Every year as storms get stronger and stronger, hail damage to meteorological instruments seems to the rise. High quality metal instrumentation is not always the answer as its weight and cost may outweigh its benefits.

hailstorm

Lightning and hail

The same air movement which causes lightning charges to build up within Cumulonimbus storm clouds are also responsible for hail stone formation. The temperature within a cloud, especially in tall Cumulonimbus clouds which can reach several kilometers into the atmosphere is many times well below freezing.

What goes up, must come down

Before microscopic water droplets, which make up the cloud, can join into a hail stone they need to crystalize on an object like a dust particle. As they grow in size, they subsequently have to be caught within a strong updraft within the cloud to keep them suspended within the cold cloud center to form a large enough hail stone that will not melt as it later falls through the warm air of the lower atmosphere. When the hail stones are large and heavy enough that the force of gravity is able to overcome the aerodynamic drag force from the updraft, they begin to fall to the ground and accelerate until they reach terminal velocity. The stronger the updraft within the cloud is, the larger the hailstones will be and the stronger the lightning activity within the cloud will be. Updraft velocity within a hail storm cloud can be estimated from the size of the hailstones if we can calculate the terminal velocity of the hail falling from the cloud.

What effects hail speed

Many studies have been done to estimate hail stone terminal velocity and each can be correct. Factors that effect hail falling speed range from:

  • Updraft / Down draft conditions under the cloud.
  • Hail stone density (average hail stone ice density is around 0.91 g/cm3 = 910 kg/m3 = 57 lb/ft3 = 57 lb/ft3
    References: http://www.monier.co.za/and What are the effects of hail on residential roofing products? by Jim D. Koontz
  • Hail stone shape and surface roughness and rotation angular velocity.
  • Hail stone density ( how much hail per unit area (m2) is falling)…stones will help reduce eachother’s aerodynamic drag and will fall faster than if falling alone.

An rough and quick estimate of hail stone falling speed has been proposed by Mr. Geerts, B. in Fall speed of hydrometeors. (April, 2000).

“Hail can fall much faster, because its diameter can be larger. Its fallspeed is approximately given by 1.4*D0.8 at sea level, the exact relationship depends on hail density and shape. For instance, a large hailstone of 8 cm (D=80 mm) weighs about 0.7 kg and falls at 48 m/s ! … The largest hailstone ever measured fell in Kansas in September of 1970: it weighed 755 grams, had a diameter of 14 cm, and fell at about 57 m/s (i.e. 207 km/h)”

From the above data we can see that the proposed simple mathematical relationship between hail speed and size is only a very rough estimate, but nevertheless a good reference point to start with.

Table summary of the above relationships between hail size and speed and weight

Hail Stone Size (mm | inches) Density(kg/m3| lb/ft3) Volume of a Sphere (4/3*π*R3) (cm3 | in3) Mass (kg | lb | slugs)  Approximate Terminal Velocity 1.4*D0.8 (m/s | mph)  Kinetic  Energy
1/2*Mass*Speed2​
(Joules)
3 mm | ~1/8 in  910 kg/m3 | 57 lb/ft3  0.014 cm3 | 0.00086 in3 0.013 g | 0.00045 oz 3.4 m/s | 7.5 mph 0.00007 J
6 mm | ~1/4 in 0.11 cm3 | 0.0069 in3 0.10 g | 0.0036 oz 5.9 m/s | 13 mph 0.0018 J
10 mm | ~3/8 in 0.52 cm3 | 0.032 in3 0.48 g | 0.016 oz 8.8 m/s | 20mph 0.019 J
12 mm | ~ 1/2 in 0.90 cm3 | 0.055 in3 0.82 g | 0.029 oz 10.2 m/s | 23 mph 0.043 J
25 mm | ~ 1 in 8.12 cm3 | 0.50 in3 7.4 g | 0.26 oz 18.4 m/s | 41mph 1.26 J
50 mm | ~ 2 in 65 cm3 | 4.00 in3 60 g | 2.1 oz 32 m/s | 72 mph 30.5 J
75 mm | ~ 3 in 220 cm3 | 13.5 in3 201 g | 7.1 oz 46 m/s | 104 mph 265 J
100 mm | ~ 4 in 524 cm3 | 32.0 in3 476 g | 16.8 oz 56 m/s | 125mph 740 J

Paint ball shooting test: Equivalent impact energy of paintballs vs hail stones.

Paintball physical parameters: Muzzle velocity = 210fps | 64m/s

Paintball Diamter
& Mass
Paintball Volume Paintball Density
Mass / Volume
Impact Velocity Kinetic  Energy
1/2*Mass*Speed2​
(Joules)
Impact Energy on cm2
Ø 17.3mm

Mass = 3.7g

4/3*π*r3 = 2.71cm3  1.37g/cm3 Range = 0m
V = 64 m/s
7.6 Joules
(see note *)
76 kJ/m2
Range = 30m,
V = 39 m/s
2.8 J
(see note **)
28 kJ/m2
Range = 60m,
V = 26 m/s
1.3 J
(see note ***)
13 kJ/m2

* Equivalent kinetic energy to a 37mm (1.5″) diameter hail stone traveling at 25m/s from table above.
** Anemometers were tested at 30 meter range which is equivalent to more than 2x the kinetic energy of a 25mm (1″) hail stone.
*** Equivalent kinetic energy to a 25mm (1″) diameter hail stone traveling at 18.5m/s from table above.

Our Anemomters and Weather Stations are tested at more than two times the impact kinetic energy of a 25mm or 1 inch hail stone.

Usefull Hail Stone Info links:

http://www.hypertextbook.com/facts/2005/AliciaKosiba.shtml
http://www-das.uwyo.edu/~geerts/cwx/
http://www-das.uwyo.edu/~geerts/cwx/notes/notes.html
http://www.riskfrontiers.com/nhq/nhq4-4tables.htm
http://www.newton.dep.anl.gov/askasci/wea00/wea00186.htm
http://www.monier.co.za/professional/hailstones.html