Projectile Motion Research Articles

Match activity profile analysis during professional men’s double pickleball tournaments

ABSTRACT The aim of this study was to analyse the activity profile of professional men’s doubles pickleball tournaments. A total of 6839 shots from eight men’s doubles matches, corresponding to the final stages of two Professional Pickleball Association (PPA) Tour tournaments were analysed. The match activity analysis included technical-tactical (shots per player, hitting locations, type of shots, ball trajectory and action and shot outcomes) as well as playing and resting time parameters (rally duration, effective playing time, resting time, work-to-rest ratio). Match duration averaged 36 ± 15.9 min, with a work-to-rest of 1:1.6 ± 0.3, while actual playing time averaged 14.0 ± 5.0 min (39% of total match time). Most points lasted between 3–9 s (67.4%) with rest times of 9–15 s (84.3%). In 60.5% of the cases, rallies involved 3–10 shots, with the forehand being the most frequent shot (40.2%). Indirect shots were more common than direct ones, with most shots being played from the transition zone (71.3%). Cross-court play (54%) dominated over parallel play and 90.8% of shots were intercepted. Winning pairs’ left-side players performed more shots per game (27.3%). This analysis provides valuable insights into the activity profile of doubles pickleball, offering guidance for improving sports’ performance.

Improvement of K-2 rifle’s live-fire accuracy using virtual reality shooting training system

Virtual reality (VR) is used in military training with simulators for marksmanship training. Despite evidence of the effectiveness of VR simulation-based training, less is known about the association between VR marksmanship training and record-fire accuracy. In addition, the VR simulations utilized in prior research were largely rooted in laser infrared technology, which does not consider the ballistic trajectory of bullets. Thus, this study was designed to examine the effect of VR-based shooting training systems, Multi-purpose Assault and sniper Rifles-shooting Simulator (MARS) training that applies a six-degree-of-freedom trajectory of a rigid body, on live-fire accuracy. The participants were divided into three groups (non-MARS training, two-MARS training, and four or more-MARS training), and their live-fire scores were compared, considering the effects of psychological variables. Additionally, the proportions of elite shooters were computed among the groups. Analysis of variance showed that individuals who were exposed to MARS training four times or more showed better K2C1 rifle live-fire accuracy than those in two-MARS training and non-MARS training. In addition, the rate of elite shooters was the highest in the four or more-MARS groups. These results demonstrate that the VR simulation training using MARS, which applies an algorithm for a six-degree-of-freedom trajectory of a rigid body, can improve the K2C1 rifle live-fire accuracy. Future studies are needed to provide stronger evidence for the optimal number of MARS training programs to improve live-fire shooting performance.

Projectile motion under quadratic air resistence via multistep-differential transformation method

The projectile motion system was examined in this study when air resistance was present (we only looked at the situation of quadratic air resistance). First, we used Newtonian mechanics to derive the equation governing the system. Second, the study focused on the projectile motion’s characteristics, namely its maximum height and maximum horizontal range. Additionally, we used simulation plots to apply the Differential Transform Method (DTM) and the Multistep Differential Transform Method (Ms-DTM) to solve the equations found. This allowed us to discuss the projectile’s trajectory. We computed the flying time and the maximum range by comparing our findings with experimental data from published research. In the end, the absolute errors were computed to find the optimal numerical approach to solve this problem.

Development of Mathematical Support and Software for Ballistic Analysis and Optimization of Active-Missile Projectile Parameters

The paper presents the results of developing mathematical and software support for internal and external ballisticsmodelling, as well as optimizing the parameters of an active-reactive projectile. A complex mathematical model of active-reactive projectile ballistic analysis includes the problem of external ballistics, the problem of internal ballistics inside the gun barrel and the problem of internal ballistics of a solid-fuel jet engine. The problem of active-reactive projectile parameteroptimization is to increase the flight range with respecttomotion stabilitycondition along the entire trajectory. Based on the mathematical model of ballistic analysis, the algorithms for solving a multi-criteria problem of active-reactive projectileparameteroptimization have been developed. The developed software package includes a block of calculation modules implementing mathematical models and computational algorithms, a database of projectile parameters and simulation results, a block for visualization the computational experiment results in the form of diagrams and tables. The software package can be used in the design and optimization of the projectileparameters of artillery systems implementing the active-reactive throwingprinciple. The results of mathematical modeling and optimization of parameters are considered using the example of the designed active-reactive projectile for the 152 mm artillery system. To improve the projectilestability on the trajectory during jet engineoperation, it is proposed to install ribs at an angle to the projectile axis on the inner surface of the nozzle so as to create extra torque. Based on the developed model, the optimal characteristics of firing an active-reactive projectile of caliber 152 mm are determined. The results of internal and external ballisticsproblem solutionfor an active-reactive projectile obtained by means ofthe software package for ballistic process modeling are presented. The main problem of internal ballistics inside the gun barrel, the problem of internal ballistics of a solid-fuel jet engine, the direct problem of external ballistics of an active-reactive projectile and the study of the projectile motion stability along the trajectory are solved. Optimal parameters of internal and external ballistics, providing the maximum firing range of an active-reactive projectile with respect toitsmotionstability along the entire trajectory, are found.

Foul Detection for Table Tennis Serves Using Deep Learning

Detecting serve fouls in table tennis is critical for ensuring fair play. This paper explores the development of foul detection of table tennis serves by leveraging 3D ball trajectory analysis and deep learning techniques. Using a multi-camera setup and a custom dataset, we employed You Only Look Once (YOLO) models for ball detection and Transformers for critical trajectory point identification. We achieved 87.52% precision in detecting fast-moving balls and an F1 score of 0.93 in recognizing critical serve points such as the throw, highest, and hit points. These results enable precise serve segmentation and robust foul detection based on criteria like toss height and vertical angle compliance. The approach simplifies traditional methods by focusing solely on the ball motion, eliminating computationally intensive pose estimation. Despite limitations such as a controlled experimental environment, the findings demonstrate the feasibility of artificial intelligence (AI)-driven referee systems for table tennis games, providing a foundation for broader applications in sports officiating.

Pedagogical strategy of teaching-learning projectile throwing in third year baccalaureate students of the “Santa Rita Educational Unit”

A pedagogical strategy is presented for teaching projectile launching to third-year high school students at the Santa Rita Educational Unit. It is focused on teaching concepts such as parabolic trajectory, initial velocity and launch angle, which are fundamental. to understand the motion of projectiles in physics. To facilitate this learning, the PhET interactive simulator was used, which allowed students to manipulate different variables and observe how these affect the behavior of the projectiles in real time. The methodology was implemented in three phases: a theoretical introduction to the key concepts, an interactive experimentation phase with the PhET simulator, and an evaluation based on theoretical and practical tests. In addition, this pedagogical strategy seeks to promote active and participatory learning, where Students become protagonists of their own learning process, exploring and discovering the effects of changes in launch parameters. The result was the evaluation of the students, which was carried out through tests that combined theoretical questions about the principles of projectile movement and practical exercises that required them to apply what they learned in simulations.

Research on the Aerodynamic and External Ballistic Characteristics of Bullets Based on Low-Temperature Meteorological Factors

Abstract To further investigate the aerodynamic and ballistic trajectory characteristics of a certain type of ammunition under the influence of low-temperature meteorological factors, based on computational fluid dynamics and rigid body dynamic trajectory equations, numerical calculations and analysis of the aerodynamic characteristics and 6-degree-of-freedom rigid body ballistic trajectory, as well as low-temperature environmental ballistic trajectory flight tests, were conducted on this type of ammunition. The research shows that under constant atmospheric pressure, as the ambient temperature decreases, the pressure on the bullet surface increases, the aerodynamic parameters of the bullet decrease, and the convergence trend of the bullet’s ballistic trajectory angle of attack weakens significantly; under constant low-temperature, as the atmospheric pressure decreases, the pressure on the bullet surface decreases, the changes in the aerodynamic parameters of the bullet are small, and the convergence trend of the bullet’s ballistic trajectory angle of attack increases.

A058: The Impact of Multi-Directional Training on Change-of-Direction Speed and Short-Distance Sprint Ability in Tennis Student-Athletes

Objective: Tennis, characterized by rapid multi-directional sprints, involves lateral movements along the baseline constituting approximately 70% of gameplay, with each single movement covering around 3 meters. On average, there are 2-4 direction changes per point, and each stroke requires 0.4 seconds. Recognizing the imperative need for tennis players to rapidly change direction and execute short-distance sprints, influenced by factors like the ball's trajectory, opponent's movements or disguise movements, this study aimed to investigate the impact of three weeks of multi-directional sprint training on the change-of-direction speed and short-distance sprint ability of tennis student-athletes. Methods: Nineteen male tennis athletes with an ITN5 level or above from Beijing Sport University, with no lower limb injuries or surgery history in the past six months, were randomly assigned to the multi-directional sprint training group (RR group, 9 subjects) and the fixed-route multi-directional sprint training group (FR group, 10 subjects). Independent sample t-tests for height, weight, age, and ITN level indicated no significant differences between the two groups (P > 0.05). Utilizing equipment such as the Agility Training Instrument, SmartSpeed, high-speed cameras, and marked buckets, the study conducted multi-directional sprint training in a 3x3 m experimental area. Training modes included: (1) sequentially passing through the fixed training route of the sensor panel, and (2) random signal-directed directional movement training. The experimental intervention comprised three stages: (1) First week: 15 sessions = 3 times × 5 sets; (2) Second week: 20 sessions = 4 times × 5 sets; (3) Third week: 25 sessions = 5 times × 5 sets. Spider Run and T-drill tests were conducted before and after the intervention to assess change-of-direction speed, along with a 5m straight sprint test to evaluate short-distance sprint ability. Results: The Shapiro-Wilk (S-W) test confirmed that each group's data followed a normal distribution, with no differences in various indicators between the RR and FR groups before the intervention. Data analysis revealed significantly higher Spider Run, T-drill, and 5m straight sprint scores in both groups after the intervention compared to pre-intervention (P < 0.05). There were no significant differences between the two groups in improving change-of-direction speed and straight sprint ability test scores (P > 0.05). Conclusion: Three weeks of multi-directional sprint training effectively enhanced the change-of-direction speed and short-distance straight sprint ability of tennis student-athletes.

Tangential and Normal Acceleration Components in Projectile Motion

Tangential and Normal Acceleration Components in Projectile Motion

Визначення критичної швидкості пробиття мішеней зі сплавів алюмінію та магнію

The motion of a non-deformable kinetic projectile of cylindrical shape in a continuous homogeneous semi-infinite medium is considered based on the well-known Alekseevsky-Tate model. As a result of solving the differential equation of motion of the impactor, the dependence of its speed on the penetration depth was obtained. The boundary conditions are: before penetrating the target, the speed of the impactor is equal to the critical penetration speed, and after penetrating the thickness of the target, the speed of the impactor is equal to zero. A simple formula for calculating the critical velocity of target penetration Vcr is obtained based on this dependence. This formula does not contain empirical coefficients. Therefore, the calculation of Vcr requires a minimum of information about both the material of the projectile and the target. An improved equation for calculating the resistance of the target material is also proposed. For targets from aluminum and magnesium alloys, critical penetration rates depending on their thickness were theoretically calculated and penetration curves were plotted. Also, the critical penetration velocity for targets from these alloys was determined experimentally during ballistic tests the results of the authors' own research and taken from the literature. A good agreement between the experimental data and theoretical calculations of the critical penetration velocity is observed, with the calculation error not exceeding 4%. With regard to the assessment of the critical thickness of the target, the maximum error will be about 5%, the average – 2,5%. It is assumed that in order to provide the reliable guaranteed protection against a known projectile, it is necessary to overestimate by 4% the calculated value of the critical penetration velocity while designing the protective element. Keywords: equation of motion, impactor, target, critical velocity, aluminum alloys, magnesium alloys.

Numerical Simulation Model of Projectile In-bore Motion Parameters Based on Interior Ballistics Theory

Abstract In modern warfare, artillery systems serve as crucial equipment, and their firing accuracy directly impacts their overall capability to strike targets. Especially under local warfare conditions, the demand for shooting accuracy of large-caliber artillery and small-caliber naval guns is increasingly high. This paper focuses on the interior ballistics design of artillery by constructing an accurate model of the projectile’s in-bore motion.

Research on Guidance and Control Method of UAV for Ground Attack Missions

Abstract On the modern battlefield, suicide drones have a low ability to break through the air defense fire network when using traditional ballistics against ground targets. The adoption of ballistic trajectory with landing constraints can effectively improve the survivability of missiles and the attacking effect on ground targets. Starting from the pure proportional navigation, the relationship between the ballistic angular rate and the target line-of-sight angular rate of the traditional proportional guidance is expanded to the relationship between the missile’s overload and the target’s line-of-sight angle, so as to realize the effect of controlling the missile’s overload to indirectly control the ballistic angle to the target’s line-of-sight angle of convergence, which ensures the fast tracking of the target and at the same time, makes the missile attack the target’s trajectory more gently. Attacking the target with the overload control method guarantees that the overload of the missile during the guidance process is within a reasonable range, which effectively reduces the probability of missing the target. By selecting appropriate proportional navigation coefficients and incorporating bias terms with controlled descent angles, a three-dimensional guidance and control method is designed to achieve precise targeting with longitudinal descent angle constraints on fixed ground targets. This guidance and control method remains effective even under hypersonic conditions, as verified through hardware-in-the-loop simulation, confirming its effectiveness and precision.

Simulation study of aerodynamic parameters of small unmanned aerial vehicle (UAV) dropped munitions

Abstract Based on the method of computational fluid dynamics, fluent software is used to simulate and calculate the aerodynamic parameters of small unmanned aerial vehicle projectiles. The drag coefficient, lift coefficient, and pitching moment coefficient of the projectile under different angles of attack and different throwing velocities are obtained by establishing a three-dimensional model of the projectile, dividing the computational grid, and setting up the relevant initial conditions. The results are analyzed, and the results of the computation can provide a basis for the calculation of the ballistic trajectory of the projectile.

Research on ballistic correction technique based on Pontryagin’s Minimum Principle

Abstract The research endeavor focuses on optimizing ballistic trajectories for correction mortar shells, employing Pontryagin’s Minimum Principle (PMP) grounded in energy conservation. A controlled particle ballistic model is established for the corrective projectiles, facilitating the derivation of control strategies targeting ballistic attributes. Leveraging MATLAB’s simulation capabilities, this study explores the variable tendencies of trajectory incline, tangential overload, and projectile velocity under a semi-constrained framework—fixed launch points and flexible terminal states. Simultaneously, the corrective efficacy of projectiles is validated. Simulation outcomes affirm that integrating PMP with the projectiles’ mathematical model constitutes a potent approach to resolving ballistic optimization challenges, thereby enhancing trajectory precision and overall projectile performance. This work underscores the significance of optimal control methodologies in advancing projectile technology.

Stochastic evolution of projectile motion during artillery exterior ballistic

Abstract In order to analyze the variation law of the flight distance error of the unpowered projectile with time, the probability density function (PDF) of projectile flight distance is calculated by the probability density evolution method (PDEM) based on 6 degrees of freedom rigid ballistic equation with random parameters of the projectile. A test example shows that the calculated results of PDEM are consistent with Monte Carlo (MC) method, which further verifies the effectiveness. In addition, the evolution of projectile flight distance and its error is analyzed within the given ranges of projectile parameter error, which provides a reference for the general design of artillery.

A refined prediction model for the initial disturbances of the projectile in the self-propelled gun

Abstract In the gun launch process, the continuous propellant combustion provides power and energy for the projectile. Due to the gap between the projectile and barrel, the high-speed motion of the former is generally accompanied by contact and collision with the latter. Meanwhile, the gun also recoils under the propellant gas. Notably, the above complex motion of the system causes the initial disturbances of the projectile and muzzle. Previous launch dynamic models usually neglect the influence of the gun recoil on the combustion and flow in the chamber. However, the gun recoil inevitably further increases the chamber’s free space, resulting in the calculation deviations of projectile and muzzle disturbances. The above deviations ultimately determine the firing accuracy and firing stability prediction. To study the in-bore projectile motion and subsequent external ballistic process more accurately, an improved coupled calculation method of launch dynamics is developed. This work combines the interior ballistic two-phase flow dynamics considering the gun recoil, in-bore projectile motion theory, multibody system dynamics, and necessary high-precision numerical schemes. The launch process of the 155 mm self-propelled gun is studied. As the results show, the calculated vibration characteristics, dynamic response, and interior ballistic performance indexes are consistent with measured ones, verifying the feasibility of the above method. In addition, the initial disturbances of the projectile with and without considering the recoil’s influence on the combustion and flow in the chamber is discussed. The work in this paper provides an accurate tool to predict the initial disturbances of the projectile.

Precise calculation for underwater internal ballistics based on bi-directional coupling

Abstract An accurate calculation method for underwater internal ballistics considering motion resistance is proposed based on bi-directional coupling. The resistance of the projectile against water is often neglected in underwater classical internal ballistic modelling, leading to less precise calculations. In this paper, the mutual influence of the projectile motion and the water current is considered comprehensively by establishing a bi-directional coupling model of the fluid and the projectile. The launching process of the underwater projectile is simulated in detail using a combination of computational fluid dynamics (CFD) and classical internal ballistics (CIB). The numerical simulation results show that the bi-directional coupling model has high accuracy in predicting the trajectory, initial velocity and pressure distribution. Compared with the traditional bi-directional coupling model, the bi-directional coupling model can reflect the actual situation more accurately, which significantly improves the reliability and accuracy of underwater ballistics research. The research results of this paper provide new theoretical support for underwater ballistic design and are of great significance for improving the performance of underwater weapon systems.

Criterion Validity and Reliability of a New Medicine Ball Rotational Power Test.

Hardy, SGJ, Stelzer-Hiller, OW, Edwards, KM, and Freeston, J. Criterion validity and reliability of a new medicine ball rotational power test. J Strength Cond Res XX(X): 000-000, 2024-This study assessed the validity and reliability of 2 medicine ball rotational power assessments, the novel push for maximum velocity by radar (MBvel), and the commonly used push for maximum distance by tape measure (MBdis), against the criterion reference 3-dimensional motion capture (MoCap) to identify the best-practice field-based assessment. Fifteen professional female cricketers volunteered for 2 testing sessions each comprising of a specific warm-up and 24 (12 MBvel, 12 MBdis) maximal throws of a 2-kilogram medicine ball. Radar velocity and tape measure distance were compared with MoCap velocity and projectile motion calculated distance overall, and by dominant and nondominant sides. Statistical analysis included intraclass correlations (ICCs) for accuracy (1, 1) and reliability (3,1), Bland-Altman plots for bias precision and limits of agreement, linear regression (R2) for variance, and Pearson's (r) for correlation. Significance was set α = 0.05. MBvel demonstrated excellent accuracy (ICC = 0.97 [0.97-0.98]), and nearly perfect agreement for bias (-0.09%) and precision (1.49%). Side-to-side analysis showed the same profile for MBvel dominant (ICC = 0.96 [0.95-0.97], bias -0.15%, precision = 1.55%) and nondominant sides (ICC = 0.97 [0.96-0.98], bias -0.05%, precision = 1.53%). MBvel demonstrated excellent reliability overall (ICC = 0.94 [0.82-0.98]) for dominant (ICC = 0.88 [0.69-0.97]) and nondominant sides (ICC = 0.93 [0.80-0.98]). MBdis showed poor accuracy (ICC = 0.38 [0.28-0.47]), large bias (12.43%), lower precision (4.55%), and moderate reliability (ICC = 0.72 [0.32-0.90]). The MBvel assessment validly and reliably measures rotational power performance, enabling practitioners to profile, benchmark, and assess the quality in the field.

Uncovering the mechanical secrets of the squirting cucumber

Rapid movement is rare in the plant kingdom, but a prerequisite for ballistic seed dispersal. A particularly dramatic example of rapid motion in plants is the squirting cucumber ( Ecballium elaterium ) which launches its seeds explosively via a high-pressure jet. Despite intriguing scientists for centuries, the exact mechanism of seed dispersal and its effect on subsequent generations remain poorly understood. Here, through a combination of experimentation, high-speed videography, quantitative image analysis, and mathematical modeling, we develop a full mechanical description of the process. We quantify the turgor pressure driving ballistic ejection, and uncover key mechanical interactions between the fruit and stem both prior to and during seed ejection, including the unique feature that fluid is redistributed from fruit to stem prior to ejection, a developmental event that goes against the paradigm of rapid seed ejection but which is of key importance in successful dispersal for Ecballium . Combining modeling elements, we quantify and simulate the ballistic trajectories of seeds, which are dispersed over distances greater than 2,000 times their length. We demonstrate how together these mechanical features contribute to a nearly uniform distribution of seeds away from the parent plant. Parametric variation of key developmental events in the modeling framework indicates how a suite of adaptive features in combination drives the spatial distribution of offspring over consecutive generations, and suggests that ballistic seed dispersal has a stabilizing effect on population dynamics by reducing intraspecific competition.

Big fish can't jump? Allometry of terrestrial jumping in cyprinodontiform fishes.

Teleost fishes that emerge onto land must produce effective terrestrial movements to return to the water. Using the Cyprinodontiformes as a model system, we examined a terrestrial behavior termed the tail-flip jump across a size range of individuals representing three species of aquatic killifishes (Gambusia affinis, Poecilia mexicana, and Jordanella floridae) and two species of amphibious killifishes (Kryptolebias marmoratus and Fundulus heteroclitus) to identify potential effects of size (mass) on jumping performance. The ballistic trajectory equation was used to partition the contributions of velocity (determined by acceleration and contact time) and takeoff angle to jump distance. Despite differences in size (over an order of magnitude) all fishes took off from the ground at ∼45°. However, in terms of total displacement, aquatic and amphibious killifish species scaled differently in their ability to perform the tail-flip jump. Aquatic killifishes decrease in total jump distance as mass increases; however, amphibious killifishes increase in total jump distance as mass increases. Aquatic killifishes cannot produce adequate accelerations at larger sizes, but amphibious killifishes produce similar accelerations despite over an order of magnitude size difference. Because of this, amphibious killifish species are able to maintain fast takeoff velocities at large body sizes. Distinct scaling patterns may be generated by differences in body shape. Aquatic killifishes have a fusiform body shape, with most of their body mass in the anterior of the body, while amphibious killifishes have a more uniform body shape that reduces their overall mass present in the anterior body. We hypothesize that reduced mass in the anterior body facilitates raising the head over the tail to prepare for takeoff. In contrast with amphibious species, the negative scaling relationship seen in body size vs. displacement in aquatic killifishes implies an upper size limit to producing the tail-flip jump for fish species that infrequently encounter the terrestrial environment.