Vertical Axis Research Articles

Mathematical Analysis of a Navier–Stokes Model with a Mittag–Leffler Kernel

In this paper, we establish the existence and uniqueness results of the fractional Navier–Stokes (N-S) evolution equation using the Banach fixed-point theorem, where the fractional order β is in the form of the Atangana–Baleanu–Caputo fractional order. The iterative method combined with the Laplace transform and Sumudu transform is employed to find the exact and approximate solutions of the fractional Navier–Stokes equation of a one-dimensional problem of unsteady flow of a viscous fluid in a tube. In the domains of science and engineering, these methods work well for solving a wide range of linear and nonlinear fractional partial differential equations and provide numerical solutions in terms of power series, with terms that are simple to compute and that quickly converge to the exact solution. After obtaining the solutions using these methods, we use Mathematica software Version 13.0.1.0 to present them graphically. We create two- and three-dimensional plots of the obtained solutions at various values of β and manipulate other variables to visualize and model relationships between the variables. We observe that as the fractional order β becomes closer to the integer order 1, the solutions approach the exact solution. Lastly, we plot a 2D graph of the first-, second-, third-, and fourth-term approximations of the series solution and observe from the graph that as the number of iterations increases, the approximate solutions become close to the series solution of the fourth-term approximation.

Mapping Visit Behaviors in a Virtual Art Gallery to Visitor Engagement Profiles Using Latent Class Analysis

Virtual art galleries represent a rapidly growing and potentially unique context for art engagement, but little is known about the psychological nature of these experiences. To better characterize virtual art gallery visits, we quantified a set of in-depth behaviors related to art viewing, navigation, and intensive art engagement in a virtual gallery. Data included coordinate position and gaze proxy data, recorded from 264 unconstrained participant visits to a virtual gallery that contained 24 diverse artworks curated throughout 3 rooms. Nine classified visit behaviors—related to the overall visit, navigation, art viewing, and deep engagement—were used in a latent class analysis as indicators for estimating possible visitor engagement classes. The analysis resulted in a 4-class model which classified visitors as disengaged, typical, engaged, and revisitors. Finally, we examined how each class differed in terms of their art knowledge, personality, and other individual differences. Significant differences were found for several variables, including aesthetic fluency, openness to experience, extraversion, age, and nausea.

Sex Chromatin in New Hampshire Cocks

Sex chromatin (SC) is defined as inactive X chromosome in the female somatic cells, it condensed as heterochromatic at interphase of the nucleus and appears like nuclear satellite projection, and only female cells contain SC in mammals. Different ages of cocks: immature (8,16 weeks old), growing (24 weeks old) and production age (32,48 weeks old) , were studied to detect the sex chromatin (SC) with it's various shapes :Sessile nodule(SS), Drum stick(DS), Tear drop(TD) and Club shape(CS) in the blood lymphocytes of blood smears prepared from WBCs of 45 New Hampshire(NH) strain cocks. Also SC measurements were detected which include: vertical (V) and horizontal (H) axes, SC area (SCA), nuclear area (NA), and the ratio(R) between these two areas. . Results show that SC is present in the male chicken blood lymphocytes in all ages. There is no significant difference in the incidence of the SC or its various measurements between ages, but the vertical axis was recorded a significant (P

Anisotropies related to representational gravity.

Four experiments examined whether representational gravity, in which memory for the location of a previously-viewed target is displaced in the direction of implied gravitational attraction, occurs uniformly across a target. Participants viewed stationary, vertically-moving, or horizontally-moving targets of different sizes and at different heights within the picture plane. After a target vanished, participants indicated the remembered location of the top edge or bottom edge of that target. Significant anisotropies were found, as the remembered location of the top edge was displaced downward, whereas the remembered location of the bottom edge was not displaced or was displaced upward. Anisotropies along the vertical axis were not influenced by whether participants knew prior to target presentation which edge to remember or by whether targets were stationary or moved vertically, although there was a trend foranisotropies along the vertical axis to be reduced when targets moved horizontally. Larger targets and targets higher in the picture plane resulted in larger displacement when targets were stationary, although effects of size and height were diminished when targets were moving. If the top edge and bottom edge of a target are considered analogous to the trailing edge and leading edge of a moving target, respectively, then anisotropies related to representational gravity are similar to anisotropies previously reported for representational momentum for horizontally-moving targets (as direction of implied gravitational attraction is downward). The existence of such anisotropies has implications for the representation of space and for the localization of and interaction with stimuli in the environment.

Ducted wind turbines: A review and assessment of different design models

Wind energy technology is progressing at an accelerated pace due to the growing global demand for renewable energy, particularly horizontal axis wind turbines (HAWTs). Ducted wind turbines (DWTs) have emerged as a promising enhancement to traditional horizontal axis wind turbines, demonstrating substantial improvements in efficiency and power output. This study presents a comprehensive evaluation of four distinct designs for DWTs, with a focus on critical factors including efficiency, cost-effectiveness, durability, and environmental sustainability. Among the designs analyzed, the Diffuser configuration emerges as the most advantageous in terms of cost, delivering energy more economically than the Nozzle-Diffuser design. The durability analysis underscores the Diffuser design’s superior longevity, indicated by a durability index of 0.9, reflecting its robust construction and low maintenance demands. Additionally, the Diffuser design is shown to be highly environmentally sustainable, achieving an Environmental Impact Score of 0.91, highlighting its minimal carbon footprint and high recyclability. The study concludes that the Diffuser design offers a balanced and effective solution, combining cost efficiency, durability, and environmental considerations while maintaining competitive efficiency levels.

Effect of Implant Analog Design and Additively Manufactured Casts' Printing Layer Thickness on the Linear and Angular Accuracy of Analogs for Direct Digital Workflow: An In Vitro Study.

To evaluate how implant analog design and printing layer thickness affect the linear and angular accuracy of implant analogs in additively manufactured casts, comparing with conventional implant analogs in stone casts. A reference cobalt chromium mandibular model with a single implant was digitized with an industrial optical scanner and scan bodies compatible with a pressure/friction fit (S) or a screw-retained (N) implant analog for direct digital workflow. These scans were used to fabricate casts with 50 μm (S-50 and N-50) and 100 μm (S-100 and N-100) layer thickness (n=10). Ten stone casts were made after single-step closed-tray polyvinylsiloxane impressions of the model (CNV). All casts were digitized with the same metal scan body and scanner used to digitize the master model, and these scans were superimposed over the scan of the master model to measure the linear (x, y, and z-axes) and angular (XY and YZ planes) deviations (Geomagic Control X). The precision of measured deviations was defined with the average deviation values. Generalized linear model analysis was used to compare the deviations within implant analogs for direct digital workflow, while 1-way analysis of variance and Dunnett's test were used to compare these analogs and conventional analogs (α = .05) Results. The analog design affected the linear deviations (y-axis), while the interaction between the analog design and the layer thickness, and the analog design affected the angular deviations (XY plane, P ≤ .030). S analogs had lower linear and angular deviations than N analogs, and S-50 led to lower angular deviations than N-50 (P ≤ .030). CNV led to higher linear accuracy (y-axis) than N-50, N-100, and S-100 and led to lower angular deviations than all test groups (XY plane) (P ≤ .025). The analogs in S-50 casts had positional trueness similar to or higher than those in other test groups and their accuracy was mostly similar to those in CNV casts. Implant analogs for direct digital workflow deviated more towards lingual and gingival, and conventional analogs deviated more towards buccal, occlusal, and distal. All analogs had a tendency to tilt towards lingual and distal.

RP-Net: A Robust Polar Transformation Network for rotation-invariant face detection

Face detection is challenging in unconstrained environments, where it encounters various challenges such as orientation, pose, and occlusion. Deep convolutional neural networks, particularly cascaded ones, have greatly improved detection performance but still struggle with rotating objects due to limitations in the Cartesian coordinate system. Although data augmentation can mitigate this issue, it also increases computational demands. This paper introduces the Robust Polar Transformation Network (RP-Net) for rotation-invariant face detection. RP-Net converts the complex rotational problem into a simpler translational one to enhance feature extraction and computational efficiency. Additionally, the Advanced Spatial-Channel Restoration (ASCR) module optimizes facial landmark detection within polar domains and restores critical details lost during transformation. Experimental results on benchmark datasets show that RP-Net significantly improves rotation invariance over traditional CNNs and surpasses several state-of-the-art rotation-invariant face detection methods.

Nanoindentation creep response of Ti–6Al–4V ELI alloy manufactured via laser powder bed fusion

The anisotropic creep response in both the XY and XZ planes of Ti–6Al–4V ELI manufactured by powder bed fusion (PBF) was examined under nanoindentation creep loading at room temperature, ranging from nm to μm scales. The stress exponent values of 4.06–4.30, rationalised through threshold stress, indicate that the creep behaviour is primarily dominated by dislocation gliding. Creep displacement results show that the anisotropic creep behaviour in the XY and XZ planes of the as-built, and heat treatment enhances the creep resistance of the XZ plane, while there is no significant difference in creep displacement between the as-built and heat-treated XY planes. Due to the higher dislocation density and compressive residual stress in the XY plane compared to the XZ plane, the creep resistance is higher in the XY plane for the as-built. It is highlighted that compressive residual stress is more relieved in the XY plane than in the XZ plane through heat treatment. The heat treatment results in improved creep resistance due to the formation of the Widmanstätten structure and β precipitates, which can impede dislocation movement under creep loading. The combination of residual stress and microstructural effects leads to anisotropic creep behaviour, suggesting that the anisotropy is inherited from the additive manufacturing process at micron scales.

GB-SAR geocoding considering the radar attitude inclination angles for building facade deformation extraction

ABSTRACT The process of engineering construction typically impacts the nearby existing buildings, causing either localized or widespread deformation of these structures. The application of deformation monitoring technology enables the timely identification of damage or uneven deformation, thereby facilitating the implementation of appropriate maintenance and repair actions. This paper explores the application of ground-based synthetic aperture radar (GB-SAR) in building facade deformation monitoring. GB-SAR acquires two-dimensional (2D) images and measures deformation along the line of sight (LOS) direction through interference calculation. In order to accurately determine the location of deformation and retrieve the elevation information of image pixels, it is usually required to utilize external three-dimensional (3D) data to reconstruct the 3D coordinate of these pixels, which is known as geocoding, or georeferencing. In the case of the GB-SAR system, it is necessary for the observer to measure the angles between the antenna orientation, the radar movement direction and the reference plane of the local surveying coordinate system. Nevertheless, the measurement of these attitude angles may be overlooked in practice, and the impact of small attitude angles or their measurement errors on GB-SAR geocoding may be disregarded, which directly affects the slant range projection (SRP) calculation of the external 3D data, thereby leading to biased 3D coordinate reconstruction of GB-SAR pixels. This paper proposes a method to calculate the SRP coordinates of point cloud data considering the attitude inclination angles of radar sensor, and perform matching calculations on the high-quality pixels (HQPs) with the point cloud after SRP to extract building facade deformation. The results demonstrate that the method is capable of effectively mitigating the influence of the radar attitude inclination angles, resulting in a reduction of the average deviation of 3D coordinates to approximately one-third of the value without consideration of the sensor’s attitude in a real-world building monitoring experiment.

A Gauss kernel non-local stress-driven plate theory

This study presents a novel stress-driven formulation, incorporating Kirchhoff’s plate assumptions and accounting for the non-local size-dependent feature in both plate geometric axes, which is practical, especially near the origin of the axis in the polar coordinates. The presented formulation does not impose any additional constraints on the elastic radial curvatures, which are known as constitutive boundary conditions. Therefore, taking into account the non-local behavior in both radial and circumferential directions does not lead to an overconstrained problem. The study focuses on the analysis of a circular plate with an outer radius (R), thickness (h), and the length scale parameter (L). The governing differential equations are derived in Cartesian coordinates and then transformed to the polar coordinates to analyze circular plates. When R tends to infinity, the governing equation is solved analytically. Using the Galerkin technique, a finite element solution is presented for the analysis of a bounded circular plate with a clamped boundary condition at the outer radius R. The study discusses the size effects and the gradient properties of functionally graded plates in stress-driven non-local theory. It reveals that while increasing the non-local parameter results in a reduction of transverse displacement, the moments remain unaffected.

Constructing 3D SPAD distribution using hyperspectral LiDAR point cloud by PROSPECT model inversion

ABSTRACT Accurately estimating leaf chlorophyll concentrations in a three-dimensional (3D) manner is crucial for precisely monitoring crop growth and development. To reduce destructive detection and achieve real-time estimation, researchers often utilize crop leaves’ SPAD (Soil and Plant Analyzer Development) to represent relative chlorophyll content. However, SPAD measurement is time-consuming and laborious work. Many inversion methods have been proposed to estimate SPAD based on one-dimensional reflectance or two-dimensional spectral images, which rely on external light sources and also cannot obtain 3D distribution. Hyperspectral LiDAR (HSL), as an active remote sensing technology, can acquire target spatial and spectral data simultaneously, making 3D SPAD inversion and reconstruction possible. This research aims to invert SPAD values with HSL spectral information aided by the PROSPECT model and reconstruct 3D SPAD distribution with HSL spatial information. Firstly, we constructed new ratio chlorophyll indices (RCI) based on the multi-feature analysis method with the PROSPECT model and HSL spectral data. Next, we employed RCIs to modify the Look-Up Table (LUT) cost function (SPAD-LUT) of the PROSPECT model, which was validated with the ANGERS dataset. Then, we conducted SPAD inversion with HSL spectral information from vegetable crop samples and integrated the inverted SPAD values into their corresponding 3D coordinates, achieving 3D SPAD distribution reconstruction. The predicted values of the model inversion with the HSL dataset are consistent with the measured SPAD (R2 = 0.421, RMSE = 10.615). The results indicate that our method can invert sample SPAD values and reconstruct their distribution with HSL point cloud despite their complex spatial structure.

Heat transfer enhancement of PCM in the triple-pipe helical-coiled latent heat thermal energy storage unit and complete melting time correlation

Secondary flows induced in helical-coiled pipes significantly enhance the thermal storage performance of latent heat thermal energy storage units. This paper presents a three-dimensional model of a triple-pipe helical-coiled system to investigate the melting characteristics of phase change material within it. A correlation for the complete melting time was developed based on the simulation results. The findings indicate that the thermal-hydraulic fields of the heat transfer fluids and phase change material deflect from the vertical central axis at cross-sections. The secondary flows within the inner pipe are more effective in enhancing melting than those in the outer pipe. Melting performance improves with increasing inner pipe diameter, coil diameter (from 100 mm to 160 mm), inclination angle, or heat transfer fluid temperature, or decreasing helical pitch. The inner pipe diameter, helical pitch and heat transfer fluid temperature exhibit more pronounced influences. An inner pipe diameter of 30 mm, a coil diameter of 160 mm, a helical pitch of 80 mm, an inclination angle of 90°, a heat transfer fluid temperature of 360 K, and a heat transfer fluid Reynolds number of 2000, respectively produce a faster melting process. The developed correlation for the triple-pipe helical-coiled pipe thermal storage unit accurately predicts 96 % of the 45 data within ±11 %.

Extraction of isotropic and anisotropic components for optical surface micro-metrology based on the two-dimensional power spectral density analysis

Extraction of surface characteristics is essential during surface processing and optical inspections. In this work, we propose a new extraction method by dividing the global feature within multiple directions into isotropic and anisotropic components and combining noise filtration, two-dimensional component extraction, and fast reconstruction. The mathematical descriptions of global and local features were derived. The noise by holes, scratches, and finite sampling points was restrained by Bearing Ratio analysis, Hough transform, and Welch window operation. The isotropic and anisotropic surface components were extracted in the two-dimensional power spectral density domain, reconstructed in the two-dimensional Fourier domain, and inversed in Cartesian coordinates. Five surfaces with anisotropic structural characteristics ranging from zero to two dimensions were analyzed. The general applicability was proved according to the consistency between surface processing methods and extracted results. A chemical mechanical polishing experiment was designed and accomplished to verify the sensitivity of the extraction method. The subtle variation in surface morphology was captured on the reconstructed surfaces near the polishing end-point, confirming its detectability on weak anisotropic components. This process-oriented surface extraction method can achieve qualified results without transcendental knowledge of surface conditions and offers openness to various surface evaluation criteria by statistical roughness indicators, which supports surface inspection for multiple surface processing techniques.

Smart dimensional quality assessment of embedded steel plates based on images and laser data fusion

Abstract Accurate and efficient positioning is critical to ensuring the dimensional quality assessment of embedded steel plates. However, traditional manual measurement methods struggle to efficiently measure and evaluate these plates. Vision-based measurement methods offer advantages such as high resolution, fast data acquisition, and processing speed, allowing accurate measurement of 2D coordinates. LiDAR can capture highly accurate point clouds, due to the unordered nature of point clouds, processing and analysis require significant computational resources. This paper proposes a method for smart 3D localization of embedded steel plates using image and laser data. (1) We introduce an improved Rectangular Diagonal Constraint Harris (RDC-Harris) corner detection method and achieve subpixel 2D corner detection of embedded plates based on deep learning；(2) Given a calibrated camera-LiDAR, we develop a smart detection algorithm guided by 2D image bounding boxes, achieving 3D corner localization. In indoor testing and engineering applications, this method effectively ensures the dimensional quality of embedded steel plates. Compared to traditional manual inspection, the measurement efficiency reaches 10 minutes per station, with an accuracy of 2.12 mm.

Hybrid Orientation and Position Collaborative Motion Generation Scheme for a Multiple Mobile Redundant Manipulator System Synthesized by a Recurrent Neural Network.

To enable distributed multiple mobile manipulator systems to complete collaborative tasks safely and stably, this article investigates and presents a motion generation scheme that considers both orientation and position coordination based on a distributed recurrent neural network. Moreover, physical limits are also considered. Specifically, the orientation and position coordination constraints and physical limits are modeled separately as equality and inequality constraints with coupled variables. Subsequently, a motion generation scheme for multiple mobile manipulators based on quadratic programming is established. Finally, a distributed linear variational inequality-based primal-dual neural network is constructed to solve the motion generation scheme and obtain the motion trajectories of all the mobile manipulators. The simulation results demonstrate that the hybrid orientation and position collaboration motion generation scheme effectively addresses the position and orientation coordination problem for multiple mobile manipulator systems. Compared to other schemes, the proposed scheme based on a distributed computing structure greatly enhances the stability of the system. Additionally, the proposed approach introduces orientation coordination and physical limits, which increases the practicality of the system.

A comprehensive study of the effect of scanning strategy on IN939 fabricated by powder bed fusion-laser beam

This study provides a comprehensive investigation into the effects of different scanning strategies on the material properties of IN939 fabricated using the PBF-LB process. The scanning strategies examined included alternating bi-directional scanning with rotation angles of 0°, 45°, 67°, and 90° between adjacent layers (named as shown), as well as alternating chessboard scanning with rotation angles of 67° and 90° (named as Q67° and Q90°). The results revealed that the 45° and 67° samples had the highest relative density, while the 0° and Q67° samples showed the highest average porosity. Moreover, various types of cracks, including solidification, solid-state, and oxide-induced cracks, were observed. Among the bi-directional scan samples, the 0° sample displayed the most extensive cracking and the highest σmax residual stress values in both XZ and XY planes. Conversely, the 45° and 67° samples exhibited fewer cracks. Notably, the lowest σmax residual stress in the XZ planes among the bi-directional scan samples was observed in the 67° sample. Additionally, microstructural analyses indicated differences in grain size and morphology, among the samples. Texture analysis indicated that the 0° and 90° samples exhibited strong cube textures, whereas the texture intensity weakened for the 45° and 67° samples. Moreover, the alternating chessboard scanning strategy led to rougher surfaces (higher Sa and Sz values) compared to the alternating bi-directional scanning strategy, regardless of the rotation angles. Furthermore, the microhardness values among the samples showed minimal variance, ranging between 321 ± 14 HV and 356± 7 HV.

Impact of postoperative spinal malalignment on postoperative health-related quality of life after long-level fixation for degenerative lumbar scoliosis: does residual coronal angularity matter?

This study evaluates the influence of spinal malalignment on health-related quality of life (HRQOL) in a long-level fusion spine. This was a retrospective analysis of 121 consecutive patients with DLS after long-segment fusion. HRQOL and radiographic parameters were collected at final follow-up. For postoperative residual Cobb angle (CA), patients were divided as follows: group (0) (CA < 10°), group (+) (CA 10°∼20 °), and group (++) (CA > 20°). For postoperative coronal vertical axis (CVA), patients were separated as follows: group (0) (CVA < 2cm), group (+) (CVA 2 ∼ 3cm), and group (++) (CVA > 3cm). Patients were also grouped by the sagittal modifiers as group (0), group (+), and group (++) according to the Scoliosis Research Society (SRS)-Schwab classification, respectively. Visual analog scale (VAS) for back was significantly lower in CA 10°∼20° group compared to other groups. Patients with remnant CA > 20° showed worse Oswestry Disability Index (ODI), SRS-22 and the 36-item Short Form Health Survey (SF-36) - physical component scores (PCS). Sagittal vertical axis (SVA) showed significant correlation with HRQOLs after surgery, and the statistical significance of ODI, SRS-22 and SF-36 scores was observed among subgroups. In long-level fused spine, residual CA > 20° resulted in worse clinical outcomes and was recommended to avoid during surgery. And 10° to 20° residual CA was acceptable in DLS patients and even better than Cobb angle < 10° in several HRQOLs, therefore strictly pursing upright alignment seems unnecessary. SVA also showed effectiveness in assessing HRQOL in the fixed spine.

A Top Model of Urban Residents’ Subjective Well-Being in China

Past research on subjective well-being (SWB) in Western society and China has revealed various contributing factors. This study conducted a series of interviews with Chinese urban residents to systematically analyze those factors based on Bronfenbrenner’s Ecological System Theory. The results revealed that 5 layers, 23 factors, and 55 elements, many of which had distinct Chinese characteristics, contributed to Chinese urban residents’ SWB. The Top Model of SWB, visualized as a spinning top or gyroscope, showcased the interdependent layers of factors impacting Chinese urban residents’ SWB. At its vertical axis is a time dimension as residents often reflect on factors by comparing their present situation with the past and the future. Discussion regarding each layer, the primary factors that comprise each layer, links between the layers, and the impact of a time dimension was included to substantiate the proposed model. The discussions focus on the study’s contribution to SWB literature, public policy-making, and future research on urban Chinese residents’ SWB.

Design and kinematics analysis of a cable-stayed notch manipulator for transluminal endoscopic surgery

The friction between the joints of the continuum manipulator with discrete joints brings great difficulties to kinematic modeling. The traditional driving wire arrangement limits the load capacity of the manipulator. A cable-stayed notch manipulator for transluminal endoscopic surgery is proposed, and a driving force coupling kinematic mode is established. The manipulator is fabricated from a superelastic Nitinol tube with bilaterally cut rectangular notches and is actuated by a stay cable. By applying the comprehensive elliptic integral solution (CEIS) for large deformation beams, the bending angle of each elastic beam is obtained, and the kinematics from the driving space to the joint space is formed. According to the bending angle of each elastic beam, the expression of the manipulator in Cartesian space can be obtained by geometric analysis. The kinematics from the joint space to the Cartesian space is established. The outer diameter of the manipulator is only 3.5 mm, and the inner diameter can reach 2 mm, allowing instruments to pass through. The maximum error of the manipulator movement is less than 5%. The load capacity of the manipulator has been verified through the stiffness experiments, and the maximum load of the manipulator can reach 400 g. The cable-stayed notch manipulator can be accurately modeled on the base of CEIS, and its motion accuracy can meet the needs of engineering applications. The compact size and excellent load capacity of the manipulator make it potential for application in transluminal endoscopic surgical robots.

Impact of scapula anatomical landmark positioning on scapular orientation using CT-based 3D models: an intra-observer repeatability and inter-observer reproducibility study

HypothesisThe primary objective of this study was to assess intra-observer repeatability and inter-observer reproducibility of the 3D coordinates of a set of scapula anatomical landmarks obtained by manual positioning on conventional supine CT-scan based scapula surface models. The secondary objective was to assess intra-observer repeatability and inter-observer reproducibility of the resulting 3D scapular orientation. It was hypothesized that the 3D scapular orientation reliability would be better or similar than established reliability of intra-operative baseplate positioning (i.e. version and inclination) in reverse total shoulder arthroplasty (rTSA). MethodsThree anatomical landmarks, i.e. acromial angle (AA), inferior angle (IA), and trigonum scapulae (TS), were manually positioned on 81 scapula surface models using updated landmark definitions. These models were obtained by the segmentation of CT-scan images acquired from patients undergoing elective rTSA procedures at the Department of Surgery at Geneva University Hospitals between May 2022 and December 2023. This procedure was repeated 3 times per scapula by 3 independent observers. A set of parameters corresponding to the 3D landmark coordinates (expressed in an average scapula coordinate system) and the 3D scapular orientation (expressed as three angles related to the retraction/protraction, lateral/medial rotation, and internal/external rotation) were computed. Intra-observer repeatability and inter-observer reproducibility were assessed for each of these parameters using an intra-class correlation as a relative reliability metric. Standard error of measurement (SEM) was also reported as an absolute reliability metric. ResultsIntra-observer ICC and inter-observer ICC ranged from poor to moderate for AA, poor to excellent for IA, and poor to excellent for TS. However, low SEM, ranging from 0.4 mm to 2.4 mm for intra-observer repeatability and from 0.2 mm to 1.8 mm for inter-observer reproducibility, were obtained for every coordinate of each anatomical landmark. This results in poor to moderate intra-observer ICC and inter-observer ICC for scapula angular orientation. Again, low SEM, ranging from 0.4° to 0.8° for intra-observer repeatability and 0.4° to 0.6° for inter-observer reproducibility, were obtained, arguing for reliable measurements. Discussion and ConclusionThis study demonstrates that manual positioning of the three scapula anatomical landmarks recommended by the International Society of Biomechanics can be performed in a reliable manner across measures and observers on surface bone models obtained from CT-scan images. However, a clear and standardized definition of these landmarks is needed to ensure consistency across measurements.