Triangulation station

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A triangulation station, also known as a trigonometrical point, and sometimes informally as a trig, is a fixed surveying station, used in geodetic surveying and other surveying projects in its vicinity.

The station is usually set up by a government with known coordinates and elevation published. Numerous stations are installed on summits for purposes of visibility and prominance. A graven metal plate on the top of a pillar may provide a mounting point for a theodolite or reflector, often using some form of kinematic coupling to ensure reproducible positioning.

Trigonometrical stations form networks of triangulation. Positions of all land boundaries, roads, railways, bridges and other infrastructure can be accurately located by the network, a task essential to the construction of modern infrastructure. Apart from the known stations set up by government, some temporary trigonometrical stations are set up near construction sites for monitoring the precision and progress of construction.

Some trigonometrical stations use the Global Positioning System for convenience. Its accuracy factors in ionospheric and tropospheric propagation delay errors.

Although stations are no longer required for many modern surveying purposes, they remain useful to hikers and even aviators as navigational aids. Particular small triangles on maps mark summits, for example.

The nomenclature for triangulation stations varies regionally: they are generally known as trigonometrical stations or triangulation stations in North America, trig points in the United Kingdom, trig pillars in Ireland, trig stations or trig points in Australia and New Zealand,^[1] and trig beacons in South Africa.

In the 1820s, much of New South Wales was unsurveyed territory to the European arrivals. To aid the mapping of the country, the science of trigonometic surveying was introduced by Major Thomas Mitchell who had been brought out to the colony as Assistant Surveyor General of New South Wales. The freestanding peak of Mount Jellore was selected as the first trigonometric summit for his triangulation survey of the countryside. In 1828 Mitchell headed south from Sydney with a small party and camped at the base of the basalt, making daily excursions to the top. While his convict crew cleared the summit of trees, Mitchell plotted and measured distant peaks and sketched the skyline.

A national geodetic survey and adjustment carried out in the early 1970s in Australia has left a legacy of trig stations, many consisting of a ground mark with a black quadripod (pyramid frame) supporting a visible disc above the ground mark.^[2]

• 
  Australia's first trig
• 
  Trigonometrical station, NSW, Australia
• 
  Trig point atop Mount Wellington, Tasmania

Many trigonometrical stations were placed on hilltops around Hong Kong. They strongly resemble those used in other former British colonial territories such as Australia, consisting of a white column topped with a black band.

• 
  A trigonometrical station in Chek Lap Kok Scenic Hill, Hong Kong

In Japan, there are five classes of triangulation stations (三角点, sankakuten, lit. 'three corner points'):

Class 1 (一等三角点, ittō sankakuten)

They are installed approximately every 40 kilometres (25 mi), with smaller ones (as necessary) about every 25 kilometres (16 mi).^[3] There are about 1000 throughout Japan. The pillars are 18 centimetres (7.1 in) on a side, and each pillar is anchored with two very large perpendicular rocks buried underground.^[4]

Class 2 (二等三角点, nitō sankakuten)

They are installed approximately every 8 kilometres (5.0 mi). There are about 5000 throughout Japan, and the pillars are 15 centimetres (5.9 in) on a side. Each pillar is anchored with a very large perpendicular rock buried underground.

Class 3 (三等三角点, santō sankakuten)

There are about 32,000 installed throughout Japan, with one approximately every 4 kilometres (2.5 mi). The pillars are 15 centimetres (5.9 in) on a side, and each pillar is anchored with a large perpendicular rock buried underground.

Class 4 (四等三角点, yontō sankakuten)

They are installed approximately every 2 kilometres (1.2 mi), and there are about 69,000 throughout Japan. The pillars are 12 centimetres (4.7 in) on a side, and each pillar is anchored with a large perpendicular rock buried underground.

Class 5 (五等三角点, gotō sankakuten)

These markers were installed in 1899 and are the predecessors to the modern triangulation stations used in Japan today. They are generally not used anymore since the installation of the Class 1-4 stations. Some of them still exist at various locations throughout Japan.

• 
  Class 3 triangulation point in Shiroyama Park in Inagi, Tokyo

As of August 2023^[update] there are 5,765 trig stations in New Zealand. They are placed on top of hills and are usually black and white.^[5]

• 
  Trig station on top of Mount Maunganui

South Africa has a network of approximately 28,000 trig beacons, established by the Chief Directorate: National Geo-spatial Information (historically known as the Trigonometrical Survey).^[6] These beacons are typically white-painted concrete pillars supporting black metal plates in a cross shape, installed on mountains, hills or tall buildings.

• 
  Trig beacon on the summit of Lion's Head in Cape Town

In Spain there are 11,000 triangulation stations, concrete structures which typically consist of a cylinder 120 cm high and 30 cm in diameter over a concrete cubic base.

They were erected by the Instituto Geográfico Nacional, usually painted in white, and can be marked with a metallic label with the warning: "The destruction of this sign is punishable by law."

• 
  Trigonometric station on the top of Peñalara mountain (Spain)

In the United Kingdom, trig points are typically concrete pillars and were erected by the Ordnance Survey.

The process of placing trig points on top of prominent hills and mountains began in 1935 to assist in the accurate retriangulation of Great Britain. The Ordnance Survey's first trig point was erected on 18 April 1936 near Cold Ashby, Northamptonshire. In low-lying or flat areas some trig points are only a few metres above sea level and one is even at −1 m (near Little Ouse, Cambridgeshire, TL61718 89787).^[7] When all the trig points were in place, it was possible in clear weather to see at least two other trig points from any one trig point, but subsequent vegetation growth means that this is not necessarily still the case. Careful measurements of the angles between the lines-of-sight of the other trig points then allowed the construction of a system of triangles which could then be referenced back to a single baseline to construct a highly accurate measurement system that covered the entire country.

In most of the UK, trig points are truncated square concrete (occasionally stone) pyramids or obelisks tapering towards the top. On the top a brass plate with three arms and a central depression is fixed, known as a "spider": it is used to mount and centre a theodolite used to take angular measurements to neighbouring trig points. A benchmark is usually set on the side, marked with the letters "O S B M" (Ordnance Survey Bench Mark) and the reference number of the trig point on a plaque called a "flush plate". Within and below the visible trig point, there are concealed reference marks whose National Grid References are precisely known. The standard trig point design is credited to Brigadier Martin Hotine (1898–1968), head of the Trigonometrical and Levelling Division of the Ordnance Survey.^[8] Many of them are now disappearing from the countryside as their function has largely been superseded by aerial photography and digital mapping using lasers and GPS. To quote from a page at the OS site: "Like an iceberg, there is more of trig pillar below the surface than above it."^[9] From the same source: "Today the receivers that make up the OS Net network are coordinated to an accuracy of just 3 mm over the entire length of Great Britain."

• 
  A trig point near Wootton Wawen, Warwickshire, England
• 
  Sign at Triangulation Point 3M of the Israeli Cassini Soldner measuring system outside Ofakim.

The United States National Geodetic Survey (NGS) and predecessor agencies manages the National Spatial Reference System (NSRS), which includes permanent survey marks for horizontal position (latitude and longitude), height, or gravity. Some marks have information for both horizontal position and height. Some marks were established by NGS. Others were established by other organizations, such as state highway departments, but are included in the database that makes up the NSRS. Information about marks is available to the public online. The number of points in the NSRS is over 1,500,000.^[10]

The image is the spire of the Fair Haven, Vermont First Baptist Church, a horizontal survey mark (triangulation station), and is described in the NGS National Spatial Reference System under the permanent ID OD1373.

• 
  Fair Haven First Baptist Church

• Struve Geodetic Arc
• Bilby tower
• Boundary marker
• Geodesy
• Ordnance Survey
• Retriangulation of Great Britain
• Survey marker
• Trigpointing is a pastime in which people individually go out, find and log the location of trig points.
• Cover of Martyn Bennett's album Grit

Wikimedia Commons has media related to Trig points.

• TrigpointingUK
• GPS Waypoints of all UK Trigpoints
• Photos of examples of trig points in the UK on geograph.org.uk
• Database of trig points in the United Kingdom
• Repères de nivellement. French I.G.N
• Serveur de fiches (maps). French I.G.N
• Database of trig points in New Zealand Archived 16 December 2015 at the Wayback Machine
• "Trig pillars we salute you", blog post from UK Ordnance Survey