Variations in the Free-Fall Velocities of Hail Jim D. Koontz, RRC, PE Jim D. Koontz & Associates, Inc. 3120 North Grimes, Hobbs, NM 88240 Phone: 575-392-7676 • E-mail: jim@jdkoontz.com RC I I n t e r n a t i o n a l C o n v e n t i o n a n d T r a d e S h ow • Ma rc h 1 4 – 1 9 , 2 0 1 9 K o o n t z • 1 Abstract Hailstorms account for billions of dollars of damage a year to roofing systems. Mitigating this damage is dependent on properly understanding the effect of hail’s impact on roofing systems. Prior research on this issue has depended primarily on data from the National Bureau of Standards (NBS) document, NBS 23, from August 1969, authored by Sidney Greenfeld. The NBS published data stating the free-fall velocities of spherical ice of various sizes with an assumed density of .89 to .91. Resultant kinetic energy was calculated for each of these sizes. This research was based on theoretical data generated by J.A.P. Laurie of the National Building Research Institute in Pretoria, South Africa. The NBS research assumes spherical ice and does not consider other relevant factors such as shape, surface area, air temperature, humidity, and barometric pressure. To study the effect of these variations in meteorological factors and physical properties of hail, a vertical wind tunnel has been utilized by Jim D. Koontz & Associates. Ice spheres with different shapes, surface areas, and densities have been tested in a vertical wind tunnel with variations in other relevant meteorological factors. This study measures the true free-fall velocity and resultant kinetic energy generated by variations in hail. The information produced will be compared to the NBS data to aid researchers in performing roof damage assessments as a result of hail impact and in developing hail-resistant roofing products. Speaker Jim D. Koontz, RRC, PE – Jim D. Koontz & Associates, Inc. – Hobbs, NM JIM D. KOONTZ, president of his firm, is a graduate of Tulane University with a BS in engineering and an MBA. Koontz has been involved in the roofing industry since 1960 and began testing roofing material in 1976. He has experience as a roofer, estimator, consultant, lecturer, researcher, and expert witness. Koontz was first published in 1984 and has numerous articles relating to roofing material/product research to his credit. This includes research on single-ply products as well as hail/wind research on numerous roofing systems. 2 • Koontz RCI International Convention and Trade Show • MarcRCh 14-19, 2019 ABSTRACT On a yearly basis, hail damage results in millions of dollars in business for the roofing industry. Prior hail research has depended primarily on data from the National Bureau of Standards (NBS) document NBS 23,1 authored by Sidney Greenfeld. The NBS publication contains calculated data on the free-fall/terminal velocities of ice spheres 1 to 3 in. in diameter with an assumed density of .89 g/cm3 to .91 g/cm3. Resultant kinetic energy is reported for the various hail sizes. Terminal velocity increases with the size of hail. As a result, impact energy increases exponentially with hail size. This research was based on theoretical data generated by J.A.P. Laurie, National Building Research Institute, Pretoria, South Africa.2 The NBS research is a theoretical model that assumes ice spheres with densities of pure ice and does not consider other factors. The purpose of this study is to measure the effects of shape, surface area, density, air temperature, humidity, and barometric pressure on the free-fall velocities of hailstones. Table 1, included in the NBS paper, has been widely relied upon by Factory Mutual, UL, the American Society for Testing and Materials (ASTM), and others to define impact energy for hail. BACKGROUND Jim D. Koontz & Associates, Inc. (JDKA) has been performing hail testing on different roofing systems for over 30 years. Ice spheres are produced in molds which approximate the .91 grams/cm3 as listed by the NBS (Figure 1). The ice spheres are placed in a barrel, similar to a muzzleloader. The ice spheres are then propelled with compressed air from a pneumatic launcher (Figure 2). The air pressure within the tank of the pneumatic launcher is controlled to one-hundredth of a lb. per sq. in. (psi). The pneumatic valve, or trigger mechanism, is also controlled to one-hundredth of a psi. Once the hailstone is fired, the velocity is measured with a ballistic timer. During the testing at JDKA’s laboratory, it was first observed that when firing hailstones of the same size, density, and Variations in the Free-Fall Velocities of Hail RCI International Convention and Trade Show • MarcRCh 14-19, 2019 Koontz • 3 Table 1. Terminal velocities and energies of hailstonesa *Read from graphs in reference {9}. inches cm ft/s mi/hr (m/sec) ft lbs Joules 1 (2.5) 73 50 (22.3) <1 (<1.36) 1 1/4 (3.2) 82 56 (25.0) 4 (5.42) 1 1/2 (3.8) 90 61 (27.4) 8 (10.85) 1 3/4 (4.5) 97 66 (29.6) 14 (18.96) 2 (5.1) 105 72 (32.0) 22 (29.80) 2 1/2 (6.4) 117 80 (35.7) 53 (71.9) 2 3/4 (7.0) 124 85 (37.8) 81 (109.8) 3 (7.6) 130 88 (39.6) 120 (162.7) Diameter Terminal Velocity Approximate impact energy Table 1 – National Bureau of Standards (NBS) 23. Figure 2 – Pneumatic hail gun. Figure 1 – Ice spheres. at the same tank pressures, variations in the terminal velocity occurred. After considerable testing, it was determined that the variations in velocity were the result of changes in the barometric pressure and temperature. These variations in terminal velocity prompted the work of this study. FREE FALL – TERMINAL VELOCITY As a hailstone begins to fall, it is initially acted upon by gravity. When a hailstone reaches its maximum altitude and starts to drop, it accelerates due to gravity. The downward force is: Force = Mass x Acceleration (F = M x A) As the hailstone falls through the atmosphere, it is acted upon by air. Friction or resistance from air on the falling hailstone produces an upward pressure, aka drag force. The faster the hailstone falls, the greater the resultant air pressure or drag force on the hailstone. At some point, the force of gravity and the upward air pressure are equal, at which time the hailstone will fall at terminal velocity (Figure 3). The terminal velocity, however, may change, depending upon atmospheric conditions, density, and shape of the hailstone. KINETIC ENERGY The impact force for any hailstone is dependent upon two factors: the mass of the hailstone and the terminal velocity. Once mass and terminal velocity are known, the kinetic energy of the hailstone can be calculated: Kinetic Energy = ½ Mass x Velocity2 BAROMETRIC PRESSURE Altitude is height above sea level. At higher altitudes, the air density is lower and air is also cooler. Gravity pulls more air molecules towards the earth’s surface. Air molecules at higher altitudes spread out more. The air density and barometric pressure decreases (Table 2). As hail falls, the air density increases, and the hail will slow somewhat with higher density and warmer air. The temperature of air at sea level, under typical conditions, averages 59˚F. Increasing altitude results in a decrease of barometric pressure and temperature. The rate of decrease of temperature is 3.6˚F for every 1000 feet. The temperature, however, can be much colder in a cloud during a storm event. SURFACE AREA/DENSITY OF HAIL A perfect symmetrical ice sphere has a volume, V = 4/3 ℿ R3, and a surface area, A = 4 ℿ R2 (Figure 4), if one assumes the density of the hail per NBS 23 is .90 grams/cm3 or .0325 pounds/in3. By examining the ratio of weight to surface area, it can be seen that there is a linear relationship to terminal velocity. The greater the weight per surface area, the greater the terminal velocity as a result of relatively less air resistance for higher-weight hailstones. Thus, the larger the hail, the faster it falls. A hailstone with a non-spherical shape will have a greater weight-to-surface ratio and, Figure 3 – Hailstone terminal velocity. Table 2 – Barometric pressure vs. altitude. 4 • Koontz RCI International Convention and Trade Show • MarcRCh 14-19, 2019 theoretically, should have greater drag or wind resistance resulting in a slower free-fall terminal velocity. Studies by the Insurance Institute for Business and Home Safety3 (IBHS) utilized a 3-D scanning laser to measure 40 hailstones in the field following hail events. Models of the actual hailstones allowed for an accurate calculation of the volume of naturally occuring hail. The hailstones were also tested in compression. The research showed variations in hailstone densities, but larger hailstones exhibited a density closer to pure ice: .9 grams/cm3. Studies by Heymsfied, Giammanco, and Wright4 also confirm that as hail increases in size above three centimeters, it becomes less spherical. Another research paper by Giammanco, Brown, Grant, Dewey, Hodel, and Stumpf5 of the IBHS confirmed variations in compressive strength of naturally occuring hailstones. JDKA TESTING To study the effect variations of meteorological factors and physical properties of hail have on terminal velocities, JDKA utilized a vertical wind tunnel (Figure 5). Air is drawn from the bottom of the wind tunnel and is exhausted through the top. Hailstones of different sizes, densities, and surface areas are placed in the wind tunnel. Air velocity is then increased to the point where the ice sphere begins to float. Air velocities, barometric pressures, humidity levels, and temperature are recorded (Figure 6). NBS 23 Initial tests were performed with symmetrical spherical hail with densities of approximately .90 grams/cm3. The terminal velocities recorded in the laboratory Figure 4 – Symmetrical sphere. Table 3 – Ratio of weight to surface area. Table 4 – Terminal velocity, weight, and surface area. Figure 5 – Vertical wind tunnel. Diameter of Radius Volume Surface Weight of Ratio NBS- Hail (Inches) (Cubic Area Hail (Weight to Calculated (Inches) Inches) (Square (Pounds) Surface Terminal Inches) Area) Velocity (Feet/Second) 1 .5 .52 3.14 .017 .005 73 1.5 .75 1.77 7.07 .058 .008 90 2.0 1.0 4.19 12.57 .136 .011 105 2.5 1.25 8.18 19.63 .266 .014 117 3.0 1.50 14.14 28.27 .460 .016 130 RCI International Convention and Trade Show • MarcRCh 14-19, 2019 Koontz • 5 were compared to the theoretical velocities listed by NBS (Table 5). The testing shows a general correlation between the NBS theoretical terminal velocity and the laboratory-measured terminal velocity. The velocities of laboratory hailstones where higher than listed by the NBS for hailstones 1.5 to 2.0 in. Laboratory hailstones above 2.5 and 3.0 in. exhibited a terminal velocity below the NBS data. The NBS data most likely assumed standard atmospheric conditions. The laboratory testing was performed at an elevation of 3620 ft. above sea level. VARIATION IN HAILSTONE DENSITY Previous research on the physical properties of hailstones by IBHS5 found wide variation in the densities of naturally occurring hailstones. Utilizing carbonated water, JDKA produced 1-in.-diameter hailstones with densities varying from .84 g/cm3 to .89 g/cm3. The terminal velocity decreased from 73.3 ft./sec. to 70.8 ft./sec. NONSYMMETRICAL ICE SPHERES Ice spheres with different shapes, surface areas, and densities have been tested. Plastic spheres with irregular shapes are initially fabricated on a 3-D digital printer (Figure 7). The plastic spheres, Figures 8 and 9, are then used to make molds to create irregularly shaped hailstones (Figure 10). Irregularly shaped 1-in. hailstones had a reduced velocity of up to 4.5 ft./sec. Irregularly shaped 1.5-in. hailstones had a reduced velocity of 11.2 ft./sec. FINDINGS TO DATE • Symmetrical spherical hailstones with a higher density fall faster, have less aerodynamic drag, and develop a greater kinetic energy at the point of impact. Larger spherical hailstones have an impact energy close to the theoretical work performed by Laurie and NBS. • Hailstones with a lower density fall at a slower terminal velocity and have a reduced impact energy at the point of impact. • Hailstones with a greater ratio of surface area to density fall at a slower velocity with a lower impact energy. • Higher barometric pressures result Figure 6 – Floating hailstone, terminal velocity. Figure 7 – 3-D digital printer. Table 5 – NBS theoretical vs. laboratory testing. 6 • Koontz RCI International Convention and Trade Show • MarcRCh 14-19, 2019 in higher densities of air; thus, slower hailstone free-fall velocities. • The original work by Laurie and the NBS is conservative with respect to the amount of impact energy imparted to roof systems. Nonspherical hailstones and hailstones with greater surface areas fall at a slower terminal velocities and thus, have lower impact energies. The impact energies reported by the NBS are most likely on the high end of impact energies experienced in real-world hailstone events. Additional research in this area is being performed. Data related to this research will be presented in future papers. REFERENCES 1. Sidney Greenfeld. National Bureau of Standards. NBS 23. August 1969. 2. J.A.P. Laurie. Hail and Its Effects on Buildings. National Building Research Institute. South Africa. 1960. 3. Ian M. Giammanco, Benjamin R. Maiden, Heather E. Estes, and Tanya M. Brown-Giammanco. “Using 3D Laser Scanning Technology to Create Digital Models of Hailstones.” Insurance Institute of Business and Home Safety. July 28, 2017. 4. Andrew J. Heymsfield, Ian M. Giammanco, and Robert Wright. “Terminal Velocities and Kinetic Energies of Natural Hailstones.” November 25, 2014. 5. Ian M. Giammanco, Tanya M. Brown, Rosemarie G. Grant, Douglas L. Dewey, Jon D. Hodel, and Robert A. Stumpf. “Evaluating the Hardness Characteristics of Hail Through Compressive Strength Measurements.” Journal of Atmospheric and Oceanic Technology. November 2015. 6. Ibid. Figure 10 – Irregularly shaped ice sphere mold with hailstone. Figure 8 – Plastic spikey sphere. Figure 9 – Plastic knobby sphere. RCI International Convention and Trade Show • MarcRCh 14-19, 2019 Koontz • 7
