Surface Tilt Angle Research Articles

Optimal intersurface stability for unicompartmental femoral component design with two pegs placed on the distal resection surface:5 mm peg length incrementand 10° peg inclination.

The present study aimed to identify the optimal design of the unicompartmental femoral component through parameter analysis and stability evaluation. A finite element (FE) analysis was applied to analyse and adjust the parameter combinations of the anterior tilt angle of the posterior condyle resection surface, the position of the peg, the length of the pegand the inclination angle of the peg, resulting in 10 different FE models. Setting three knee flexion angles of 8.4° (maximum load state during walking), 40° (maximum load state during stair climbing)and 90° (maximum load state during squatting exercise), quantitatively analysing the micromotion values of the bone-prosthesis interfaceand defining a weighted scoring formula to evaluate the stability of different FE models. The validity of the FE analysis was verified using the Digital Image Correlation (DIC) device. The errors between the FE analysis and the DIC test at three flexion angles were 5.6%, 1.7%and 11.1%. The 10 different femoral component design models were measured separately. The FE analysis demonstrated that the design with a 0° anterior tilt angle of the posterior condyle resection surface, both pegs placed on the distal resection surface, lengthened 5 mm pegsand a 10° peg inclination angle provided the best stability. The current study proposed a method for evaluating the stability of the femoral component design. The optimal intersurface stability design of the unicompartmental femoral component was achieved with two pegs placed on the distal resection surface, a 5-mm peg length incrementand a 10° peg inclination. These results might provide a reference for the selection of unicompartmental femoral components in clinical practice and therefore improve the survival rate of future unicompartmental knee arthroplasty. Level III.

Study on the Lubricating Characteristics of the Oil Film of the Slipper Pair in a Large Displacement Piston Pump

Due to the large size of the bottom surface, the slipper pair of the large displacement piston pump (LDPP) will form a larger linear speed difference in the inner and outer positions of the slipper relative to the center of the swash plate during high-speed rotation. It is more likely to lead to the slipper overturning, which makes the slipper partially worn. To make improvements, the comprehensive performance of the slipper pair of the LDPP, the motion law of the slipper pair of the LDPP was explored. Firstly, a mathematical model of the oil film thickness of the slipper pair of the LDPP under the state of residual compression force is established, based on the consideration of the linear velocity difference formed by the high-speed rotation of the large bottom surface slipper and the theory of dynamics and thermodynamics. Secondly, the impact of rotational speed, piston chamber pressure and oil temperature on the oil film thickness of the slipper pair was simulated and analyzed. Finally, to measure the oil film thickness of the slipper pair, oil film thickness measuring equipment was created, and the accuracy of the mathematical model was verified. The study revealed the changing rules of the oil film thickness and tilt angle of the bottom surface of the slipper pair under various working conditions. The consistency of the simulation and test findings demonstrates that the mathematical model can accurately describe influencing elements and changing rules of the LDPP slipper pair’s oil film lubrication characteristics.

Surface wettability effects on self-cleaning efficacy: Outdoor experimental study

Self-cleaning coatings of photovoltaic (PV) panel and building glass have received a great deal of attention over the last two decades, using both hydrophobic and hydrophilic treatments. Here, we present a comparison study of the outdoor self-cleaning performances of superhydrophilic, hydrophobic and superhydrophobic glass coatings, over 200 days, using different tilt angles. It was found that the average transmission of all the samples linearly decreased over time after rainfall. We have defined relative self-cleaning efficacy (RSCE), using the average transmission difference of coated and uncoated samples, at a given tilt angle. We have found that the RSCE depends on both surface wettability and tilt angle. The superhydrophobic coating was found to have the best RSCE, with the superhydrophilic coating next, although both superhydrophobic and superhydrophilic coating have similar RSCE when cleaned by rainfall. Surprisingly, the RSCE is higher at a lower tilt angle for all the samples, despite a higher transmission at a higher tilt angle, suggesting that the RSCE is higher at lower tilt angles due to weaker interaction between dust particles and the surfaces.

Optimization and test of ginger-shaking and harvesting device based on EDEM software

Considering the challenges posed by the elevated excavation resistance and substantial soil content of ginger blocks, a specialized digging and harvesting device was designed. The device primarily consists of a digging shovel, shaking fence, hydraulic cylinder, lifting arm and other devices. The mechanical characteristics of the digging device and the mechanism of soil crushing were analysed, and the key factors affecting excavation resistance and soil crushing were determined as follows: forward speed Vm, shaking soil frequency f, shovel surface tilt angle ɑ, shaking fence tilt angle β. To determine the influence rules of key factors on excavation resistance and soil flow, a ginger virtual simulation model of EDEM was constructed. Through the utilization of a target optimization method, an improved parameter combination for evaluating the performance of the ginger harvest operation was established. The optimized parameters were as follows: forward speed of 0.35 m/s, shaking soil frequency of 4.0 Hz, shaking fence inclination at 26.0°, and digging shovel inclination at 9.0°. The field test results show that the ginger harvest effect was good, the ginger block contained fewer impurities such as soil, the harvester operation was stable, and there was no congestion and rollover phenomenon. The forward resistance of the excavation harvesting device was found to be 1368.8 N, the soil content was 4.6 %, and the relative error with the expected result was 7.30 %, thereby meeting the requirements of ginger harvesting and the use requirements of users.

Effect of attack angles on droplet impact on textured metal surfaces: Droplet morphisms, surface tilt angles, droplet deformation

The experimental results of the water droplet impact on the tilted metal substrates are given. To establish the effect of the texture on the spreading of droplets, parallel-directed scratches were applied using a grinding machine. To analyze the shape of water droplets after impingement, topological-based data analysis (TDA) was used. The TDA showed that the droplet could be represented as a group of trivial topological structures: spheres, discs, and hemispheres. The latter creates the prerequisites for the development of relatively simple mathematical models that describe the complex processes of liquid droplets impacting on tilted, textured substrates. Moreover, the time dependence of the droplet contact line (L) and the left and right contact angles (LCA and RCA) on a textured surface were established. It was shown that anisotropic modification of the substrate has a significant effect on the characteristics and conditions of the spreading of the coolant droplets.

Assessment of reliability and validity of a handheld surface spine scanner for measuring trunk rotation in adolescent idiopathic scoliosis

PurposeTo assess the reliability and validity of a handheld scanner (SpineScan3D) for trunk rotation measurement in adolescent idiopathic scoliosis (AIS) subjects, as compared with Scoliometer.MethodsThis was a cross-sectional study with AIS subjects recruited. Biplanar spine radiographs were performed using an EOS imaging system with coronal Cobb angle (CCA) determined. The angle of trunk rotation (ATR) was measured using Scoliometer. SpineScan3D was employed to assess the axial rotation of subjects’ back at forward bending, recorded as surface tilt angle (STA). Intra- and inter-examiner repeats were conducted to evaluate the reliability of SpineScan3D.Results97 AIS patients were recruited. Intra- and inter-examiner reliability of STA measures were good to excellent in major thoracic and lumbar curves (p < 0.001). A strong correlation was found between STA and ATR measures in both curve types (p < 0.001) with a standard error of the ATR estimate of between 1 and 2 degrees from linear regression models (R squared: 0.8–0.9, p < 0.001). A similar correlation with CCA was found for STA and ATR measures (r: 0.5–0.6, p < 0.002), which also demonstrated a similar sensitivity (72%-74%) and specificity (62%-77%) for diagnosing moderate to severe curves.ConclusionSpineScan3D is a handheld surface scanner with a potential of wide applications in subjects with AIS. The current study indicated that SpineScan3D is reliable and valid for measuring trunk rotation in AIS subjects, comparable to Scoliometer. Further studies are planned to investigate its measurements in coronal and sagittal planes and the potential of this device as a screening and monitoring tool.Trial registration number (date of registration)HKUCTR-2288 (06 Dec 2017).Level of evidenceLevel III.

Infrared thermography monitoring of rock faces – Potential and pitfalls

Rock surface temperatures are of fundamental importance for studies on weathering, rockfall and permafrost. Point temperature measurements may not reflect the small-scale variability of temperature as a function of micro-topography. To close this gap, infrared thermography (IRT) seems to be a simple and promising approach. However, there are several pitfalls in terms of interpretation, as radiation temperatures depend on emissivity and reflectivity of the rock, which in turn are influenced by rock type, surface roughness, wetness, surrounding weather conditions, and angle to the camera axis.We performed laboratory and exemplary field experiments in order to estimate the magnitude of possible errors. We used rough and smooth (sawn) specimen of six different stone types in wet and dry condition and took IRT images at different tilt angles between camera axis and rock surface. Furthermore, we applied the approach to a small rock outcrop (approx. 3 × 3 m) and to a rockwall (approx. 100 × 100 m).The results of the laboratory measurements show that the temperature error increases with increasing tilt angle of the rock surface. Depending on the nature of the reflected surroundings, radiation temperatures can be warmer or cooler than sensor temperatures. In typical settings, the error is low (<0.5 K) up to a tilt of 40° but it may increase to >1 K at tilt angles of 50° and more. Smooth and wet surfaces tend to be more prone to deviations.The field examples confirm the results of the laboratory tests. But they show that spatial differences in temperature can still be detected as the “true” differences are usually larger than the magnitude of error. We suggest to reduce the error of the IRT image by correcting temperatures using a high-resolution surface model.

ANALYTICAL INVESTIGATION ON THE CONDENSATION PERFORMANCE OF VERTICAL, TILTED AND HORIZONTAL SURFACES FOR PASSIVE WATER HARVESTING

Condensate harvesting is the phenomenon of obtaining water from water vapor in the humid air condensing on a surface. The idea is a passive technique with no additional energy consumption, yet condensation performance of a surface varies with many parameters. This study analytically investigates the condensation performance of the vertical, tilted, and horizontal water harvesting systems. First, viscous effects, inertia, and gravitational forces are examined in detail to express the evolution of boundary layer in condensation film. Then the condensation performance of each surface orientation and tilt angles are documented and compared for all flow conditions. Although vertical surfaces have higher condensate harvesting performance compared to the tilted and horizontal systems, the condensation rate is only about 2% lower up to 15⁰ tilt angle. When the harvesting surface is tilted at 30⁰, the condensation rate of the laminar film decreases by 3.5%, while the reduction is 4.7% in wavy-turbulent film condensation. The results indicate that the change in condensation rate is more evident just after 45⁰ tilt. Furthermore, 89⁰ tilted surfaces experience 63.7% and 74.1% lower condensate harvesting in laminar and wavy-turbulent regimes, respectively. In addition, identical horizontal surfaces produce only one fifth condensation rate of a vertical system.

Effect of a surface polarized layer on the optical properties of a nematic cell

The optical properties of a cell of nematic liquid crystal presenting a tilted surface polarization submitted to an electric field are theoretically investigated. The origin of the surface polarization is assumed to be related to the interaction of the nematic molecules with the substrate and to the polar order due to the cell filling procedure. The analysis shows that the coupling of the surface polarization with the external field has different effects on the two surfaces limiting the sample. On one of them, the coupling gives rise, in an unbounded sample, to a continuous variation of the easy angle, whereas on the other one it is responsible for a first-order like transition of the easy axis orientation. For a sample of finite thickness our analysis shows that in the presence of a coupling between the two surfaces, operated by the elastic properties of the liquid crystal, the abrupt variation of the easy axis on one of the surfaces induces also on the other surface a discontinuity on the nematic surface orientation. The optical transmission of the cell versus the amplitude of the applied voltage, for an impinging monochromatic linearly polarized light, presents a discontinuity for the critical voltage at which the first-order transition of the surface tilt angles appears.

Particle-Size-Dependent Analysis of the Impact of Temperature, Humidity, and Tilt Angle on Soiling

Natural soiling—the deposition of dust onto surfaces—is a very complex problem and influenced by different factors, such as weather conditions, dust type, or surface properties. To investigate the individual impact of various factors and parameters, laboratory and outdoor soiling tests were performed for uncoated glass samples and glass samples with an antisoiling coating. For this, an advanced experimental setup was used operating at controlled environmental conditions. A detailed microscopic investigation with particle size analysis was performed to better understand the underlying physics of soiling effects and its influencing parameters, including relative humidity, surface temperature, tilt angle, and properties of the sample surface (i.e., glass coatings). Various effects were identified, which must not be neglected for correct interpretation of soiling test results. The article shows that particle rebound, natural convection, thermophoresis, capillary condensation, and adhesion properties of the surface have a substantial impact on soiling.

Exploring the Effects of Wetting and Free Fatty Acid Deposition on an Atomistic Hair Fiber Surface Model Incorporating Keratin-Associated Protein 5-1.

The complex development of cosmetic and medical formulations relies on an ever-growing accuracy of predictive models of hair surfaces. Hitherto, modeling efforts have focused on the description of 18-methyl eicosanoic acid (18-MEA), the primary fatty acid covalently attached to the hair surface, without explicit modeling of the protein layer. Herein, the molecular details of the outermost surface of the human hair fiber surface, also called the F-layer, were studied using molecular dynamics (MD) simulations. The F-layer is composed primarily of keratin-associated proteins KAP5 and KAP10, which are decorated with 18-MEA on the outer surface of a hair fiber. In our molecular model, we incorporated KAP5-1 and evaluated the surface properties of 18-MEA through MD simulations, resulting in 18-MEA surface density, layer thickness, and tilt angles in agreement with previous experimental and computational studies. Subsequent models with reduced 18-MEA surface density were also generated to mimic damaged hair surfaces. Response to wetting of virgin and damaged hair showed rearrangement of 18-MEA on the surface, allowing for water penetration into the protein layer. To demonstrate a potential use case for these atomistic models, we deposited naturally occurring fatty acids and measured 18-MEA's response in both dry and wet conditions. As fatty acids are often incorporated in shampoo formulations, this work demonstrates the ability to model the adsorption of ingredients on hair surfaces. This study illustrates, for the first time, the complex behavior of a realistic F-layer at the molecular level and opens up the possibility of studying the adsorption behavior of larger, more complex molecules and formulations.

Incorporating theoretical and practical approaches to assess the amount of sunlight captured by a tilted surface in a tropical climate

Global solar radiation can theoretically be approximated in terms of tilt and azimuth of the surface regarding the impossibility of simultaneous measurement of solar radiation at various surface tilt and azimuth angles. Moreover, the random and anisotropic nature of diffuse radiation in a tropical climate makes it extremely difficult to estimate global solar radiation accurately as a function of surface tilt and azimuth angles. This study aims to develop a novel experimental and theoretical approach in the form of a computational network in order to determine a precise combined model integrated with global horizontal solar radiation to evaluate global tilted solar radiation in a tropical climate. Obtained results revealed that precisely estimation of the global tilted solar radiation was possible, by combining geometric factors for the tilted beam solar radiation, a combination of Gueymard and Louche models for the tilted diffuse solar radiation, and isotropic ground reflectance model for the ground reflected radiation, along with global horizontal solar radiation. It was observed that the accuracy of the model developed was higher for the partly sunny sky compared to the cloudy and rainy sky, estimates were more accurate on south-facing surfaces, and the model's accuracy declined with the increasing tilt angle of the surface. The statistical analysis exhibited excellent agreement between the measured data and simulation results, considering the value of normalized mean absolute error (nMAE %), normalized root mean squared error (nRMSE %), and mean absolute percentage error (MAPE %), which were in the ranges 0.22–0.94, 0.27–1.11, and 0.23–1.02, respectively for estimating global tilted solar radiation in various regions of Peninsular Malaysia, and they were respectively found in the range of 10.2–27.5%, 16.1–38.9%, and 6.0–17.8%, for evaluating the monthly optimum tilt angle towards the south, that leads to a loss of solar energy from 1.3 to 5.4 kWh/m2/year in Peninsular Malaysia. This search revealed that the experimental and theoretical approach employed in this study can be extended to more climatic regions.

Experimental Demonstration of Light-Trapping Transparent Electrode Geometries

The intrinsic trade-off between conductivity and transparency has long impeded the development of truly transparent electrodes. Recently, a transparent electrode design was introduced that promised remarkably high electrical conductivity while allowing near-complete transmission of incident light into the underlying optical device. The approach is based on the use of metallic wires with inclined surfaces, embedded in a transparent dielectric film. Light reflected by metallic regions of the sample can be recovered by total internal reflection, resulting in efficient trapping of light incident on conductive regions. Prototype electrode geometries were fabricated by multiphoton lithography and selective chemical deposition. Light trapping is observed by optical microscopy and laser scanning experiments for surface tilt angles exceeding 25°. Approximately 60% of light reflected by the metallic electrode surface was recovered through total internal reflection. The presented approach could lead to optoelectronic devices with significantly improved performance across a wide spectral bandwidth.

VISUALIZATION RESEARCH OF DROPLET FREEZING ON AN INCLINED TITANIUM SURFACE

Freezing of droplets on inclined cold surfaces was investigated through their visualization. A DSA100 Droplet Surface Analyzer was employed to study the effects of surface tilt angle and temperature on the phase transition time of droplets of various sizes. The post-freezing contact diameter and contact angle between the droplets and the titanium surface were measured and analyzed. From these experimental studies and the related analysis it appears that the freezing time of droplets on cold surfaces at different tilt angles (15&amp;deg;, 30&amp;deg;, 45&amp;deg;, 60&amp;deg;, 75&amp;deg;, and 90&amp;deg;) is the longest when the bottom plate is tilted at 45&amp;deg;. As the tilted surface temperature is reduced, the droplet shape as it froze hardly changes with increasing tilt angle, and at the same time the freezing time of the droplets at each inclination angle is further reduced with decreasing bottom plate temperature. The experiments show that the deformation of a freezing 20-&amp;mu;L droplet on an inclined cold surface is more pronounced than that of a 1-&amp;mu;L droplet. The phase transition time of a large-volume droplet also decreases as the cold plate inclination increases. Thermodynamic equations are also employed to explain the longest droplet phase transition time which occurs at an inclination of 45&amp;deg;.

Fast wafer focus measurement system for photolithography using on-axis structure illumination method

Wafer focus-measuring system (WFMS) with high efficiency and robustness is crucial to ensure the exposure quality when advanced optical projection photolithography method is applied. In this work, we proposed a structure-illumination based wafer focus measuring system (SI-WFMS) which requires only single-step sampling process to implement the measurement of vertical defocus distance of exposure area, with less than 0.06 μm error. Both the surface profile and tilt angle of the wafer are also available to be rapidly measured through SI-WFMS, thereby saving the time of the measuring process and improving the manufacturing efficiency.

Stability analysis and design of an unmanned deformable vehicle during coupled reconfiguration motion

An unmanned deformable vehicle, which is a new type of robot combining a car and a robot, can drive at high speed with wheels and walk with steps. An unmanned deformable vehicle is prone to tipping instability when reconfigured between the automotive and humanoid states. The following work reported herein addresses these issues. The kinematic model of an unmanned deformed vehicle during the coupled reconfiguration process was established. The zero moment point (ZMP) theory was used as the stability criterion, and based on the requirement for stability during the reconstruction process, a genetic algorithm was used to find the optimal value of the support state foot landing position for the parking and driving coupled reconfiguration, and for the optimal value of the driving acceleration of the deformed vehicle during the driving coupled reconfiguration. On the basis of the optimal foot landing position, the total reconfiguration time threshold, deformed vehicle driving acceleration threshold, and support surface tilt angle threshold were analysed and calculated in accordance with stability requirements during the reconfiguration. Finally, the stability performance of the optimised system was verified through prototype testing.

A numerical study on the natural convective heat loss of an isothermal upward-facing cylindrical cavity

• Uncovered the influences of surface temperature, tilt angle and aperture area. • Developed an empirical correlation with high prediction accuracy. • Proposed a strategy that reduces the air velocity to control convective heat loss. The development of second-stage concentrators and lens systems facilitates the application of upward-facing cavities in solar energy utilization. To design a cavity with high efficiency and low cost, convective heat loss must be determined then controlled. Taking the commonly used isothermal cylindrical cavities as the object, natural convective heat loss characteristics were analysed numerically. The influences of surface temperature, tilt angle and aperture ratio were elaborated. Results show that the natural convective heat loss keeps increasing with increasing aperture ratio. As the tilt angle reduces, the natural convective heat loss increases before attaining a maximum at about −30° after which it drops. In short, the natural convective heat loss is proportional to the air velocity, the higher the air velocity, the larger the heat loss. A strategy controlling the air velocity is thus proposed to control the convective heat loss. Unlike isoflux conditions, a clockwise vortex forms inside the cavity for the tilt angle less than −30°. Large prediction errors are presented for using previous correlations to predict the natural convection heat loss of upward-facing cylindrical cavities. Hence, a novel empirical correlation based upon the influence characteristics of studied factors and with high accuracy is developed.

Experimental study of effect of glass cover tilt angle of solar still in winter season of India’s composite climate

• Solar still’s performance in the winter season with nocturnal productivity. • Model-2 (TA 30°) above latitude angle performed good with 1660 ml/m2 yield, 17.25 % efficiency, and 1.1 % exergy efficiency . • Effect of covering condenser surface by insulating material in nocturnal yield. • Low tilt angle causes back drop of condensate into the basin. • Effect of wind velocity on outer surface temperature of condenser in daylight. The present work consists of an experimental investigation to find the effect of the tilt angle of the condenser surface of solar still (SS) on distilled water productivity and efficiency in the winter season in the metrological condition of Varanasi (25.2623°N, 82.9894°E), India. In this experiment, three models were fabricated with different tilt angles having the same basin areas. The first two models were single basin single slope (SBSS) type SS having tilt angles of 25° and 30° in southward facing. The third model was a single basin double slope (SBDS) type SS having a tilt angle of 15° facing toward the east–west direction. Generally, the latitude angle is used as a tilt angle however the present study revealed that the tilt angle varies according to season (sun-earth positioning) and affects productivity. The findings show the temperature difference between basin water and condenser glass cover is limited which is the driving force of the desalination process. The results showed that model-1, 2, and 3 give maximum yield of 760, 925, 320 ml/m 2 of distilled water with maximum thermal and exergy efficiency of 17.15 % and 0.6 %, 17.25 % and 1.1 %, and 7 % and 0.3 % respectively over seven hours span. This investigation also reveals the heat retaining capacity of SS and effect of polystyrene coverage on glass cover that helps to obtain maximum nocturnal yield of 435, 735, 320 ml/m 2 from model-1, 2, and 3 respectively on different days that make total distilled output to 1195, 1660, 560 ml/m 2 on a particular day. In design perspective, the proper selection of tilt angle facilitates the seamless gliding of condensate to collecting troughs that mitigate the loss of condensate that falls into the basin before reaching to trough.

Making the Urban Sky View Factor With Numerical Models Consistent With Radiation Heat Transfer Theory

Abstract This work proposes a method for removing the inconsistency between the numerical models used for determining the sky view factor (SVF) in an urban environment and fundamental radiation heat transfer theory. For this purpose, a transformation of the coordinate system from global to surface was developed, which corrected the measurement of the angular coordinates of the elements in the discretized sky vault. The transformation was deployed in a published numerical model and was validated in a non-urban environment with a widely used analytical expression for the SVF, with which it was found to be in excellent agreement. The method was subsequently applied to an urban scenario, and the results were compared with the original numerical model. The proposed method provides a better determination of the SVF as a function of the surface azimuth and tilt angle.

Toward Terrain Effects on GNSS Interferometric Reflectometry Snow Depth Retrievals: Geometries, Modeling, and Applications

Accurate and high temporal-spatial resolution snow depth retrieval using the Global Navigation Satellite System Interferometric Reflectometry (GNSS-IR) has become a popular topic. The terrain is a significant issue affecting GNSS-IR snow depth retrieval. This study explores detailed information about the problems and new solutions to this issue. The main conclusions include but are not limited to the following aspects: 1) Reflections from Below the Antenna (RBA) is the primary geometrical relationship of the GNSS multipath signal for snow depth retrieval; 2) The proposed GSnow_TERR model considers the terrain effects by incorporating the surface tilt angle (γ) into the derivative of the multipath relative phase (φ) with respect to the satellite elevation angle ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</i> ). Unlike the previous region-by-region solutions, the new model has a definite physical meaning which considers the γ as an independent non-negligible variable; 3) The new model performs well for repeatable and non-repeatable GNSS tracks. The former agrees with the PBO H2O product with r <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = 0.97 and a slightly 1 ~ 2 cm improvement in the RMSE. The latter agrees with the baseline two-step clustering method for GLONASS, Galileo, and BDS, with r <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = 0.96 and RMSD = 1.11 cm. The rate of data utilization increases by a mean value of 38.21% for non-repeatable tracks. The performance of the model in practical applications is consistent with theoretical analysis. The findings of this study provide a valuable reference for future GNSS-IR snow depth research and applications.