Tip Geometry Research Articles

The effect of fan-type inducer blade tip geometry on cavitation behavior and noise in an industrial centrifugal pump

Cavitation is one of the biggest problems in industrial centrifugal pumps because it causes serious vibration and noise. Therefore, there is a demand for pump manufacturers to prevent problems due to the cavitation before delivering products to the site. Noise is considered to increase due to the development of cavitation at the tip of the inducer blades. In this study, the location of cavitation development was controlled by changing the inducer blade tip geometry to reduce noise. A centrifugal pump with a fan-type inducer was operated to measure noise at various cavitation numbers and flow rates with a microphone set up on the outer wall near the inducer. A visualization experiment using an acrylic casing around the inducer, a high-speed camera, and strobe light was also conducted to observe the behavior of cavitation development. The relationship between cavitation form and noise was investigated in detail.

Atomistic understanding of ductile-to-brittle transition in single crystal Si and GaAs under nanoscratch

Ensuring ductile removal in a grinding process is crucial for achieving the desired finish on a hard and brittle single crystal. This study provides new insights into the material removal processes in Si and GaAs single crystals, exploring their deformation behaviour using Berkovich and Conical tips to replicate contact from a fixed abrasive grit. Experimental observations are compared with Molecular Dynamic (MD) simulations to uncover the atomistic deformation mechanisms during the ductile-to-brittle transition (DBT). Notable plastic deformation and minimal cracking were consistently observed in Si, irrespective of the tips used. MD simulations supported this observation, revealing pronounced chip formation indicative of ductile material removal. The resistance to cracking in Si was attributed to amorphization induced by localized high contact stresses. In contrast, GaAs showed a propensity for cracking, with MD simulations revealing dislocation and slip band formation, and cracks emerging in the areas of substantial plastic deformation. These findings address phenomena not previously discernible in experimental studies due to the challenge of real-time observation. Moreover, the tip geometry was shown to significantly influence stress distribution, impacting deformation and crack formation in GaAs. This study also reveals limitations in predicting the critical depth for DBT in both Si and GaAs throught the amended Bifano, Dow, and Scattergood (aBDS) models and MD simulation, offering nuanced insights into these challenges that have not been extensively explored. It was found that the experimental results exceeded predictions by an order of magnitude. These discrepancies underscore the aBDS model's disregard for essential material properties and tip geometry, while the disparities between MD simulation and experiment are primarily attributed to the inherent limitations in the simulated length scales and challenges in detecting initial subsurface cracks.

Multi-objective optimization design of aerothermal performance for turbine blade squealer tip with inclined suction-side rim

To optimize the inclined rim design, multi-objective optimization was numerically conducted on the suction-side rim of the squealer tip in the GE-E3 rotor blade. The RANS equations, incorporating with the standard k-ω model, were numerically solved. Through the implementation of a Kriging surrogate model coupled with the NSGA-II evolutionary optimization technique, six geometric parameters on the suction-side rim went through iterative optimization. This process yielded three optimized squealer tip geometries on the Pareto front: Structure 1 with minimum total pressure loss, Structure 2 with optimal comprehensive aerothermal performance, and Structure 3 with minimum tip heat load. Comparative analysis revealed that with the inner and external wall inclined toward the cavity and passage respectively, the optimization results in a 3 %–11 % reduction in tip heat load, accompanied by an 8.5 %–10.2 % reduction in aerodynamic loss, facilitated by an attenuated upper passage vortex (UPV) and strengthened tip leakage vortex (TLV). The critical inclined region of the external rim wall, spanning 7 %–80 %, influences the exit total pressure loss distribution. The inclined inner wall upstream of 50 % Cax obstructs coolant jets from exiting the cavity, reducing the heat load on the cavity bottom. However, the inclined external wall from 66 % to 90 % Cax amplifies the impingement of the scraping vortex (SV), increasing local heat transfer. The thermal behavior of Structure 1 is sensitive to changes in tip clearance, whereas Structure 2 and 3 show more robust advantages. As the clearance increased, the aerodynamic losses associated with the TLV rise for all three optimized tips, but losses from the UPV remain similar. This study provides a novel approach for designing efficient squealer tip geometries incorporating an inclined rim.

Mapping the composite nature of clay matrix in mudstones: integrated micromechanics profiling by high-throughput nanoindentation and data analysis

AbstractMudstones and shales serve as natural barrier rocks in various geoenergy applications. Although many studies have investigated their mechanical properties, characterizing these parameters at the microscale remains challenging due to their fine-grained nature and susceptibility to microstructural damage introduced during sample preparation. This study aims to investigate the micromechanical properties of clay matrix composite in mudstones by combining high-speed nanoindentation mapping and machine learning data analysis. The nanoindentation approach effectively captured the heterogeneity in high-resolution mechanical property maps. Utilizing machine learning-based k-means clustering, the mechanical characteristics of matrix clay, brittle minerals, as well as measurements on grain boundaries and structural discontinuities (e.g., cracks) were successfully distinguished. The classification results were validated through correlation with broad ion beam-scanning electron microscopy images. The resulting average reduced elastic modulus (Er) and hardness (H) values for the clay matrix were determined to be 16.2 ± 6.2 and 0.5 ± 0.5 GPa, respectively, showing consistency across different test settings and indenter tips. Furthermore, the sensitivity of indentation measurements to various factors was investigated, revealing limited sensitivity to indentation depth and tip geometry (when comparing Cube corner and Berkovich tip in a small range of indentation depth variations), but decreased stability at lower loading rates. Box counting and bootstrapping methods were applied to assess the representativeness of parameters determined for the clay matrix. A relatively small dataset (indentation number = 60) is needed to achieve representativeness, while the main challenges is to cover a representative mapping area for clay matrix characterization. Overall, this study demonstrates the feasibility of high-speed nanoindentation mapping combined with data analysis for micromechanical characterization of the clay matrix in mudstones, paving the way for efficient analysis of similar fine-grained sedimentary rocks.

AN EXPERIMENTAL RIGHT ATRIUM PLATFORM TO ASSESS RECIRCULATION IN HEMODIALYSIS CATHETERS

Hemodialysis (HD) is a treatment supporting decreased kidney function, via a catheter inserted into the heart’s Right Atrium (RA). Recirculation is a source of inefficiency for treatment, where blood is dialyzed again due to poor catheter design. Lab-testing is still relatively unexplored, hence, a mechanical testing system was designed with the intention of providing a consistent and repeatable environment for testing HD catheters. System geometry was composed using a Computer-Aided Design (CAD) model of a heart, with the RA scaled to appropriate dimensions, and a PolyDiMethylSiloxane (PDMS) model produced through 3D printing and negative wax casting. Pulsatile blood flow was mimicked by peristaltic pumps driving a blood analogue (BA). Recirculation was induced by adding dyed BA to the system via the catheter and measured using a colorimeter. The developed platform was initially evaluated using two catheters, demonstrating the capability to accurately replicate atrial hemodynamic conditions. Two step-tipped catheters, A and B, were tested at 350 ml/min, producing recirculation values of 13.11% and 18.58%, respectively. The results exhibit the ability of the system developed to evaluate HD catheter performance, with the potential to explore a wider range of tip geometries relevant to clinical preference. Furthermore, this advancement towards an anatomically accurate lab-based test system could be paired with computational methods to progress the evaluation of such medical devices and enhance their development.

Bayesian reconstruction of 3D particle positions in high-seeding density flows

Abstract Measuring particles' three-dimensional (3D) positions using multi-camera images in fluid dynamics is critical for resolving spatiotemporally complex flows like turbulence and mixing. However, current methods are prone to errors due to camera noise, optical configuration and experimental setup limitations, and high seeding density, which compound to create fake measurements (ghost particles) and add noise and error to velocity estimations. We introduce a Bayesian Volumetric Reconstruction (BVR) method, addressing these challenges by using probability theory to estimate uncertainties in particle position predictions. Our method assumes a uniform distribution of particles within the reconstruction volume and employs a model mapping particle positions to observed camera images. We utilize variational inference with a modified loss function to determine the posterior distribution over particle positions. Key features include a penalty term to reduce ghost particles, provision of uncertainty bounds, and scalability through subsampling. In tests with synthetic data and four cameras, BVR achieved 95% accuracy with less than 3% ghost particles and an RMS error under 0.3 pixels at a density of 0.1 particles per pixel (ppp). This shows 57% to 97% less ghost particles and 1.3 to 2 times lower RMS error than standard MART and IPR reconstructions. In an experimental Poiseuille flow measurement, our method closely matched the theoretical solution. Additionally, in a complex cerebral aneurysm basilar tip geometry flow experiment, our reconstructions were dense and consistent with observed flow patterns. Our BVR method effectively reconstructs particle positions in complex 3D flows, particularly in situations with high particle image densities and camera distortions. It distinguishes itself by providing quantifiable uncertainty estimates and scaling efficiently for larger image dimensions, making it applicable across a range of fluid flow scenarios.

Information transfer between tip leakage vortex and blade aerodynamic force of a compressor cascade

The compressor blade exhibits intricate flow patterns near stall conditions, with the tip leakage vortex and the main flow shedding vortex from the blade's trailing edge identified as factors influencing the blade's aerodynamic force oscillation. The tip leakage vortex is recognized as the primary contributor to flow structures during non-synchronous vibration (NSV), although existing compressor NSV reduced order models often attribute the fluid oscillation to the passage flow shedding vortex. A tool capable of distinguishing between flow structures and blade aerodynamic force is crucial for resolving this discrepancy. Detached eddy simulations (DES) in a compressor cascade form the basis for gathering data on vortex structures and blade aerodynamic force. This study employs an information thesis method to elucidate the cause-and-effect relationship between the tip leakage vortex and blade aerodynamic force. Through a series of unsteady single passage simulations and experimental validation, the mechanisms leading to variations in blade aerodynamic force are demonstrated. Notably, this research utilizes Proper Orthogonal Decomposition (POD) mode time coefficients in span and axial directions to represent dynamic information on vortex structures. Additionally, transfer entropy is introduced as a metric to evaluate the causal interaction between turbulent flow of the tip leakage and the blade's aerodynamic force, marking a significant advancement. The analysis of information transfer entropy aids in identifying the vortex structure with a stronger relationship to aerodynamic force, a critical finding. By applying this approach, the study examines tip leakage vortex structures in various tip clearance sizes concerning aerodynamic force. The Tip3C and Tip5C tip geometries exhibit tip leakage vortex features with radial vortex characteristics and backflow, akin to structures associated with non-synchronous vibration. These tip vortex structures in the Tip3C and Tip5C tip geometry cascades demonstrate substantial correlations with aerodynamic force oscillation on the blade surface. Conversely, the Tip1C tip geometry cascade displays distinct tip leakage vortex features compared to Tip3C and Tip5C, with weaker ties to blade aerodynamic force oscillation. As simulation models progress, consideration of vortex structures in the passage and leakage vortex at the leading edge is imperative for accurate predictions of aerodynamic force oscillation response.

Monodisperse Porous Emitter Materials for Ion Electrospray Propulsion

Electrospray spacecraft propulsion typically uses commercially available porous glass materials for their emitter components. The quality of this emitter material is crucial to the operation of the thrusters, as nonuniformities in the pore distribution can lead to differential propellant flow rates, variation in tip geometries, and less-than-optimal performance of the thruster. The focus of this work is on the development of new porous materials that are more uniform and can mitigate these issues caused by nonuniformities present in current commercially available porous materials. A silica nanoparticle photo-curable resin solution is developed to create high-uniformity porous substrates to improve tip geometry and overall thruster performance.

The effect of rail crown film hole injection angle and blowing ratio on the flow and cooling performance of the squealer tip in a turbine blade

Squealer tip is considered as an efficient and reliable tip geometry design in leakage loss control and thermal load reduction in heavy-duty gas turbine blade. The cooling and aerodynamic characteristics of a squealer tip with different film hole parameters are investigated after validating the numerical approach. Firstly, superior aerodynamic and cooling performance of the rail crown film hole (RCFH) scheme is proved by comparing three squealer tip structures. Subsequently, two kinds of injection angles (streamwise injection α and normal injection β) and three angle values (35°, 90°, and 145°) are studied in RCFH schemes. Finally, a compound angle scheme consisting of optimal α and β is investigated at blowing ratios (M) varying from 0.5 to 2.0. In varied α hole schemes, the velocity of the coolant can be divided into the radial and streamwise components, the effects of which on leakage control are complementary, leading to minimal sensitivity of total leakage flow rate (LFR) to α. Increasing and decreasing α can both enhance the coolant attachment on the rail crown surface compared with the radial injected scheme. In varied β hole schemes, more coolant momentum is used to resist the leakage flow as β increases, which results in remarkable LFR reduction. Moreover, the back-press effect of leakage flow on the coolant is markedly enhanced, improving the utilization of coolant. In compound angle scheme, increasing M leads to enhanced impingement on clearance flow, and the maximum values of average film cooling efficiency (η) on the rail crown and cavity floor appear at M = 1.0 and M = 1.5, respectively.

Innovative tool designs to improve formability in case of single point incremental forming

Single point incremental forming (SPIF) is one of the dieless sheet metal forming processes that offer flexibility in the customized fabrication of required parts. Improvement in formability in the case of SPIF has been one of the burning issues in the metal-forming fraternity in the past decades. In the present study, different tool tip geometries, namely hemispherical, elliptical, en-grooved, and triangular tool tips, were employed in the SPIF of 0.8 mm thick CRCA (cold rolled close annealed) steel, and the influence on the forming height was assessed in reference to the commonly used hemispherical tool tip. It was observed that tool geometry has a significant influence on forming height obtained with SPIF, and a maximum of 27% increase in forming height was observed with the en-grooved tool tip with a considerable reduction in the forming force required.

Numerical investigation on the use of various blade tips for the helicopter's main rotor blade in forward flight regarding aerodynamic performance and HSI noise considerations

The goal of this research is to investigate aerodynamic performance and high-speed impulsive (HSI) noise of various blade tips for the helicopter's main rotor in forward flight. For this purpose, three-dimensional compressible flow field around the rotor blades is numerically simulated by the solution of the unsteady Reynolds averaged Navier-Stokes (URANS) equations with the "SST k-ω" turbulence model. Solution is quantified by the calculation of torque, drag, and thrust coefficients of CQ, CD, CT, and L/D ratio. HSI noise on the rotor plane is assessed by the calculation of sound pressure level at certain points of the flow field using the Ffowcs Williams-Hawking (FW-H) equation. Blade tips are eleven and include anhedral, dihedral, Eagle and combinations of them, and also Blue Edge and rectangular. The combinations are inspired by the tip configurations of the fixed wings. In this regard effects of the tip geometry parameters including curvature and height of its parts have been considered as well. All of the tips are examined for two flight conditions of Caradonna and Tung two-blade rotor with fixed pitch angle and time-varying pitch angles. Based on the present results, it is found that blade tips of dihedral family do not improve the aerodynamic performance of the helicopter blade. Also, addition of anhedral part to the blade tip improves the L/D ratio. According to the present acoustic analysis, it was seen that after the Blue Edge, the Eagle tip stands in order of priority. For the condition of Caradonna and Tung two-blade rotor with tip Mach number of 0.8 and advance ratio of 0.2, HSI noise of the Eagle-tip blade decreases by 2.39 % compared to that of the two-blade rotor with rectangular tip. However, the aerodynamics performance of the Eagle tip is much better than that of the Blue Edge.

Quantification of Gravitational Effects on Nasal Tip Geometry

Introduction: It is widely accepted in plastic surgery that patient positioning can affect the geometry of the nasal tip due to downward gravitational forces. However, empirical data supporting this principle is lacking. The primary objective of this study is to quantify gravitational effects on nasal tip geometry by calculating changes in tip rotation and projection between the supine and upright positions. This analysis will help further assess whether gravity affects the actual positional rotation of the nasal tip or if its impact is solely relative to neighboring landmarks. Methods: This study is a prospective case series that obtains upright and supine nasal measurements in 20 subjects. The nasolabial, nasofrontal, and columellar-facial angles, as well as the Goode, Crumley, Simon, and Powell ratios are used to calculate nasal tip rotation and projection changes. Results: Mean nasolabial angle demonstrated a statistically significant tip derotation of 3.2° in the upright position relative to supine. Mean nasofrontal angle and mean columellar-facial angle did not significantly differ between positions. The nasal tip appeared relatively less projected in the upright position using the Simon and Crumley methods, whereas no significant difference was seen with the Powell and Goode methods. Conclusion: Gravity can influence the apparent nasal tip geometry by altering lip position and length, but it does not impact the true nasal tip geometry when the upper lip is excluded as a reference point.

Experimental Investigation of Tip Design Effects on the Unsteady Aerodynamics and Heat Transfer of a High-Speed Turbine

Abstract While modern engine manufacturers devote significant efforts to the development of reliable and efficient machines, the introduction of novel, optimized components in the hot gas path represents a risky opportunity. Accurate experimental and numerical data are critical to assess the impact of new technologies on the harsh engine environment. The present study addresses the impact of a selection of high-performance rotor blade tips on the aerodynamic and heat flux field of a high-pressure turbine (HPT) stage. A combined numerical and experimental approach is employed to characterize the interaction of the tip leakage flow with the rotor secondary flows and the casing heat transfer mechanisms for each individual tip geometry. The turbine stage is tested at engine-scaled conditions in the rotating turbine facility of the von Karman Institute. In the present study, the turbine rotor is operated in rainbow configuration to allow the simultaneous testing of multiple blade tip geometries. Reynolds-averaged Navier–Stokes (RANS) simulations are employed to predict the aerodynamic and thermal fields of the individual profiles using test-calibrated boundary conditions. Isothermal steady computations are performed at different wall temperatures to compute the adiabatic wall temperature and the heat transfer convective coefficient. Low-order models are used to represent the over-tip thermal field and the driving heat transfer mechanisms. The time-resolved outlet flow is characterized using a vortex tracking technique and high-frequency aerodynamic measurements to identify the rotor secondary flow structures.

Effect of crack tip geometry and in situ compression rolling on fracture failure mechanisms in poly-lactic acid (PLA) extrusion-based additive manufacturing

Effect of crack tip geometry and in situ compression rolling on fracture failure mechanisms in poly-lactic acid (PLA) extrusion-based additive manufacturing

Mass-manufacturable scintillation-based optical fiber dosimeters for brachytherapy

Scintillation-based fiber dosimeters are a powerful tool for minimally invasive localized real-time monitoring of the dose rate during Low Dose Rate (LDR) and High Dose Rate (HDR) brachytherapy (BT). This paper presents the design, fabrication, and characterization of such dosimeters, consisting of scintillating sensor tips attached to polymer optical fiber (POF). The sensor tips consist of inorganic scintillators, i.e. Gd2O2S:Tb for LDR-BT, and Y2O3:Eu+4YVO4:Eu for HDR-BT, dispersed in a polymer host. The shape and size of the tips are optimized using non-sequential ray tracing simulations towards maximizing the collection and coupling of the scintillation signal into the POF. They are then manufactured by means of a custom moulding process implemented on a commercial hot embossing machine, paving the way towards series production. Dosimetry experiments in water phantoms show that both the HDR-BT and LDR-BT sensors feature good consistency in the magnitude of the average photon count rate and that the photon count rate signal is not significantly affected by variations in sensor tip composition and geometry. Whilst individual calibration remains necessary, the proposed dosimeters show great potential for in-vivo dosimetry for brachytherapy.

Numerical investigation of elastomeric solid cutting: Enhancing cut initiation for minimally invasive biological tissue cutting

Abstract Minimizing tissue damage during blade cutting is vital for optimal surgical outcomes. However, the elastomeric properties of tissues require that they be considerably deformed before cut initiation, resulting in physical damage. Thus, the blade indentation depth required for cut initiation must be reduced by enhancing the cut-initiation ability of a process. In this study, factors that influence the cut initiation of elastomeric solids are identified by investigating the tensile stress states beneath the blade that trigger cut initiation. Finite element simulations are used to analyze interfacial interactions between the blade and workpiece and their relation to the stress states. Results show that the distribution of the in-plane stretch of the workpiece surface along the blade surface plays a key role in determining the stress states and the resulting cut-initiation ability. The effects of process parameters, including interfacial friction, blade tip geometry, blade motion, and workpiece size, are examined and discussed by analyzing the corresponding in-plane surface stretch distribution. This study offers a fundamental understanding of cut initiation in elastomeric solid cutting for improving surgical cutting tasks.

Tip Vortex Study of a Rotor with Double-Swept Blade Tips

An experimental aerodynamic study was conducted, analyzing the wake structure of a four-bladed model rotor with a forward-backward swept tip geometry inspired by the ONERA-DLR “Etude d´un Rotor Aéroacoustique Technologiquement Optimisé”-design. Similar tip designs are used on some modern helicopter main rotors. The experiments were conducted at the Rotor Test Facility Göttingen (RTG) in hover-like conditions using a stereoscopic high-speed particle image velocimetry system. The results are compared with those of a reference rotor using a conventional parabolic blade tip. The test parameters include both constant-pitch cases and pitch-oscillating cases with a cyclic swashplate input. The constant-pitch tests show a two-step stall behavior for the double-swept tip, with the first step characterized by a reduced thrust slope and a reduced rotor efficiency. This effect is explained by a repositioning and a structural change of the tip vortex generation. The pitch-oscillating cases show that the double-swept tip results in an earlier tip stall compared to the parabolic geometry while maintaining high thrust levels. The dynamic tip stall yields a break-down of the wake’s tip vortex system, which is replaced by a spanwise band with small-scale turbulent structures and trailed vorticity, but no large-scale vortices.

Compensation Method for Correcting the Topography Convolution of the 3D AFM Profile Image of a Diffraction Grating

Any 3D AFM image is a convolution of the geometry of the AFM tip and the profile of the scanned sample, especially when the dimensions of the scanned sample are comparable to those of the AFM tip shape. The precise profile of the scanned sample can be extracted from the 3D AFM image if the geometry of the AFM tip is known. Therefore, in order to separate the geometry of the AFM probe tip from the 3D AFM image of a diffraction grating with a rectangular profile and to correct for the topographic convolutions induced by the AFM probe tip, a method is used to quantitatively evaluate the geometry of the AFM probe tip, including the tip radius and the included angle. A model for reconstructing the measured AFM image is proposed to correct topography convolutions caused by the AFM tip shape when scanning a diffraction grating with rectangular profiles. A series of experiments were performed to verify the effectiveness of the proposed AFM tip geometry evaluation method, and comparison experiments were conducted to demonstrate the feasibility and reliability of the proposed reconstruction model.

Principle and antimicrobial efficacy of laser-activated irrigation: A narrative review.

In the last two decades, the activation of root canal irrigants with pulsed lasers as an adjunct in root canal treatment has become increasingly popular. This narrative review explains the physical basics and the working mechanism of laser-activated irrigation (LAI), explores the parameters influencing LAI efficacy, considers historical evolutions in the field and summarizes laboratory and clinical evidence with emphasis on the antimicrobial action of LAI. Cavitation is the driving force behind LAI, with growing and imploding vapour bubbles around the laser tip causing various secondary phenomena in the irrigant, leading to intense liquid dynamics throughout the underlying root canal. High-speed imaging research has shown that laser wavelength, pulse energy, pulse length and fibre tip geometry are parameters that influence this cavitation process. Nevertheless, this has not resulted in standardized settings for LAI. Consequently, there is significant variability in studies assessing LAI efficacy, complicating the synthesis of results. Laboratory studies in extracted teeth suggest that, with regard to canal disinfection, LAI is superior to conventional irrigation and there is a trend of higher antimicrobial efficacy of LAI compared to ultrasonic activation. Clinical evidence is limited to trials demonstrating similar postoperative pain levels after LAI versus no activation or ultrasonic activation. Clinical evidence concerning the effect of LAI on healing of apical periodontitis as yet is scarce.

Microfabricated double-tilt apparatus for transmission electron microscope imaging of atomic force microscope probe.

Atomic force microscopy (AFM) uses a scanning stylus to directly measure the surface characteristics of a sample. Since AFM relies on nanoscale interaction between the probe and the sample, the resolution of AFM-based measurement is critically dependent on the geometry of the scanning probe tip. This geometry, therefore, can limit the development of related applications. However, AFM itself cannot be effectively used to characterize AFM probe geometry, leading researchers to rely on indirect estimates based on force measurement results. Previous reports have described sample jigs that enable the observation of AFM probe tips using Transmission Electron Microscopy (TEM). However, such setups are too tall to allow sample tilting within more modern high-resolution TEM systems, which can only tilt samples less than a few millimeters in thickness. This makes it impossible to observe atomic-scale crystallographic lattice fringes by aligning the imaging angle perfectly or to view a flat probe tip profile exactly from the side. We have developed an apparatus that can hold an AFM tip for TEM observation while remaining thin enough for tilting, thereby enabling atomic-scale tip characterization. Using this technique, we demonstrated consistent observation of AFM tip crystal structures using tilting in TEM and found that the radii of curvature of nominally identical probes taken from a single box varied widely from 1.4nm for the sharpest to 50nm for the most blunt.