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.

**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 |
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Hail Stone Size (mm | inches) |
Density(kg/m^{3}| lb/ft^{3}) |
Volume of a Sphere (4/3*π*R^{3}) (cm^{3} | in^{3}) |
Mass (kg | lb | slugs) |
Approximate Terminal Velocity 1.4*D^{0.8 }(m/s | mph) |
Kinetic Energy1/2*Mass*Speed ^{2}(Joules) |

3 mm | ~1/8 in | 910 kg/m^{3} | 57 lb/ft^{3} |
0.014 cm^{3} | 0.00086 in^{3} |
0.013 g | 0.00045 oz | 3.4 m/s | 7.5 mph | 0.00007 J |

6 mm | ~1/4 in | 0.11 cm^{3} | 0.0069 in^{3} |
0.10 g | 0.0036 oz | 5.9 m/s | 13 mph | 0.0018 J | |

10 mm | ~3/8 in | 0.52 cm^{3} | 0.032 in^{3} |
0.48 g | 0.016 oz | 8.8 m/s | 20mph | 0.019 J | |

12 mm | ~ 1/2 in | 0.90 cm^{3} | 0.055 in^{3} |
0.82 g | 0.029 oz | 10.2 m/s | 23 mph | 0.043 J | |

25 mm | ~ 1 in | 8.12 cm^{3} | 0.50 in^{3} |
7.4 g | 0.26 oz | 18.4 m/s | 41mph | 1.26 J | |

50 mm | ~ 2 in | 65 cm^{3} | 4.00 in^{3} |
60 g | 2.1 oz | 32 m/s | 72 mph | 30.5 J | |

75 mm | ~ 3 in | 220 cm^{3} | 13.5 in^{3} |
201 g | 7.1 oz | 46 m/s | 104 mph | 265 J | |

100 mm | ~ 4 in | 524 cm^{3} | 32.0 in^{3} |
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 |
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Paintball Diamter& Mass |
Paintball Volume |
Paintball DensityMass / Volume |
Impact Velocity |
Kinetic Energy1/2*Mass*Speed ^{2}(Joules) |
Impact Energy on cm^{2} |

Ø 17.3mm
Mass = 3.7g |
4/3*π*r^{3} = 2.71cm^{3} |
1.37g/cm^{3} |
Range = 0m V = 64 m/s |
7.6 Joules (see note *) |
76 kJ/m^{2} |

Range = 30m, V = 39 m/s |
2.8 J (see note **) |
28 kJ/m^{2} |
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Range = 60m, V = 26 m/s |
1.3 J (see note ***) |
13 kJ/m^{2} |

** 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