Separation Angle Research Articles

Wind tunnel measurements on the effects of leading edge geometry on surface pressures and wake flow of finite blunt plate

In this paper, the surface wind pressure distribution and wake flow of finite blunt plates with different leading edge geometries are investigated. Particle image velocimetry and surface pressure measurement are performed on five typical leading-edge plates in a uniform wind. The results show that the wind pressure distribution on the blunt plate surface is largely affected by the leading-edge geometry. Specifically, as the leading edge angle increases from 60° to 180°, the peak values of the mean pressure coefficient and peak suction pressure coefficient decrease by 20.1 % and 11.6 % respectively. Meanwhile, the peak value of the r.m.s pressure coefficient increases from 0.041 to 0.126 and gradually approaches the mid-axis of blunt plate. In addition, larger separation angles lead to an increase in the reattachment length from 0.7d to 5.26d, but monotonically decrease the characteristic frequency of the plate. The analysis of the wake velocity field shows that an increase in leading-edge angle leads to an increase in the length of the low-velocity recirculation zone in the wake from 0.7d to 1.1d, and both the turbulent kinetic energy and Reynolds stress are larger in this region. Meanwhile, the flow streamlines and vorticity distribution become more unstable and complex, exhibiting a faster rate of evolution. Furthermore, the extraction of the wake structure using a proper orthogonal decomposition shows that the aerodynamic shape of leading edge has a limited effect on the large-scale vortex structure, but significantly affects small-scale vortex structure of high-order modes.

Polarization splitters with designable separation angles based on polarization holography of tensor theory.

We propose a simple and inexpensive method for the fabrication of polarization splitters with designable separation angles and a controllable active area, based on polarization holography of tensor theory. First, we design two polarization holograms that reconstruct waves with only p- or s-polarization components, respectively. Then, after we recorded these two holograms on the same position of the recording material using the interference approach, as a result, a polarization splitter could readily be prepared. The separation angles of fabricated polarization splitters can be easily adjusted by changing the interference angle, and the active area can also be easily modified by changing the sizes of the interference beams and recording material during the recording process. The experimental results verify the reliability and accuracy of this method. We believe that this work may broaden the application field of polarization holography.

CFD modelling of steel desulfurisation in a gas-stirred ladle

ABSTRACT Low sulfur content is crucial in secondary steelmaking to enhance steel quality. The desulfurization rate is influenced by slag-steel interactions, including slag eye size and interfacial mass transfer coefficient. Gas-stirred ladles can impact the interaction through stirring conditions such as argon flow rate and dual plug separation angle. Using a 3D CFD simulation model, the effects of different stirring conditions on the desulfurization rates, molten steel flow, and slag-steel interfacial behaviors were investigated. Results showed that 180° separation angle leads to higher desulfurization efficiency than 90°. A higher argon gas flow rate increases desulfurization rate, and using 20 SCFM (8.92×10-3 Nm3/s) argon flow rate for both plugs resulted in higher desulfurization rate than using 5 SCFM (2.23×10-3 Nm3/s) for one plug and 20 SCFM for the other. The smallest desulfurization efficiency was observed when using 5 SCFM for both plugs.

基于最优采摘参数的猕猴桃采摘末端执行器设计与试验

A kiwifruit harvesting end effector was designed and developed to improve the efficiency of mechanized kiwifruit harvesting. Firstly, the automated kiwifruit picking process was determined according to the kiwifruit orchard working environment. Secondly, the end-effector was designed and analyzed based on the principle of kiwifruit picking. Finally, an orchard experiment was conducted with the clamping force, rotation angle and rotation speed of the end-effector as test factors, and the separation success rate, separation time and damage rate of kiwifruit fruit as test indicators. A regression model between the test factors and test indicators was established using a quadratic fitting equation to analyze the influence between the test factors and indicators. The experimental results showed that the optimal parameter was a clamping force of 3.05 N, a separation angle of 65.75°, and a separation speed of 60.03°/s. The results of the study provide theoretical basis and technical support for automated kiwifruit harvesting.

Low-coherence snapshot phase-shifting diffraction phase microscope

We proposed a Wollaston-prism-based snapshot phase-shifting diffraction phase microscope (WP-SPDPM) for low-coherence snapshot quantitative phase imaging and videography. Wollaston prism separates two orthogonally linearly polarized beams with high degrees of polarization at a sufficiently small separation angle; one of the beams passing through a pinhole serves as the reference beam. Four phase-shifted interferograms are simultaneously acquired with a polarization camera to accurately retrieve a high spatial resolution phase map. The system is nearly common-path in configuration and can achieve a large slope range and high accuracy. In addition to the ability to resist environmental noise, the WP-SPDPM is suitable for phase measurement using low-coherence light. The accuracy and large measurable slope range of the proposed system is validated and compared experimentally with a commercial profilometer. We believe WP-SPDPM is a powerful tool for the accurate and robust quantitative phase measurement and has a significant potential of the real-time phase imaging.

Experimental and numerical study of hooked-end steel fiber-reinforced concrete based on the meso- and macro-models

In this study, several three-point-bending (TPB) experiments were conducted to investigate the influence of fiber content on the fracture behavior of hooked-end steel fiber-reinforced concrete (SFRC). Subsequently, a numerical meso-model was proposed based on the application of the cohesive/volumetric finite element method, which allows the pervasive fracture along non-prescribed trajectories to be captured accurately. The bond-slip relation and traction-separation relation of the fiber–concrete interface were both considered. Consequently, the accuracy of the meso-model was validated through the experiments conducted in this study. The influence of the separation angle of the SFRC fracture interface on the bridging effect of the fibers was investigated using the proposed model. Finally, based on the conclusions obtained from the experiments and meso-model, a macro-model of SFRC was proposed to improve the computational efficiency, which was validated considering two different experimental cases.

An analytical solution of the rope-sheave contact in static conditions based on a bristle model

This paper presents an analytical solution for the rope-sheave contact problem in static conditions, also applicable to belt-pulley problems and similar mechanisms. The rope is assumed under constant and unequal loads at the two ends, as in an elevator when the brake is acting on the drive sheave and the weights of the cabin and counterweights are different. The rope is assumed to behave as a rod without bending stiffness. Assuming a bristle model for the rope-sheave contact and Coulomb friction, the balance of forces in a differential slice of the rope is used to obtain a closed-form solution for the axial force field and the normal and tangential contact force fields. This analytical solution is found first in the case of a bristle model with tangential flexibility but axially rigid. Then, the model is extended to axially flexible bristles, that allows the rope to sheave relative penetration. The solution is valid until one cross-section of the rope achieves the saturated tangential friction force. The value of the axial load when this condition is met is identified. If the high-load further increases, the rope in contact with the sheave is separated in two areas, the area next to the low-load remains fully stuck to the sheave while the area next to the high-load shows exactly the saturated friction force. This paper calculates the angle of separation between the two areas and the axial force field and normal and tangential contact force fields, being all these functions piece-wisely defined. Finally, the paper presents numerical results for a particular example of all the analytical solutions.

KINEMATIC ANALYSIS OF HIP JOINT MODIFICATIONS IN SWITCH LEAP: COMPENSATORY MECHANISMS DUE TO REDUCED MOBILITY IN THIS AREA

ABSTRACT. Artistic gymnastics include a series of artistic elements where the joints’ mobility represents an essential factor for the accuracy of the execution in both beam and floor routines. The reduced mobility is responsible for the occurrence of compensatory movements. This type of repetitive and long-term compensations can damage the joints involved in execution of an accurate switch leap element. The aim of the study was to analyze the compensatory mechanisms due to reduced mobility in the hip joint that can occur during the execution of a switch leap. 6 female gymnasts (8-10 years) from C.S.S.1 Timisoara have been analyzed when they executed switch leap on the floor. The kinematic analysis was carried using inertial sensors for movement tracking technology. The evaluated parameters were: leg separation angle (LSA), lateral pelvic tilt (LPT) and pelvic rotation (PR). The data revealed a LSA of 137.5± 2.239° which corresponds to the second level of penalty (0.30 points). The compensatory movements were revealed by the level of LPT and pelvic rotation. Depending on the front leg, the compensatory tilt, represented by the elevation of the hip joint, was found on the right or left part accordingly. Regarding the pelvic rotation, this is performed in the backward direction on the same part with the tilt. The kinematic analysis of the switch leap element provides supplementary data that can be taken into consideration by the gymnasts and coaches during the training period in order to reduce the risk of injuries and the risk of falling from the beam.

Resolution analysis on light-field particle image velocimetry.

With rapid developments in light-field particle image velocimetry (LF-PIV) based on single-camera, dual-camera, and dual-camera with Scheimpflug lenses, comprehensive quantitative analysis and careful evaluation of their theoretical spatial resolutions are essential to guide their practical applications. This work presents a framework for and better understanding of the theoretical resolution distribution of various optical field cameras with different amounts and different optical settings in PIV. Based on Gaussian optics principles, a forward ray-tracing method is applied to define the spatial resolution and provides the basis of a volumetric calculation method. Such a method requires a relatively low and acceptable computational cost, and can easily be applied in dual-camera/Scheimpflug LF-PIV configuration, which has hardly been calculated and discussed previously. By varying key optical parameters such as magnification, camera separation angle, and tilt angle, a series of volume depth resolution distributions is presented and discussed. By taking advantage of volume data distributions, a universal evaluation criterion based on statistics that is suitable for all three LF-PIV configurations is hereby proposed. With such a criterion, the pros and cons of the three configurations, as well as the effects of key optical parameters, can then be quantitatively illustrated and compared, thus providing useful guidance on the configuration and optical parameter selections in practical implementations of LF-PIV.

Auxetic properties of a tangram-inspired metamaterial

This paper explores a new anisotropic auxetic system that consists of rotating rhombi and right triangles by inspiration from tangram pieces. The Poisson’s ratio was developed by geometrical analysis on the representative unit with prescribed boundary requirements. Upon assigning rotational stiffness to the hinges, the Young’s modulus was established by matching the potential energy stored in the spiral springs with the strain energy of the deformation for the homogenized continuum. Results indicate that the on-axes Poisson’s ratio and dimensionless Young’s moduli are governed by the shapes and separation angles of the rigid units which, in turn, determine the dimension of the representative unit of the metamaterial. For the special case where the Poisson’s ratio is −1 when stretched on either axis, the Young’s moduli are equal. For this special case, the separation angles and the on-axes Young’s moduli increase monotonically with the shape descriptor of the rigid units. The capability of combining rotating rigid units of quadrilateral and triangular shapes suggests that new combinations of mechanical properties can be designed from rotation-based auxetic systems.

Source separation and arrival angle estimation using a single acoustic vector sensor

Extracting individual time signatures from two angularly-separated sources overlapping in time and bandwidth typically requires coherent array processing on multiple hydrophones, a process whose performance is degraded by limited aperture and spatial aliasing. Vector sensors, which measure both acoustic pressure and particle velocity, can measure an acoustic field’s directionality in a single, compact sensor package. Standard beamforming techniques can be applied to the outputs of a vector sensor to suppress one source’s signal, but its efficacy is limited by the angular insensitivity of the resulting cardioid beam pattern. Here we use fundamental physical principles to demonstrate that measurements on a 2-D vector sensor can completely determine the azimuths, amplitudes, and relative phases of two horizontal plane waves of the same frequency, achieving source separation and direction-of-arrival estimates for both. Interference between the waves creates a reactive intensity whose orientation is perpendicular to the bisector of the two wavenumber vectors. This observation leads to closed-form inversion formulas. Data examples of the technique are illustrated using overlapping humpback whale songs off Hawaii, and on weak airgun and bowhead whale signals embedded within intense directional noise from a nearby drilling site in the Beaufort Sea. [Work sponsored by ONR TFO.]

Cross flow over two heated cylinders in tandem arrangements at subcritical Reynolds number using large eddy simulations

This study analyses the heat transfer and flow characteristics of cross-flow over two heated infinite cylinders in a tandem (in-line) configuration. Non-isothermal Large Eddy Simulations (LES) using the dynamic Smagorinsky model were conducted at a fixed Reynolds number of 3,000 (based on the free stream velocity and the cylinder diameter). A range of cylinder gap ratios (1.0≤L/D≤5.0) was investigated (in increments of 0.25) with two different Prandtl numbers Pr=0.1 and 1.0. Results show that the flow structures vary according to the order of the patterns: (i) Extended body regime: without attachment for low L/D (1.0-1.25) where cylinders behave as a single bluff body with top–bottom vortex shedding, (ii) Shear layer reattachment regime: with reattachment for moderate L/D (1.5-3.75) where the detached shear layer from the upstream cylinder reattaches to the downstream cylinder, and (iii) Co-shedding regime: for high gap ratios (3.75≤L/D≤5.0) a phenomenon called “jumping”, where the two cylinders behave as isolated bluff bodies. Furthermore, it was observed that the average Nusselt number of both cylinders experience a drastic variation at a critical spacing ratio (between 3.75≤L/D≤4.0). For L/D≤3.0, the average Nusselt number of the upstream cylinder was found to be higher than that of the downstream one. However, for spacing ratios L/D>3.0, the average Nusselt number was similar for both cylinders. For the downstream cylinder, the maximum Nusselt number was located at the separation angle and was found to be independent of the spacing ratio.

Variance of the Hellings-Downs correlation

Gravitational waves (GWs) create correlations in the arrival times of pulses from different pulsars. The expected correlation $\mu(\gamma)$ as a function of the angle $\gamma$ between the directions to two pulsars was calculated by Hellings and Downs for an isotropic and unpolarized GW background, and several pulsar timing array (PTA) collaborations are working to observe these. We ask: given a set of noise-free observations, are they consistent with that expectation? To answer this, we calculate the expected variance $\sigma^2(\gamma)$ in the correlation for a single GW point source, as pulsar pairs with fixed separation angle $\gamma$ are swept around the sky. We then use this to derive simple analytic expressions for the variance produced by a set of discrete point sources uniformly scattered in space for two cases of interest: (1) point sources radiating GWs at the same frequency, generating confusion noise, and (2) point sources radiating GWs at distinct non-overlapping frequencies. By averaging over all pulsar sky positions at fixed separation angle $\gamma$, we show how this variance may be cleanly split into cosmic variance and pulsar variance, also demonstrating that measurements of the variance can provide information about the nature of GW sources. In a series of technical appendices, we calculate the mean and variance of the Hellings-Downs correlation for an arbitrary (polarized) point source, quantify the impact of neglecting pulsar terms, and calculate the pulsar and cosmic variance for a Gaussian ensemble. The mean and variance of the Gaussian ensemble may also be obtained from the previous discrete-source confusion-noise model in the limit of a high density of weak sources.

Numerical investigation of flow past a circular cylinder modified with a single groove at low Reynolds number

Flow past a circular cylinder modified by grooves is one of the passive control techniques to control the drag and lift forces. The presence of grooves tends to reduce the hydrodynamic drag and lift. The aim of this work was to numerically investigate the influence of a single groove modification on a circular cylinder and how it was impacting the hydrodynamic coefficients based on its position and shape at low Reynolds numbers. Three types of grooves were considered, namely, dimple, square, and triangular, with identical width and depth which is 0.1 times the diameter. The Reynolds numbers considered were 100, 150, and 200. The computational domain was set to a blockage ratio of 0.01 after carrying out a detailed domain independence test. It was observed that the drag and lift reduction was maximum at groove location 90° with the decrements being more for the square groove shape. The viscous drag showed a decrease in its values for all the groove positions located on the flow-facing side of the cylinder; however, the pressure drag showed an increment in its values for these groove locations, and these increments were relative of larger magnitudes, thus influencing a net increase in the total mean drag when compared to the smooth case; this was evident at groove locations 120° and 150°. The vorticity patterns for the grooves located on the front side showed large irregularities in magnitude between the anticlockwise and the clockwise vortices with the groove side vortices being of larger magnitudes, and for the wake side, the irregularities were negligible. The coefficient of pressure and separation angles were also investigated. The CP vs θ plots showed discontinuity at groove locations with abrupt variations at the front face of the cylinder; for the wake side grooves, these discontinuities were low and almost coincided with the CP vs θ plots of the smooth cylinder. The grooves located at 90° showed a delay in separation and at 60° the boundary layer tends to detach earlier.

Circuit representation, experiment and analysis of parallel-cell triboelectric nanogenerator

Typical simulation using finite element for designing triboelectric nanogenerator (TENG) needs high computational resources. Equivalent circuit modeling as a less computationally intensive method has great potential for TENG simulation but it is only used for simple structures in the literature. In this work, taking parallel-cell triboelectric nanogenerator (PC-TENG) as an example, we establish an equivalent circuit representation for TENG with complex structures. The boundary effect and the parasitic capacitance, which are normally ignored in the existing simple circuit models in the literature, are considered in the equivalent circuit modeling by comparison with finite element simulation and experiment. With the validated equivalent circuit model of the PC-TENG, a parametric study demonstrates the influence of various critical parameters (separation angle α from 0° to 90°, excitation frequency from 1 Hz to 10 Hz, and excitation amplitude truncation percentage from 0 % to 100 %) on the electrical outputs of the PC-TENG, showing that PC-TENG can obtain the optimal outputs at α > 15°, 10 Hz and a truncation percentage of 50 %. The methodology based on the proposed circuit representation paves the way for holistic modeling, evaluation and optimization for complex TENG design.

Mathematical modeling of the parameters of an electro-optic modulator in the Mach–Zehnder interferometer configuration based on thin lithium niobate films

Subject of study. An electro-optic modulator in a Mach–Zehnder interferometer configuration based on ridge waveguides made of a thin lithium niobate film was studied. Aim of study. The study aimed to mathematically model the parameters of an electro-optic modulator in a Mach–Zehnder interferometer configuration based on ridge waveguides made of a thin lithium niobate film. Method. The dependence of the optical losses introduced by a Y-branch splitter on the angle of the splitter was investigated using a beam propagation method based on the fast Fourier transform. Main results. The results of mathematical simulation of the parameters of the electro-optic modulator in the Mach–Zehnder interferometer configuration based on thin lithium niobate films were presented. The dependence of the optical losses, introduced by the Y-splitter, on the waveguide separation angle was obtained. Images of interference patterns occurring in the output waveguide were examined. A comparison revealed that the effectiveness of the proposed interferometer configuration was higher than that of the alternative solutions available in the literature. The novelty of the results is that the configuration of the electro-optic modulator investigated in this study was fabricated in the form of an integrated optical circuit based on ridge waveguides of thin-film lithium niobate. Such a solution enables a reduction in the dimensions of the final device and increases the sensitivity compared with that of existing analogs based on bulk electro-optic crystals. Additionally, owing to the use of a semiconductor substrate, an electronic circuit can possibly be integrated into the substrate, which enables the implementation of an electro-optic sensor system on a single chip. Practical significance. The method for interference pattern analysis proposed in this study provides information on the magnitude of the voltage applied to the arm of the interferometer and enables the development of requirements for its further modernization for increasing the accuracy of measurements and developing optoelectronic devices based on thin lithium niobate films, including integrated optical electric-field sensors.

Semiempirical Model of the Drag Force Acting on an Obstacle in Downward Dense Particle Flows as per the Flow-Around Behavior

Determination of the flow-around drag force acting on an internal when particles downwardly flow around the internal is important for the safety of internals in the downward particle flow channel. In this study, the flow behaviors of particles downwardly flowing around different obstacles were investigated and a semiempirical drag force model was proposed based on the characteristics of the flow patterns. The proposed model was validated and key coefficients were correlated using the experimental data. The results indicate that there were three featured flow zones when particles downwardly flowed around an obstacle: the flow stagnant zone (disappear for triangular/conical obstacle), the slip-shear flow zone, and the flow separation zone. The stagnant zone angle and the flow separation angle were proposed to depict transition points of three flow zones when particles flowed around a cylindrical/spherical obstacle, and the two angles were found independent of the flow condition. A drag force model as per the flow patterns was proposed. The model decomposed the drag force into the compression force, the shear force, and the confinement force. The expressions of the compression stress, the shear stress, the effective area, and the confinement force were given. The mathematical form of the proposed model was validated and key coefficients in this model were also correlated using the experimental data. The average error of the drag force model was ±7.6% while the maximum error was within ±15%.

Effects of Ground Slopes on Erector Spinae Muscle Activities and Characteristics of Golf Swing.

(1) Background: 'Slope' refers to the position faced by golfers on the course. Research on the recruitment strategies of thoracolumbar erector spinae during golf swings on different slopes may help us to understand some underlying mechanisms of lower back pain. (2) Purpose: The purpose of the present study is to assess electromyography (EMG) patterns of the erector spinae muscles (ES) and the kinematics of the trunk and swing parameters while performing golf swings on three different ground slopes: (1) no slope where the ball is level with the feet (BLF), (2) a slope where the ball is above the feet (BAF), and (3) a slope where the ball is below the feet (BBF). Furthermore, the present study evaluates the effect of slope on the kinematics of the trunk, the X-factor angle, and the hitting parameters. (3) Methods: Eight right-handed recreational male golfers completed five swings using a seven-iron for each ground slope. Surface electromyograms from the left and right sides of the ES thoracolumbar region (T8 and L3 on the spinous process side) were evaluated. Each golf swing was divided into five phases. Kinematics of the shoulder, trunk, and spine were evaluated, and the ball speed, swing speed, carry, smash factor, launch angle, and apex were measured using Caddie SC300. (3) Results: The muscle activity of the BAF and BBF slopes was significantly lower than that of the BLF slope during the early follow-through phase of the thoracic ES on the lead side (i.e., left side) and during the acceleration and early follow-through phases of the lumbar ES on the lead side. The lead and trail side (i.e., right side) lumbar ES were more active during acceleration than the thoracic ES. Additionally, the trends of the lead and trail sides of the thoracolumbar regions on the three slopes were found to be the same across the five phases. Trunk angle and X-factor angles had no significant differences in address, top of backswing, or ball impact. The maximum separation angles of the X-factor appeared in the early phase of the downswing for all the three slopes. Regarding smash factor and launch angle, there were no significant differences between the three slopes. The ball speed, swing speed, carry, and apex were higher on BLF than on BAF and BBF slopes. (4) Conclusion: The findings suggest that amateur golfers face different slopes with altered muscle recruitment strategies. Specifically, during the acceleration phase of the golf swing, the BAF and the BBF slopes, compared with the BLF slope, significantly underactivated the lead side thoracolumbar erector spinae muscles, thereby increasing the risk of back injury. Changes in muscle activity during critical periods may affect neuromuscular deficits in high-handicap players and may have implications for the understanding and development of golf-related lower back pain. In addition, the X-factor angle was not affected by the slope, however, it can be found that the hitting parameters on the BLF slope are more dominant than on the other slopes.

Control over Vortex Shedding and Drag Force on a Circular Obstacle Using a Pair of Downstream Splitter Plates in a Transient Flow

The current work is an analysis of the laminar, two‐dimensional, and transient flow over a circular cylinder with a two‐branched splitter plate. For complex nonlinear governing equations, the finite element method is used as a computational approach. The objective of the current study is to determine the best conditions using geometrical characteristics along with the impact of Reynolds number Re.The geometric parameters, α which is the angle of separation between the pair of splitter plates of length L and G/D which is the gap from diameter ratio of the splitter plate to cylinder diameter, are the controlling tools for the present study. Due to its little impact on flow characteristics, it was discovered that using a two‐branched splitter plate in Reynolds numbers under 100 is not desirable. A complete vortex shedding has been achieved with α = 0° and G/D = 2 at Re = 100 and also the periodic behavior of velocity has been controlled. The least drag force is observed at an angle of 30° between the two plates compared to another angle of 0°. It is not advised to use two splitter plates at angles more than 30° because this will not further contribute in the drag reduction. Since the gap to diameter ratio between the splitter plates and the cylinder increased up to a significant value, the overall control on hydrodynamic effects is achieved. It is concluded that the maximum drag reduction of 48% over the cylinder has taken place when the Re is 200, α is 30°, and G/D is 2.

The effect of shock wave properties on the release timings of solar energetic particles

Context. Fast and wide coronal mass ejections (CMEs) and CME-driven shock waves are capable of accelerating solar energetic particles (SEPs) and releasing them in very distant locations in the solar corona and near-Sun interplanetary space. SEP events have a variety of characteristics in their release times and particle anisotropies. In some events, specifics of the SEP release times are thought to be difficult to reconcile with the scenario that a propagating shock wave is responsible for the SEP release. Aims. Despite the apparent difficulties posed by the shock scenario, many studies have not considered the properties of the propagating shock waves when making a connection with SEP release. This could probably resolve some of the issues and would help us to delve into and understand more important issues such as the effect of the shock acceleration efficiency on the observed characteristics of the SEP timings and the role of particle transport. This study aims to approach these issues from the shock wave perspective and elucidate some of these aspects. Methods. We constructed a simple 2D geometrical model to describe the propagation and longitudinal extension of a disturbance. We used this model to examine the longitudinal extension of the wave front from the eruption site as a function of time, to calculate the connection times as a function of the longitudinal separation angle, and to determine the shock parameters at any connection point. We examined how the kinematic and geometric properties of the disturbance could affect the timings of the SEP releases at different heliolongitudes. Results. We show that the extension of a wave close to the solar surface may not always indicate when a magnetic connection is established for the first time. The first connection times depend on both the kinematics and geometry of the propagating wave. A shock-related SEP release process can produce a large event-to-event variation in the relationship between the connection and release times and the separation angle to the eruption site. The evolution of the shock geometry and shock strength at the field lines connected to an observer are important parameters for the observed characteristic of the release times.