# Review of Impact Factors of the Velocity of Large Hailstones for Laboratory Hail Impact Testing Consideration

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Hailstone Properties in Current Standard Testing Procedures

## 3. The Terminal Velocity of Hailstones

_{t}for a given hailstone, an equation derived from the net force that, based on the drag force, acts on a solid object can be used.

_{a}the air density, A describes the cross-sectional area of the hailstone normal to the airflow, and denotes C

_{d}the drag coefficient [30]. An assumption that has often been made for hailstones is a spherical shape. If this assumption is applied to the equation above, the expression for the terminal velocity of such a hailstone becomes

_{h}[30,31,32,33]. When the terminal velocity of hailstones is discussed in theory, this equation is often calculated and used. It is a theoretical model that only holds if a variety of assumptions are fulfilled. Many of the properties that have an impact on the terminal velocity of the hailstone, such as size, shape, density, and other relevant factors, can have a wide range. The following sections closely examine these factors and how they influence the actual velocity obtained by the equation.

#### 3.1. Density of Hailstones

^{−3}was observed as the “mean density of conical graupel” [36]. Earlier observations found densities for soft graupel ranging from 0.5 to 0.7 g cm

^{−3}[37]. Densities of 0.8 to 0.9 g cm

^{−3}have been measured [38]. A slightly closer range was found for the mean density values of hailstones between 0.82 and 0.87 g cm

^{−3}[34]. These are all less than the density of pure ice. Due to its open molecular structure, the density of pure ice at 0 °C is 0.917 g cm

^{−3}[39,40]. Looking at larger hailstones with a more devastating effect on structures, it was found that the mean density is often closer to 0.9 g cm

^{−3}[20]. Some even mention that large, heavy hailstones have a density close to that of pure ice [21]. Three-dimensional scanning technology, in recent research, supports a density close to pure ice for larger hailstones [41]. The density of hailstones is an essential factor for the investigation of the terminal velocity of hailstones. Because of the large variety of properties, the exclusive use of diameter is a limited approach to predicting the terminal velocity. For material testing with a focus on larger, more devastating hailstones, the assumption of density close to pure ice is often used.

#### 3.2. The Drag Coefficient and Reynolds Number

^{2}or as the frontal area (1/4)πd

^{2}” [47], and it is proportional to this reference area, the square of the velocity, and the air density [47]. The drag coefficient and the Reynolds number are dependent on each other [48,49]. There is “a trend towards a decreasing drag coefficient with an increasing Reynolds number” [30]. The drag coefficient, being part of the equation for the terminal velocity of a hailstone, becomes problematic when the drag coefficient is assumed to be specific to a single hailstone [19]. The drag coefficient usually ranges between 0.4 and 0.6 [50], or even from 0.45 up to 0.8 [51], depending on the size and the surface roughness of the given hailstone. A good fit over a considerable size of hailstones for the drag coefficient was found to be a value of 0.6, especially if hailstones are approximately spherical [52,53].

_{h}= 917 kg/m

^{3}. For the air, a density of ρ

_{a}= 1.225 kg/m

^{3}, and the acceleration due to gravity is g = 9.81 m/s

^{2}is used.

#### 3.3. The Spherical Shape of Hailstones

#### 3.4. The Effect of Air Density

^{3}at 260 K (−13.15 °C) and 1.089 kg/m

^{3}at 320 K (46.85 °C) [67]. The air density is also affected by the altitude. There is a decrease in air density with an increasing altitude [68,69]. The decrease in the global-mean density by altitude is approximately exponential, with a surface density at sea level of about 1.2 kg/m

^{3}[69]. This means that with an increase in altitude, the terminal velocity of hailstones also increases [70] if all other factors were to be the same.

^{3}and 1.45 kg/m

^{3}based on Equation (2) for hailstones with diameters of 2 cm to 10 cm in 2 cm increments, to illustrate the influence of this factor on the velocity and therefore its kinetic energy. For the other values that are involved in the terminal velocity equation, the density of the hailstone is assumed at ρ

_{h}= 917 kg/m

^{3}, the drag coefficient is assumed to be CD = 0.60, and the acceleration due to gravity is g = 9.81 m/s

^{2}.

^{−3}to 1.45 kg m

^{−3}. It again illustrates the significant influence of a factor involved in the calculation of the terminal velocity of hailstones.

#### 3.5. Empirical Models to Determine Terminal Velocity

^{0.8}for diameter D in cm for hailstones up to a size of 8.00 cm, where v is in m/s [73]. This is a model that gives values close to another equation, which is v = 1.4 × D

^{0.8}[74] with D in mm for this equation. Significantly lower terminal velocities come from the equations found by other research groups as they looked at hail with a diameter of around 2.00 to 3.00 cm (0.79 to 1.18 inch). One study noted hailstones as large as roughly 2.50 cm (0.98 inches) in diameter and used the expression v = 11.45 × D

^{0.5}, where the diameter D is to be in cm [30]. The other group determined the expression v = 8.445 × D

^{0.553}(D in cm) specifically fitted for observations of hailstones smaller than a diameter of 2.00 cm (0.79 inches) [75]. A recent corrigendum based on Insurance Institute for Business and Home Safety (IBHS) measurements derives the terminal velocity of hail with v = 7.6 × D

^{0.89}for diameters less than 1.50 cm and v = 8.4 × D

^{0.67}for diameters larger than 1.50 cm [58]. However, another research study used v = 15 × D

^{0.5}(with D in cm) for spheroidal bodies as an empirical formula for the terminal velocity of hailstones [53]. This equation is very close to the one used nowadays by ASTM International standards. To determine the resistance of solar collector covers to hail, they use v = 14.04 × D

^{0.5}(with D in cm) [13], and to determine the resistance of photovoltaic modules to hail, they use v = 4.44 × D

^{0.5}(for D in mm) [14]. While these two equations from ASTM International use cm and mm for the diameter D, respectively, it is important to note that v = 14.04 × D

_{[cm]}

^{0.5}= 4.44 × D

_{[mm]}

^{0.5}. Figure 3 summarizes the several models discussed previously and shows the terminal velocity of hailstones in m/s for specific diameters in cm.

## 4. Hailstone Velocity in Combination with Wind

_{r}of hailstones that is important to determine the kinetic energy upon impact. The accompanying wind during a hailstorm has a direct influence on the total velocity of the hailstone [23] and makes hailfall combined with wind the more damaging type of hailfalls [63]. It is also known that horizontal wind can increase the hailstone velocity above its terminal velocity, which results in a higher impact kinetic energy [8].

_{r}) to a horizontal wind speed component (v

_{w}) component as well as the terminal velocity of a given hailstone (v

_{t}).

_{R}. However, if the wind is from the north, the hailstone may have only a glancing impact. A conservative approach in hail impact testing is to take a worst-case approach.

_{h}= 917 kg/m

^{3}, the drag coefficient is assumed to be CD = 0.60, for the air, a density of ρ

_{a}= 1.225 kg/m

^{3}is used, and the acceleration due to gravity is g = 9.81 m/s

^{2}.

_{R}of the different sized hailstones for horizontal wind speeds of 0 m/s, 15 m/s, 20 m/s, and 30 m/s and downdraft speeds of 0 m/s, 5 m/s, and 10 m/s. The resulting hailstone speed combines the terminal velocity v

_{t}and both the horizontal wind speed v

_{w}and downdraft speed v

_{d}using the following equation

## 5. Conclusions

_{T}. Overall, the review shows a great deal of variability in hail events, thus elucidating the varied and often conflicting results and formulations in this field of study.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Fraile, R.; Berthet, C.; Dessens, J.; Sánchez, J.L. Return periods of severe hailfalls computed from hailpad data. Atmos. Res.
**2003**, 67–68, 189–202. [Google Scholar] [CrossRef] - Vinet, F. Climatology of hail in France. Atmos. Res.
**2001**, 56, 309–323. [Google Scholar] [CrossRef] - Webb, J.; Elsom, D.M.; Reynolds, D.J. Climatology of severe hailstorms in Great Britain. Atmos. Res.
**2001**, 56, 291–308. [Google Scholar] [CrossRef] - Lozowski, E.P.; Strong, G.S. On the Calibration of Hailpads. J. Appl. Meteorol. Clim.
**1978**, 17, 521–528. [Google Scholar] [CrossRef][Green Version] - World Meteorological Organization (WMO). Technical Regulations: Volume II—Meteorological Service for International Air Navigation, 2018th ed.; World Meteorological Organization: Geneva, Switzerland, 2018. [Google Scholar]
- National Weather Service. Severe Weather Definitions. n. d. Available online: https://www.weather.gov/bgm/severedefinitions (accessed on 3 August 2020).
- Kumjian, M.R.; Gutierrez, R.; Soderholm, J.S.; Nesbitt, S.W.; Maldonado, P.; Luna, L.M.; Marquis, J.; Bowley, K.A.; Imaz, M.A.; Salio, P. Gargantuan Hail in Argentina. Bull. Am. Meteorol. Soc.
**2020**. [Google Scholar] [CrossRef][Green Version] - Schuster, S.S.; Blong, R.J.; Leigh, R.J.; McAneney, K.J. Characteristics of the 14 April 1999 Sydney hailstorm based on ground observations, weather radar, insurance data and emergency calls. Nat. Hazards Earth Syst. Sci.
**2005**, 5, 613–620. [Google Scholar] [CrossRef][Green Version] - Noon, R. Forensic Engineering Investigation; CRC Press: Boca Raton, FL, USA, 2001. [Google Scholar]
- Greenfeld, S.H. Hail Resistance of Roofing Products; Building Research Division, US Institute for Applied Technology: Washington, DC, USA, 1969. [Google Scholar]
- Lucy, R.R.; Petty, S.E. Hail Damage Assessments to Low-Sloped Roof Systems. In Forensic Engineering: Damage Assessments for Residential and Commercial Structures; Petty, S.E., Ed.; CRC Press: Boca Raton, FL, USA, 2013; pp. 119–159. [Google Scholar]
- Olson, R.; Juntikka, R.; Asp, L.E. High Velocity Hail Impact on Composite Laminates—Modelling and Testing. In Dynamic Failure of Composite and Sandwich Structures; Abrate, S., Castanié, B., Rajapakse, Y.D.S., Eds.; Springer: Dordrecht, The Netherlands, 2013; pp. 393–426. [Google Scholar]
- E44 Committee. Practice for Determining Resistance of Solar Collector Covers to Hail by Impact with Propelled Ice Balls 2015; ASTM International: West Conshohocken, PA, USA, 2015. [Google Scholar]
- E44 Committee. Test Method for Determining Resistance of Photovoltaic Modules to Hail by Impact with Propelled Ice Balls 2019; ASTM International: West Conshohocken, PA, USA, 2019. [Google Scholar] [CrossRef]
- F07 Committee. Test Method for Hail Impact Resistance of Aerospace Transparent Enclosures; West ASTM International: West Conshohocken, PA, USA, 2005. [Google Scholar] [CrossRef]
- FM Approvals. Specification Test Standard for Impact Resistance Testing of Rigid Roofing Materials by Impacting with Freezer Ice Balls July 2005; FM Approvals: West Gloucester, RI, USA, 2005. [Google Scholar]
- UL Standard. Standard for Impact Resistance of Prepared Roof Covering Materials 1/25/2010. Available online: https://standardscatalog.ul.com/ProductDetail.aspx?productId=UL2218 (accessed on 10 December 2020).
- Schleusener, R.A.; Jennings, P.C. An Energy Method for Relative Estimates of Hail Intensity. Bull. Am. Meteorol. Soc.
**1960**, 41, 372–376. [Google Scholar] [CrossRef] - Long, A.B.; Matson, R.J.; Crow, E.L. The Hailpad: Construction and Materials, Data Reduction, and Calibration; Citeseer: Boulder, CO, USA, 1979. [Google Scholar]
- Browning, K.A.; Ludlam, F.H.; Macklin, W.C. The density and structure of hailstones. Q. J. R. Met. Soc.
**1963**, 89, 75–84. [Google Scholar] [CrossRef] - Vittori, O.; di Caporiacco, G. The density of hailstones. Nubila
**1959**, 2, 51–57. [Google Scholar] - Insurance Institute for Business & Home Safety. Impact Resistance Test Protocol for Asphalt Shingles. 2019. Available online: https://ibhs.org/wp-content/uploads/2019/06/ibhs-impact-resistance-test-protocol-for-asphalt-shingles.pdf (accessed on 24 October 2020).
- Laurie, J.A.P. Hail and Its Effects on Buildings; Council for Scientific and Industrial Research: Pretoria, South Africa, 1960. [Google Scholar]
- Petty, S.E. Synthetic Storm Damage (Fraud) to Roof Surfaces. In Forensic Engineering: Damage Assessments for Residential and Commercial Structures; Petty, S.E., Ed.; CRC Press: Boca Raton, FL, USA, 2013; pp. 161–182. [Google Scholar]
- List, R. Zur Aerodynamik von Hagelkörnern. ZAMP
**1959**, 10, 143–159. [Google Scholar] [CrossRef] - Decker, F.W.; Calvin, L.D. Hailfall of 10 September 1959 Near Medford, Oregon. Bull. Am. Meteorol. Soc.
**1961**, 42, 475–481. [Google Scholar] [CrossRef][Green Version] - Bilham, E.G.; Relf, E.F. The dynamics of large hailstones. Q. J. R. Met. Soc.
**1937**, 63, 49–62. [Google Scholar] [CrossRef] - Mandal, G.; Kumar, A.; Sharma, D.C.; Kumar, H. Comparative Analysis of Different Air Density Equations. MAPAN
**2013**, 28, 51–62. [Google Scholar] [CrossRef] - Böhm, H.P. A General Equation for the Terminal Fall Speed of Solid Hydrometeors. J. Atmos. Sci.
**1989**, 46, 2419–2427. [Google Scholar] [CrossRef] - Matson, R.J.; Huggins, A.W. The Direct Measurement of the Sizes, Shapes and Kinematics of Falling Hailstones. J. Atmos. Sci.
**1980**, 37, 1107–1125. [Google Scholar] [CrossRef][Green Version] - Knight, C.A.; Knight, N.C. Hailstorms. In Severe Convective Storms; Doswell, C.A., Ed.; American Meteorological Society: Boston, MA, USA, 2001; pp. 223–254. [Google Scholar] [CrossRef]
- Wisner, C.; Orville, H.D.; Myers, C. A Numerical Model of a Hail-Bearing Cloud. J. Atmos. Sci.
**1972**, 29, 1160–1181. [Google Scholar] [CrossRef] - List, R. Properties and Growth of Hailstones. In Thunderstorm Morphology and Dynamics; Kessler, E., Ed.; University of Oklahoma Press: Washington, DC, USA, 1982; pp. 409–445. [Google Scholar]
- Prodi, F. Measurements of Local Density in Artificial and Natural Hailstones. J. Appl. Meteorol.
**1970**, 9, 903–910. [Google Scholar] [CrossRef][Green Version] - Heymsfield, A.J. A Technique for Investigating Graupel and Hail Development. J. Clim. Appl. Meteorol.
**1983**, 22, 1143–1160. [Google Scholar] [CrossRef] - Heymsfield, A.J. The Characteristics of Graupel Particles in Northeastern Colorado Cumulus Congestus Clouds. J. Atmos. Sci.
**1978**, 35, 284–295. [Google Scholar] [CrossRef][Green Version] - List, R. Kennzeichen atmosphärischer Eispartikeln: 1. Teil. J. Appl. Math. Phys. (ZAMP)
**1958**, 9, 180–192. [Google Scholar] [CrossRef] - List, R. Kennzeichen atmosphärischer Eispartikeln: 2. Teil. J. Appl. Math. Phys. (ZAMP)
**1958**, 9, 217–234. [Google Scholar] [CrossRef] - Olovsson, I. Snow, Ice and Other Wonders of Water: A Tribute to the Hydrogen Bond; World Scientific: New Jersey, NJ, USA, 2016. [Google Scholar]
- Allan, H.H. Properties of ice and supercooled water. In CRC Handbook of Chemistry and Physics: A Ready-Reference Book of Chemical and Physical Data, 95th ed.; Haynes, W.M., Ed.; CRC Press: Boca Raton, FL, USA, 2014; pp. 6–12. [Google Scholar]
- Giammanco, I.M.; Maiden, B.R.; Estes, H.E.; Brown-Giammanco, T.M. Using 3D Laser Scanning Technology to Create Digital Models of Hailstones. Bull. Am. Meteorol. Soc.
**2017**, 98, 1341–1347. [Google Scholar] [CrossRef] - Knight, C.A.; Schlatter, P.T.; Schlatter, T.W. An Unusual Hailstorm on 24 June 2006 in Boulder, Colorado. Part II: Low-Density Growth of Hail. Mon. Weather. Rev.
**2008**, 136, 2833–2848. [Google Scholar] [CrossRef] - Giammanco, I.M.; Brown, T.M.; Grant, R.G.; Dewey, D.L.; Hodel, J.D.; Stumpf, R.A. Evaluating the Hardness Characteristics of Hail through Compressive Strength Measurements. J. Atmos. Ocean. Technol.
**2015**. [Google Scholar] [CrossRef] - Battan, L.J.; Wilson, D.S. “Hail” on a Mountain in Arizona. J. Appl. Meteorol. (1962–1982)
**1969**, 8, 592–595. [Google Scholar] [CrossRef][Green Version] - Knight, C.A.; Knight, N.C. Quenched, Spongy Hail. J. Atmos. Sci.
**1973**, 30, 1665–1671. [Google Scholar] [CrossRef][Green Version] - Morgan, G.M.; Towery, N.G. On the Role of Strong Winds in Damage to Crops by Hail and Its Estimation with a Simple Instrument. J. Appl. Meteorol.
**1976**, 15, 891–898. [Google Scholar] [CrossRef][Green Version] - Torenbeek, E.; Wittenberg, H. Flight Physics: Essentials of Aeronautical Disciplines and techNology, with Historical Notes; Springer: Dordrecht, The Netherlands; London, UK, 2009. [Google Scholar]
- Abraham, F.F. Functional Dependence of Drag Coefficient of a Sphere on Reynolds Number. Phys. Fluids
**1970**, 13, 2194. [Google Scholar] [CrossRef] - Heymsfield, A.; Szakáll, M.; Jost, A.; Giammanco, I.; Wright, R. A Comprehensive Observational Study of Graupel and Hail Terminal Velocity, Mass Flux, and Kinetic Energy. J. Atmos. Sci.
**2018**, 75, 3861–3885. [Google Scholar] [CrossRef] - Magono, C. Thunderstorms; Elsevier: Amsterdam, The Netherlands; Oxford, UK, 1980. [Google Scholar]
- Macklin, W.C.; Ludlam, F.H. The fallspeeds of hailstones. Q. J R. Met. Soc.
**1961**, 87, 72–81. [Google Scholar] [CrossRef] - Dennis, A.S. Weather Modification by Cloud Seeding; Academic Press: New York, NY, USA, 1980. [Google Scholar]
- Gokhale, N.R. Hailstorms and Hailstone Growth, 1st ed.; State University of New York Press: Albany, NY, USA, 1975. [Google Scholar]
- Theis, A.; Borrmann, S.; Mitra, S.K.; Heymsfield, A.J.; Szakáll, M. A Wind Tunnel Investigation into the Aerodynamics of Lobed Hailstones. Atmosphere
**2020**, 11, 494. [Google Scholar] [CrossRef] - Wang, P.K.; Chueh, C.-C.; Wang, C.-K. A numerical study of flow fields of lobed hailstones falling in air. Atmos. Researc.
**2015**, 160, 1–14. [Google Scholar] [CrossRef] - Wang, P.K.; Chueh, C.-C. A numerical study on the ventilation coefficients of falling lobed hailstones. Atmos. Res.
**2020**, 234, 104737. [Google Scholar] [CrossRef] - Heymsfield, A.; Wright, R. Graupel and Hail Terminal Velocities: Does a “Supercritical” Reynolds Number Apply? J. Atmos. Sci.
**2014**, 71, 3392–3403. [Google Scholar] [CrossRef] - Heymsfield, A.; Szakáll, M.; Jost, A.; Giammanco, I.; Wright, R.; Brimelow, J. Corrigendum. J. Atmos. Sci.
**2020**, 77, 405–412. [Google Scholar] [CrossRef] - Heymsfield, A.J.; Giammanco, I.M.; Wright, R. Terminal velocities and kinetic energies of natural hailstones. Geophys. Res. Lett.
**2014**, 41, 8666–8672. [Google Scholar] [CrossRef] - Cheng, L.; English, M.; Wong, R. Hailstone Size Distributions and Their Relationship to Storm Thermodynamics. J. Clim. Appl. Meteorol.
**1985**, 24, 1059–1067. [Google Scholar] [CrossRef][Green Version] - Huggins, A.; Crow, E.L.; Long, A.B. Errors in Hailpad Data Reduction. J. Appl. Meteorol.
**1980**, 19, 733–747. [Google Scholar] - Koontz, J.D. What Are the Effects of Hail on Residential Roofing Products? Available online: https://www.semanticscholar.org/paper/What-are-the-effects-of-hail-on-residential-roofing-Koontz/e4d3f6c1a57462efdd39f5aa1ec740bf2809208e (accessed on 10 December 2020).
- Morgan, G.M., Jr.; Summers, P.W. Hailfall and Hailstorm Characteristics. In Thunderstorm Morphology and Dynamics; Kessler, E., Ed.; University of Oklahoma Press: Washington, DC, USA, 1982; pp. 363–408. [Google Scholar]
- Gessler, S.E.; Petty, S.E. Hail Fundamentals and General Hail-Strike Damage Assessment Methodology. In Forensic Engineering: Damage Assessments for Residential and Commercial Structures; Petty, S.E., Ed.; CRC Press: Boca Raton, FL, USA, 2013; pp. 23–67. [Google Scholar]
- Knight, N.C. Hailstone Shape Factor and Its Relation to Radar Interpretation of Hail. J. Clim. Appl. Meteorol.
**1986**, 25, 1956–1958. [Google Scholar] [CrossRef][Green Version] - Picard, A.; Davis, R.S.; Gläser, M.; Fujii, K. Revised formula for the density of moist air (CIPM-2007). Metrologia
**2008**, 45, 149–155. [Google Scholar] [CrossRef] - Lemmon, E.W. Thermophysical Properties of Air. In CRC Handbook of Chemistry and Physics: A Ready-Reference Book of Chemical and Physical Data, 95th ed.; Haynes, W.M., Ed.; CRC Press: Boca Raton, FL, USA, 2014; pp. 6–15, 6–20. [Google Scholar]
- Benson, T. Earth Atmosphere Model. 2014. Available online: https://www.grc.nasa.gov/WWW/K-12/rocket/atmosmet.html (accessed on 29 May 2019).
- Salby, M.L. Fundamentals of Atmospheric Physics; Academic Press: San Diego, CA, USA; London, UK, 1995. [Google Scholar]
- DvS, R. A Giant Hailstone from Kansas in Free Fall. J. Appl. Meteorol.
**1972**, 11, 1008–1011. [Google Scholar] - U.S. Department of the Interior Geological Survey. Elevations and Distances in the United States; U.S. Department of the Interior Geological Survey: Washington, DC, USA, 2001.
- Auer, A.H., Jr. Distribution of Graupel and Hail with Size. Mon. Weather Rev.
**1972**, 100, 325–328. [Google Scholar] [CrossRef] - Pruppacher, H.R.; Klett, J.D. Microphysics of Clouds and Precipitation; Springer: Dordrecht, The Netherlands, 2010. [Google Scholar]
- Geerts, B. Fall Speed of Hydrometeors. Available online: http://www-das.uwyo.edu/~geerts/cwx/notes/chap09/hydrometeor.html (accessed on 10 May 2019).
- Knight, N.C.; Heymsfield, A.J. Measurement and Interpretation of Hailstone Density and Terminal Velocity. J. Atmos. Sci.
**1983**, 40, 1510–1516. [Google Scholar] [CrossRef][Green Version] - Jenkins, D.R.; Mathey, R.G. Hail Impact Testing Procedure for Solar Collector Cover. STIN
**1982**, 83, 22841. [Google Scholar] - Changnon, S.A. Hail sensing and small-scale variability of windblown hail. J. Weather Modif.
**1973**, 5, 30–42. [Google Scholar] - Sioutas, M.; Meaden, T.; Webb, J.D. Hail frequency, distribution and intensity in Northern Greece. Atmos. Res.
**2009**, 93, 526–533. [Google Scholar] [CrossRef] - Browning, K.A. The Structure and Mechanisms of Hailstorms. In Hail: A Review of Hail Science and Hail Suppression; Foote, G.B., Foote, G.B., Knight, C.A., Eds.; American Meteorological Society: Boston, MA, USA, 1977; pp. 1–43. [Google Scholar]
- Strauch, R.G.; Merrem, F.H. Structure of an Evolving Hailstorm, Part III: Internal Structure from Doppler. Radar. Mon. Weather Rev.
**1976**, 104, 588–595. [Google Scholar] [CrossRef][Green Version] - Fujita, T.T. The Downburst: Microburst and Macroburst; The University of Chicago: Chicago, IL, USA, 1985. [Google Scholar]
- Wilson, J.W.; Wakimoto, R.M. The Discovery of the Downburst: T. T. Fujita’s Contribution. Bull. Am. Meteorol. Soc.
**2001**, 82, 49–62. [Google Scholar] [CrossRef] - Microburst. In An Illustrated Dictionary of Aviation, 1st ed.; Kumar, B.; de Remer, D.; Marshall, D.M. (Eds.) McGraw-Hill: New York, NY, USA, 2004. [Google Scholar]
- Williams, E.; Boldi, B.; Matlin, A.; Weber, M.; Hodanish, S.; Sharp, D.; Goodman, S.; Raghavan, R.; Buechler, D. The behavior of total lightning activity in severe Florida thunderstorms. Atmos. Res.
**1999**, 51, 245–265. [Google Scholar] [CrossRef][Green Version] - Savory, E.; Parke, G.A.; Zeinoddini, M.; Toy, N.; Disney, P. Modelling of tornado and microburst-induced wind loading and failure of a lattice transmission tower. Eng. Struct.
**2001**, 23, 365–375. [Google Scholar] [CrossRef] - Encyclopædia Britannica. Microburst. 2019. Available online: https://academic-eb-com.lib-e2.lib.ttu.edu/levels/collegiate/article/microburst/52495 (accessed on 15 June 2019).
- Holmes, J.; Oliver, S. An empirical model of a downburst. Eng. Struct.
**2000**, 22, 1167–1172. [Google Scholar] [CrossRef] - Kim, J.; Hangan, H. Numerical simulations of impinging jets with application to downbursts. J. Wind Eng. Ind. Aerodyn.
**2007**, 95, 279–298. [Google Scholar] [CrossRef] - Mason, M.S.; Wood, G.S.; Fletcher, D.F. Numerical simulation of downburst winds. J. Wind Eng. Ind. Aerodyn.
**2009**, 97, 523–539. [Google Scholar] [CrossRef] - Gunter, W.S.; Schroeder, J.L. High-resolution full-scale measurements of thunderstorm outflow winds. J. Wind Eng. Ind. Aerodyn.
**2015**, 138, 13–26. [Google Scholar] [CrossRef] - Choi, E.C.; Hidayat, F.A. Gust factors for thunderstorm and non-thunderstorm winds. J. Wind Eng. Ind. Aerodyn.
**2002**, 90, 1683–1696. [Google Scholar] [CrossRef] - Lombardo, F.T.; Smith, D.A.; Schroeder, J.L.; Mehta, K.C. Thunderstorm characteristics of importance to wind engineering. J. Wind Eng. Ind. Aerodyn.
**2014**, 125, 121–132. [Google Scholar] [CrossRef]

**Figure 1.**Relationship between spherical hailstone diameter and terminal velocity for different drag coefficients.

**Figure 2.**Terminal velocity of different sized hailstones (diameter in cm) at varying air densities.

**Figure 4.**Relationship between the resultant velocity (v

_{r}), wind speed (v

_{w}), and terminal hailstone velocity (v

_{t}).

**Table 1.**Effect of vertical and horizontal wind speed on the resulting velocity compared to the terminal velocity of different sized hailstone.

Hailstone Diameter (cm) | Vertical Wind Speed (m/s) | Horizontal Wind Speed (m/s) | Resulting Hailstone Velocity (m/s) | Increase Compared to Terminal Velocity (%) |
---|---|---|---|---|

2 | 0 | 0 | 18.07 | 0 |

15 | 23.48 | 30 | ||

20 | 26.95 | 49 | ||

30 | 35.02 | 94 | ||

5 | 0 | 23.07 | 28 | |

15 | 27.51 | 52 | ||

20 | 30.53 | 69 | ||

30 | 37.84 | 109 | ||

10 | 0 | 28.07 | 55 | |

15 | 31.82 | 76 | ||

20 | 34.46 | 91 | ||

30 | 41.08 | 127 | ||

6 | 0 | 0 | 31.29 | 0 |

15 | 34.70 | 11 | ||

20 | 37.14 | 19 | ||

30 | 43.35 | 39 | ||

5 | 0 | 36.29 | 16 | |

15 | 39.27 | 25 | ||

20 | 41.44 | 32 | ||

30 | 47.09 | 50 | ||

10 | 0 | 41.29 | 32 | |

15 | 43.93 | 40 | ||

20 | 45.88 | 47 | ||

30 | 51.04 | 63 | ||

10 | 0 | 0 | 40.40 | 0 |

15 | 43.09 | 7 | ||

20 | 45.08 | 12 | ||

30 | 50.32 | 25 | ||

5 | 0 | 45.40 | 12 | |

15 | 47.81 | 18 | ||

20 | 49.61 | 23 | ||

30 | 54.41 | 35 | ||

10 | 0 | 50.40 | 25 | |

15 | 52.58 | 30 | ||

20 | 54.22 | 34 | ||

30 | 58.65 | 45 |

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## Share and Cite

**MDPI and ACS Style**

Dieling, C.; Smith, M.; Beruvides, M.
Review of Impact Factors of the Velocity of Large Hailstones for Laboratory Hail Impact Testing Consideration. *Geosciences* **2020**, *10*, 500.
https://doi.org/10.3390/geosciences10120500

**AMA Style**

Dieling C, Smith M, Beruvides M.
Review of Impact Factors of the Velocity of Large Hailstones for Laboratory Hail Impact Testing Consideration. *Geosciences*. 2020; 10(12):500.
https://doi.org/10.3390/geosciences10120500

**Chicago/Turabian Style**

Dieling, Christian, Milton Smith, and Mario Beruvides.
2020. "Review of Impact Factors of the Velocity of Large Hailstones for Laboratory Hail Impact Testing Consideration" *Geosciences* 10, no. 12: 500.
https://doi.org/10.3390/geosciences10120500