keywords : Tactical Ballistic Missile(전술탄도미사일), Target Designation(표적 지정), Kepler Law(케플러 법칙), Cueing Data(큐잉 정보), Engagement Control System(교전통제시스템)

Trajectory of a short radio wave in the multilayer ionosphere

Abstract: An exact solution of the ray trajectory equation in the spherically symmetric ionosphere is derived by approximating the height distribution of the electron density by a set of quasi-linear and quasi-parabolic functions.

Device for counting shot bullet

Abstract: PROBLEM TO BE SOLVED: To provide a device for counting shot bullets, configured to always obtain a result of artillery live-fire training and accurate response of a trainer who has implemented the trainingSOLUTION: A range-side ballistic trajectory detector 1A disposed near a shooting place P side and a target-side ballistic trajectory detector 2A disposed near a target device TA side are used on a shooting line Ls connecting the shooting place P and the target T A controller 6 counts the number of shot bullets by comparing the bullets detected by the shooting place-side ballistic trajectory detector 1A and the target-side ballistic trajectory detector 2A

Modeling and Simulation of Electromagnetic Railgun’s Exterior Ballistic Trajectory

Abstract: A method for studying the characteristics of electromagnetic railguns exterior ballistic trajectory is present. For electromagnetic railguns high muzzle velocity and wide range,which make it cover the whole near space, an proper atmospheric environment model and an mathematical model of motion are proposed to describe the railguns exterior ballistic trajectory. By comparing the trajectory performance and velocity variation between electromagnetic railgun and conventional gun, railguns advantage in velocity and range as well as its lethality over conventional gun is testified and its potential application value is shown. Results indicate that electomagnetic railgun has the capability to intercept the missile or other type of military targets, and it is critical to get a tradeoff between mass of projectile and muzzle velocity.

A mathematical model derivation of general fire control problem and solution scenario

Abstract: This paper seeks to investigate the calculation of the prediction angle of the fire control problem. An integrated prediction angle of fire control system including a movable gun and line-of-sight tracker was derived analytically. Numerical methods developed over many years will be used to calculate the prediction angle components (lead, curvature correction, and jump correction). The most challenging computational problem associated with fire control has always been determined using projectile trajectory. Prediction equations of motion must be solved simultaneously to determine the location of the future point of impact. Because targets are small and move rapidly in three dimensions, a system of automatic computation and transmission of firing data to the gun had become necessary to the satisfactory solution of the fire control problem. In this paper, we will make use of the numerical theory to develop an accurate and efficient scheme for predicting the present and future position of a manoeuvring target.