Kinetic or Impact Energy (Ke) = ½(mass)(velocity)2
Without the influence of wind, an object (in this case, a hailstone) falling straight down will eventually reach a constant velocity (terminal velocity or free-fall velocity) in which it no longer accelerates due to the drag force from air. The calculations that have been used in the research to replicate the free-fall velocities of hailstones is based on conservative assumptions that the density of a hailstone is equivalent to that of freezer-made ice and that the surface area of a hailstone is nearly equivalent to that of a sphere. These assumptions are conservative when compared with actual hail events in that a hailstone will have less density and weight than freezer-made ice, and the surface area (i.e. shape) of a hailstone is less aerodynamic than that of an actual sphere. In short, a hailstone will be lighter and slower than a freezer-made ice ball of the same diameter. The following table summarizes the free-fall velocities and impact energies associated with various diameters of hailstones with values approximated by ice balls used in laboratory studies.
The values in the above table identify impact energies of hailstones falling straight down, but it is known that hail events are generally influenced by a horizontal component, too (i.e., wind). Wind affects the angle of impact and the terminal velocity, and therefore would increase the impact energy of a hailstone. Due to the horizontal wind component, hail will not strike all roof slopes (on most roofs) with the same kinetic energy because roof angles and their orientations vary. Using trigonometry, one can calculate a resultant velocity of hailstones based on various wind speeds by using the following equation:
a2+b2 = c2
Using the above equation, we can now derive the terminal velocity when hailstones are influenced by both the vertical (i.e. free-fall) and horizontal (wind) components. The following chart displays the effects of wind velocities on impact energies for various hailstone diameters.
The research that has been done on hailstone impacts to the most common roofing material in the United States (asphalt shingles) indicates that the threshold diameter that a hailstone must be in order to cause functional damage to a three-tab, asphalt shingle is 1 inch in diameter. The following chart displays the impact energies of hailstones at free-fall velocities (i.e., no wind) and with wind speeds ranging from 20 to 150 miles per hour.
The chart shows that in order for a ½-inch hailstone to reach the same impact energy as a free-falling 1-inch hailstone, wind speeds must be about 135 miles per hour. It also shows that in order for a ¾-inch hailstone to reach the same impact energy as a free-falling 1-inch hailstone, wind speeds must be around 65 miles per hour. Note that the calculated impact energy in these charts assumes a worst-case scenario with the impact angle perpendicular to the surface being impacted. As the impact angle departs from 90 degrees, the surface being impacted will receive more of a glancing blow, and thus the impact energy will decrease. For example, the impact energy of a free falling 1-inch hailstone would be reduced about 25 percent if the roof being impacted has a pitch of 7 to 12. This is why it is critical to understand from which direction a hail event originated when performing a study for hail damage to a pitched roofing surface. In order for small hailstones to have enough kinetic energy to damage three-tab asphalt shingles, they must be propelled by significant wind speeds AND impact the surface at 90 degrees. To satisfy both of these conditions, ¾-inch-diameter hail must accompany 65 mph winds, the hail must hit a roof slope on the windward side of the house, and the pitch of that slope would have to be 19 to 12. Similarly, ½-inch-diameter hail must accompany 135 mph winds, the hail would have to hit a roof slope on the windward side of a house, and the pitch of that roof slope would have to be 48 to 12. The sketches below illustrate how impractical these conditions are considering most residential roof slopes have pitches between 3 to 12 and 14 to 12. Therefore, the conditions for small hail to be able to cause damage to asphalt shingles are very rare.