Arc Length Research Articles

A nonlinear low frequency quasi zero stiffness vibration isolator using double-arc flexible beams

There is an increasing demand for integrated small vibration isolators in precision sensing instruments and medical equipment. Therefore, a quasi-zero stiffness (QZS) vibration isolator with double-arc flexible beams (D-AFB) is proposed. The QZS isolator consists of D-AFB units, the base, platform, fixture, guide rail, and linear bearing. The static performance of D-AFB is analyzed using the FEA method, and the QZS condition is obtained. The harmonic balance method (HBM) and the pseudo arc length method (PALM) are used to solve the dynamic equations of the nonlinear system, and the analytical solutions of displacement transmissibility and Force transmissibility are derived. In theory, the initial frequency is 77.6 % lower than that of the equivalent linear system. The QZS characteristic of D-AFB is verified by static experiment, and the low-frequency isolation performance of the QZS isolator is verified by dynamic experiment under constant amplitude and constant acceleration excitation. The D-AFB has a simple structure and can easily satisfy QZS conditions. So the D-AFB can be customized according to load requirements. Multiple vibration isolation loads can be obtained by adjusting the assembly of the D-AFB. The QZS isolator can adapt to load changes within 10 % and has an isolation effect on vibrations above 4 Hz. The idea of designing a QZS isolator with D-AFB as an array unit has a good research prospect and great application value in meeting the requirements of miniaturization and integration.

Determination of global geodetic parameters using satellite laser ranging to Galileo, GLONASS, and BeiDou satellites

The new Global Navigation Satellite System (GNSS) satellites, including GLONASS, Galileo, and BeiDou system, are equipped with Laser Retroreflector Arrays (LRA) to support Satellite Laser Ranging (SLR) tracking, which contributes to the estimation of global geodetic parameters. In this study, we estimate the global geodetic parameters using the SLR observations to GNSS satellites and also investigate the effects of different data processing strategies on the estimated Earth Rotation Parameters (ERP), geocenter motion, and terrestrial scale. The results indicate that setting range bias parameters for each satellite-station pair can effectively account for the satellite-specific biases induced by LRAs, leading to smaller Root Mean Square Errors (RMSE) of the post-fit SLR residuals. Furthermore, estimating the range biases for each satellite-station pair improves the accuracy of the estimated station coordinates and ERP. We also examine the impact of different arc lengths on the estimates of ERP, geocenter motion, and terrestrial scale. The results show that extending arc length can significantly reduce the formal error of ERP. The 7-day strategy produces the smallest RMSEs of 473 microarcseconds and 495 microarcseconds for the estimated X- and Y-component of pole coordinates, and 52 microseconds for length-of-day, respectively. However, the estimated geocenter motion is less affected by the arc length, even the shortest 1-day arc strategy can capture the seasonal variations of geocenter motion in Z component. For scale estimation, extending the arc length notably improves the accuracy of the estimated station coordinates and scale, but this advantage becomes less noticeable in longer arcs. The 7-day solution also obtains the closet scale results compared to ITRF2014, with the RMSE of 2.10 × 10–9.

Enhancing Bi2Te2.70Se0.30 Thermoelectric Module Performance through COMSOL Simulations

This research employs the COMSOL Multiphysics software (COMSOL 6.2) to conduct rigorous simulations and assess the performance of a thermoelectric module (TEM) meticulously crafted with alumina (Al2O3), copper (Cu), and Bi2Te2.70Se0.30 thermoelectric (TE) materials. The specific focus is on evaluating diverse aspects of the Bi2Te2.70Se0.30 thermoelectric generator (TEG). The TEM design incorporates Bi2Te2.70Se0.30 for TE legs of the p- and n-type positioned among the Cu layers, Cu as the electrical conductor, and Al2O3 serving as an electrical insulator between the top and bottom layers. A thorough investigation is conducted into critical parameters within the TEM, which include arc length, electric potential, normalized current density, temperature gradient, total heat source, and total net energy rate. The geometric configuration of the square-shaped Bi2Te2.70Se0.30 TEM, measuring 1 mm × 1 mm × 2.5 mm with a 0.25 mm Al2O3 thickness and a 0.125 mm Cu thickness, is scrutinized. This study delves into the transport phenomena of TE devices, exploring the impacts of the Seebeck coefficient (S), thermal conductivity (k), and electrical conductivity (σ) on the temperature differential across the leg geometry. Modeling studies underscore the substantial influence of S = ±2.41 × 10−3 V/K, revealing improved thermal conductivity and decreased electrical conductivity at lower temperatures. The findings highlight the Bi2Te2.70Se0.30 TEM’s high potential for TEG applications, offering valuable insights into design and performance considerations crucial for advancing TE technology.

Microstructure evolution and property strengthening of Ti2AlNb alloys prepared by multi-wire arc-directed energy deposition

Ti2AlNb alloys are expected to have applications in the aerospace field because of their excellent high-temperature performance and moderate density. Multi-wire arc-directed energy deposition (MWA-DED) technology enables the in-situ formation of Ti2AlNb alloys. However, Ti2AlNb alloys fabricated by MWA-DED face challenges such as compositional segregation and poor mechanical properties. In this study, high-performance Ti2AlNb alloys were efficiently prepared using MWA-DED technology, and their microstructure evolution was systematically analyzed. Hot-wire technology was proposed to assist in melting the TiNb wire to minimize the difference in the physical properties of the two wires. A pre-alloy droplet transfer mode with a large arc length was developed to eliminate composition segregation. The results showed that the Ti2AlNb alloys exhibited a homogeneous composition that matched the target Ti-22Al-23 Nb. Lots of strengthening phases (O phases higher than 90%) were precipitated throughout the sample. Temperature fields calculated from finite element simulation revealed that the precipitated phases were attributed to the “in-situ” heat treatment during deposition. The ultimate tensile strength and elongation reached 1002 MPa and 8% at room temperature, and 756 MPa and 8.3% at high temperature (650 ℃), respectively. The outstanding mechanical properties of Ti2AlNb alloys fabricated by MWA-DED are superior to those of cast and previously reported additively manufactured alloys. This study proposes novel ideas for additive manufacturing of high-performance Ti2AlNb alloys.

Optimization design and 3D printing of curvilinear fiber reinforced variable stiffness composites based on polar coordinate sweeping

The 3D printing of curvilinear fiber reinforced variable stiffness structures (CFRVSSs) provides new opportunities for innovative design and fabrication of complex components in response to rising demand for high-performance and lightweight components in aerospace, railway, and other fields. In this paper, we get rid of the limitations of existing research on the structure of open-hole plates and aim to investigate complex structures with large curvature. Considering the characteristics of 3D printing and service load, an optimization design method based on polar coordinate sweeping was proposed for CFRVSSs. The consistency factors between the fiber distribution (direction, content) and stress distribution (direction, magnitude) were established. Through quantitative analysis, the directional consistency factor between the optimized local fibers and stresses was enhanced by a factor of 3.69, and the correspondence factor between the fiber content and the stress magnitude was enhanced by a factor of 3.8. Furthermore, the calculation method for curve spacing and curve arc length based on polar coordinate sweeping were proposed to minimize the forming errors caused by CFRVSSs 3D printing. The design and fabrication of a high-speed rail tie rod structure were carried out using the optimization design method and 3D printing process in current research. As a result, the ultimate tensile strength of the optimized curvilinear fiber reinforced tie rod structure increased by 156 % compared to the unoptimized straight-line fiber reinforced tie rod structure. The method proposed in this study has a wide range of applications for the design and fabrication of complex components with large curvature in the engineering field.

Planning of Geometric Road Bend Using Spiral Circle Spiral Types (Case Study at STA. 11.800 to STA. 12.200) Jarak Village Roads in Jombang Regency, Indonesia

Jarak Village, Jombang Regency in Indonesia has a conditions of the geometric structure of a narrow road with sharp turns. In addition, the village has many tourist attractions, so it often attracts tourist to vacation. Tourist arrivals will affect the economy, it is necessary to evaluate the geometric planning of road bends that have a elevation more than three percent its mean do not match the standard Highway Department of Indonesian method, therefore it is carried out using the Spiral Circle Spiral (SCS) calculation. The purpose of this research is to plan the geometric road bend using the SCS type to produce a plan on a bend with a design that meets the standard of the Highways method. The method in this research was a survey of the geometric conditions the roads. From the geometric condition data that was analysis would be carried out using the SCS type Highway Department of Indonesian method, with radius analysis on bends, and horizontal alignment visibility. The results of the research showed a transition curve (Ls). For more discuss can be describe the arc length and spiral angle will be calculated so that an road bend design is obtained.

Relationship between lymphocytes and idiopathic macular hole

BackgroundAn idiopathic macular hole (IMH) is a full-thickness anatomic defect extending from the internal limiting membrane to the photoreceptor layer of the macula without any known cause. Recently, clinical laboratory markers of systemic inflammatory status derived from complete blood counts have been evaluated in ocular diseases. This study aimed to explore whether they could predict the development and progression of IMHs.MethodsA retrospective review of 36 patients with IMH and 36 sex-and-age-matched patients with cataracts was conducted. We collected complete blood counts of all participating individuals and calculated systemic immunoinflammatory indicators. The maximum base diameter of the IMH (BD), minimum diameter of the IMH (MIN), height of the IMH (H), area of the intraretinal cyst (IRC), and curve lengths of the detached photoreceptor arms were measured on optical coherence tomography (OCT) images. We used these values to calculate the macular hole index (MHI), tractional hole index (THI), diameter hole index (DHI), hole form factor (HFF), and macular hole closure index (MHCI). We performed a receiver operating characteristic (ROC) curve analysis of 30 patients with IMH who were followed up 1 month after surgery.ResultsLymphocyte counts were significantly higher in the IMH group. No other significant differences were observed between the IMH and control groups. Lymphocyte counts in the IMH group were significantly negatively correlated with MIN and BD and were significantly positively correlated with MHI, THI, and MHCI. However, lymphocyte counts were not significantly correlated with H, IRC, DHI, and HFF. In the ROC analysis, BD, MIN, MHI, THI, and MHCI were significant predictors of anatomical outcomes. According to the cut-off points of the ROC analysis, lymphocyte counts were compared between the above-cut-off and below-cut-off groups. Lymphocyte counts were significantly higher in the MIN ≤ 499.61 μm, MHI ≥ 0.47, THI ≥ 1.2, and MHCI ≥ 0.81 groups. There were no significant differences between the above-cut-off and below-cut-off BD groups.ConclusionsAlthough inflammation may not be an initiating factor, it may be involved in IMH formation. Lymphocytes may play a relatively important role in tissue repair during the developmental and postoperative recovery phases of IMH.

A numerical calculation of arc length and area using some spline quasi-interpolants

In this paper, we propose two methods to approach numerically the length of curves and the area of surface of revolution created by rotating a curve around an axis. The first is based on an approximation of functions by quadratic spline discrete quasi-interpolant and calculating its exact length. The second method consists toapproximate the values of the first derivatives by those of cubic spline discrete quasiinterpolant. Those values are used to provide a quadrature formula to calculate the integral giving the length. In both methods, we prove that the order of convergence is O(h^4). The theoretical results given in this work are justified by some numerical examples.

Ultra-Compact Orthoplanar Spring via Euler-Spiral Flexures

Orthoplanar springs are single-component compliant mechanisms that can be fabricated from sheet material and undergo deflection orthogonal to the plane of the mechanism. They are useful in applications where spatial constraints are significant. An Euler spiral is a curve whose curvature is linearly proportional to the arc length allowing for the curve to assume a flat position under a load. In this work, orthoplanar spring and Euler-spiral concepts are synthesized to create a single-component spring mechanism that lies flat under a load. Where traditional planar springs under a load will take on an out-of-plane contour, the Euler-spiral orthoplanar spring lies completely flat under a load. The relationship between the load needed to flatten the orthoplanar Euler-spiral spring and its physical geometry is examined. A use case where the Euler-spiral orthoplanar spring is utilized as a deployment mechanism for a mid-flight emerging antenna on the surface of a flight body is presented.

Mode I fracture propagation and post-peak behavior of sandstone: Insight from AE and DIC observation

Microcracks generated at the crack tip, particularly in quasi-brittle materials such as sandstone, give rise to a non-linear region known as the fracture process zone (FPZ), which cannot be analyzed using linear elastic fracture mechanics (LEFM). To gain insights into the nonlinear fracturing behavior of rock, this study conducted three-point bending experiments on sandstone beams with prefabricated notch. Stable mode-Ⅰ fracture propagation during the post-peak stage was achieved by the monotonic increment of crack mouth opening displacement (CMOD) measured by a clip gauge. The acoustic emission (AE) and digital image correlation (DIC) techniques were utilized to visually track the detailed crack propagation process from both micro and macro perspectives. Nonlinear fracture parameters, including FPZ length, were identified by AE and DIC measurements and compared with the theoretical calculation. A nonlinear fracture criterion relating applied load, equivalent crack length, and stress intensity factor were established, from which the theoretical CMOD-P curve at the post-peak stage were obtained and validated with experimental measurement from MTS machine. The results reveal that microcracks formulating the FPZ materialize in the pre-peak stage, with the majority emerging post-peak to facilitate the propagation of the traction-free crack and FPZ in the loading direction, as evidenced by AE locations and DIC displacement gradient. Throughout the crack propagation process, over 65 % of microcracks are estimated to be tensile mode based on both AF/RA and polarity analysis, aligning with anticipated outcomes from macroscopic three-point bending fracture tests. Energy dissipation primarily occurs within the FPZ to facilitate separation of crack faces, with the dissipated energy region advancing towards the beam boundary. By integrating AE source locations and DIC displacement gradient, the FPZ length of the 3-point-bending sandstone specimens is determined to be lp = 8.1 mm, slightly exceeding the theoretical FPZ lengths calculated by the Irwin model (lp = 7.0 mm) and the Dugdale-Barenblatt model (lp = 7.6 mm). Using a non-linear fracture criterion that incorporates the FPZ and employing the in-time equivalent crack length measured by AE and DIC as an intermediate variable, the theoretical applied load-crack length curve during the post-peak stage is calculated, showing close agreement with load cell measurements with a negligible error of approximately 2 %. Furthermore, the theoretical post-peak CMOD vs. load curve aligns with experimentally obtained results, demonstrating a non-linear crack propagation speed at a constant CMOD rate, wherein crack propagation speed decreases as crack length increases.

Incidence and analysis of intraoperative complications in femtosecond laser-assisted cataract surgery: a large-scale cohort study to establish the learning curve

AimsTo assess the safety of femtosecond laser-assisted cataract surgery (FLACS) based on surgical parameters and intraoperative complications analysis and to determine the length of the learning curve for FLACS.MethodsA prospective...

A Stochastic Methodology for EV Fast-Charging Load Curve Estimation Considering the Highway Traffic and User Behavior

The theoretical impact of the electric vehicle (EV) market share growth has been widely discussed with regards to technical and socioeconomic aspects in recent years. However, the prospection of EV scenarios is a challenge, and the difficulty increases with the granularity of the study and the set of variables affected by user behavior and regional aspects. Moreover, the lack of a robust database to estimate fast-charging stations’ load curves, for example, affects the quality of planning, allocation, or grid impact studies. When this problem is evaluated on highways, the challenge increases due to the reduced number of trips related to the reduced number of charger units installed and the limited EVs range, which influence user anxiety. This paper presents a methodology to estimate the highway fast-charging station operation condition, considering regional and EV user aspects. The process is based in a block of traffic simulation, considering the traffic information and highway patterns composing the matrix solution model. Also, the output block estimates charging stations’ operational conditions, considering infrastructure scenarios and simulated traffic. A Monte Carlo simulation is presented to model entrance rates and charging times, considering the PDF of stochastic inputs. The results are shown for the aspects of load curve and queue length for one case study, and a sensibility study was conducted to evaluate the impact of model inputs.

Positioning Error Estimation Method for Short-Arc Angles-Only Initial Orbit Determination

The development of space surveillance capabilities has received increased emphasis with time. Suitable evaluation parameters are investigated to analyze the effects of multiple factors on short-arc angles-only initial orbit determination. This investigation is crucial for designing surveillance system parameters. In this paper, the orbit determination equations where the target state is linear were derived by assuming that Lagrangian coefficients are constant and taking the minimum residual sum as the optimization objective. From this paper’s analysis, it was demonstrated that because the position uncertainty distribution primarily lies in the line-of-sight vector, the upper limit of relative positioning error (RPE) can be used as the evaluation parameter of the determination accuracy in scenarios where a high-orbit target is observed by a low-orbit sensor observes. An empirical relationship was also found, indicating that the upper limit of RPE is proportional to the observation error, −2.5 power of the observation arc length, and the 0.5 power of the observation interval.

A Shape Memory Polymeric Shield for Protecting Corneal Endothelium During Phacoemulsification.

The purpose of this study was to explore the protective effect of a shape memory polymeric shield on corneal endothelium during phacoemulsification in rabbits. Poly-(glycerol dodecanedioate) (PGD) with a transition temperature of 24.416°C was prepared to make a shape memory shield with a thickness of 100µm, an arc length of 14 mm, and a radius of curvature of 8.8 mm. In the control group, a phaco-tip with bevel-down was used to simulate injury to the corneal endothelium by phacoemulsification in rabbits. In the experimental group, the pre-cooled and curled shape memory shield was injected into and removed from the anterior chamber before and after phaco-power release. Anterior segment optical coherence tomography (AS-OCT), confocal microscope, trypan blue/alizarin red staining, and scanning electron microscope were performed to measure endothelial damage after surgery. One day postoperatively, the lost cell ratio of the control group and the experimental group were 28.08 ± 5.21% and 3.50 ± 1.43%, respectively (P < 0.0001), the damaged cell ratios were 11.83 ± 2.30% and 2.55 ± 0.52%, respectively (P < 0.0001), and the central corneal thicknesses (CCT) were 406.75 ± 16.74µm and 340. 5 ±13.48µm, respectively (P < 0.0001). Seven days postoperatively, the endothelial cell density (ECD) of the control group and the experimental group were 1674 ± 285/mm2 and 2561 ± 554/mm2, respectively (P < 0.05). The above differences were all statistically significant. This PGD based shape memory shield has a protective effect on corneal endothelium during phacoemulsification. It reduces postoperative corneal edema and ECD decrease in the short term after surgery. The shape memory PGD "shield" in this study may have a use in certain human patients with vulnerable corneas of low endothelial cell count or shallow anterior chambers.

Orbit determination of Earth-Moon libration point navigation constellation based on Inter-satellite links

Earth-Moon libration point navigation constellation has a merit of fully covering the cislunar space and providing navigation services with merely a small number of satellites. Furthermore, this type of constellation itself can achieve orbit determination by using only its Inter-satellite links (ISL) owing to the well-known gravitational asymmetry near the libration points. This paper adopts a representative four-satellite navigation constellation including three satellites located near the libration point L3, L4, L5, and an extra one in Distant Retrograde Orbit (DRO), and studies the orbit determination accuracy of the constellation under two conditions: establishing ISLs within itself (called Solely libration point satellites) and establishing additional ISLs with BeiDou Navigation Satellite System (BDS) (called Libration + BeiDou satellites). The simulation results indicate that, for the Solely libration point satellites scenario with the 1 m range error and solar radiation pressure (SRP) error with the level of 10% deviation between ball model and macro model, the final orbit accuracies for L3, L4, L5, and DRO satellites can respectively achieve 11.3 m, 12.7 m, 12.6 m, and 7.3 m. Reducing the link interval can significantly shorten the arc length to achieve final accuracy, whileas it has less impact on the final orbital accuracy. When the link interval is set as 240, 60, 10, and 2 min, the arc lengths at the final accuracy of better than 15 m are about 35, 29, 23, and 20 days, respectively. To balance the communication burden and the orbit determination arc length, the recommended ISL building interval is 10 min. Errors coming from range measurement model and dynamic model, in addition, are key factors in orbit determination, which can result in meters to tens of meters of orbital accuracy. For the Libration + BeiDou satellites scenario, the augmented ISLs to BDS can substantially improve constellation orbital accuracy and shorten the orbit determination arc length. When the DRO satellite attached to the Geostationary Earth Orbit (GEO), Inclined Geosynchronous Orbit (IGSO), and Medium Earth Orbit (MEO) satellites of BDS respectively, the improved accuracy are 37.1%, 61.2%, and 42.2%, while the shortened arc length are 20.1%, 28.3%, and 28.1%, respectively. The research findings presented in this paper can serve as a reference for the construction and assessment of navigation constellations in the Earth-Moon system.

Arc Length Spacing-Driven Cooperative Elliptical Encircling Control of Robots: Design and Experiments

Most studies of cooperative enclosing control are centered around moving along the shared circle with available position information. Note that Global Positioning System (GPS) is typically inaccessible under hostile scenar- ios, and elliptical circumnavigation may provide a more flexible and high-efficiency entrapping solution, whilst the non-orthogonality of axial and tangential velocities and the lack of GPS enable elliptical entrapping to be more challeng- ing, and the related outcomes are still rare. Following this line, a novel coordinated error in terms of arc length spacing is skillfully formulated and included in elliptical encircling control to characterize cooperative behaviors without trigg- ering frequent speed variation and unstable observation. Particularly, to remedy the dependence on accessible global position, a new bearing-based estimator under a local frame is proposed to recover the relative coordinate, then a modified cooperative elliptical encircling control strategy is formulated without entailing global position data. Lyapunov stability analysis demonstrates that all error variables are ultimately bounded. Both simulations and experiments are implemented to illustrate the efficacy of proposed control algorithm.

Automatically Sketching Auroral Skeleton Structure in All‐Sky Image for Measuring Aurora Arcs

AbstractThe auroral arc is the typical track of the interaction between the solar wind and the Earth's magnetosphere. A sketch of skeletons for arc‐like aurora is usually used to describe auroral structures, such as vortex, fold and curl structures, etc. With artificial intelligence technologies, sketching auroral skeleton structure (AuroSS) in all‐sky images enables automatic detection and measurement of aurora arcs in very large amounts of ground‐based auroral observation data. The skeleton is a highly characterizing topological structure that has been extensively studied in the field of computer vision. However, AuroSS is not the medial axis of auroral shapes and a large number of accurate AuroSS annotations are not available. It is difficult to detect AuroSS by using an unsupervised or fully‐supervised method. In this paper, we formulate the automatic AuroSS extraction to learn a mapping from an all‐sky auroral image to a ridge style AuroSS. Without accurate AuroSS annotations, emission ridge and coarse localization of aurora are incorporated to generate pseudo‐labels of AuroSS. A series of functional weakly supervised models are trained and cascaded to achieve AuroSS detection. Experimental results on auroral images obtained from all‐sky imagers at Yellow River Station (YRS) show that the detected AuroSS is consistent with that of human visual perception. Based on the obtained AuroSS, the orientations and lengths of auroral arcs can be estimated automatically. By browsing the temporal variation in arc orientation from dusk to dawn, we can acquire synoptic observations of auroral activities at YRS.

Feasibility analysis of deep steep riser based on co-rotational coordinate method

DSR (Deep steep riser) is a new riser structure that reduces the ultra-high-tension load caused by the riser self-weight. In this paper, the mechanical behavior of DSR under different buoyancy module configurations and different ocean currents is studied. The finite element model of DSR is established based on co-rotational coordinate method. The model is solved by arc length method. The accuracy of the numerical method is verified by Abaqus software. Then, the effects of buoyancy module length and buoyancy factor on DSR are analyzed. Finally, the influence of different current incidence angles and velocities on DSR is evaluated. The results show that the DSR model based on the co-rotational coordinate method can effectively simulate the nonlinear behavior of large deformation of DSR. The method is simple, flexible and computationally efficient. This method can quickly improve the efficiency of numerical calculation in static analysis of deepwater riser. And DSR is feasible under certain conditions.

Near-Earth Asteroids Orbit Determination by DRO Space-Based Optical Observations

In response to the problem that ground-based optical monitoring systems cannot monitor near-Earth asteroids which are in the direction too close to the Sun on the celestial sphere, we raise a method that tracks and determines the orbit of asteroids by Distant Retrograde Orbit (DRO) platforms with optical monitoring. Through data filtering by visibility analysis and the initial orbit information of the asteroids provided by Jet Propulsion Laboratory (JPL), the asteroids’ orbits are determined and compared with the reference orbit. Simulation results show that with a measurement accuracy of two arcseconds and an arc length of three years, the orbit determination accuracy of the DRO platform for near-Earth asteroids selected in the simulation example can reach tens of kilometers, especially the asteroids with Atira orbits to an accuracy of fewer than ten kilometers. In conclusion, the near-Earth asteroids monitoring systems based on DRO platforms are capable to provide sufficient monitoring effectiveness which enables precisely tracking of the target asteroids and forecast of their positions.

Horizontal Curve Safety Performance Evaluation Based on Naturalistic Vehicle Lane Position Data

Performance-based design is a renewed approach for project decision-making to specifically address the purpose and needs of projects by providing design flexibility. Resources to evaluate roadway design based on safety performance are an important need for transportation practitioners. In this study, naturalistic driving study (NDS) data were used to estimate the safety effect of elements that influence driving behavior on rural undivided two-lane horizontal curves. Available data included 3,292 horizontal curves and 150,233 traversals, which required a significant data processing effort to conduct data cleaning and quality assessment. From the safety surrogates evaluated and methods implemented, lane position provided the most consistent and statistically significant results. Centerline and edge line encroachment events were modeled with the negative binomial using traffic volume and curve geometry as the predictor components. Encroachment estimates were associated with observed crashes from state data to convert encroachments to crashes. Predictor variables such as curve radius showed a decreasing trend in predicted crashes as curve radius increased. Similarly, as shoulder or lane width increased, predicted crashes decreased. Crash estimates derived from safety surrogates were used to develop an analytical tool aimed at practitioners for curve design considerations. Data input includes curve radius, shoulder width, lane width, curve length, traffic volume, expected service life, and construction cost. The economic assessment provides a quantitative measure for practitioners to evaluate alternative curve designs by assessing the tradeoffs between safety and costs of implementation.