Projectile Motion Research Articles

Properties of Gaze Strategies Based on Eye-Head Coordination in a Ball-Catching Task.

Visual motion information plays an important role in the control of movements in sports. Skilled ball players are thought to acquire accurate visual information by using an effective visual search strategy with eye and head movements. However, differences in catching ability and gaze movements due to sports experience and expertise have not been clarified. Therefore, the purpose of this study was to determine the characteristics of gaze strategies based on eye and head movements during a ball-catching task in athlete and novice groups. Participants were softball and tennis players and college students who were not experienced in ball sports (novice). They performed a one-handed catching task using a tennis ball-shooting machine, which was placed at 9 m in front of the participants, and two conditions were set depending on the height of the ball trajectory (high and low conditions). Their head and eye velocities were detected using a gyroscope and electrooculography (EOG) during the task. Our results showed that the upward head velocity and the downward eye velocity were lower in the softball group than in the tennis and novice groups. When the head was pitched upward, the downward eye velocity was induced from the vestibulo-ocular reflex (VOR) during ball catching. Therefore, it is suggested that skilled ball players have relatively stable head and eye movements, which may lead to an effective gaze strategy. An advantage of the stationary gaze in the softball group could be to acquire visual information about the surroundings other than the ball.

Understanding and Differentating General and Special Relativity

This article stresses the importance of comprehending projectile motion for its extensive applications in both science and real-world contexts. This understanding not only enhances our grasp of physics and mathematics but also demonstrates how straightforward motions can embody complex scientific concepts.

Numerical simulation of the coupled dynamics model of the projectile engraving process

AbstractThe projectile engraving process directly influences the projectile motion in‐bore and impacts the firing accuracy, firing safety, and barrel life of the gun. For this reason, attention has been focused on this research topic. To address the limitations of the “instantaneous engraving” hypothesis adopted in the classical interior ballistic theory, the VUAMP user subroutine, one of ABAQUS's secondary development interfaces, is utilized in this paper to realize the modeling and numerical simulation of a coupled dynamics model of the projectile engraving process. In addition to facilitating engineering applications, a polynomial fitting formula of the engraving resistance obtained by simulation is proposed and then used as a supplement to establish a closed and solvable interior ballistic model considering the projectile engraving process. By comparing with test data, the simulation accuracy of the coupled dynamics model is verified. Simulation results reveal that the engraving process takes 3.8 ms, accounting for 26% of the whole launch process, which takes 14.6 ms, demonstrating that the process is not instantaneous. The results of this paper can serve as a reference for future studies on the coupled solution of the projectile engraving process and interior ballistics of guns or gun‐like equipment.

A comprehensive analysis of the ‘coming and going’ phenomenon of the projectile motion of a sphere under air resistance

We have analyzed the ‘coming and going’ phenomenon of the projectile motion of a sphere using experimental data correlations that span the entire range of Reynolds numbers. We have modeled the drag force using an analytical expression for the drag coefficient and performed a numerical analysis to compute the critical angle as a function of the sphere’s initial speed, radius, and mass. Our results indicate that the critical angle behaves analogously to the drag coefficient as a function of the Reynolds number. This study is significant as it deals with a drag force not limited to any specific flow regime and may help undergraduate students and science instructors delve deeper into the subject.

A pre-longitudinal screen of performance in an integrated assessment of throwing and catching competence

ABSTRACT Background: The ability to adapt motor skill performance to a variety of conditions is vital to success in physical activity settings. Valid and reliable measurements of motor competence (MC) are critical for understanding its impact on physical health. Many widely used MC assessments evaluate the performance of isolated motor skills, place performers in highly standardized environments, and limit opportunities to adapt performance. Consequently, evaluations of motor skill performance using these tools may not adequately differentiate motor skill levels. Assessing MC in more dynamic performance contexts may enhance the utility of MC measures. Purpose: The purpose of this study was to examine the developmental validity of scores on a combined throwing and catching assessment. Data Collection and Analysis: Data were collected on a convenience sample (n = 873, n female = 320, age = 14.7 years ± 4.2). Participants threw a regulation tennis ball against a wall from a distance three times their standing height and caught it as many times as possible in 30 s. Performers were free to use any throwing pattern (e.g. over/underarm) or task strategy (e.g. speed, trajectory of ball, ball bouncing, one- or two-handed catch). The highest number of catches between two 30-second trials was used for analysis. Descriptive statistics were calculated for the total sample and for males and females separately. Pearson correlations were used to evaluate the relationship between throw-catch assessment (TCA) scores and age. We evaluated the relationship between TCA score, sex, and age via hierarchical regression with TCA score as the dependent variable using three models: (1) Participant sex as the sole predictor, (2) sex and age as predictors, and (3) sex, age, and the quadratic term for age (age2). Additionally, we evaluated the reliability of scores on TCA assessment trials via intraclass correlations (ICCs) using a two-way, fixed effects model. Results: The mean TCA score was 11.34 (± 5.44; M females = 9.18 ± 4.80, M males = 12.59 ± 5.40). Strong relationships were observed between TCA score and age (r = .743, r females = .698, r males = .746; all significant at p < .001). Significant increases in model fit were observed at each stage of the hierarchical regression (Model 1: R 2 = .091, p < .01; Model 2: ΔR 2 = .484, p < .01; Model 3: ΔR 2 = .009, p < .01), with the final model indicating significant effects for sex (β male = 1.95, p < .01), age (β = 2.01, p < .01) and age2 (β = –.04, p < .01) on TCA score (R 2 = .584, F 3,869 = 406.7, p < .001). Finally, there was good reliability between scores on the two TCA trials (ICC = .875, F 872,873 = 14.97, p < .001). Discussion: These data provide preliminary evidence for the developmental validity of the TCA across childhood to young adulthood. The ability to differentiate skill levels across a wide age-range can enhance the ability to track MC across the lifespan and better understand the relationship between covariates of MC across the lifespan. These data provide support for a MC assessment that can be used by researchers and practitioners to evaluate throwing and catching skill in a swift and ecologically valid way.

Determination of a car speed - analysis of projectile motion from a muddy puddle

Drops from a muddy puddle produce a distinct pattern on the side doors of a car driving through the puddle. This pattern was studied to determine the speed of the car. We can conceive at least two different models for pattern formation. We can decide in favor of one of the models by using different representations of the data. The activity is based on a rich context-based problem of projectile motion and offers epistemological insight into how physics research works by forming and testing hypotheses and using alternative representations.

On the possibility of changing the trajectory of a projectile or rocket based on aerodynamic impact in the shock wave zone

A physical hypothesis is proposed that it is possible to change the design trajectory of the projectile on the basis of mechanical action on the entire volume of shockwave zones with a unilateral, asymmetric presence of the second projectile. Deviating from the original trajectory results in a positive result when it comes to a defensive task. A new semi-empirical model has been developed and compiled, which allows you to calculate the trajectory of the projectile taking into account the air resistance to movement. In the new model, it is recommended that only four easily detectable values​ ​ be used in upcoming experiments: the initial departure speed , the maximum altitude , the maximum flight range and the full time. The calculation scheme uses iterative calculations. On the basis of which the values ​ ​ of numerical coefficients in the semi-empirical model are specified. The physical idea that external powerful laser radiation can heat the side surface of the projectile and the entire zone of wave jumps of the seal is justified. On one side of the semi-plant, that is, it is one-way heating. The asymmetrical thermal state on both sides of the missile may cause the missile or projectile to deviate from the previously assigned heading. This circumstance is also in favor of the proposed idea.

Development of a 2-D Motion Tracker Application Project Assisted By Computer Vision to Enhance Student’s Laboratory Skills

The lecture method that is often applied by the teacher in class can also cause the learning experience of students to not be optimal; as a result, students only understand the theory and concept of projectile motion. One method that can be used to learn physics is the experimental method. This study aims to produce a projectile motion tracker application project and describe the effect of applying this application project in the physics learning process, especially related to students' laboratory skills. The research method used is research and development (RD), using the 4-D development model (Define, Design, Develop, and Disseminate). Pre- and post-test results were obtained from 74 high school students to assess their laboratory skills before and after treatment. The instruments used were questionnaires and tests. The results show that the projectile motion tracker application project can be employed as a tool for physics education, based on expert test results with very good categories in language, visual appearance, and software engineering. In addition, based on the results of the practicality test for teachers and students, the test results were in the very practical category, respectively, from the aspects of ease of use, attractiveness, efficiency, and usefulness. The results of students' pre- and post-test on their laboratory skills show that the projectile motion tracker application project can enhance students' laboratory skills. The projectile motion tracker application project can be used as an alternative by teachers, lecturers, or education practitioners to support teaching and learning activities.

ViSTec: Video Modeling for Sports Technique Recognition and Tactical Analysis

The immense popularity of racket sports has fueled substantial demand in tactical analysis with broadcast videos. However, existing manual methods require laborious annotation, and recent attempts leveraging video perception models are limited to low-level annotations like ball trajectories, overlooking tactics that necessitate an understanding of stroke techniques. State-of-the-art action segmentation models also struggle with technique recognition due to frequent occlusions and motion-induced blurring in racket sports videos. To address these challenges, We propose ViSTec, a Video-based Sports Technique recognition model inspired by human cognition that synergizes sparse visual data with rich contextual insights. Our approach integrates a graph to explicitly model strategic knowledge in stroke sequences and enhance technique recognition with contextual inductive bias. A two-stage action perception model is jointly trained to align with the contextual knowledge in the graph. Experiments demonstrate that our method outperforms existing models by a significant margin. Case studies with experts from the Chinese national table tennis team validate our model's capacity to automate analysis for technical actions and tactical strategies. More details are available at: https://ViSTec2024.github.io/.

Trajectory of a golf ball on a sloping green

Calculations are presented on the trajectory of a golf ball that rolls across the inclined surface of a golf green. The ball follows a curved path and comes to a stop at a point displaced at an angle to the initial launch direction. It is shown that the displaced angle is independent of the launch speed but depends on the launch angle and the ratio of the incline angle to the coefficient of rolling friction. The stopping distance is proportional to the launch speed squared. A simple experiment is described to check the calculations.

DYNAMIC CHARACTERISTICS OF TIME-VARYING CONTROL SYSTEM OF THE ROCKET’S ROTATIONAL MOVEMENT

The rocket motion control system is time-varying, because its parameters during flight depend on the trajectory point and fuel consumptions. In the available sources, due attention is not paid to the development of a mathematical apparatus of an applied value for the quan- titative assessment of the dynamic characteristics of a time-varying system.&#x0D; The purpose of the work is to justify the possibility of an algorithm building for calcu- lating the parameters of a link with constant parameters, which is equivalent to a time- varying system in terms of dynamic characteristics at the selected trajectory section.&#x0D; The link’s parameters are found by using the criterion of equivalence of the array of values of the motion model’soutput signal and the analytical solution of the link’s differential equation for a given sequence of input signals. This makes it possible to use the mathematical apparatus of stationary systems to determine the indicators of the disturbances compensation.&#x0D; The model of the control system of the rocket’s rotational movement in one plane is taken as a linear differential equation with time-varying parameters without taking into ac- count the executive device inertia and other disturbances. The link with constant parameters is a fractional-rational function of the second order, for the determination of which a se- quence of signals is applied to the input of the system model, the duration of which depends on the desired stability margin on the roots plane of the characteristic polynomial.&#x0D; Using the example of a time-varying system for controlling the rocket’srotational movement in the yaw plane, the possibility of determining the parameters of the transition process of compensation for the disturbances characteristic of it is shown for the selected tra- jectory section.&#x0D; The obtained results can be used in the design of a motion control system with time- varying parameters.&#x0D; The next stage of the research is an assessment of the complexity level of the calcula- tion algorithm when increasing the order of the system’smathematical model.

That’s out! How expert umpires make leg-before-wicket judgements in cricket

ABSTRACT Despite evidence that elite-level cricket umpires are highly accurate in making leg-before-wicket (LBW) judgements, there is limited understanding as to how they make these judgements. In this study, we explored the explicit LBW decision-making expertise of elite-level cricket umpires (N = 10) via 10 individual semi-structured interviews. Using thematic analysis, we aimed to identify the sources of information that umpires incorporate into their decision-making process. Results indicated that umpires engage in intentional pre-delivery information-gathering to guide their expectations, and to set context-specific parameters as to what would constitute an LBW dismissal. Not only do umpires use information about the ball trajectory, but they also use additional information about the condition of the pitch, the action-capabilities and susceptibilities of players, and the unique requirements of different match formats. Umpires reported employing a gaze-anchor strategy when gathering information for each delivery and described the process of this information as initially intuitive, before engaging in deeper post-hoc reasoning. Findings highlight the importance of including contextual information when exploring officials’ decisions and may inform future training interventions for cricket umpires.

A Mechanistic Model and Experiments on Bedrock Incision and Channelization by Rockfall

AbstractRockfall and rock avalanches are common in steep terrain on Earth and potentially on other planetary bodies such as the Moon and Mars. Since impacting rocks can damage exposed bedrock as they roll and bounce downhill, rockfall might be an important erosive agent in steep landscapes, even in the absence of water. We developed a new theory for rockfall‐driven bedrock abrasion using the ballistic trajectories of rocks transported under gravity. We calibrated this theory using laboratory experiments of rockfall over an inclined bedrock simulant. Both the experiments and the model demonstrate that bedrock hillslopes can be abraded by dry rockfall, even at gradients below the angle of repose, depending on the bedrock roughness. Feedback between abrasion and topographic steering of rockfall can produce channel‐like forms, such as bedrock chutes, in the absence of water. Particle size has a dominant influence on abrasion rates and runout distances, while the hillslope angle has a comparatively minor influence. Rockfall transport is sensitive to bedrock roughness; terrain with high friction angles can trap rocks creating patches of rock cover that affect subsequent rockfall pathways. Our results suggest that dry rockfall can play an important role in eroding and channelizing steep, rocky terrain on Earth and other planets, such as crater degradation on the Moon and Mars.

A novel metaheuristic inspired by horned lizard defense tactics

This paper introduces HLOA, a novel metaheuristic optimization algorithm that mathematically mimics crypsis, skin darkening or lightening, blood-squirting, and move-to-escape defense methods. In crypsis behavior, the lizard changes its color by becoming translucent to avoid detection by its predators. The horned lizard can lighten or darken its skin, depending on whether or not it needs to decrease or increase its solar thermal gain. The skin darkening or lightening strategy is modeled by including the stimulating hormone melanophore rate( α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}-MHS) that influences these skin color changes. Further, the move-to-evasion strategy is also mathematically described. The horned lizard’s shooting blood defense mechanism, described as a projectile motion, is also modeled. These strategies balance exploitation and exploration mechanisms for local and global search over the solution space. HLOA performance is benchmarked with sixty-three optimization problems from the literature, testbench problems provided in IEEE CEC- 2017 “Constrained Real-Parameter Optimization”, analyzed for dimensions 10, 30, 50, and 100, as well as testbench functions from IEEE CEC-06 2019 “100-Digit Challenge”. Moreover, three real-world constraint optimization applications from IEEE CEC2020 and two engineering problems, the multiple gravity assist optimization and the optimal power flow problem, are also studied. Wilcoxon and Friedman statistics tests compare the HLOA algorithm results against ten recent bio-inspired algorithms. Wilcoxon shows that HLOA provides the optimal solution for most testbench functions more effectively than competing algorithms. At the same time, the Friedman statistics test ranks the HLOA first, and the n-dimensional analysis shows that it performs better on the constrained optimization problems for dimensions 50 and 100. The source code is free and available from https://www.mathworks.com/matlabcentral/fileexchange/159658-horned-lizard-optimization-algorithm-hloa.

Table tennis players use superior saccadic eye movements to track moving visual targets.

Table tennis players perform visually guided visuomotor responses countlessly. The exposure of the visual system to frequent and long-term motion stimulation has been known to improve perceptual motion detection and discrimination abilities as a learning effect specific to that stimulus, so may also improve visuo-oculomotor performance. We hypothesized and verified that table tennis players have good spatial accuracy of saccades to moving targets. University table tennis players (TT group) and control participants with no striking-sports experience (Control group) wore a virtual reality headset and performed two ball-tracking tasks to track moving and stationary targets in virtual reality. The ball moved from a predetermined position on the opponent's court toward the participant's court. A total of 54 conditions were examined for the moving targets in combinations of three ball trajectories (familiar parabolic, unfamiliar descent, and unfamiliar horizontal), three courses (left, right, and center), and six speeds. All participants primarily used catch-up saccades to track the moving ball. The TT group had lower mean and inter-trial variability in saccade endpoint error compared to the Control group, showing higher spatial accuracy and precision, respectively. It suggests their improvement of the ability to analyze the direction and speed of the ball's movement and predict its trajectory and future destination. The superiority of the spatial accuracy in the TT group was seen in both the right and the left courses for all trajectories but that of precision was for familiar parabolic only. The trajectory dependence of improved saccade precision in the TT group implies the possibility that the motion vision system is trained by the visual stimuli frequently encountered in table tennis. There was no difference between the two groups in the onset time or spatial accuracy of saccades for stationary targets appearing at various positions on the ping-pong table. Table tennis players can obtain high performance (spatial accuracy and precision) of saccades to track moving targets as a result of motion vision ability improved through a vast amount of visual and visuo-ocular experience in their play.

Numerical–experimental study on the stability mechanism of tail slapping motion of supercavitation projectile

Tail slapping is considered to be a prominent mode for facilitating the movement of supercavitating projectiles underwater. Stability mechanism of the tail slapping and stability criterion of projectiles was numerically investigated in this paper. A numerical method was conducted to calculate the free flight of projectiles by combining the finite volume method, the mixture multiphase model, and a dynamic meshing scheme. The accuracy and applicability of the numerical calculation method are verified by experiments. Three typical stability modes of tail slapping motion, namely, stable, conditionally stable, and unstable, were identified through the free flight numerical simulations of projectiles with varying length-to-diameter ratios under different initial angular velocities. The stability criterion of projectiles was proposed, indicating that the tail slapping stability can be determined by analyzing the curve of the moment variation with the angle of attack at any velocity above 200 m/s. Furthermore, it was found that the stable projectiles possess inherent motion states that are exclusively determined by their structural features and are unaffected by the initial motion conditions.

A Semantic Tree-Based Fast-Moving Object Trajectory Tracking Algorithm for Table Tennis

Table tennis is a popular sport around the world. A key technology in table tennis education and analysis system is reconstructing the trajectory of the fast-moving ball from videos. Typically the table tennis ball is too small and barely visible in the video, making it difficult to be recognized directly by detection models like YOLO. However, table tennis balls usually has obvious motion features, which are usually not found in similar false targets. It inspired the authors to first find all candidate targets and then use the motion features of table tennis ball to select them out. In this article, the authors propose a tree-based algorithm named T-FORT to track the ball and reconstruct its trajectory. Specifically, they consider all the possible objects in a tree-framework, and identify the real target by integrating visual features and moving patterns. The authors conduct a set of experiments on three datasets to evaluate the effectiveness and performance of the proposed algorithm. The experimental results show that the proposed method is more precise than existing algorithms, and is robust in various scenarios.

Ballistic Capture Analysis Using the Energy Transition Domain

In the framework of the planar Circular Restricted Three-Body Problem (CR3BP) and for a given value of the Jacobi constant, a necessary condition for a ballistic capture is a passage through zero two-body energy, which defines a region in the synodic plane called energy transition domain (ETD). The latter is the locus of points where the zero-energy condition and selected Jacobi constant are simultaneously fulfilled. This paper shows how an ETD can be described analytically and exploited for the efficient computation and insightful classification of the complete set of ballistic capture trajectories in the planar problem. The new methodology is applied to different three-body systems and highlights the influence of the three-body energy on key aspects of the capture mechanism, such as prograde to retrograde transition. Other interesting results concern three-body energy limits, collisions, long-duration captures, altitude range throughout the capture process, and the origin of ballistic capture orbits.

Adaptive Kalman Filter for Real-Time Visual Object Tracking Based on Autocovariance Least Square Estimation

Real-time visual object tracking (VOT) may suffer from performance degradation and even divergence owing to inaccurate noise statistics typically engendered by non-stationary video sequences or alterations in the tracked object. This paper presents a novel adaptive Kalman filter (AKF) algorithm, termed AKF-ALS, based on the autocovariance least square estimation (ALS) methodology to improve the accuracy and robustness of VOT. The AKF-ALS algorithm involves object detection via an adaptive thresholding-based background subtraction technique and object tracking through real-time state estimation via the Kalman filter (KF) and noise covariance estimation using the ALS method. The proposed algorithm offers a robust and efficient solution to adapting the system model mismatches or invalid offline calibration, significantly improving the state estimation accuracy in VOT. The computation complexity of the AKF-ALS algorithm is derived and a numerical analysis is conducted to show its real-time efficiency. Experimental validations on tracking the centroid of a moving ball subjected to projectile motion, free-fall bouncing motion, and back-and-forth linear motion, reveal that the AKF-ALS algorithm outperforms a standard KF with fixed noise statistics.

The influence of pitcher handedness on pitch-calling behavior: Insights from fMRI study on baseball umpires.

This functional magnetic resonance imaging study delves into the impact of experience and pitcher handedness on the pitch-calling behavior of baseball umpires. Expert and intermediate umpires were asked to make ball/strike calls on videotaped pitches of left- and right-handed pitchers and rate their certainty for the call while undergoing scanning. Behavioral results replicated previous findings that expert umpires were more certain but not more accurate or quicker than intermediate umpires, suggesting that, as sports officials, umpires may learn to project confidence to maintain control of the game. At the neural level, expert umpires exhibited more extensive and pronounced activations within the action observation network, dorsal striatum, and cerebellum. These heightened neural responses were probably associated with their enhanced visual processing abilities for pitching action and ball trajectory, honed over years of officiating. Notably, both expert and intermediate umpires exhibited decreased accuracy when judging pitches from left-handed pitchers compared to right-handed ones. These challenges in accuracy corresponded with weaker neural activations in the aforementioned brain regions, implying difficulties in processing specific visual details of the rarely encountered left-handed pitchers. Moreover, slightly longer reaction times and reduced uncertainty were observed particularly for left-handed ball pitches, as revealed by lower activation in the right premotor cortex, highlighting issues with predictive processing. In summary, our findings shed light on the influence of pitcher handedness on the pitch-calling behavior of baseball umpires and extend the current understanding of the perceptual and decision-making behavior of sports officials.