A tall order

Geodetic method

*Its the oldest known method but one of the most accurate. Early scientific measurements of mountains were made by Greek authors Dicaearchus,Eratosthenes and Xenagoras.

*It uses three processesLevelling,measurement of triangles and determination of distance of a mountain visible at sea.

Method: Similar triangles,usually right triangles,are compared using a hodometer. Other distance measuring instruments include Dioptra,Quadrant,ancient astrolabe,ancient cross-staff and Gnomon.

Barometric Method

This is based on the premise that if a mercury column is held up by air pressure,the column is shorter at higher altitudes. Eventually Edmund Haley devised a formula: 0.0144765 H 900 (log 30-log h),where 30 inches is the height of mercury at sea-level; h is its height at the place of observation; and H is the elevation. However,the method could never accurately link mountain height to barometric height.

Thermometric Method

*This is based on the concept of boiling point of water at different altitudes; the boiling point of water falls with a rise in height.

*Henri Victor Regnault constructed an instrument called hypsometer for thermometric measurement. The formula used was: h 295 (100-t),where h is expressed in metres,t in degrees centigrade.

In 1854,Mount Washington was measured by all 3 methods. It came to 6,288 ft (1,917 m) by primary triangulation,used by the US Coast Survey,to 6,280 ft by the process of levelling,6,206 ft by barometer method,and 6,116 feet by boiling point method. It was determined that the results given by the barometer,however erratic,wander less from those by the levelling instrument than the other results.

Modern Measurement

Photogrammetry

An alternative method,it is commonly used by the UK to measure its hills and peaks. It involves flying over the area to be measured and taking overlapping,high-resolution photos from which a 3D representation is created. Measurements can then be taken that translate directly to positions and heights in the real world. This method allows large areas to be surveyed quickly and safely and to an accuracy of 3-4 m.

GPS

The most accurate method,which Nepal is using for Mount Everest,involves using GNSS (Global Navigation Satellite System). An instant position is determined but the height is not very accurate. For greater accuracy,the GNSS unit has to remain stationary and record data for a period of time.

GPS second method

A GPS receiver is planted on top of the mountain. Scientists then time how long it takes for radio signals to travel between the receiver and orbiting satellites. This yields enough data to determineto within a centimetrethe elevation of the receiver relative to the satellite,which sits at a known distance from the centre of the Earth. But that doesnt determine the height above sea level. The height of the ocean surface is believed to differ by more than 100 m across the globe. So scientists try to estimate where the sea level would be if the water were lapping up against or indeed flowing through the base of the mountain. The final calculation may not be that precise.

Mountains can be measured from different base points

From sea level: Measuring elevation from the sea level is one of the most widely accepted techniques. When measuring from sea level,Mount Everest is the uncontested tallest mountain of the world,with a peak that rises 8,848 m above sea level.

From its base: Some measurements are taken from the base of the mountain itself,even if the base is above sea level. Measured in this manner,Mauna Kea,whose base is at the bottom of the Pacific Ocean,is the worlds tallest at 10,203 m. This beats Mount Everest even though Mauna Keas elevation is only 4,205 m at its peak.

Mount Lamlam,whose base is deep in the Mariana Trench in the Pacific,is another mountain which could be tallest when measured from the base. Though reports about its height differ,one report puts its height,when measured from the base,at 11,527 m,making it taller than Mauna Kea.

From surrounding terrain: When measuring Mount Everest,the elevation of the plateauon which it is situatedfrom the sea level is also included in the mountains height. But if its vertical rise was measured from the surrounding terrain,Everest would lose to Mount McKinley,whose elevation from the sea level is otherwise lower than Mount Everest,but its vertical rise is about 5,500 m,compared to Mount Everests 3,700 m.

From centre of Earth: When measured from the centre of the Earth,the worlds tallest mountain is Chimborazo,which is 6,384 km at its peak. However,its elevation is only 6,268 m above sea level. It is located in Ecuador,near the equator,which gives it an advantage,because the Earth bulges slightly in the middle.

Tallest Mountains how they were measured

Mount Everest: 8,848/8,850 metres,Himalayan range

Both Nepal and China,the two countries the mountain straddles,officially recognise the 8,848 m height. China recently said the height be recognised as 8,844.43 m. Mount Everest was identified in 1841,but its height was measured seven years later from a distance of 177 km because at that time Tibet and Nepal kept their borders closed. Then the official elevation was calculated at 9,205 m. By 1954,it was recognised as the tallest mountain in the world. In 1856,Andrew Waugh announced Everest (then Peak XV) as 8,840 m high. The elevation of 8,848 m was first determined by an Indian survey in 1955. It was subsequently reaffirmed by a 1975 Chinese measurement at 8,848.13 m. In both cases the snow cap,not the rock head,was measured. In May 1999,an American Everest Expedition stationed a GPS unit into the highest bedrock. Rock head elevation was found to be 8,850 m and snow/ice elevation was 1 m higher.

K2: 8,610 metres,Karakoram (2nd highest in the world)

In 1986,the summit was measured using GPS and laser distance metres for the first time. The measurement was performed from Concordia at a distance of about 15 km. The ellipsoidal height turned out to be 8,579 m,while the geoidal height of K2 turned out to be 8,616 m. A March 1987 measurement indicated that the summit might be higher than Everest,but later that year Everest was re-measured by a similar method and found to be 237 m taller. In 1996,a research expedition set out to verify this 8,616 m height using a combination of modern equipment,triangulation and trigonometry. The elevation of the rock top of Mount K2 was computed as 8,614.27 m.

Kilimanjaro: 5,895 metres (highest in Africa)

In 1889,Dr Hans Meyer on his third attempt finally became the first person to conquer the summit. He claimed that he had climbed 6,045 m. But,the colonial authorities in Germany adjusted the figure to 5,892 m,and it remained the official height until 1952,when Kilimanjaro was mapped by British cartographers. The new official altitude was then determined at 5,895 m. However,the UN Environment Programme/World Conservation Monitoring Centre,in their official factsheet about Kilimanjaro National Park mentions the height of Kilimanjaro as 5,893 m. In 1999,a team of specialists re-measured Kilimanjaro,using the newly available GPS technology and the summit shrunk by 2.45 m to 5,892.55 m. In 2008 the exercise was repeated and according to measurements taken by GPS and gravimeter methods,Kilimanjaros height was estimated to be 5,891.8 m.

Complied by: shreya sengupta; illustration: Pradeep Yadav