Rain Droplets Research Articles

Wind speed effects on rainfall-induced salinity and temperature anomalies at the sea surface microlayer at mid-latitudes

Sea surface salinity (SSS) and temperature (SST) can serve as proxies to detect freshwater fluxes at the sea surface during precipitation. Widely unknown, however, is the impact of precipitation (droplet sizes and velocities) and wind speed on the sea surface microlayer (SML), the <1 mm boundary layer between atmosphere and ocean. We used the autonomous surface vehicle HALOBATES in the German Bight, North Sea, to collect SSS and SST data with high vertical resolution at 7 depths in the top meter, spaced 10–30 cm apart, including the SML. During two rain events with similar maximum rainfall intensity, the magnitude and persistence of the resulting salinity anomaly (between SML and 100 cm depth) was dependent on wind speed. The maximum rate of change of salinity in the SML was 4 times faster with high wind speeds: 0.009 g kg min−1 at low wind speeds, 0.037 g kg min−1 at high wind speeds. A threshold of about 5 m s−1 determined whether stratification occurred in the near-surface layer or freshwater mixed with the underlying layers during precipitation. Strong winds still caused salinity changes in the near-surface layer and SML, but the water mixed rapidly with the underlying water masses. The SML salinity was affected by droplet distributions with smaller droplets, as small droplets stay at the surface. Salinity and temperature changes in the SML were >9 times higher than at 100 cm depth (−0.037 g kg min−1 vs. −0.004 g kg min−1) and still detectable during very high wind speeds. Overall, these results contribute to a better understanding of the vertical distribution of freshwater in the surface ocean and its dependence on rain intensity, wind speed, and droplet properties, helping to improve understanding of the fate of freshwater in a changing ocean due to climate warming.

Femtosecond-Laser-Enabled Geometric Microengineering of PZT Films for Boosted Piezoelectric Response and Rainfall Monitoring Demonstration.

Geometric microengineering of the active layer in a piezoelectric sensor has emerged as a hot topic to improve performance but meets challenges due to the brittle nature of piezoelectric ceramics. Here, we demonstrate that fs-laser-induced compressive stress leads to film bulging in the nanoscale and forms various shapes of nanostructures, including nanobumps, nanovolcanoes, and nanocaves on Pb1.1Zr0.52Ti0.48O3 (PZT) films, in a single-step, mask-free, large-scale, and rapid fashion. Highly reproducible 3D profiles of the nanostructures are finely controlled by carefully adjusting the laser energy density around the ablation threshold. Evaluation of piezoelectric response to external pressure pulses shows that the PZT films patterned with 450 nm high nanobumps exhibit a 30% increase in output voltage compared to flat PZT films. In a rainfall monitoring test, the PZT films patterned with 450 nm high nanobumps show a significantly enhanced response with varying rain droplet volumes and falling frequencies. Geometric microengineering of PZT films using a femtosecond laser direct writing route provides a guideline for material design in a wide range of microsensor applications.

Estimation of energy available in rain droplets from meteorological rainfall data

Abstract Even though the amount of rainfall is well documented in the reports of the India Meteorological Department (IMD), the rainfall energy available in different parts of India is unknown to the best of our knowledge. This paper reports a theoretical framework to convert the meteorological rainfall data to rainfall energy. The amount of rainfall over the south-west Monsoon period of 2022 is first converted to an average rainfall rate. Using the information on rain droplet size distribution for a rainfall of a given rainfall rate, the total energy contained in the rainfall is derived. In this, both the kinetic and surface energies of rain droplets of different sizes are considered. Based on the developed theoretical framework, rainfall map of India is converted to rainfall energy map showing states/union territories with maximum and minimum rainfall energy. Furthermore, for selected states in India, the districts showing maximum and minimum rainfall energy are also highlighted. The framework developed in the present study would help attempts to develop efficient rain energy harvesting systems.

Evaluation of Autoconversion Representation in E3SMv2 Using an Ensemble of Large‐Eddy Simulations of Low‐Level Warm Clouds

AbstractIn numerical atmospheric models that treat cloud and rain droplet populations as separate condensate categories, precipitation initiation in warm clouds is often represented by an autoconversion rate , which is the rate of formation of new rain droplets through the collisions of cloud droplets. Being a function of the cloud droplet size distribution (DSD), the local is commonly parameterized as a function of DSD moments: cloud droplet number and mass concentrations. When applied in a large‐scale model, the grid‐mean must also include a correction, or enhancement factor, to account for the horizontal variability of the cloud properties across the model grid. In this study, we evaluate the Au representation in the Energy Exascale Earth System Model version 2 (E3SMv2) climate model using large‐eddy simulations (LES), which explicitly resolve cloud droplet spectra, and therefore the local , as well as its spatial variability. The analysis of an ensemble of warm low‐level cloud cases shows that the E3SMv2 formulation represents the reasonably well compared to the horizontally averaged explicitly computed rate from LES. The agreement, however, comes from a combination of an underestimated E3SM‐tuned local rate and an overestimated subgrid cloud variability enhancement factor. The latter bias is traced to neglecting the horizontal variability of and its co‐variability with in parameterizing the grid‐mean .

Tailoring of Self-Healable Polydimethylsiloxane Films for Mechanical Energy Harvesting.

Triboelectric nanogenerators (TENGs) have emerged as potential energy sources, as they are capable of harvesting energy from low-frequency mechanical actions such as biological movements, moving parts of machines, mild wind, rain droplets, and others. However, periodic mechanical motion can have a detrimental effect on the triboelectric materials that constitute a TENG device. This study introduces a self-healable triboelectric layer consisting of an Ecoflex-coated self-healable polydimethylsiloxane (SH-PDMS) polymer that can autonomously repair mechanical injury at room temperature and regain its functionality. Different compositions of bis(3-aminopropyl)-terminated PDMS and 1,3,5-triformylbenzene were used to synthesize SH-PDMS films to determine the optimum healing time. The SH-PDMS films contain reversible imine bonds that break when the material is damaged and are subsequently restored by an autonomous healing process. However, the inherent stickiness of the SH-PDMS surface itself renders the material unsuitable for application in TENGs despite its attractive self-healing capability. We show that spin-coating a thin layer (≈32 μm) of Ecoflex on top of the SH-PDMS eliminates the stickiness issue while retaining the functionality of a triboelectric material. TENGs based on Ecoflex/SH-PDMS and nylon 6 films show excellent output and fatigue performance. Even after incisions were introduced at several locations in the Ecoflex/SH-PDMS film, the TENG spontaneously attained its original output performance after a period of 24 h of healing. This study presents a viable approach to enhancing the longevity of TENGs to harvest energy from continuous mechanical actions, paving the way for durable, self-healable mechanical energy harvesters.

Fatigue damage mechanics approach to predict the end of incubation and breakthrough of leading edge protection coatings for wind turbine blades

The state of the surface of the leading edge of wind turbine blades is important for optimal aerodynamic performance. Rain erosion leads to damage and roughness on the leading edge. In this study, we present an approach to predict the level of roughness of the leading edge based on fatigue damage accumulation due to impacts of rain droplets. Impact simulations of droplets on the protective coating layer are coupled with rain erosion test data and fatigue S-N curves. Fatigue damage values are then related to surface roughness levels. An approach to extract S-N curve parameters from a rain erosion test and then make predictions for other coatings based only on the output of impact simulations is presented and tested against test data. Both the end of incubation and coating breakthrough times are predicted with this approach. Stress, strain and energy density values were used as fatigue damage indicators and the respective predictions were compared to each other. It was found that the maximum principal strain gave the best predictions and matched the experimental trends.

Preparation of protective coatings for the leading edge of wind turbine blades and investigation of their water droplet erosion behavior

The damage caused by rain droplet erosion to the leading edge of wind turbine blades is extremely severe. To reduce this issue, in this study, hydroxyl-terminated polybutadiene (HTPB) and isophorone diisocyanate (IPDI) were used as the polyurethane (PU) polyol and curing agent, respectively, to prepare a PU coating with a high resistance to water droplet erosion (WDE) for the protection of the leading edge of wind turbine blades. The effect of n (–NCO):n (–OH) (R-value, n is the molar ratio) on the mechanical properties and WDE resistance of PU coatings, the relationship between the two performances, and the influence of the erosion conditions on the WDE behavior were investigated for the first time. The results show the existence of a correlation between the mechanical properties (hardness, impact, flexibility, and tensile strength) and WDE resistance of the coating. While, a better abrasion resistance is found not to result in a better WDE resistance. The PU coating with an R-value of 1.2 shows an optimal WDE resistance in both atomization and jet erosion experiments. In atomized droplet erosion (ADE) experiments, the change in erosion velocity accelerates the incubation period of coating erosion damage and increases the erosion rate. In jet droplet erosion (JDE) experiments, the damage to the coating is closely related to the erosion angle, reaching a maximum at an impact angle of 60°. Furthermore, in the ADE experiments, various erosion morphologies, such as pits, grooves, cracks, and stepped texture, are observed on the damaged coating surface. While, regarding the JDE experiments, holes, grooves, and cracks are observed. Such damage is caused by the combined effects of water hammer pressure, lateral jets, and local permeation.

Prediction of the dynamic pressure drop of filter media loaded with water mists based on the deposited droplet mass distributions and pore network model

Predicting the pressure drop of a filter is necessary, especially regarding the jump in the dynamic pressure drop of a filter without pre-filters when clogged by rain or fog droplets. However, the efficient prediction method for the pressure drop in cylinder filters loading with water mists in the pore network faces limitations due to the high requirements for microscopic images of materials and the need to consider for the increasing holding droplet capacity of filters. In this study, a systematic method that takes into account the distributions of the deposited droplet mass within the water-absorbed filter medium layers in the pore network model (PNM) was developed. The pore geometry and distributions were determined from 2D microstructure images, and the dynamic deposited droplet mass and water-absorbing capacity of fibers were combined with the changing saturation to optimize the PNM for calculating the dynamic pressure drop of the filter media. Specifically, the empirical equation of the self-defined equivalent single fiber filtration efficiency (ESFFE) describes the relationship between the changing single fiber filtration efficiency and the deposited droplet mass. The optimized PNM is suitable for predicting the behavior of bibulous wood cellulose fiber filter media. The dynamic pressure drop shows a slight increase before surging, following the typical “channel and jump” model. Although the calculations deviate slightly from the experimental results with 25 % deviations, this systematic method effectively predict the jump in pressure drop of the tested filter medium. Therefore, this systematic method for predicting pressure drop of filters holds promise in anticipating unsafe pressure drop jumps in filters installed in coastal areas.

How leading edge roughness influences rain erosion of wind turbine blades?

Rain erosion of wind turbine blades is observed very commonly and is a concerning issue. Damage on the leading edge of blades leads to loss of aerodynamic efficiency. The mechanisms of damage initiation are not yet fully understood. This study focuses on the effect of existing surface damage or roughness of the leading edge of blades on impact stresses and erosion rates for the protective coating layer. The main mechanisms of interaction between impacting rain droplets and surface irregularities of a polyurethane-based coating are examined through finite element simulations and high-stress areas are identified. The results of the simulations reveal that areas inside erosion pits experience larger von Mises stresses than other undamaged areas. This could be explained by increased velocity as the water flows into erosion pits, observed in the simulations. At the same time, impacts on rough and damaged areas cause large stress values over a larger area than impacts on flat surfaces, due to the interaction with surface damage. These two observations could be the cause for faster erosion rates near damaged areas, as observed in experimental images during rain erosion testing. The predicted elevated stresses due to initial roughness or pre-existing damage could lead to faster damage growth, and to erosion pits growing wider and deeper.

Prediction of rain erosion damage progression using disdrometer rain data: The importance of liquid water content

Wind turbine blade erosion poses a significant challenge to the durability and performance of wind turbines. Modeling of rain erosion damage, considering atmospheric conditions, improves our understanding of the progression of leading-edge erosion on wind turbine blades. In this study, we investigate the impact of varying raindrop characteristics on rain erosion damage development. We analyse 2.5 years of data from a disdrometer, which measures the size and velocity of falling rain droplets, at Risø campus. Various post-processing methods of the disdrometer data are used for estimating representative droplet diameters and fall velocities for each rain event. We compare measured droplet fall velocities with theoretical terminal velocities, revealing a necessity for revising theoretical approaches to raindrop fall velocity for erosion damage modeling. The measured rain rates and representative fall velocities are used to calculate the liquid water content in the air. We introduce a bin-wise summation method for estimating the liquid water content, circumventing the need for representative droplet assumptions. As this method provides the most accurate input for the damage model, we benchmark the other post-processing methods against it and employ it to evaluate bias estimates of associated damage predictions. The largest bias (22%) in accumulated damage is found with an arithmetic mean droplet diameter approach and the smallest bias (-2%) with the median volume estimation method for damage model input. Furthermore, we demonstrate that, for a given rainfall volume, smaller droplets contribute to larger accumulated damage compared to larger droplets.

Efficient and stable coupling of the SuperdropNet deep-learning-based cloud microphysics (v0.1.0) with the ICON climate and weather model (v2.6.5)

Abstract. Machine learning (ML) algorithms can be used in Earth system models (ESMs) to emulate sub-grid-scale processes. Due to the statistical nature of ML algorithms and the high complexity of ESMs, these hybrid ML ESMs require careful validation. Simulation stability needs to be monitored in fully coupled simulations, and the plausibility of results needs to be evaluated in suitable experiments. We present the coupling of SuperdropNet, a machine learning model for emulating warm-rain processes in cloud microphysics, with ICON (Icosahedral Nonhydrostatic) model v2.6.5. SuperdropNet is trained on computationally expensive droplet-based simulations and can serve as an inexpensive proxy within weather prediction models. SuperdropNet emulates the collision–coalescence of rain and cloud droplets in a warm-rain scenario and replaces the collision–coalescence process in the two-moment cloud microphysics scheme. We address the technical challenge of integrating SuperdropNet, developed in Python and PyTorch, into ICON, written in Fortran, by implementing three different coupling strategies: embedded Python via the C foreign function interface (CFFI), pipes, and coupling of program components via Yet Another Coupler (YAC). We validate the emulator in the warm-bubble scenario and find that SuperdropNet runs stably within the experiment. By comparing experiment outcomes of the two-moment bulk scheme with SuperdropNet, we find that the results are physically consistent and discuss differences that are observed in several diagnostic variables. In addition, we provide a quantitative and qualitative computational benchmark for three different coupling strategies – embedded Python, coupler YAC, and pipes – and find that embedded Python is a useful software tool for validating hybrid ML ESMs.

Let It Snow: Designing Snowfall Experience in VR

We present Snow, a cross-modal interface that integrates cold and tactile stimuli in mid-air to create snowflakes and raindrops for VR experiences. Snow uses six Peltier packs and an ultrasound haptic display to create unique cold-tactile sensations for users to experience catching snowflakes and getting rained on their bare hands. Our approach considers humans' ability to identify tactile and cold stimuli without masking each other when projected onto the same location on their skin, making illusions of snowflakes and raindrops. We design both visual and haptic renderings to be tightly coupled to present snow melting and rain droplets for realistic visuo-tactile experiences. For multiple snowflakes and raindrops rendering, we propose an aggregated haptic scheme to simulate heavy snowfall and rainfall environments with many visual particles. The results show that the aggregated haptic rendering scheme demonstrates a more realistic experience than other schemes. We also confirm that our approach of providing cold-tactile cues enhances the user experiences in both conditions compared to other modality conditions.

Multi-Phase flow simulation for transient analysis of ballast drainage behavior and shoulder cleaning effect

This paper presents multi-phase flow simulations to analyze the transient transport of rain droplets through rail ballast and its dependence on fouling conditions and shoulder cleaning. The entire process consisting of random rain droplet injection, droplet migration through the air, falling on the ballast surface, drainage through the void spaces between ballast aggregates, and running off the ballasts are modeled. A computational fluid dynamics (CFD) model is developed, in which the volume of fluid (VOF) method and Darcy-Forchheimer's equation are employed to capture the gas–liquid mixture interface and consider fouling-induced flow resistance, respectively. The model is implemented as an interFoam solver in the OpenFOAM CFD tool. A method for determining trapped moisture inside the fouled and moderately fouled ballast layers is also presented. Parametric simulations are conducted to investigate the effect of fouling conditions, more specifically, Fouling Index (FI), Fouling Profile (FP), and shoulder cleaning on ballasts' drainage performance and time-dependent moisture accumulation and penetration. The results indicate that severe congestion in fouled ballast is responsible for higher moisture accumulation, slower penetration, and poorer drainage of ballast. Shoulder cleaning is an effective measure to reopen flow passage and restore drainage capability, in particular, for the fouled ballast.

Droplet Injection for Multiphase Rainfall Simulations on Dynamically Refined Mesh for Effective Interface Capturing

This paper presents a volume of fluid (VOF) model for multiphase rainfall simulation that injects rain droplets as a continuous phase alongside the adaptive mesh refinement (AMR) method to resolve air-water interfaces. An approach based on multi-level domains and a pseudo-random algorithm is proposed to determine injection locations in a random and non-intrusive manner with the least bias. Face zones instead of faces are adopted as constituent elements for droplet injection to prevent droplet fragmentation due to a change of face IDs caused by AMR. Correspondingly, a new multi-level address system is introduced to establish the correspondence among subdomains at different levels. The model is applied to multiphase flow VOF simulation for parametric 2-D and 3-D rainfall analysis. The results are verified by the data reported in the literature. It demonstrates that the model can efficiently simulate realistic rainfall phenomena, capture the droplet interface, and preserve droplet injection uniformity.

Evaluation of offshore wind turbine blades coating thickness effect on leading edge protection system subject to rain erosion

During operation, wind turbine blades are subjected to a wide range of environmental and loading conditions and blade erosion can have a negative impact on performance and power production. The layer-wise thickness of a leading edge coating system can have a substantial effect on erosion rate due to rain droplet impact, which can result in a variety of complex failure modes, such as delamination of the coating-substrate interface. The objective of this work to develop single droplet numerical models to investigate the influence of elastic stress wave developments generated during impact. Following that, a single rain droplet FE parametric research was performed with different coating materials, coating and filler putty thicknesses. It is shown that stiffer coatings lead to higher stresses. Furthermore, thicker coatings can result in lower stress transfer to the filler material. The empirical equations developed for coating thickness and filler putty thickness were found to be in good agreement with each other. This detailed baseline investigation can help in understanding the effect of coating and filler putty thickness on rain erosion rate, as well as analysing different coating designs using empirical equations for the development of more durable leading edge protection coatings for wind turbine blade applications.

Estimation of Surface Sensible Heat Flux due to Precipitation over CONUS and Its Impact on Urban Extreme Precipitation Modeling

Abstract The surface sensible heat flux induced by precipitation (QP) is a consequence of the temperature difference between the surface and the rain droplets. Despite its seemingly negligible nature, QP is frequently omitted from both meteorological and climatological models. Nevertheless, it is important to acknowledge the numerous occasions in which the instantaneous values of QP can be significant, particularly during extreme precipitation events. This study undertakes a comprehensive assessment of QP across the contiguous United States (CONUS) utilizing high-resolution reanalysis, observational data, and numerical modeling to examine the influence of QP on precipitation and the surface energy budget. The findings indicate that the spatial distribution of QP climatology is analogous to that of precipitation, with magnitudes ranging from 2 to 3 W m−2 predominantly over the Midwest and Southeast regions. A seasonal analysis of QP reveals that the highest values occurring during the June–August (JJA) period, averaging 3.18 W m−2. Peak QP values of approximately 4 W m−2 are observed during JJA over the Great Plains region. We hypothesize that the QP during an extreme precipitation event would be nonnegligible and have a significant impact on the local weather. To test this conjecture, we perform high-resolution simulations with and without QP during an extreme precipitation event over the Chicago Metropolitan Area (CMA). The results show that the QP may be a dominant factor compared to other components of surface heat flux during the zenith of precipitation hours. Also, QP has the potential to not only diminish precipitation but also alter and reconfigure the remaining surface energy budget components.

Rain droplet impact stress analysis for leading edge protection coating systems for wind turbine blades

Rain droplet impact stress analysis for leading edge protection coating systems for wind turbine blades

Mesoscale Characteristics of Exceptionally Heavy Rainfall during 4–6 May 2023 in Jiangxi, China

A long-lasting rainfall event exceeding historical extremes took place in Jiangxi, China, from May 4 to 6, 2023. Because of the concentrated duration of precipitation, it led to significant water accumulation in the northern, central, and southern regions of Jiangxi. The objective of this study was to investigate the weather mechanisms underlying this extreme rainstorm in Jiangxi. By examining detailed observational data, the mesoscale weather characteristics and environmental conditions of the event can be obtained. These findings offer valuable insights for future weather forecasting and warnings. It was observed that after the Huanghuai cyclone moved eastward into the sea, the cold air on its western side shifted northward and converged with the warm, moisture-laden air mass in Hunan and Jiangxi provinces. This convergence of air masses triggered the heavy rainstorm event. The peak precipitation period occurred from midnight on May 5 to 0800 BJT on May 6. Concerning the macroscopic precipitation characteristics, multiple mesoscale convective systems (MCSs) originated in Hunan during this period and progressed eastward along the shear line toward the central part of Jiangxi. As for the microscopic precipitation features, the total precipitation amount was closely linked to the duration of heavy rain droplets. The rainfall distribution in the raindrop spectrum also served as a valuable reference for understanding the persistence and size of precipitation. The temporal pattern of the combined reflectivity echo along 27.5° N indicated that from 2000 BJT on May 5 to the early morning of May 6, there was a rapid development of a weaker MCS after passing through the Luoxiao Mountains. This development resulted in a “train effect” in the central region of Jiangxi. The presence of a 200 hPa divergence area, high vertical ascent rate, and abundant water vapor contributed to the formation of a narrow area of heavy rainstorms in central Jiangxi. Additionally, the falling area of heavy rain coincided with the front of the 500 hPa low trough. In the northern part of Jiangxi, the occurrence of heavy precipitation was influenced by the equivalent temperature front area. Favorable conditions, including water vapor, dynamics, and thermal factors, further supported the occurrence of heavy precipitation.

Fatigue S-N curve approach for impact loading of hyper- and visco-elastic leading edge protection systems of wind turbine blades

Computational evaluation of leading edge erosion remains challenging due to the high-strain rate loading conditions caused by impact of the wind turbine blade leading edge with rain droplets and other environmental particles. Here, a methodology is proposed for obtaining an S-N curve which can be used for impact fatigue evaluation of hyper- and viscoelastic leading edge protection systems for wind turbine blades, in the relevant strain rate domain. Two material systems (hard and soft polyurethane (PU)) are characterised experimentally by dynamic mechanical analysis (DMA) and static tensile tests. Time-temperature superposition is applied to the raw DMA data in order to obtain the material’s mastercurve, describing its visco-elastic behaviour in an expanded strain rate domain. The Yeoh (hyperelastic) and prony series (vis-coelastic) material model parameters are calibrated and form the input for a 2D-axisymmetric finite element model, in which Single Point Impact Fatigue Test (SPIFT) testing conditions are simulated. The stress field experienced by the coating during SPIFT testing is obtained and combined with the experimental measurements, allowing the determination of the material systems S-N curve, in the relevant strain rate domain. Results for a hard and soft PU coating system are compared with rain erosion test (RET) data. The RET data shows higher lifetime for the hard PU systems, a tendency that can be predicted when comparing the S-N curve for the hard and soft PU system. This methodology can be utilised in computational lifetime evaluation of leading edge coating systems. Furthermore, the methodology has the potential to partly alleviate the need of RET in the development and comparison of next-generation leading edge protection systems.

Comparative study on the water droplet erosion behavior between stretched and casted aeronautical PMMA

Rain droplet erosion is a potential threat in aviation, especially for forward-facing components such as windshields of aircraft. To comprehend and mitigate such hazards, a comparative study was conducted on two kinds of commonly used aeronautical PMMA materials: casted and biaxially stretched. The study aimed to investigate the water droplet erosion (WDE) behavior and the underlying damage mechanism. A modified pulsed water jet erosion facility was constructed to mimic the impact of successive water droplets. The influence of impact velocity on the WDE behavior was explored and quantitative evaluations of volume loss, surface entrance area, and erosion depth were conducted. Results revealed that the increase in impact velocity leads to faster damage initiation and a larger erosion rate. Compared with the stretched sample, the casted sample exhibits higher erosion resistance. The stretched sample exhibits a funnel-shaped cavity with a flat bottom, while the casted sample shows a tapered crater with shallow depth. The cavity shape can influence the subsequent flow fields and stress distribution, thereby affecting the development of erosion entrance and depth. Microscopic analysis of the erosion cavities revealed different damage mechanisms at each stage of erosion. The stretched sample exhibited exfoliation of fine flakes and denudation of large pieces due to stress waves and lateral jet-induced shear, whereas hydraulic penetration had a more pronounced effect on the casted sample. The cushioning effect of the water film was also studied, noting a gradual reduction in its effectiveness with increasing impact velocity.