Projectile Motion Research Articles

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.

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.

How Seam Inclination Influences Cricket Ball Swing

Abstract. Cricket, a sport with origins in 16th century England, involves players attempting to manipulate the lateral motion of the ball to outwit the batsman. This is often achieved by adjusting the seam inclination or altering the ball's surface roughness. This paper specifically investigates how seam inclination affects cricket ball swing through computational fluid dynamics (CFD) simulations. The focus of the study is on conventional swing for both non-rotational and rotational cricket balls. The results indicate that seam inclination significantly influences swing, with an optimal angle between 58 to 60 degrees for the maximum lateral force of non-rotational cricket. This finding provides valuable insights into the mechanics of conventional swing and offers guidelines for bowlers to enhance their performance. The research explores the complex interplay between the ball's aerodynamics, seam inclination, and the resulting swing. By utilizing CFD simulations, the study delves into the underlying fluid dynamics that govern the ball's trajectory and the generation of lateral forces.

New metrics for measuring 2D uniformity in stirring system based on reconstruction of the particle trajectory

In industrial mixing systems, the evaluation method is a crucial indicator for measuring mixing uniformity. This study proposes an assessment method that combines a method for positioning using dual cameras and a point pattern density fluctuation (PD) method based on disordered hyperuniformity. This study employs a method for positioning using dual cameras to investigate the motion trajectories of tracer balls and achieve a 3D reconstruction process. The reconstructed 3D systems are cross-sectioned through on the axis of the stirring paddle to form a 2D planar diagram of the tracer ball trajectories. The PD method is used to evaluate the mixing effectiveness of the 2D trajectory points, establishing evaluation metrics for the 2D mixing system. To ensure the accuracy of the PD method, a feasibility analysis was conducted using the conductometry. A relationship model between λ and mixing time was established, with a Pearson correlation coefficient (r) of -0.9867, indicating a strong negative linear correlation. The relationship between the planes and whole 3D space was analyzed in terms of the whole and the discrete perspective, as well as the existing methods were compared with other approaches. This study not only deepens the theoretical understanding of evaluating mixing uniformity but also provides a crucial foundation and theoretical basis for process optimization of stirring systems and design of stirred reactors. It offers valuable references and insights for engineering design and technological improvements in related fields.

Measurement and Dynamic Analysis of the Centroid Trajectories of Angular-Contact Ball Bearing Cages

When a high-speed rolling bearing cage comes into contact with rollers, it experiences random movement due to friction and collision, which significantly impacts the overall performance of the bearing. To further investigate the motion law of cages, a test bench for a 7010C angular-contact bearing cage was constructed. This setup utilized laser sensors to obtain changes in attitude and displacement during operation. After analyzing how cage deflection errors influenced trajectory measurements, corrections were applied to the measurement results. Additionally, an investigation was conducted into the effects of varying rotational speeds on the dynamic performance of the cage. Simulations were performed using ADAMS software, which verified both the effectiveness of the measuring method and the testing results. The findings indicated that within the tested range of rotational speeds, the centroid trajectory stability of the cage gradually improved as rotational speed increased and then began to show a tendency to deteriorate. Furthermore, there existed a negative correlation between the deflection error of the cage and the centroid trajectory stability.

Study on vortex structure and hydrodynamic characteristics of water-exit projectile with shoulder ventilation

During the vertical motion of a water-exit projectile, the gas stored inside is expelled from the shoulder under the effect of pressure differential, forming a ventilated cavity covering the surface of the projectile. This paper explores the vortex structure characteristics of the surface ventilated cavity through numerical simulation and summarizes its impact on the hydrodynamic characteristics of the water-exit projectile. It was found that the end of the shoulder ventilated cavity presents a periodic vortex shedding form. And the existence of the shoulder ventilated cavity can reduce the vertical resistance of the projectile, improve the vertical movement speed, and play a role in load reduction and drag reduction. Additionally, the lateral displacement of the projectile at the moment of water exit decreases by approximately 45.2%, and the deviation angle reduces by about 55.6%, significantly improving the stabilization of its water exit posture. This indicates that the presence of the shoulder ventilated cavity can effectively enhance the hydrodynamic performance of the projectile.

Interceptive abilities in autism spectrum disorder: Comparing naturalistic and virtual visuomotor tasks.

A growing body of research reveals that autistic individuals exhibit motor coordination challenges. Multiple theoretical frameworks propose that the seemingly disparate features of autism may arise from a common underlying process: a diminished ability to make predictions. Sensorimotor skills, such as catching a ball, critically rely on predicting the ball's trajectory as well as anticipatory coordination of the entire body. Here, we assessed four different naturalistic and virtual interception tasks with 31 neurotypical and 23 autistic children (ages 7-12). In a naturalistic setting, participants caught the ball either with their hands or a hand-held funnel with an enlarged catch area that also prevented the ball from bouncing off. A virtual setup reduced whole-body demands, as children only moved a paddle to catch or bounce a ball on a screen. Control tasks, involving rapid reaching to grasp a static object and quiet standing, which largely eliminated the requirements for prediction, were also tested. Results from all task variations demonstrated that autistic children completed fewer successful interceptions, suggesting that predictive requirements, inherent to all interception tasks, played a critical role. Effect sizes in the virtual tasks were smaller. Correlations of the task metrics with behavioral assessments rendered the strongest correlations with Praxis scores. The control tasks showed no differences between autistic and neurotypical children. These findings lend support to the emerging hypothesis that predictive challenges are present in autism. Further research with larger sample sizes will help identify to what extent these visuomotor differences may inform core domains of autism.

Application of computational methods in problems of aeroballistics. determination of conjugate throwing angles and construction of ballistic trajectories

The problem of aeroballistics of non-reactive artillery projectiles is studied by means of a simplified mathematical model. The following problems are considered as separate subproblems: initial value problem, determination of the horizontal range of a projectile (4th order Runge-Kutta method with modification of polynomial interpolation); optimization problem (Powell's method), determination of the angles of maximum range — the throwing angles at which the maximum horizontal range is achieved; the boundary value problem (shooting method with Newton-Raphson method/ secant method/ polynomial interpolation), determination of throwing angles at a given distance and the problem of finding conjugate trajectories — the low and high angled trajectories, which achieve the same horizontal range of the projectile at different throwing angles; the inverse geodesy problem (Vincenty's formulae), determination of the geodesic distance between two geographical points on the WGS-84 non-spherical Earth model. The following characteristics are graphically illustrated as a function of throwing angles: horizontal and vertical ranges, maximum vertical and horizontal velocity components, magnitudes of terminal velocities, impact angle, and flight time of projectiles. The existence of conjugate trajectories is established and the strategy of sequential firing of projectiles with the aim of simultaneously hitting the target along different trajectories is determined. The programming of the numerical methods, the algorithm for solving the problem, and the visualization elements were implemented using the MATLAB application package, and the developed methodology and software have demonstrated their effectiveness and the possibility of their practical application.

Embeddedness of Earth's gravity in visual perception.

Falling objects are commonplace in daily life, requiring precise perceptual judgments for interception and avoidance. We argue that human judgments of projectile motion arise from the interplay between sensory information and predictions constrained by Newtonian mechanics. Our study investigates how individuals perceive falling objects under various gravitational conditions, aiming to understand the role of internalized gravity in visual perception. Through meticulously controlling the available information, we demonstrated that these phenomena cannot be explained solely by simple heuristics nor representational momentum. Instead, we found that the perceptual judgments of humans (n = 11, 13, 14, and 11, respectively, in Experiments 1, 2, 3, and 4) are influenced by a combination of sensory information and gravity predictions, highlighting the role of internalized physical constraints in the perception of projectile motion.

Developing the Proficiency Level of Sophomore Fisheries Students through Contextualized Comics in Projectile Motion

Projectile motion finds applications in day-to-day activities and many of the students find it hard to grasp and comprehend. In this study, the goal was to craft and utilize a contextualized comics that serves as an intervention tool to address students’ low achievement on some concepts of kinematics, with emphasis on projectile motion. The study used one group pretest-posttest experimental design to investigate the effectiveness of the intervention tool. The paired t-test was also employed to compare students’ performance before and after using the contextualized comics. Shapiro-Wilk test was also utilized to determine whether the data follows a normal distribution in comparing the tests used. The participants of this study were 20 sophomore fisheries students. The contextualized comics was utilized by the students after the pre-test. Findings have remarkably revealed that before the utilization of the contextualized comics, participants were identified as not proficient on the concepts of projectile motion. This implies that the students did not master the lesson as prevailed in their MPS of 12.8% which is within the “not proficient” bracket. After the conduct of intervention with the contextualized comics, the students significantly scored higher in their post-test resulting in an MPS of 75.2% which falls under the “proficient” level. Through the validation of Shapiro-Wilk test which follows normal distribution, there is a significant difference between pre-test and post-test scores after the implementation of the contextualized comics where p < 0.001. Thus, it signifies that the contextualized comics was an effective intervention tool to enhance students’ performance on the least learned topic in physics.

Real-Time Table Tennis Scoring and Player Position Tracking System Using Computer Vision

This study focuses on developing a system that uses state-of-the-art computer vision techniques to improve the accuracy and efficiency of table tennis tracking. The table tennis ball's trajectory and movement are tracked automatically by the system using a mobile camera array, allowing for real-time score updates without the need for human participation. This method guarantees precise and seamless scoring, freeing players from worrying about maintaining score and allowing them to concentrate fully on the game. The system uses player pose estimation technologies in addition to real-time scoring to track and record player positions and motions during the match. The system may provide a thorough study of player motions, including tracking posture and finding important motion patterns, by gathering and analyzing skeletal data.

Role of inhibition in overcoming interferences of misconception under similar feature saliency: An eye-tracking study of the projectile motion problem

Misconceptions coexisting with scientific understanding pose significant challenges in physics education. Inhibitory control may enable individuals to overcome interference from misconceptions. However, discerning the role of inhibitory control becomes intricate when the saliency of scientific- and misconception-related features varies in a problem. This study investigates the role of inhibitory control in overcoming such misconceptions when scientific and misconception-related features are similarly salient, particularly focusing on the range-time (range determines flight time) misconception. We adopted a negative priming (NP) paradigm with the eye-tracking technique in the study. Thirty-six college physics majors participated in the experiment. In the NP paradigm, the participants first compared the flight times in a neutral (same range) or incongruent (longer range, less flight time) primes and then completed the same task in a congruent (longer range, more flight time) probe. Results revealed longer reaction times for incongruent primes compared to neutral primes and longer reaction times to respond to congruent probes following incongruent primes than when neutral primes were present beforehand, suggesting that the inhibitory control may be involved in overcoming the interference from the range-time misconception. Moreover, the eye-tracking analysis highlighted an early overt attention to the salient misconception-related feature (longer range) during primes, along with additional attentional investment necessary to inhibit the range-time misconception. During probes, an early shift of attention away from the salient misconception-related feature and a greater investment of attention on processing the congruent probes after the incongruent primes than that after the neutral primes were observed, indicating a possible effect of the previous inhibitory control in the primes on the subsequent cognitive process on the probes. These findings contribute to a deeper understanding of the cognitive process underlying physics conceptual change and provide insights into physics education. Published by the American Physical Society 2024

Electron Collimation in Twisted Bilayer Graphene via Gate-Defined Moiré Barriers.

Electron collimation via a graphene p-n junction allows electrostatic control of ballistic electron trajectories akin to that of an optical circuit. Similar manipulation of novel correlated electronic phases in twisted-bilayer graphene (tBLG) can provide additional probes to the underlying physics and device components toward advanced quantum electronics. In this work, we demonstrate collimation of the electron flow via gate-defined moiré barriers in a tBLG device, utilizing the band-insulator gap of the moiré superlattice. A single junction can be tuned to host a chosen combination of conventional pseudo barrier and moiré tunnel barriers, from which we demonstrate improved collimation efficiency. By measuring transport through two consecutive moiré collimators separated by 1 μm, we demonstrate evidence of electron collimation in tBLG in the presence of realistic twist-angle inhomogeneity.

Symmetric twin paradox for free-falling frames: Argument against the relativistic time dilation?

The twin paradox, a classical puzzle in Special Relativity (SR), is typically resolved by acknowledging the asymmetry introduced by the acceleration of one twin's frame, associated with a rocket's motion through space. A similar paradox arises without any accelerated system, involving three or more inertial systems. This is commonly resolved by employing the relativistic concepts of clock synchronization and simultaneity. Here, we reformulate the paradox for two free-falling systems, where the twins traverse identical circular orbits in opposite directions around a central mass with a spherically symmetric gravitational field. This redefined version of the paradox eliminates asymmetry inherent in the original problem. Since both frames are free-falling, they can be viewed as locally inertial according to Einstein's Equivalence Principle. Additionally, no synchronization with clocks in other frames is needed. We explore a potential resolution to the paradox and highlight that there may be a misinterpretation of the Lorentz transformation in SR.

Analysis of ballistic trajectories and its association with clinical outcomes in civilian penetrating brain injury

PurposeCivilian penetrating brain injuries (PBI) caused by firearms are a medical emergency with high rates of morbidity and mortality. The aim of this study was to evaluate the association between trajectory vectors in CT brain angiography and clinical outcomes in patients with civilian gunshots.MethodsThis is a retrospective analytical cross-sectional study that includes patients over 15 years of age with PBI due to firearms, admitted from January 2019 to December 2021 at a University Hospital in Cali, Colombia. A brain CT with angio-CT was performed the first day of admission. An XYZ coordinate system centered on the Turk’s saddle was developed. Trajectories of projectiles were plotted and compared to a patient 0 in a 3D-Slicer software. A bivariate analysis of the clinical and geometric characteristics of the trajectory was performed. Primary outcomes include mortality and disability at 6 months.ResultsTwenty-eight patients with a mean age of 27.39 ± 11.66 years were included. The vectors of non-survivors show a trend, crossing at a specific area. This area was designated as a “potential lethal zone” and inside this area, injuries around 25.3 mm from the circle of Willis, were associated with greater mortality (p < 0.005).ConclusionsIn our study PBI avoiding the ventricular system, brain stem, dorsum sellae and the circle of Willis were associated with more survivability. A “potential lethal zone” was detected and associated with poor outcome after civilian PBI due to firearms. A better evaluation of the performance of this “potential lethal zone” in larger studies will be required.

Mechanisms of speed-accuracy trade-off in tennis topspin forehand of college players

ABSTRACT This study aimed to elucidate the mechanisms underlying the speed-accuracy relationship in a tennis topspin single-handed forehand groundstroke. Groundstrokes at three different speeds by nine college players were captured, with the variability of the ball landing position evaluated as indices of accuracy. Variabilities of ball launch variables (speed, launch angle, spin, etc.) and conversion ratios from these variabilities to the variability of the ball landing position were quantified. These variabilities and their conversion ratios could be influenced by different efforts exerted to generate ball speeds and different ball trajectories required to hit a target at each speed, respectively. The speed-accuracy trade-off was observed only in the hitting direction. While the variability of the spin axis increased, it had minimal influence on the ball landing position. Conversely, the conversion ratio in the hitting direction of the velocity elevation angle significantly increased, while its variability remained unchanged. Consequently, the geometrical requirements of ball trajectories can be responsible for the speed-accuracy trade-off. Therefore, even skilled players capable of maintaining consistent ball launch variables regardless of the shot speed should deliberately choose a moderately slower ball speed to avoid an inevitable increase in the variability of the ball landing position due to geometrical requirements.

A modified bond-based peridynamic approach for rigid projectile perforation on concrete slabs

Peridynamic (PD) has a unique advantage in describing the crack growth and fragmentation of brittle materials. Concerning the dynamic behaviors and failure patterns of concrete slabs under projectile perforations, a modified bond-based PD approach maintaining both the easy implementation and computational stability characteristics was firstly developed from the following three aspects, (i) a rate-dependent PD constitutive model was proposed for describing the dynamic behaviors of concrete; (ii) a progressive damage criterion considering the tension-compression anisotropy, softening behavior, and strain rate effect of concrete was incorporated to more accurately reproduce the damage and failure of concrete; (iii) an improved micro-modulus function related to bond length was introduced to reveal the internal length effect of bond force. Then, numerical simulations of projectile perforation on concrete slabs by utilizing the developed modified bond-based PD approach, as well as the corresponding sensitivity analyses of discretization parameters including horizon size and particle spacing were performed. Based on the recommended horizon size and particle spacing, the predicted residual velocity of projectile and failure patterns of concrete slabs exhibited an excellent agreement with the test data. Furthermore, by comparisons of the traditional bond-based PD and classical finite element methods, the superiority of developed approach in describing the perforation damage of concrete targets against projectile impact was demonstrated. Finally, the modified bond-based PD approach was employed to blind simulate the projectile normal and oblique perforating multi-layered spaced concrete target plates. It was found that the modified PD model reasonably predicted the terminal ballistic trajectory, deflection angle, and residual velocity of projectile, as well as the failure patterns of target plates. The present work provides a new way to predict the terminal ballistic effect of projectile and dynamic behaviors of concrete slabs.