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  • View in gallery

    Photographs of (a) 4-cm steel ball impact, (b) 4-cm pure ice sphere impact, and (c) 80% carbonated water ice sphere impact on the same architectural composite shingle, except the product in (c) has been naturally aged for 2 years. Kinetic energy at impact for each is approximately 30 J.

  • View in gallery

    Conceptual diagram of the transition of pure ice from a ductile to a brittle failure under a compressive load with increasing strain rate.

  • View in gallery

    The field measurement device. Noted is the position of the load cell beneath the lower Delrin cylinder. The field measurement device must be oriented as shown for the test to be valid.

  • View in gallery

    Time history of compressive force measured by the field device of a laboratory ice sphere fracture.

  • View in gallery

    Compressive force measurements (a) for Instron UTM and field measurement device of seltzer/tap water mixed ice spheres shown as a function of nominal diameter and (b) compressive stress measurements for each device shown as a function of nominal diameter.

  • View in gallery

    Peak compressive force data for filtered Instron (UTM) (black) and field measurement device for seltzer/tap water mix ice spheres shown as a function of nominal (laboratory) and maximum (field) diameter.

  • View in gallery

    Mass–diameter relationship for measured hailstones from (a) 2012–13 and (b) shape factor (Knight 1986) shown as a function of major diameter.

  • View in gallery

    Compressive stress measurements shown as a function of major diameter for field observations and FM 4473 ice spheres. Error bars represent ±1 standard deviation from the mean.

  • View in gallery

    Probability distribution for compressive stress measurements from the 2012–13 field program.

  • View in gallery

    Histogram of the compressive stress of natural hailstones normalized by (a) the mean and (b) the median compressive stress of the compressive stress values obtained from pure ice sphere tests using the field measurement device.

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Evaluating the Hardness Characteristics of Hail through Compressive Strength Measurements

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  • 1 Insurance Institute for Business and Home Safety, Richburg, South Carolina
  • | 2 Technology Research and Innovation Laboratory, State Farm Mutual Automobile Insurance Company, Bloomington, Illinois
  • | 3 Insurance Institute for Business and Home Safety, Richburg, South Carolina
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Abstract

Throughout historical literature anecdotal or visual observations have been used to describe the hardness property of hailstones (e.g., hard, soft, slushy). A unique field measurement device was designed and built to apply a compressive force to the point of fracture on hailstones in the field. The device uses a pistol-grip clamp to apply a compressive load to a hailstone and integrates a fast-response load cell and associated data acquisition components to measure the applied force through the point of fracture. The strain rate applied to the stone is fast enough to produce a brittle failure, and the peak compressive force is appropriately scaled by the cross-sectional area to produce a compressive stress value. When compared to an Instron universal testing machine (UTM), the field measurement device exhibited a low bias induced by measurement hardware sampling limits. When a low-pass filter was applied to the Instron data to replicate the hardware properties of the field measurement device, good agreement was found for compressive force tests performed on laboratory ice spheres, and it was clear the device was capturing a relative measure of strength. The mean compressive stress for natural hail was similar to that of pure ice spheres, but individual thunderstorm events exhibited variability. Laboratory ice spheres also showed significant variability, which argues for large sample sizes when testing any material for impact resistance.

Corresponding author address: Ian M. Giammanco, Insurance Institute for Business and Home Safety, 5335 Richburg Rd., Richburg, SC 29729. E-mail: igiammanco@ibhs.org

Additional affiliation: Texas Tech University, Lubbock, Texas.

Abstract

Throughout historical literature anecdotal or visual observations have been used to describe the hardness property of hailstones (e.g., hard, soft, slushy). A unique field measurement device was designed and built to apply a compressive force to the point of fracture on hailstones in the field. The device uses a pistol-grip clamp to apply a compressive load to a hailstone and integrates a fast-response load cell and associated data acquisition components to measure the applied force through the point of fracture. The strain rate applied to the stone is fast enough to produce a brittle failure, and the peak compressive force is appropriately scaled by the cross-sectional area to produce a compressive stress value. When compared to an Instron universal testing machine (UTM), the field measurement device exhibited a low bias induced by measurement hardware sampling limits. When a low-pass filter was applied to the Instron data to replicate the hardware properties of the field measurement device, good agreement was found for compressive force tests performed on laboratory ice spheres, and it was clear the device was capturing a relative measure of strength. The mean compressive stress for natural hail was similar to that of pure ice spheres, but individual thunderstorm events exhibited variability. Laboratory ice spheres also showed significant variability, which argues for large sample sizes when testing any material for impact resistance.

Corresponding author address: Ian M. Giammanco, Insurance Institute for Business and Home Safety, 5335 Richburg Rd., Richburg, SC 29729. E-mail: igiammanco@ibhs.org

Additional affiliation: Texas Tech University, Lubbock, Texas.

1. Introduction

Hail events across the United States are responsible for nearly $1 billion in annual insured losses with an increasing trend attributed to changing dollar values, growing wealth, and exposure of properties at risk from severe hail (Changnon et al. 2009; Roeder 2012). Given increasing financial losses, there is a renewed interest in understanding how the physical properties of hail influence damage and developing mitigation strategies to reduce losses.

Little is known about the material properties of natural hail and how they may apply to damage potential upon impact with other materials (Kim and Kedward 2000; Schulson and Duval 2009; Swift 2013). Meteorological studies have often focused on hail growth processes, understanding the environments that support the growth of large hail, and radar detection of severe hail to support forecast and warning decision-making. The majority of these studies are thoroughly summarized by Knight and Knight (2001). The physical measurements of hailstones, such as diameter, mass, and shape, have been well quantified; however, the material properties of hail, such as hardness or strength, have not (Browning 1963; Browning and Foote 1976; Browning 1977; Macklin 1977; Foote and Knight 1977; Ziegler et al. 1983; Knight and Knight 2001; Blair and Leighton 2012; Knight et al. 2008; Heymsfield et al. 2014). Throughout historical literature hail has been qualitatively referred to as soft, slushy, or hard. This has even been used to infer damage potential, such as the event described in Knight et al. (2008), who speculated that “little property damage was likely,” following an observed hail event that produced “soft” hailstones of sizes larger than 4 cm. Quantitatively, those properties beyond the physical dimensions have not been well assessed. This is reflected in standardized material impact tests such as those developed by Underwriters Laboratory (UL; Underwriters Laboratory 2012). The UL 2218 methodology has been used to test materials for impact resistance for several decades. The test uses a steel sphere dropped from a specified height necessary to yield the same kinetic energy that a spherical hailstone of the same diameter (assuming density is that of pure ice, 0.9 g cm−3) would possess if falling at its terminal velocity. Other test methods use a sphere of pure ice propelled at a specified velocity to obtain a representative impact kinetic energy (FM Approvals 2005; FM 4473 test standard). The terminal velocity and impact kinetic energy specifications are based on the results of Bilhelm and Relf (1937), which were applied by Laurie (1960) toward material impacts. The use of ice spheres is a means to account for the material properties of hail. This need is clearly shown when a material such as a concrete tile is impacted by a steel ball using the UL 2218 standardized impact test method. The tile will typically fail, while a simple sphere of pure ice will compress and crush upon impact and the tile does not fail (Crenshaw and Koontz 2001). Other test standards apply cotton fibers within pure ice spheres to reduce the density of laboratory ice spheres to that similar to natural hail (ASTM International 2010) while strengthening the ice sphere. An example of differing damage patterns from steel ball and various ice sphere impacts on new and aged asphalt shingles is shown in Fig. 1. It is clear that the visible damage patterns differ between the three cases for which the impact kinetic energy was similar. Given the commentary in the literature and qualitative observations of damage, it is hypothesized that damage resulting from a hailstone impact can be influenced by the material properties of the projectile (e.g., hailstone) and those of the object it is encountering (e.g., roof system, siding, vehicles).To properly assess this influence, measurement of the material properties of natural hail must be made.

Fig. 1.
Fig. 1.

Photographs of (a) 4-cm steel ball impact, (b) 4-cm pure ice sphere impact, and (c) 80% carbonated water ice sphere impact on the same architectural composite shingle, except the product in (c) has been naturally aged for 2 years. Kinetic energy at impact for each is approximately 30 J.

Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0081.1

Physical measurements of the compressive strength, tensile strength, and fracture toughness of hailstones are nonexistent as result of the difficulty in performing standard material tests outside of a controlled laboratory environment (Kim and Kedward 2000; Schulson and Duval 2009; Silva 2011; Swift 2013). Capturing measurements of any of these quantities will help describe the strength of natural hail and its damage potential. For typical laboratory material strength testing, universal testing machines (UTM) are often used. These systems are capable of applying loads to materials at various strain rates in order to develop stress–strain relationships. These devices are far too cumbersome to use outside a laboratory setting. For the purposes of hail testing, often stones are shipped in cold storage for laboratory testing; however, it is speculated that cold storage may alter material properties prior to testing, such that any liquid water contained within interstices of a hailstone would freeze when placed in storage (Knight and Knight 2001). In addition, any sublimation of stones would alter their physical dimensions. Therefore, it is necessary to collect and test hailstones in situ or shortly thereafter to limit any bias due to transportation and storage.

2. Background

Hail is often referred to in historical literature as hard or soft simply as a qualitative measure of its behavior upon impact with various surfaces and materials. While damage will be strongly related to impact kinetic energy, the material properties of both hailstones and the impacted material will influence the true damage potential. The hardness property of any material is dependent on its ductility, elastic stiffness, plasticity, strain, strength, toughness, viscoelasticity, and viscosity. The ability of a material to absorb energy without failing is quantified by integrating compressive stress versus strain curve of the given material (e.g., hailstones). The uniaxial compressive stress (σc) is represented by
e1
where Fo is the peak compressive force at the moment of failure and A is the cross-sectional area along the plane in which force is applied. This is a quantity that can be effectively measured for hailstones in the field through relatively simple crush tests. A strong material possesses both high compressive strength and is also ductile. Pure ice is essentially a brittle material at relatively high strain rates under an applied compressive force (defined as the ratio of displacement rate to diameter), such that its overall strength is limited. Upon impact with a surface, a hailstone is subjected to strong compression at high strain rates. Qualitative observations of hailstones rebounding off materials (such as concrete) argue that hailstones can be hard enough to resist fracture and maintain the ability to support a load even at high strain rates generated upon impact.

The compressive stress of any material exhibits a nonlinear dependence on strain rate. Examining pure ice, at low strain rates (<10−3 s−1) it will exhibit a ductile compression. As the strain rate increases, pure ice will reach a point at which it cannot deform at a fast enough rate and cracking occurs. At even higher strain rates, cracks propagate more quickly than the ice can deform and exhibit a brittle failure. This produces a well-defined peak in the time history of compressive force during a test. The idealized compressive stress–strain rate relationship is summarized in Fig. 2. Laboratory testing has shown a general increase in compressive stress with strain rate through the transition from ductile to brittle failure (up to about 10−3 s−1), while compressive stress values level off between 10−3 and 10° s−1 (Mellor and Cole 1982; Jones 1997; Kim and Keune 2007; Shazly et al. 2009; Swift 2013). Work by Kim and Keune (2007) provided some evidence that compressive stress may begin to increase again at strain rates greater than 101 s−1. This requires that any measurement system produce a relatively uniform strain rate from test to test. The use of automated servo-driven systems to impart a compressive force has limited use in a field research vehicle setting due to space constraints.

Fig. 2.
Fig. 2.

Conceptual diagram of the transition of pure ice from a ductile to a brittle failure under a compressive load with increasing strain rate.

Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0081.1

The tensile strength of pure ice has shown less dependence on strain rate with a nearly constant value between strain rates of 10−7 and 10−1 s−1 (Hawkes and Mellor 1972; Michel 1978; Currier and Schulson 1982; Schulson et al. 1984; Druez et al. 1986; Lee and Schulson 1988). Schulson and Duval (2009) suggested that, in general, tensile strength is an order of magnitude less than compressive strength. Unfortunately, measuring this material property for hailstones is far more difficult in a field setting as discussed by Schulson and Duval (2009). Thus, for the purposes of this study, we will rely on compressive stress to serve as a proxy for the overall strength of natural hail. It is understood that capturing both quantities would allow for a more comprehensive evaluation of the strength of hailstones.

We have summarized the compressive strength of ice, but it is unclear how natural hailstones may differ. As with any material, its strength is dependent upon its microstructure. For hail, strength depends on the underlying structure of the individual grains of ice. At a larger scale, hailstones often exhibit a layered structure that is visible to the naked eye as a result of alternating growth processes. The variable nature in hail microphysical growth processes produces varying ice characteristics (e.g., clear, opaque) and influences the structure of a hailstone (Macklin 1962; Browning 1963; Knight and Knight 1968, 1973; Knight and Heymsfield 1983). The processes lead to regions of opaque ice, which contain trapped air bubbles, and other regions of relatively clear ice with discernible expansion cracks extending radially outward from the hailstone embryo (similar to a pure ice laboratory sphere). These features may provide a focus for crack development and propagation under compression (either during testing or upon impact). The strength of hail is undoubtedly linked to these processes but examining this in detail falls outside the scope of this study. Future work will hopefully begin to shed some light on these issues. With the complexity of natural hail growth, material impact methods often imply that the use of a steel ball or ice projectiles adequately represents the “most severe” hailstone-like impact for a perpendicular impact angle.

3. Measurement system

The primary objective of this study was to develop and deploy a system to measure the compressive strength of natural hail. For field measurements, a simple device was required that could produce a strain rate of approximately 10−1 s−1, had the capacity to supply and measure the compressive force, and extract the peak force applied at the point of a brittle failure. This required a mechanical functionality to supply the compressive force and adequate sensing and high-resolution data acquisition. Additional design criteria focused on the effectiveness of the system in a field setting, such that the system needed to be relatively lightweight and easy to operate inside the small space of a vehicle. One of the goals of the measurement program was to balance the cost of the complete system to enable expansion to other user groups. The resulting system integrated a manually operated field compression clamp with a load cell sensor and data acquisition module to provide an efficient means to measure the compressive force applied on a hailstone.

a. Measuring compressive strength

The general conceptual design for the mechanical device used to apply a compressive force to the sampled hailstone was a device in which a single user could manually apply the load to the hailstone. The strain rate produced by the device needed to be sufficient to yield a brittle fracture. The developed device was not intended to replace more sophisticated laboratory test equipment, such as UTMs, but instead fill a measurement gap. The device uses a modified “pistol grip” clamping handle (Fig. 3) with the load cell mounted on the bottom plate of the device. Two plates of Delrin plastic were affixed to the top and bottom plates to contact the stone during a test. The use of a plastic material mitigated melting, and high-speed photography of tests indicated minimal deformation of the material, such that its hardness was much higher than that of ice. The load cell was fitted onto a threaded steel rod beneath the lower half cylinder and was located within an aluminum shroud to protect the sensor, as shown in Fig. 3. A rigid aluminum mount was directly attached to the top portion of the clamping handle and was used to attach the upper unit of Delrin. The pistol-grip mechanism allows the user to squeeze the trigger handle (repeatedly if necessary) to apply a downward uniaxial compressive force to the specimen through the point of fracture. The downward-directed force is transferred through the bottom mount to the load cell. A drawback of the system is the lack of a constant strain rate due to the manual process in which the compressive load is applied.

Fig. 3.
Fig. 3.

The field measurement device. Noted is the position of the load cell beneath the lower Delrin cylinder. The field measurement device must be oriented as shown for the test to be valid.

Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0081.1

The primary sensing instrument used in the field measurement device is a 2.2-kN (500 lb) load cell. The sensor employs a Wheatstone bridge configuration to provide a measurement of the applied load. The load cell requires 10-Vdc input excitation voltage. The nonlinearity and hysteresis of the load cell used is 0.1% of rated output and can adequately measure 150% of its rated capacity. A signal conditioning board was integrated to amplify and scale the load cell output voltage for acquisition. The board requires a standard 12-Vdc supply to produce a ±8-Vdc analog output signal. The conditioning board has gain and balance potentiometers for calibration. The complete system can also be calibrated through the application of known weights to develop the linear calibration function. This option was used to develop a calibration curve, while the potentiometers were used to zero the system under a zero load condition.

b. Data acquisition

Acquisition of the output signal from the field measurement device is handled through a National Instruments (NI) universal serial bus (USB) module (NI USB 6009). The 14-bit module is capable of 48-kHz sampling (software controlled) on eight analog inputs (four differential channels). A National Instruments LabVIEW script is used to interface with the module and dictate the sampling rate through its onboard timing clock (configured at 100 Hz based upon signal conditioning resolution). The LabVIEW script also provides a graphical user interface for data monitoring during the test and data input (e.g., hailstone mass, dimensions), and it interfaces with a global positioning system (GPS) module to record time and position information. The amplified output voltage signal is processed through the linear calibration function to provide processed data on the applied compressive load for each test. A sample time history of a laboratory compressive force test is provided in Fig. 4, which illustrates a brittle failure of a pure ice sphere.

Fig. 4.
Fig. 4.

Time history of compressive force measured by the field device of a laboratory ice sphere fracture.

Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0081.1

c. Evaluating compressive stress

The data collected by the field system capture the time history of the applied compressive force, where the peak is the point at which the stone could not support the maximum applied load. This value (Fo) is applied to Eq. (1) to estimate the uniaxial compressive stress (σc) of the tested stone. For measurements of natural hailstones, the maximum and minimum diameters were measured. To estimate the cross-sectional area for which the load was applied, hailstones were assumed to be oblate spheroids with the cross-sectional area represented by
e2
where a is and b is [where x1 is the measured maximum diameter and y is the smallest dimension as defined by Knight (1986)]. Laboratory stones are nearly perfect spheres, but natural hailstones are more oblate and conically shaped, and can exhibit large protuberances. The assumption of oblate–spheroid shapes likely introduced a minor source of measurement error for natural hailstones. Equation (1) was applied for field and laboratory measurements to produce the estimated compressive stress.

4. Laboratory UTM and field system comparisons using ice spheres

To understand how the field measurement device compares to typical material testing instrumentation, laboratory testing on multiple sizes of modified ice spheres was conducted. An Instron 5581 UTM was used for this testing series. Identical Delrin contact plates were fitted to the Instron to maintain consistency with the field measurement device. The sampling rate of the Instron was 500 Hz. With the higher sampling resolution, this test series allowed for sampling bias concerns to be examined and quantified.

a. Validation testing

Compressive strength tests were performed on ice spheres of 3.18 cm (1.25 in.), 3.81 cm (1.5 in.), 4.45 cm (1.75 in.), and 5.08 cm (2 in.). A solution of dissolved CO2 was used in an effort to introduce bubble structures and reduce the density of test spheres below that of pure ice (~0.9 g cm−3) in an effort to mimic natural hail. This approach yielded mean density values of 0.75 g cm−3. The approach is similar to that used in the ASTM F320 (ASTM International 2010) methodology, which uses cotton fiber to reduce the density of ice used in impact testing of aerospace materials. However, the cotton fiber was shown to strengthen ice spheres beyond the strength of pure ice (Swift 2013). Test stones were made in spherical injection molds and placed in an environmental chamber at a constant temperature of −10°C for 48 h (in accordance with the FM 4473 standard for ice sphere projectiles). Spheres were randomly selected from the molds, where 50% were tested using the field measurement device and the remaining were tested with the Instron UTM. A sample size of 50 ice spheres was selected for testing in each device for each nominal size. Compressive strength tests were performed within 5 min of the ice spheres being extracted from the molds and under ambient room temperature conditions (~22°C). Test spheres typically had a surface temperature of −1° to −5°C. The displacement rate of the UTM was fixed at 0.6 cm s−1, and the rate represents the mean value found when high-speed photogrammetric analysis was conducted for three independent users of the field system during preliminary laboratory testing of similar size ice spheres. The displacement rates for the three users fell within a range of 0.55–0.64 cm s−1, producing strain rates on the order of 10−1 s−1 for ice spheres with diameters of 2.54–5.08 cm (1–2 in.). These values are large enough to produce a brittle failure of ice as described previously and fall within the zone in which compressive stress is relatively constant with strain rate.

b. Measurements

Measurements of the peak compressive force for both the Instron UTM and the field measurement device were collected for the four sizes of ice spheres. Measurements collected by both systems showed a general increase in the peak compressive force at the point of fracture, increasing with diameter (Fig. 5). When grouped by nominal diameter, a general linear trend for the mean values was observed but noted variability was present. The large standard deviations were expected given a brittle material such as ice, which has been documented in previous studies (Jones 1997; Kim and Keune 2007; Shazly et al. 2009). The sphere-to-sphere variability is likely due to several factors: impurities, trapped particulates, air bubble structures, and microfractures. These features represent possible locations where crack propagation can begin when the specimen is placed under a compressive load. As shown in Fig. 5, the field system was effective in capturing the mean linear trend but contained a measurement bias error. Applying a best-fit linear trend (not shown), the slopes from the two curves were found to be similar. This result was encouraging and indicated the field system was capable of providing a relative measure of the peak compressive force. It also identified the major source of error; which was the sampling limitations of the system, not the test method itself. The Instron UTM or any system using faster sampling rates is more effective in capturing the actual peak applied force at the point of fracture. The relative coarse sampling of the field device produced a smaller peak, as the true peak occurred between samples at a rate that the field system could not resolve. It is also noted that the Instron UTM (model 5581) sampling rate (500 Hz) used in this testing series was of lower temporal resolution than that typically used in research applications (1 kHz or greater), such that it too contained a low bias compared to the results of Swift (2013). Applying Eq. (1) to estimate the compressive stress, no linear trend with size was observed, and the mean bias error between the field measurement device and the Instron was found to be 0.12 mPa (Fig. 5).

Fig. 5.
Fig. 5.

Compressive force measurements (a) for Instron UTM and field measurement device of seltzer/tap water mixed ice spheres shown as a function of nominal diameter and (b) compressive stress measurements for each device shown as a function of nominal diameter.

Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0081.1

To investigate the bias error and the sampling limitation of the field device, several filters were applied to the raw Instron UTM compressive force time histories. Low-pass Butterworth filters with 50- and 100-Hz cutoff frequencies, and fully segmented block averages were used to downsample the raw Instron data. The 100-Hz cutoff frequency was found to yield the best results (Fig. 6). When computed, the filtered compressive stresses reduced the difference by an order of magnitude to 0.023 mPa. A two-sample Komolgorov–Smirnov test was applied to the field measurement device distribution and both filtered compressive stress distributions from the Instron UTM. In both cases, the null hypothesis of no difference between the field measurement device and filtered Instron UTM distributions was rejected. There is likely additional measurement error resulting from the nonconstant strain rate of the field measurement device. Further investigation using configurable sampling rates for Instron UTM testing, as well as different strain rates, is needed to build a relationship between compressive stress and the bias error introduced by the sampling rate. This relationship will allow for proper adjustment methods for field observations in order to be compared with historical studies and to build true stress–strain relationships. While we will present the observed compressive stress values measured in the field, caution should be used when comparing these values to those from historical studies of pure ice shapes using conventional laboratory measurement systems. To provide meaningful comparisons between laboratory ice spheres and natural hail, a significant number of pure ice spheres for several nominal diameters were tested using the field measurement device.

Fig. 6.
Fig. 6.

Peak compressive force data for filtered Instron (UTM) (black) and field measurement device for seltzer/tap water mix ice spheres shown as a function of nominal (laboratory) and maximum (field) diameter.

Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0081.1

5. Field measurements

A field measurement campaign was conducted in an effort to measure and test hailstones from thunderstorms in the Great Plains of the United States. Texas Tech University developed a similar analog compressive strength test device during the early 1980s but was unsuccessful in collecting field measurements of natural hail (M. Smith 2015, personal communication). It is believed that the field observations presented in this study represent the first quantitative measurements of the strength of natural hail. Data collected during the 2012–13 field program are used in this study, with a sample of over 900 tested hailstones collected on 14 operation days. The dataset contains observations from 22 different parent thunderstorms as summarized in Table 1, with a sample bias toward supercell thunderstorms (19 cases). Additional observations were made on four quasi-linear convective system (QLCS) events and two disorganized convective cases (based upon the classification scheme of Smith et al. 2012).

Table 1.

Summary statistics for each thunderstorm event sampled during the 2012–13 field phase.

Table 1.

a. Data

Multiple measurement teams were used in order to measure and test a large number of hailstones. Teams were responsible for collecting hail immediately following the passage of targeted thunderstorms. Hailstones were kept in insulated containers and then quickly photographed, measured, weighed, and tested for compressive strength. Typically, two to four stones were measured and tested within a 1-min period. The total measurement period was limited to 30 min. During this time, collected stones were kept in the insulated containers. Because of safety concerns, field teams remained outside the region of large hail until it was safe to proceed and begin collection efforts. This introduced a source of error from the melting of hail in addition to the rounding off of large protuberances; and it is accepted that these errors can cause some mass and diameter loss prior to collection. The effective rate in which natural stones may melt is likely a function of the total volume of hail, ambient air temperature, and the prevalence of liquid precipitation.

The influence of melting on compressive strength was investigated through laboratory testing at external temperatures of 24°C. Laboratory ice spheres (2.54-cm diameter) were randomly distributed within a 1 m2 grassy area with a concentration of approximately 50 spheres per unit area. Lag times of 10, 20, and 30 min were used. Ice spheres were collected and tested in a similar fashion to the method used in the field. While diameter and mass loss occurred, compressive stress values were variable, similar to that observed when pristine laboratory stones were tested. Any influence of melting was buried within this variability and no statistically significant trend was identified.

In the field, hailstones were collected from an approximate 25 m2 unobstructed area (usually a grassy surface) near each measurement team’s vehicle. Measurement teams made an effort to randomly select stones to obtain a representative size distribution or they attempted to measure all hail within the identified area. However, it is likely that some cases are biased toward larger diameters that did not melt before the teams arrived and hailstones that were strong enough to not fracture upon impact with the ground. Certain events also contain multiple measurement locations from within the swath of hail when time and proximity to other convection allowed (Table 1).

The maximum (x1) and minor (y) dimensions of each stone were measured and used in Eq. (2) to calculate an estimate of the cross-sectional area, which was then applied to Eq. (1) with the peak compressive force to calculate the compressive stress. For more conical-shaped stones, measurements were made in order to capture the longest dimension and the minor secondary diameter. This type of stone only comprises 5% of the dataset. For these particular stones, it is unclear how this may influence the compressive stress calculation since only one axis could be tested. Given the small percentage of these stones, it is unlikely that there was any quantifiable influence on the mean characteristics. Other stones exhibiting large protuberances (6% of the dataset) were also tested. The fracturing of the protuberances when tested was thought to possibly lead to a negative bias in the effective compressive force required to fracture the hailstone. When the raw compressive force time histories were examined, only 16 of these 54 stones were found to have exhibited a local maximum that was likely a result of the fracturing of a protuberance, while the bulk of the hailstone supported a much higher load. The data acquisition software was successful in not assigning the lower value but in capturing the larger load that the stone could physically support. It is unclear if hailstones with large protuberances may alter expected damage patterns.

The size of hailstones in the dataset ranged from 0.6 to 10.71 cm in maximum diameter. The diameter–mass relationship exhibited a power-law relation (Fig. 7). The least squares fit accounted for over 70% of the variance, and was similar to that shown by Dennis et al. (1971) and Heymsfield et al. (2014). The shape factor described by Knight (1986) was calculated for the dataset and was found to be in good agreement with past hail studies with a mean value of 0.6 (Knight 1986; Matson and Huggins 1980; Barge and Isaac 1973; Heymsfield 1978). The overall range was 0.22–1, and hailstones trended away from a purely spherical shape with size, which is similar to that found by Heymsfield et al. (2014), who used a much larger dataset (Fig. 7).

Fig. 7.
Fig. 7.

Mass–diameter relationship for measured hailstones from (a) 2012–13 and (b) shape factor (Knight 1986) shown as a function of major diameter.

Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0081.1

b. Evaluating the compressive strength of natural hail

The variability observed in natural hailstones exceeded the range of that observed in laboratory testing of both pure ice and modified spheres, with the force needed to fracture natural hailstones between 10 and 225 N (Fig. 8). Despite this large spread, the general trend in requiring a large applied force for larger and more massive stones was similar to that observed with both pure and modified ice spheres. When the peak compressive force was scaled to calculate compressive strength through the compressive stress quantity, no significant trend was present with hailstone size. The calculated compressive stress distribution ranged from 9.0 × 10−3 to a maximum of 7.5 mPa and was log-normally distributed (Fig. 9). All sampled thunderstorm events produced at least one hailstone that exceeded 1.0 mPa in compressive stress with variability in the distribution. The strongest hailstones most often were not the largest. Examining the hailstones greater than the 75th percentile of the compressive stress distribution for the complete field dataset, all fell below 3 cm in diameter. Unfortunately, the dataset is limited in sample size for hailstones larger than 3.5 cm, which would be a necessary comparison to investigate if smaller hailstones are indeed consistently stronger than giant hail (>5 cm). Currier and Schulson (1982) provided evidence that the tensile strength of ice decreases as grain size increases, and other crystalline materials (e.g., metals) also exhibit similar trends, as smaller grain sizes provide greater resistance to brittle failures (Smith and Hashemi 2006). When tested, natural hailstones often fractured into a large number of smaller pieces, consistent with a strain rate needed to produce a brittle failure of ice.

Fig. 8.
Fig. 8.

Compressive stress measurements shown as a function of major diameter for field observations and FM 4473 ice spheres. Error bars represent ±1 standard deviation from the mean.

Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0081.1

Fig. 9.
Fig. 9.

Probability distribution for compressive stress measurements from the 2012–13 field program.

Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0081.1

The mechanisms behind the large degree of variability observed could be related to the relationship between the strength and temperature of ice and how these are interplayed within the microphysical growth processes of hail. Haynes (1978) showed that the tensile and compressive strength of ice increases with lower ice formation temperatures. Between 0° and −40°C, the compressive strength of ice increased by nearly 4 times (Haynes 1978). With the typical hail growth zone falling between −10° and −30°C, one would expect some influence on hailstone strength from both the temperature profile within this region and residence time. Given an adequate sample size from parent thunderstorms, it may be possible to gain some insight into how hailstone strength may be influenced by the local storm-scale environment. While this analysis falls outside of the scope of the present study, it could help lead to forecast damage metrics for hail beyond that associated with maximum diameters and kinetic energies.

c. Ductile compression of natural hailstones

During the second year of the field program (2013), approximately 65 hailstones were measured that exhibited a ductile failure mode or were compressed into slush, despite a typical strain rate that should have produced a brittle failure. Unfortunately, this was not well documented during the first year of the program, and this information is not available for measurements made in 2012. A distinct difference was noted between stones that were ductile versus stones that were too slushy to effectively resolve a peak compressive force (<10 N). In one event (7A-2013) in the Oklahoma Panhandle, nearly all stones exhibited a ductile deformation, including stones larger than 2 cm in maximum diameter. These hailstones deformed and compressed without fracture, maintaining their shape even after the load was removed. It also appeared plausible that some stones may have even deformed on impact with the ground. Visible observations in the field and photographs of these stones suggest that nearly all were very opaque with little clear ice evident, possibly indicating low-density riming (Knight et al. 2008). Given that these types of stones were somewhat commonly observed, it supports the speculation of Knight et al. (2008) and Lozowski et al. (1991) that low-density-type stones could be more common than historical literature has been able to document.

6. Hailstone comparisons with laboratory pure ice spheres

Comparing field observations to laboratory ice spheres required additional testing of laboratory ice spheres using the field measurement system. Over 300 pure ice spheres were produced for each of the same diameters as those used in section 4 described above. Field observations of compressive stress were scaled by the mean and median of the laboratory ice sphere testing (0.61 and 0.54 mPa, respectively). This provided a relative measure of how different the strength of natural hail may be compared to that of ice spheres used in standardized material test applications. The histograms of the scaled field observations are shown in Fig. 10. For the two different scaling factors and their associated distributions, both the mean and median for each were found to be greater than 1 as a result of the large right tail to the distributions. This suggested that in general natural hail was slightly stronger than laboratory pure ice spheres produced under the FM 4473 standard. However, as shown in Fig. 10, a large portion of the scaled values fell below 1.0 and the probability of natural hail to exceed the mean (median) pure ice value was 48% (54%).

Fig. 10.
Fig. 10.

Histogram of the compressive stress of natural hailstones normalized by (a) the mean and (b) the median compressive stress of the compressive stress values obtained from pure ice sphere tests using the field measurement device.

Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0081.1

It was somewhat unexpected to find that natural hailstones, on average, were stronger than the average laboratory ice spheres; but, while examining the frequency distribution, a large portion of the field dataset had a lower compressive stress. There is a substantial amount of qualitative evidence showing hailstones rebounding off of very hard materials (e.g., concrete, asphalt). While it was not at all surprising to observe that some natural hailstones can exceed the average strength of laboratory ice spheres, the overall range of natural hailstone strength was unexpected. Impacts from pure ice spheres are often referred to as the “most severe”; however, the results presented here suggest that this may not be the case. One factor beyond the physical properties of natural hail that may help explain the results is that the manufacturing process outlined in the FM 4473 standard can lead to large and visible expansion cracks when the stones are extracted from the injection molds due to a thermal shock. King and Fletcher (1976) found that for a near-instantaneous temperature change of 15°C, the probability of cracking was near 50%. This increased to 100% for temperature changes greater than 20°C, which would be the case for any standardized tests where the ice spheres are removed from a freezer into ambient room temperature conditions. King and Fletcher (1976) also found that laboratory spheres remained intact following the thermal shock; which was also observed in the tests presented here. When these stones are compressed at high strain rates, crack propagation along these existing factures likely causes the stone to fail at a somewhat lower compressive force than if the shock-induced cracks did not exist. Despite initial fractures when the compressive force was applied, laboratory ice spheres often remained intact and maintained the ability to support an applied load. A similar process was observed at times during impact testing. During impact tests laboratory stones (manufactured in the same manner) would completely shatter, partially shatter, rebound, or essentially liquefy (T. Brown 2015, personal communication). This aspect is not well accounted for by our methodology and could be an underlying cause behind the results. It also could lead to biased impact performance ratings during product testing. Natural hailstones (when the compressive strength test was performed) often would fracture into a large number of pieces (excluding ductile compression failures) and very few remained intact, such that another test could have been performed on the remaining piece.

Microphysical processes most likely play a role as well, contributing to the differences between laboratory ice spheres and natural hail. While a significant amount of literature has been devoted toward understanding hail growth, there is little information on how these mechanisms may influence the material properties of hail. Factors such as the ratio of dry to wet growth (e.g., clear ice, opaque ice, and trapped bubble structures), the mean growth layer temperature, and other environmental conditions summarized by Knight and Knight (2001) will likely affect the compressive strength. Historical literature often discusses hardness as it relates to the density of hail (e.g., “hard and dense”). Macklin (1962) has shown that the density of ice will increase with droplet size, impact velocity, and the amount of supercooling on the surface of the stone, such that a power law can be used to describe the relationship. This suggests that as a hailstone grows and eventually descends to warmer environmental temperatures, the density of the accreted ice on the stone will be higher, and hence the density of the stones will also increase. Estimating the bulk density of natural hailstones using the maximum and minor diameters, and using an oblate–spheroid shape assumption yielded inaccurate estimates. Immersion methods such as those used by Knight and Heymsfield (1983) to obtain accurate volume measurements of hailstones were considered impractical in a field setting, and it was unclear whether the stones would then be contaminated for compressive strength testing. Peak compressive forces exhibited a clear trend with size and mass, such that one would expect a relationship between density and peak compressive force. When compressive stress is considered, no identifiable relationship was found with either size or mass. Thus, it is unclear whether the compressive stress, which is a more appropriate measure of the strength of a hailstone, will exhibit any notable relationship with bulk density.

7. Summary and discussion

The goals of this study were to develop, test, and validate a cost-effective instrumentation system to evaluate the hardness property of hail through in situ measurements of compressive strength. Despite the qualitative discussion of the hardness of hailstones throughout historical literature, it is believed that this is the first known attempt to physically measure this property. Compressive stress provided a measurement quantity required to provide a relative comparison with typical laboratory test methodologies. However, given the documented sampling bias, the magnitudes of compressive stress cannot be directly compared to those of other materials or typical laboratory measurement equipment without accounting for these differences. Additional properties, such as tensile strength, would add value to the results presented here, but those properties are difficult to measure in a field setting.

During the 2-yr program, over 900 natural hailstones were measured, tested, and photographically cataloged. The mean compressive strength was found to be higher than that observed in pure ice spheres; however, a large degree of variability was present. Natural hailstones tended to fracture into many pieces, while laboratory ice spheres often would fracture along existing expansion cracks and maintain the ability to support a compressive load. Individual thunderstorm events often produced a large spread of both hard and soft hailstones, with the hardest not necessarily representing the larger diameter stones within the given distribution. Cases were observed that produced nearly all soft stones with peak compressive stress values falling well below that of laboratory ice spheres. Larger sample sizes from parent thunderstorms are needed to extract information on how the environmental thermodynamic and kinematic profile may influence the hardness of hailstones. Proximity soundings from the inflow region of targeted thunderstorms could help in this effort. It should be noted that the dataset presented here is primarily representative of a supercell mode. Approximately 9% of the sampled hailstones were either too slushy to test (peak compressive force < 10 N) or exhibited a ductile compression. While these stones were present in most events, they represented only a small fraction of the distribution of measured hail. It is hypothesized that the ability of these types of stones to absorb energy at impact through deformation may lessen the degree of damage and that the importance of these types of hailstones in engineering applications may be minimal. As the field program continues, more effort will be made to document these types of stones and their characteristics.

The developed field measurement device succeeded in collecting a pilot dataset on the hardness property of hail. It is not intended to represent a replacement for more precise laboratory equipment, such as UTMs, but it was effective in bridging an existing measurement gap. While we present no evidence to suggest the use of ice spheres in standardized impact testing is not adequate in representing natural hail, the variability in the strength and behavior of laboratory ice spheres argues for large sample sizes in order to properly assess the impact resistance of a given material. In addition, laboratory impacts using ice spheres are not necessarily representative of the most severe impact when solely considering strength. Understanding the characteristics of natural hail is vital to improving standardized material test practices, which will help mitigate the large financial impacts of hailstorms through improved standardized test methods. Meteorologically, these types of datasets can be used for tuning and validating dual-polarimetric hail detection products (e.g., Kumjian et al. 2014), and for developing forecasting applications for the hail hazard as convection-resolving numerical models continue to improve (Gilmore et al. 2004; van den Heever and Cotton 2004; Bryan and Morrison 2012; Dennis and Kumjian 2014; Morrison et al. 2015).

Acknowledgments

Funding for the field program, laboratory testing, and analysis efforts was provided by IBHS and its member institutions. The authors wish to acknowledge D. Scott Robinett and Dr. Tim Reinhold for helping develop the initial concept for the test device. Thanks are extended to the IBHS and State Farm personnel who participated in the safe collection of the measurements presented in this study. Thanks are also extended to the State Farm Technology Research and Innovation Laboratory for performing laboratory ice sphere testing for use in this study. The authors wish to acknowledge Dr. Andrew Heymsfield and Dr. Milton Smith for their insights and helpful suggestions on an earlier version of this manuscript, and two anonymous reviewers for their commentary, which improved this work.

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