What Impact Energy from Hail Stone should Meteorological Instruments be able to Survive?
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Photo courtesy of: Raysonho @ Open Grid Scheduler / Grid Engine / Public domain
Every year as storms get stronger and stronger, hail damage to meteorological instruments seems to the rise. All metal instrumentation is not always the answer and some instruments are tougher than they look: How tough is the toughest weather station?
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 in many cases 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 crystallize on an object like a dust particle. As they grow in size, they subsequently have to be caught in a strong updraft within a cloud to keep them suspended long enough in the cold wet cloud to grow. Once the hail stones are large enough not to melt as they fall through warm air beneath the cloud, they can reach the ground and cause damage. When hail stones are large and heavy enough that the force of gravity is able to overcome the aerodynamic drag force from the updraft, their fall to the ground begins and they accelerate until reaching 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 affects 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 and in 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
Reference: http://www.monier.co.za/ and What are the effects of hail on residential roofing products? by Jim D. KoontzHail stone shape and surface roughness and rotation angular velocity.
Hail stone density (how much hail per unit area (usually m²) is falling). Close proximity of hail stones will help reduce the aerodynamic drag acting on each hail stone. Thus they will fall faster than if falling alone. They will also require a stronger updraft to keep the growing hail stones inside the cloud.
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 fall speed is approximately given by 1.4*D^0.8 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 g, had a diameter of 14 cm or 5.5 inches, and fell at about 57 m/s (207 km/h or 128 mph).”
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) | Appx. Terminal Velocity 1.4*D0.8 (m/s | mph) | Kinetic Energy = 1/2*Mass*Speed3 (Joules) | ||
| 3 mm | ~1/8 in | 910 kg/m3 | 57 lb/ft3 | 0.014 cm3 | 0.00086in3 | 0.013 g | 0.00045 oz | 3.4 m/s | 7.5 mph | 0.00007 J | ||
| 6 mm | ~1/4 in | 0.11cm3 | 0.0069 in3 | 0.10 g | 0.0036 oz | 5.9 m/s | 13 mph | 0.0018 J | |||
| 10 mm | ~3/8 in | 0.52cm3 | 0.032 in3 | 0.48 g | 0.016 oz | 8.8 m/s | 20mph | 0.019 J | |||
| 12 mm | ~ 1/2 in | 0.90cm3 | 0.055 in3 | 0.82 g | 0.029 oz | 10.2 m/s | 23 mph | 0.043 J | |||
| 25 mm | ~ 1 in | 8.12cm3 | 0.50 in3 | 7.4 g | 0.26 oz | 18.4 m/s | 41 mph | 1.26 J | |||
| 50 mm | ~ 2 in | 65cm3 | 4.00 in3 | 60 g | 2.1 oz | 32 m/s | 72 mph | 30.5 J | |||
| 75 mm | ~ 3 in | 220cm3 | 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 | 125 mph | 740 J | |||
Paint ball shooting test:
Equivalent impact energy of paintballs’ vs. hail stones follows.
| Paintball physical parameters:Muzzle velocity = 210 fps | 64 m/s | |||||
|---|---|---|---|---|---|
| Paintball Diamter & Mass | Paintball Volume | Paintball Density Mass / Volume | Impact Velocity | Kinetic Energy 1/2*Mass*Speed2 (Joules) | Impact Energy per cm2 |
| Ø17.3 mm Mass = 3.7 g | 4/3*π*r3 = 2.71 cm3 | 1.37 g/cm3 | Range = 0 m V =64 m/s | 7.6 Joules (see note *) | 76 kJ/m2 |
| Range = 30 m, V =39 m/s | 2.8 J (see note **) | 28 kJ/m2 | |||
| Range = 60 m, V =26 m/s | 1.3 J (see note ***) | 13 kJ/m2 | |||
* Equivalent kinetic energy to a 37 mm (1.5″) diameter hail stone traveling at 25 m/s from table above.
** Anemometers were tested at 30 m range which is equivalent to more than 2x the kinetic energy of a 25 mm (1″) hail stone.
*** Equivalent kinetic energy to a 25 mm (1″) diameter hail stone traveling at 18.5 m/s from table above.
Our Anemometers and Weather Stations are tested at more than two times the impact kinetic energy of a 25 mm or 1 inch hail stone. If you want to know what is the toughest weather station, please read this article: How tough is the toughest weather station?
Usefull Hail Stone Info links:
