Great Salt Lake

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https://en.wikipedia.org/wiki/Great_Salt_Lake 

 

Great Salt Lake
Ti'tsa-pa (Shoshoni)
Satellite photo from August 2018 after years of drought, reaching near-record lows. Note the difference in colors between the northern and southern portions of the lake, the result of a railroad causeway.
Location	Utah, United States
Coordinates	41°10′N 112°32′W
Type	Endorheic lake, hypersaline lake
Primary inflows	Bear, Jordan, Weber Rivers
Catchment area	21,500 sq mi (56,000 km2)
Basin countries	United States
Max. length	75 mi (121 km)
Max. width	28 mi (45 km)
Surface area	950 sq mi (2,500 km2) as of 2021
Average depth	16 ft (4.9 m), when lake is at average level
Max. depth	33 ft (10 m) average, high of 45 ft (14 m) in 1987, low of 24 ft (7.3 m) in 2021
Water volume	15,338,693.6 acre⋅ft (18.92 km3)
Surface elevation	historical average of 4,200 feet (1,300 m), 4,190.5 feet (1,277.3 m) as of 2022 March 14
Islands	8–15 (variable, see Islands)
Settlements	Salt Lake City and Ogden

The Great Salt Lake (Shoshone: Ti'tsa-pa “Bad Water”) is the largest saltwater lake in the Western Hemisphere and the eighth-largest terminal lake in the world. It lies in the northern part of the U.S. state of Utah and has a substantial impact upon the local climate, particularly through lake-effect snow. It is a remnant of Lake Bonneville, a prehistoric body of water that covered much of western Utah.

The area of the lake can fluctuate substantially due to its low average depth of 16 feet (4.9 m). In the 1980s, it reached a historic high of 3,300 square miles (8,500 km²), and the West Desert Pumping Project was established to mitigate flooding by pumping water from the lake into the nearby desert. In 2021, after years of sustained drought and increased water diversion upstream of the lake, it fell to its lowest recorded area at 950 square miles (2,500 km²), falling below the previous low set in 1963. Continued shrinkage could turn the lake into a bowl of toxic dust, poisoning the air around Salt Lake City.

The lake's three major tributaries, the Jordan, Weber, and Bear rivers together deposit around 1.1 million tons of minerals in the lake per year. Since the lake has no outlet besides evaporation, these minerals accumulate and give the lake high salinity (far saltier than seawater) and density. This density causes swimming in the lake to feel similar to floating.

The lake has been called "America's Dead Sea" and provides a habitat for millions of native birds, brine shrimp, shorebirds, and waterfowl, including the largest staging population of Wilson's phalarope in the world.

Origin

Map of Pleistocene lakes in the Great Basin of western North America, showing the path of the Bonneville Flood along the Snake River

The Great Salt Lake is a remnant of a much larger prehistoric lake called Lake Bonneville. At its greatest extent, Lake Bonneville spanned 22,400 square miles (58,000 km²), nearly as large as present-day Lake Michigan, and roughly ten times the area of the Great Salt Lake today. Bonneville reached 923 ft (281 m) at its deepest point and covered much of present-day Utah and small portions of Idaho and Nevada during the ice ages of the Pleistocene Epoch.

Lake Bonneville existed until about 16,800 years ago, when a large portion of the lake was released through the Red Rock Pass in Idaho, resulting in cataclysmic floods. With the warming climate, the remaining lake began to dry, leaving the Great Salt Lake, Utah Lake, Sevier Lake, and Rush Lake behind.

History

Stansbury's 1852 map of the Great Salt Lake and adjacent country in the Utah Territory

The Shoshone, Ute, and Paiute have lived near the Great Salt Lake for thousands of years. At the time of Salt Lake City's founding, the valley was within the territory of the Northwestern Shoshone; however, occupation was seasonal, near streams emptying from canyons into the Salt Lake Valley. One of the local Shoshone tribes, the Western Goshute tribe, referred to the lake as Pi'a-pa, meaning "big water", or Ti'tsa-pa, meaning "bad water".

There are several maps dating back to 1575 that show the Great Salt Lake at the correct latitude and longitude, within an accuracy of a few degrees. One example is a map by Nicolas Sanson dated 1650. The Great Salt Lake entered written history through the records of Silvestre Vélez de Escalante, who learned of its existence from the Timpanogos Utes in 1776. No European name was given to it at the time, and it was not shown on the map by Bernardo Miera y Pacheco, the cartographer for the expedition. Escalante had been on the shores of Utah Lake, which he named Laguna Timpanogos. It was the larger of the two lakes that appeared on Miera's map. Other cartographers followed his lead and charted Lake Timpanogos as the largest (or larger) lake in the region. As people became aware of the Great Salt Lake, they interpreted the maps to think that "Timpanogos" referred to the Great Salt Lake. On some maps, the two names were used synonymously. In time, "Timpanogos" was dropped from the maps and its original association with Utah Lake was forgotten.

In 1824, it was observed, apparently independently, by Jim Bridger and Etienne Provost. Shortly thereafter, other trappers saw it and walked around it. Most of the trappers, however, were illiterate and did not record their discoveries. As oral reports of their findings made their way to those who did make records, some errors were made. In 1843, John C. Fremont led the first scientific expedition to the lake, but with winter coming on, he did not take the time to survey the entire lake. That happened in 1850 under the leadership of Howard Stansbury (Stansbury discovered and named the Stansbury mountain range and Stansbury island). John Fremont's overly glowing reports of the area were published shortly after his expedition. Stansbury also published a formal report of his survey work which became very popular. His report of the area included a discussion of Mormon religious practices based on Stansbury's interaction with the Mormon community in Great Salt Lake City, which had been established three years earlier in 1847.

Beginning in November 1895, artist and author Alfred Lambourne spent 4 months living on the remote Gunnison Island, where he wrote a book of musing and poetry, Our Inland Sea. From November 1895 to March 1896, he was alone. In March, a few guano sifters arrived to harvest and sell the guano of the nesting birds as fertilizer. Lambourne included musings about these guano sifters in his work. Lambourne left the island early in the winter of 1896 along with the first group of guano sifters.

1930s Fresh Water Project

In the early 1930s, there was a project to dam off a third of the lake with dikes on the east side north of Salt Lake City to make a freshwater reservoir for drinking and irrigation. The project was abandoned before it got beyond the planning stage.

Causeway

The causeway across the lake was built in the 1950s by the Morrison-Knudsen construction company for the Southern Pacific Railroad as a replacement to a previously built wooden trestle, which was the major component of the Lucin Cutoff. The route is now owned and operated by Union Pacific. About 15 trains cross the 20 mi (32 km) causeway each day. Prior to December 2, 2016, the causeway constrained the flow of water between northern and southern arms, which has a significant impact on various industries surrounding the lake. The construction of a 180-foot-long (55 m) bridge created an opening of the causeway for water to flow between the arms of the lake.

Willard Bay Reservoir

Main article: Willard Bay

Willard Bay, also known as Willard Bay Reservoir or Arthur V. Watkins Reservoir is a freshwater reservoir completed in 1964, which separated, drained, and subsequently filled with fresh water from the Weber River a portion of the Great Salt Lake's northeastern arm.

West Desert Pumping Project

Record high water levels in the 1980s caused a large amount of property damage for owners on the eastern side of the Great Salt Lake, and the water started to erode the base of Interstate 80. In response, the State of Utah built the West Desert Pumping Project on the western side of the lake. It began operation on April 10, 1987. This project consists of a pumping station ^{(41°15′9.28″N 113°4′53.31″W)} at Hogup Ridge, containing three pumps with a combined capacity of moving 1,500,000 US gallons per minute (95 m³/s), an inlet canal, and an outlet canal. Also, there are 25 miles (40 km) of dikes and a 10-mile (16 km) access road between the town of Lakeside and the pumping station.

This pumping project was designed to increase the surface area of the Great Salt Lake and thus increase the rate of water evaporation. The pumps drove some of the water of the Great Salt Lake into the 320,000-acre (1300-square kilometer) Newfoundland Evaporation Basin in the desert west of the lake. A weir in the dike at the southern end of the Newfoundland Mountains regulated the level of water in the basin and it sometimes returned salty water from the evaporation basin into the main body of the Great Salt Lake.

At the end of their first year of operation, the pumps had removed about 500,000 acre-feet (620,000,000 m³) of water from the Great Salt Lake. The project was shut down in June 1989, as the level of the lake had dropped by nearly six feet (1.8 meters) since reaching its peak levels during June 1986 and March 1987. The Utah Division of Water Resources credits the project with "over one-third of that decline". In total, the pumps removed 2,730,000 acre-feet (3.37 km³) of water while they operated.

Although the pumps are no longer in use, they have been kept in place in case the level of the Great Salt Lake ever rises that high again.

Shrinking

Drought conditions, climate change, and the overuse of snowmelt have caused the Great Salt Lake to shrink considerably. As of July 2022 the Great Salt Lake occupies some 950 square miles. In 1987, it occupied some 3300 square miles. As of March 2023, the lake's highest recorded surface elevation was 4,211.2 feet on April 15, 1987; the lowest recorded surface elevation was 4,188.5 feet on December 17, 2022. In 2023, it was estimated that without policy changes, the lake would dry up in 2028, with local species killed off by overly salty water somewhat before that.

Geography

Great Salt Lake from airspace over Salt Lake City

The Great Salt Lake lends its name to Salt Lake City, originally named "Great Salt Lake City" by the president of the Church of Jesus Christ of Latter-day Saints (LDS Church), Brigham Young, who led a group of Mormon pioneers to the Salt Lake Valley southeast of the lake on July 24, 1847.

The lake lies in parts of five counties: Box Elder, Davis, Tooele, Weber, and Salt Lake. Salt Lake City and its suburbs are located to the south-east and east of the lake, between the lake and the Wasatch Mountains, but land around the north and west shores is almost uninhabited. The Bonneville Salt Flats are to the west, and the Oquirrh and Stansbury Mountains rise to the south.

The Great Salt Lake is fed by three major rivers and several minor streams. The three major rivers are each fed directly or indirectly from the Uinta Mountain range in northeastern Utah. The Bear River starts on the north slope of the Uintas and flows north past Bear Lake, into which some of Bear River's waters have been diverted via a man-made canal into the lake, but later empty back into the river by means of the Bear Lake Outlet. The river then turns south in southern Idaho and eventually flows into the northeast arm of the Great Salt Lake. The Weber River also starts on the north slope of the Uinta Mountains and flows into the east edge of the lake. The Jordan River does not receive its water directly from the Uintas; rather, it flows from freshwater Utah Lake, which itself is fed primarily by the Provo River. The Provo River does originate in the Uintas, a few miles from the Weber and Bear. The Jordan flows from the north part of Utah Lake into the south-east corner of the Great Salt Lake.

Due to the lake's shallowness, the water level can fall and rise dramatically during dry years or high-precipitation years, thereby reflecting prolonged drought or wet periods. The change in the level of lake level is strongly modulated by the Pacific Ocean through atmospheric circulations that fluctuate at low frequency. By capturing these climate oscillations while using tree-ring reconstruction of lake level, scientists can predict the lake level fluctuation onward for 5–8 years. The Utah Climate Center provides prediction of the Great Salt Lake's annual lake level. This forecast uses central tropical Pacific Ocean temperature, watershed precipitation, tree-ring data of 750+ years, and the lake level itself.

Color difference

A railroad line – the Lucin Cutoff – runs across the lake, crossing the southern end of Promontory Peninsula. The mostly solid causeway supporting the railway divides the lake into three portions: the north-east arm, north-west arm, and southern. The causeway obstructed the normal mixing of the waters of the lake, because there were only three 100-foot (30 m) breaches. Because no rivers, except a few minor streams, flow directly into the north-west arm, Gunnison Bay, it is substantially saltier than the rest of the lake. This saltier environment promotes different types of algae from those growing in the southern part of the lake, leading to a marked color difference on the two sides of the causeway. On December 1, 2016, the opening of a new 180-foot-long (55 m) bridge allowed water to flow from the southern arm of the lake into the north-west arm. At the time of opening of the causeway, the north-west arm was nearly 3 feet (90 cm) lower than the southern arm. By April 2017, the levels of both arms of the lake had risen due to spring runoff, and the north-western arm was within 1 foot (30 cm) of the southern arm.

Islands

Categorically stating the number of islands is difficult, as the method used to determine what is an island is not necessarily the same in each source. Since the water level of the lake can vary greatly between years, what may be considered an island in a high water year may be considered a peninsula in another, or an island in a low water year may be covered during another year. According to the U.S. Department of the Interior and the U.S. Geological Survey, "there are eight named islands in the lake that have never been totally submerged during historic time. All have been connected to the mainland by exposed shoals during periods of low water." In addition to these eight islands, the lake also contains a number of rocks, reefs, or shoals that become fully or partially submerged at high water levels.

The Utah Geological Survey, on the other hand, states "the lake contains 11 recognized islands, although this number varies depending on the level of the lake. Seven islands are in the southern portion of the lake and four in the northwestern portion."

The size and whether they are counted as islands during any particular year depends mostly on the level of the lake. From largest to smallest, they are Antelope Island, Stansbury Island, Fremont Island, Carrington Island, Dolphin Island, Cub Island, and Badger Island, and various rocks, reefs, or shoals with names like Strongs Knob, Gunnison Island, Goose, Browns, Hat (Bird), Egg Island, Black Rock, and White Rock. Dolphin Island, Cub Island, and Strongs Knob are in the northwestern arm. The rest are in the southern portion of the Great Salt Lake.

Sunset viewed from White Rock Bay, on the western shore of Antelope Island. Carrington Island is visible in the distance.

Black Rock, Antelope Island, White Rock, Egg Island, Fremont Island, and the Promontory mountain range are each extensions of the Oquirrh Mountain Range, which dips beneath the lake at its southeastern shore. Stansbury, Carrington, and Hat Islands are extensions of the Stansbury mountain range, and Strongs Knob is an extension of the Lakeside Mountains which run along the lake's western shore. The lake is deepest in the area between these island chains, measured by Howard Stansbury in 1850 at about 35 feet (11 meters) deep, and an average depth of 13 feet (four meters). When the water levels are low, Antelope Island becomes connected to the shore as a peninsula, as do Goose Islands, Browns Island, and some of the other islands. Stansbury Island and Strongs Knob remain peninsulas unless the water level rises well-above the average.

Lake-effect precipitation

Main article: Great Salt Lake effect

Due to the warm waters of the Great Salt Lake, lake-effect snowfalls are frequent phenomena in the surrounding area. Cold north, north-west, or west winds generally blow across the lake following the passage of a cold front, and the temperature difference between the warm lake and the cool air can form clouds that lead to precipitation downwind of the lake. It is typically heaviest in Tooele County to the east, and north into central Davis County, and can deposit excessive snowfall amounts, generally within a narrow band which is highly-dependent on the direction the wind is blowing.

The lake-effect snowfalls are more likely to occur in late fall, early winter and spring, due to the higher temperature differences between the lake and the air above it. During summer, the temperature differences can cause thunderstorms to form over the lake and drift eastward along the northern Wasatch Front. Some rainstorms may also be partially attributed to the lake effect in fall and spring. It is estimated that approximately six to eight lake effect snowstorms occur in a year, and that 10% of the average precipitation of Salt Lake City can be attributed to the lake effect.

Hydrology

Map of Great Salt Lake

Because of its high salt concentration, the lake water is unusually dense, and most people can float more easily than in other bodies of water, particularly in Gunnison Bay, the saltier north arm of the lake.

Water levels have been recorded since 1875, averaging about 4,200 feet (1,300 m) above sea level. Since the Great Salt Lake is a shallow lake with gently sloping shores around all edges except on the south side, small variations in the water level greatly affect the extent of the shoreline. The water level can rise dramatically in wet years and fall during dry years. The water level is also affected by the amount of water flow diverted for agricultural and urban uses. The Jordan and Weber rivers, in particular, are diverted for other uses. In the 1880s, Grove Karl Gilbert predicted that the lake – then in the middle of many years of recession – would virtually disappear except for a small remnant between the islands.

A 2014 study used tree rings collected in the watershed of the Great Salt Lake to create a 576-year record of lake level reconstruction. The lake level change is strongly modulated by Pacific Ocean-coupled ocean/atmospheric oscillations at low frequency and therefore reflects the decadal-scale wet/dry cycles that characterize the region. By capturing these climate oscillations as well as utilizing the tree-ring reconstruction of lake level change, researchers were able to predict the lake level fluctuation onward for as long as 5–8 years.

The Great Salt Lake differs in elevation between the south and north parts. The causeway for the Lucin Cutoff divides the lake into two parts. The water-surface elevation of the south part of the lake is usually 0.5 to 2 feet (15–61 cm) higher than that of the north part because most of the inflow to the lake occurs from the south.

Salinity

Most of the salts dissolved in the lake and deposited in the desert flats around it reflect the concentration of solutes by evaporation; Lake Bonneville itself was fresh enough to support populations of fish. More salt is added yearly via rivers and streams, though the amount is much less than the relict salt from Bonneville.

The salinity of the lake's main basin, Gilbert Bay, is highly variable and depends on the lake's level; it ranges from 5 to 27% (50 to 270 parts per thousand). For comparison, the average salinity of the world ocean is 3.5% (35 parts per thousand) and 33.7% in the Dead Sea. The ionic composition is similar to seawater, much more so than the Dead Sea's water; compared to the ocean, the Great Salt Lake's waters are slightly enriched in potassium and depleted in calcium. Dissolved ions do not necessarily increase or decrease in step with changes of total dissolved solids. For example, in October 1903, dissolved solids tallied 27.72% and by February 1910 they were down to 17.68%, with chlorine, sodium and sulfate levels substantially lower, but over the same time calcium, magnesium and potassium increased, with the increase of magnesium especially pronounced.

Ecosystem

American avocets at Bear River Migratory Bird Refuge

 

Mountains of the Great Salt Lake in winter.

 

Modern stromatolites (cyanobacteria) growing along the western shore of Antelope Island near Elephant Head.

The high salinity in parts of the lake makes them uninhabitable for all but a few species, including brine shrimp, brine flies, and several forms of algae. The brine flies have an estimated population of over one hundred billion and serve as the main source of food for many of the birds which migrate to the lake. However, the fresh- and salt-water wetlands along the eastern and northern edges of the Great Salt Lake provide critical habitat for millions of migratory shorebirds and waterfowl in western North America. These marshes account for approximately 75% of the wetlands in Utah. Some of the birds that depend on these marshes include: Wilson's phalarope, red-necked phalarope, American avocet, black-necked stilt, marbled godwit, snowy plover, western sandpiper, long-billed dowitcher, tundra swan, American white pelican, white-faced ibis, California gull, eared grebe, peregrine falcon, bald eagle, plus large populations of various ducks and geese.

There are twenty-seven private duck clubs, seven state waterfowl management areas, and a large federal bird refuge on the Great Salt Lake's shores. Wetland/wildlife management areas include the Bear River Migratory Bird Refuge; Gillmor Sanctuary; Great Salt Lake Shore lands Preserve; Salt Creek, Public Shooting Grounds, Harold Crane, Locomotive Springs, Ogden Bay, Timpie Springs, and Farmington Bay Waterfowl Management Areas.

Several islands in the lake provide critical nesting areas for various birds. Access to Hat, Gunnison, and Cub islands is strictly limited by the State of Utah in an effort to protect nesting colonies of American white pelican (Pelecanus erythrorhynchos). The islands within the Great Salt Lake also provide habitat for lizard and mammalian wildlife and a variety of plant species. Some species may have been extirpated from the islands. For example, a number of explorers who visited the area in the mid-1800s (e.g. Emmanuel Domenech, Howard Stansbury, Jules Rémy) noted an abundance of yellow-flowered "onions" on several of the islands, which they identified as Calochortus luteus. This species today occurs only in California; however, at that time the name C. luteus was applied to plants that later were named C. nuttallii. A yellow-flowered Calochortus was first named as a variety of C. nuttallii but was later separated into a new species, C. aureus. This species occurs in Utah today, though apparently no longer on the islands of the Great Salt Lake.

Because of the Great Salt Lake's high salinity, it has few fish, but they do occur in Bear River Bay and Farmington Bay when spring runoff brings fresh water into the lake. A few aquatic animals live in the lake's main basin, including centimeter-long brine shrimp (Artemia franciscana). Their tiny, hard-walled eggs or cysts (diameter about 200 micrometers) are harvested in quantity during the fall and early winter. They are fed to prawns in Asia, sold as novelty "Sea-Monkeys," sold either live or dehydrated in pet stores as a fish food, and used in testing of toxins, drugs, and other chemicals. There are also two species of brine fly, as well as protozoa, rotifers, bacteria and algae.

Salinity differences between the sections of the lake separated by the railroad causeway result in significantly different biota. A phytoplankton community dominated by green algae or cyanobacteria (blue-green algae) tint the water south of the causeway a greenish color. North of the causeway, the lake is dominated by Dunaliella salina, a species of algae which releases beta-carotene, and the bacteria-like haloarchaea, which together give the water an unusual reddish or purplish color. The dense, high-salinity water of the North Arm flows back through the causeway into the Southern portion of the lake, creating a deep brine layer there.

Migratory birds on the Great Salt Lake

Although brine shrimp can be found in the arm of the lake north of the causeway, studies conducted by the Utah Division of Wildlife Resources indicate that these are likely transient. Populations of brine shrimp are mostly restricted to the lake's south arm.

In the two bays that receive most of the lake's freshwater inflows, Bear River Bay and Farmington Bay, the diversity of organisms is much higher. Salinities in these bays can approach that of fresh water when the spring snow melt occurs, and this allows a variety of bacteria, algae and invertebrates to proliferate in the nutrient-rich water. The abundance of invertebrates such as gnat larvae (chironomids) and back swimmers (Trichocorixa) are fed upon extensively by the huge shorebird and waterfowl populations that utilize the lake. Fish in these bays are fed upon by diving terns and pelicans.

Pink Floyd the flamingo

A solitary Chilean flamingo, named Pink Floyd after the English rock band, wintered at the Great Salt Lake. He escaped from Salt Lake City's Tracy Aviary in 1987 and lived in the wild, eating brine shrimp and socializing with gulls and swans. A group of Utah residents suggested petitioning the state to release more flamingos in an effort to keep Floyd company and as a possible tourist attraction. Pink Floyd was last seen in Idaho, in the area of Camas National Wildlife Refuge in 2005.

Elevated mercury levels

During a survey in the mid-1990s, U.S. Geological Survey and U.S. Fish and Wildlife Service researchers discovered a high level of methylmercury in the Great Salt Lake with 25 nanograms per liter of water. For comparison, a fish consumption advisory was issued at the Florida Everglades after water there was found to contain 1 nanogram per liter. The extremely high methylmercury concentrations have been only in the lake's anoxic deep brine layer (monimolimnion) below a depth of 20 feet (6.1 m), but concentrations are also moderately high up in the water column where there is oxygen to support brine shrimp and brine flies.

The toxic metal shows up throughout the lake's food chain, from brine shrimp to eared grebes and cinnamon teal.

The finding of high mercury levels prompted further studies, and a health advisory warning hunters not to eat common goldeneye or northern shoveler, two species of duck found in the lake. It has been stated that this does not pose a risk to other recreational users of the lake.

After later studies were conducted with a larger number of birds, the advisories were revised and another was added for cinnamon teal. Seven other species of duck were studied and found to have levels of mercury below EPA guidelines, thus being determined safe to eat.

A study in 2010 suggested that the main source of the mercury is from atmospheric deposition from worldwide industry, rather than local sources. As water levels rise and fall, mercury accumulation does as well. About 16% of the mercury is from rivers, and 84% is from the atmosphere as an inorganic form, which is converted into more toxic methyl mercury by bacteria which thrive in the more saline water of the North arm affected by the causeway. A 2020 study found high concentrations of mercury in the lake's sediments, a consequence from smelting and mining activities in the surrounding mountains. The mercury and other metals can contaminate the overlying water, and in turn, move into brine shrimp and other organisms.

Commerce

Solar evaporation ponds in the Northeast portion of the lake. Fremont Island is visible to the South (top of image)

Great Salt Lake contributes an estimated $1.3 billion annually to Utah's economy, including $1.1 billion from industry (primarily mineral extraction), $136 million from recreation, and $57 million from the harvest of brine shrimp.

Solar evaporation ponds at the edges of the lake produce salts and brine (water with high salt quantity). Minerals extracted from the lake include: sodium chloride (common salt), used in water softeners, salt lick blocks for livestock, and to melt ice on local roadways (food-grade salt is not produced from the lake, as it would require costly processing to ensure its purity); potassium sulfate, used as a commercial fertilizer; and magnesium-chloride brine, used in the production of magnesium metal, chlorine gas, and as a dust suppressant. US Magnesium operates a plant on the southwest shore of the lake, which produces 14% of the worldwide supply of magnesium, more than any other North American magnesium operation. Mineral-extraction companies operating on the lake pay royalties on their products to the State of Utah, which owns the lake.

Brine shrimp

The harvest of brine shrimp cysts during fall and early winter has developed into a significant local industry, with the lake providing 35% to 45% of the worldwide supply of brine shrimp, and cysts selling for as high as $35 per pound ($77/kg). Brine shrimp were first harvested during the 1950s and sold as commercial fish food. In the 1970s, the focus changed to their eggs, known as cysts, which were sold primarily outside the US as food for shrimp, prawns, and some fish. Today, these are mostly sold in East Asia and South America. The amount of cysts and the quality are affected by several factors, but salinity is most important. The cysts will hatch at 2 to 3% salinity, but the greatest productivity is at salinities above about 10%. If the salinity drops near 5% to 6%, the cysts will lose buoyancy and sink, making them more difficult to harvest.

The causeway across the lake was built in the 1950s as a replacement to a wooden trestle. Prior to December 2, 2016, the causeway constrained the flow of water between northern and southern arms, which has a significant impact on various industries surrounding the lake. The construction of a 180-foot-long (55 m) bridge created an opening of the causeway for water to flow between the arms of the lake.

The northern arm of the lake has a much higher salinity, to the point that the native brine shrimp cannot survive in its waters. In the southern portion of the lake, where the vast majority of the fresh water inlets are found, the salt level can dip below what is necessary for the brine shrimp to survive. With the opening of the bridge, the salinity of the northern arm of the lake will likely drop as less saline water from the southern arm of the lake flows into the northern arm. The brine shrimp harvesting industry could benefit from the freer flow of water. There were concerns from the brine shrimp harvesting industry that the conditions in the southern arm of the lake were becoming too saline for the brine shrimp, following several years of lower precipitation in the lake's watershed. The precipitation in the watershed was above normal for the water year beginning on October 1, 2016. The additional water allowed the levels of both arms of the lake to rise, creating better conditions for a healthy brine shrimp population.

Oil and minerals

Great Salt Lake Minerals Company (a subsidiary of Compass Minerals) extracts minerals from the northern bay. The company potentially benefited from the higher salinity of the north-west arm of the lake but had difficulty accessing water from the lake because of lower water level. Prior to the opening of the causeway, the intake channels had to be extended to reach the water.

Morton Salt, Cargill Salt, Broken Arrow Salt and the Renco Group's U.S. Magnesium each extract minerals from the southern bay and could benefit from a more natural mixture of water between the two sides of the lake.

The lake's north arm contains deposits of oil, but it is of poor quality and it is not economically feasible to extract and purify it. As of 1993, approximately 3,000 barrels (480 m³) of crude oil had been produced from shallow wells along the shore. The oil field at Rozel Point produced an estimated 10,000 barrels (1,600 m³) of oil from 30 to 50 wells, but has been inactive since the mid-1980s. Oil seeps in the area had been known since the late 19th century, and attempts at production began in 1904. Industrial debris from this field remained in place near Spiral Jetty until a cleanup effort by the Division of Oil, Gas and Mining and the Division of Forestry, Fire, and State Lands was completed in December 2005.

Recreation

The lake is one of Utah's largest tourist attractions. Antelope Island State Park is a popular tourist destination that offers panoramic views of the lake, hiking and biking trails, wildlife viewing and access to beaches.

The State of Utah operates a marina on the south shore of the lake at Great Salt Lake State Park and another in Antelope Island State Park. With its sudden storms and expansive spread, the lake is a great test of sailing skills. Single mast, simple sloops are the most popular boats. Sudden storms and lack of experience on the part of boaters are the two most dangerous elements in boating and sailing on the Great Salt Lake.

Dramatically fluctuating lake levels have inhibited the creation and success of tourist-related developments. There is also a problem with pollution from industrial and urban effluent, as well as a natural "lake stink" caused by the decay of insects and other wildlife, particularly during times of low water.

Saltair

The original Saltair, c. 1900

 

Main article: Saltair (Utah)

Three resorts have operated under the name Saltair on the southern shore of the lake since 1893. Rising and lowering water levels have affected each iteration.

The first Saltair pavilion was destroyed by fire on April 22, 1925. A new pavilion was built and the resort was expanded at the same location by new investors, but after being closed for several years, it was destroyed by arson in 1970. The second Saltair included a fun house and a dancing venue.

The current Saltair serves as a concert venue. The new resort was completed in 1981, approximately a mile (1600 m) west of the original.

Garfield Beach Resort

Garfield Beach Resort, 1888

The Garfield Beach Resort was established by Captain Thomas Douris in 1881 and was originally called Garfield Landing. The resort was located near Black Rock outside of the town of Corinne, and patrons traveled to it via the steamboat General Garfield. After the expansion of the resort, the General Garfield was replaced by two steamers, the Susie Riter and the Whirlwind. The iconic General Garfield was moored to the dock as a landmark. The main attraction of the resort was a massive pavilion 400 feet from shore. It covered 165 by 400 feet (50 by 122 m) and included 300 feet (91 m) of covered deck. The success of Garfield Beach eventually overtook the neighboring Black Rock resort. In 1887, the resort was purchased by the Utah and Nevada railroad. They improved the site by adding an array of bathhouses, a restaurant, and other amenities, including a bowling alley. The resort was the Salt Lake's first to have an electric generator, which powered its many concerts, and parties held atop the pavilion tower. Garfield Beach was the most popular Salt Lake resort until Saltair was built in 1893. The resort was put out of service by a fire in 1904.

Arts and culture

Robert Smithson's Spiral Jetty

Spiral Jetty

The northwest arm of the lake, near Rozel Point, is the location for Robert Smithson's work of land art, Spiral Jetty (1970), which is only visible when the level of Great Salt Lake drops below 4,197.8 feet (1,279.5 m) above sea level.

Oolitic sand

The lake and its shores contain oolitic sand, small, rounded, or spherical grains of sand that are made up of a nucleus (generally a small mineral grain) and concentric layers of calcium carbonate (lime) and look similar to very small pearls.

Whales in the Great Salt Lake

Local legend maintains that in 1875, entrepreneur James Wickham had two whales released into the Great Salt Lake, with the intent of using them as a tourist attraction. The whales are said to have disappeared into the lake and been subsequently sighted multiple times over a number of months, but there have never been any confirmed sightings of the whales since the time of their supposed release. Scientists believe they could not have survived due to the high salinity of the lake. 

Lake monster

In mid-1877, J. H. McNeil was with many other Barnes and Co. Salt Works employees on the lake's north shore in the evening. They claimed to have seen a large monster with a body like a crocodile and a horse’s head in the lake. They claimed this monster attacked the men, who quickly ran away and hid until morning. This creature is regarded by some to have simply been a buffalo in the lake. Thirty years prior, "Brother Bainbridge" claimed to have sighted a creature that looked like a dolphin in the lake near Antelope Island. This monster is called by some the North Shore Monster.

Analog computer

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Analog_computer

 

A page from the Bombardier's Information File (BIF) that describes the components and controls of the Norden bombsight. The Norden bombsight was a highly sophisticated optical/mechanical analog computer used by the United States Army Air Force during World War II, the Korean War, and the Vietnam War to aid the pilot of a bomber aircraft in dropping bombs accurately.

 

TR-10 desktop analog computer of the late 1960s and early 1970s

An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities (analog signals) to model the problem being solved. In contrast, digital computers represent varying quantities symbolically and by discrete values of both time and amplitude (digital signals).

Analog computers can have a very wide range of complexity. Slide rules and nomograms are the simplest, while naval gunfire control computers and large hybrid digital/analog computers were among the most complicated. Complex mechanisms for process control and protective relays used analog computation to perform control and protective functions.

Analog computers were widely used in scientific and industrial applications even after the advent of digital computers, because at the time they were typically much faster, but they started to become obsolete as early as the 1950s and 1960s, although they remained in use in some specific applications, such as aircraft flight simulators, the flight computer in aircraft, and for teaching control systems in universities. Perhaps the most relatable example of analog computers are mechanical watches where the continuous and periodic rotation of interlinked gears drives the second, minute and hour needles in the clock. More complex applications, such as aircraft flight simulators and synthetic-aperture radar, remained the domain of analog computing (and hybrid computing) well into the 1980s, since digital computers were insufficient for the task.

Timeline of analog computers

See also: History of computing hardware § Analog computers

Precursors

See also: Timeline of computing hardware before 1950

This is a list of examples of early computation devices considered precursors of the modern computers. Some of them may even have been dubbed 'computers' by the press, though they may fail to fit modern definitions.

The Antikythera mechanism, dating between 150 and 100 BC, was an early analog computer.

The Antikythera mechanism, a type of device used to determine the positions of heavenly bodies known as an orrery, was described as an early mechanical analog computer by British physicist, information scientist, and historian of science Derek J. de Solla Price. It was discovered in 1901, in the Antikythera wreck off the Greek island of Antikythera, between Kythera and Crete, and has been dated to c. 150~100 BC, during the Hellenistic period. Devices of a level of complexity comparable to that of the Antikythera mechanism would not reappear until a thousand years later.

Many mechanical aids to calculation and measurement were constructed for astronomical and navigation use. The planisphere was first described by Ptolemy in the 2nd century AD. The astrolabe was invented in the Hellenistic world in either the 1st or 2nd centuries BC and is often attributed to Hipparchus. A combination of the planisphere and dioptra, the astrolabe was effectively an analog computer capable of working out several different kinds of problems in spherical astronomy. An astrolabe incorporating a mechanical calendar computer and gear-wheels was invented by Abi Bakr of Isfahan, Persia in 1235. Abū Rayhān al-Bīrūnī invented the first mechanical geared lunisolar calendar astrolabe, an early fixed-wired knowledge processing machine with a gear train and gear-wheels, c. AD 1000.

The sector, a calculating instrument used for solving problems in proportion, trigonometry, multiplication and division, and for various functions, such as squares and cube roots, was developed in the late 16th century and found application in gunnery, surveying and navigation.

The planimeter was a manual instrument to calculate the area of a closed figure by tracing over it with a mechanical linkage.

A slide rule. The sliding central slip is set to 1.3, the cursor to 2.0 and points to the multiplied result of 2.6.

The slide rule was invented around 1620–1630, shortly after the publication of the concept of the logarithm. It is a hand-operated analog computer for doing multiplication and division. As slide rule development progressed, added scales provided reciprocals, squares and square roots, cubes and cube roots, as well as transcendental functions such as logarithms and exponentials, circular and hyperbolic trigonometry and other functions. Aviation is one of the few fields where slide rules are still in widespread use, particularly for solving time–distance problems in light aircraft.

In 1831–1835, mathematician and engineer Giovanni Plana devised a perpetual-calendar machine, which, through a system of pulleys and cylinders, could predict the perpetual calendar for every year from AD 0 (that is, 1 BC) to AD 4000, keeping track of leap years and varying day length.

The tide-predicting machine invented by Sir William Thomson in 1872 was of great utility to navigation in shallow waters. It used a system of pulleys and wires to automatically calculate predicted tide levels for a set period at a particular location.

The differential analyser, a mechanical analog computer designed to solve differential equations by integration, used wheel-and-disc mechanisms to perform the integration. In 1876 James Thomson had already discussed the possible construction of such calculators, but he had been stymied by the limited output torque of the ball-and-disk integrators. A number of similar systems followed, notably those of the Spanish engineer Leonardo Torres y Quevedo, who built several machines for solving real and complex roots of polynomials; and Michelson and Stratton, whose Harmonic Analyser performed Fourier analysis, but using an array of 80 springs rather than Kelvin integrators. This work led to the mathematical understanding of the Gibbs phenomenon of overshoot in Fourier representation near discontinuities. In a differential analyzer, the output of one integrator drove the input of the next integrator, or a graphing output. The torque amplifier was the advance that allowed these machines to work. Starting in the 1920s, Vannevar Bush and others developed mechanical differential analyzers.

Modern era

Analog computing machine at the Lewis Flight Propulsion Laboratory circa 1949.

Heathkit EC-1 educational analog computer

The Dumaresq was a mechanical calculating device invented around 1902 by Lieutenant John Dumaresq of the Royal Navy. It was an analog computer that related vital variables of the fire control problem to the movement of one's own ship and that of a target ship. It was often used with other devices, such as a Vickers range clock to generate range and deflection data so the gun sights of the ship could be continuously set. A number of versions of the Dumaresq were produced of increasing complexity as development proceeded.

By 1912, Arthur Pollen had developed an electrically driven mechanical analog computer for fire-control systems, based on the differential analyser. It was used by the Imperial Russian Navy in World War I.

Starting in 1929, AC network analyzers were constructed to solve calculation problems related to electrical power systems that were too large to solve with numerical methods at the time. These were essentially scale models of the electrical properties of the full-size system. Since network analyzers could handle problems too large for analytic methods or hand computation, they were also used to solve problems in nuclear physics and in the design of structures. More than 50 large network analyzers were built by the end of the 1950s.

World War II era gun directors, gun data computers, and bomb sights used mechanical analog computers. In 1942 Helmut Hölzer built a fully electronic analog computer at Peenemünde Army Research Center as an embedded control system (mixing device) to calculate V-2 rocket trajectories from the accelerations and orientations (measured by gyroscopes) and to stabilize and guide the missile. Mechanical analog computers were very important in gun fire control in World War II, the Korean War and well past the Vietnam War; they were made in significant numbers.

In the period 1930–1945 in the Netherlands, Johan van Veen developed an analogue computer to calculate and predict tidal currents when the geometry of the channels are changed. Around 1950, this idea was developed into the Deltar, a hydraulic analogy computer supporting the closure of estuaries in the southwest of the Netherlands (the Delta Works).

The FERMIAC was an analog computer invented by physicist Enrico Fermi in 1947 to aid in his studies of neutron transport. Project Cyclone was an analog computer developed by Reeves in 1950 for the analysis and design of dynamic systems. Project Typhoon was an analog computer developed by RCA in 1952. It consisted of over 4,000 electron tubes and used 100 dials and 6,000 plug-in connectors to program. The MONIAC Computer was a hydraulic analogy of a national economy first unveiled in 1949.

Computer Engineering Associates was spun out of Caltech in 1950 to provide commercial services using the "Direct Analogy Electric Analog Computer" ("the largest and most impressive general-purpose analyzer facility for the solution of field problems") developed there by Gilbert D. McCann, Charles H. Wilts, and Bart Locanthi.

Educational analog computers illustrated the principles of analog calculation. The Heathkit EC-1, a $199 educational analog computer, was made by the Heath Company, US c. 1960. It was programmed using patch cords that connected nine operational amplifiers and other components. General Electric also marketed an "educational" analog computer kit of a simple design in the early 1960s consisting of two transistor tone generators and three potentiometers wired such that the frequency of the oscillator was nulled when the potentiometer dials were positioned by hand to satisfy an equation. The relative resistance of the potentiometer was then equivalent to the formula of the equation being solved. Multiplication or division could be performed, depending on which dials were inputs and which was the output. Accuracy and resolution was limited and a simple slide rule was more accurate. However, the unit did demonstrate the basic principle.

Analog computer designs were published in electronics magazines. One example is the PEAC (Practical Electronics analogue computer), published in Practical Electronics in the January 1968 edition. Another more modern hybrid computer design was published in Everyday Practical Electronics in 2002. An example described in the EPE hybrid computer was the flight of a VTOL aircraft such as the Harrier jump jet. The altitude and speed of the aircraft were calculated by the analog part of the computer and sent to a PC via a digital microprocessor and displayed on the PC screen.

In industrial process control, analog loop controllers were used to automatically regulate temperature, flow, pressure, or other process conditions. The technology of these controllers ranged from purely mechanical integrators, through vacuum-tube and solid-state devices, to emulation of analog controllers by microprocessors.

Electronic analog computers

Polish analog computer AKAT-1 (1959)

 

EAI 8800 Analog computing system used for hardware-in-the-loop simulation of a Claas tractor (1986)

The similarity between linear mechanical components, such as springs and dashpots (viscous-fluid dampers), and electrical components, such as capacitors, inductors, and resistors is striking in terms of mathematics. They can be modeled using equations of the same form.

However, the difference between these systems is what makes analog computing useful. Complex systems often are not amenable to pen-and-paper analysis, and require some form of testing or simulation. Complex mechanical systems, such as suspensions for racing cars, are expensive to fabricate and hard to modify. And taking precise mechanical measurements during high-speed tests adds further difficulty.

By contrast, it is very inexpensive to build an electrical equivalent of a complex mechanical system, to simulate its behavior. Engineers arrange a few operational amplifiers (op amps) and some passive linear components to form a circuit that follows the same equations as the mechanical system being simulated. All measurements can be taken directly with an oscilloscope. In the circuit, the (simulated) stiffness of the spring, for instance, can be changed by adjusting the parameters of an integrator. The electrical system is an analogy to the physical system, hence the name, but it is much less expensive than a mechanical prototype, much easier to modify, and generally safer.

The electronic circuit can also be made to run faster or slower than the physical system being simulated. Experienced users of electronic analog computers said that they offered a comparatively intimate control and understanding of the problem, relative to digital simulations.

Electronic analog computers are especially well-suited to representing situations described by differential equations. Historically, they were often used when a system of differential equations proved very difficult to solve by traditional means. As a simple example, the dynamics of a spring-mass system can be described by the equation ${\displaystyle m\ddot{y}+d\dot{y}+cy=mg}$, with ${\displaystyle y}$ as the vertical position of a mass ${\displaystyle m}$, ${\displaystyle d}$ the damping coefficient, ${\displaystyle c}$ the spring constant and ${\displaystyle g}$ the gravity of Earth. For analog computing, the equation is programmed as ${\displaystyle \ddot{y}=-\frac{d}{m}\dot{y}-\frac{c}{m}y-g}$. The equivalent analog circuit consists of two integrators for the state variables ${\displaystyle -\dot{y}}$ (speed) and ${\displaystyle y}$ (position), one inverter, and three potentiometers.

Electronic analog computers have drawbacks: the value of the circuit's supply voltage limits the range over which the variables may vary (since the value of a variable is represented by a voltage on a particular wire). Therefore, each problem must be scaled so its parameters and dimensions can be represented using voltages that the circuit can supply —e.g., the expected magnitudes of the velocity and the position of a spring pendulum. Improperly scaled variables can have their values "clamped" by the limits of the supply voltage. Or if scaled too small, they can suffer from higher noise levels. Either problem can cause the circuit to produce an incorrect simulation of the physical system. (Modern digital simulations are much more robust to widely varying values of their variables, but are still not entirely immune to these concerns: floating-point digital calculations support a huge dynamic range, but can suffer from imprecision if tiny differences of huge values lead to numerical instability.)

Analog circuit for the dynamics of a spring-mass system (without scaling factors)

 

Damped motion of a spring-mass system

The precision of the analog computer readout was limited chiefly by the precision of the readout equipment used, generally three or four significant figures. (Modern digital simulations are much better in this area. Digital arbitrary-precision arithmetic can provide any desired degree of precision.) However, in most cases the precision of an analog computer is absolutely sufficient given the uncertainty of the model characteristics and its technical parameters.

Many small computers dedicated to specific computations are still part of industrial regulation equipment, but from the 1950s to the 1970s, general-purpose analog computers were the only systems fast enough for real time simulation of dynamic systems, especially in the aircraft, military and aerospace field.

In the 1960s, the major manufacturer was Electronic Associates of Princeton, New Jersey, with its 231R Analog Computer (vacuum tubes, 20 integrators) and subsequently its EAI 8800 Analog Computer (solid state operational amplifiers, 64 integrators). Its challenger was Applied Dynamics of Ann Arbor, Michigan.

Although the basic technology for analog computers is usually operational amplifiers (also called "continuous current amplifiers" because they have no low frequency limitation), in the 1960s an attempt was made in the French ANALAC computer to use an alternative technology: medium frequency carrier and non dissipative reversible circuits.

In the 1970s, every large company and administration concerned with problems in dynamics had an analog computing center, such as:

• In the US: NASA (Huntsville, Houston), Martin Marietta (Orlando), Lockheed, Westinghouse, Hughes Aircraft
• In Europe: CEA (French Atomic Energy Commission), MATRA, Aérospatiale, BAC (British Aircraft Corporation).

Analog–digital hybrids

Analog computing devices are fast, digital computing devices are more versatile and accurate, so the idea is to combine the two processes for the best efficiency. An example of such hybrid elementary device is the hybrid multiplier where one input is an analog signal, the other input is a digital signal and the output is analog. It acts as an analog potentiometer upgradable digitally. This kind of hybrid technique is mainly used for fast dedicated real time computation when computing time is very critical as signal processing for radars and generally for controllers in embedded systems.

In the early 1970s, analog computer manufacturers tried to tie together their analog computer with a digital computer to get the advantages of the two techniques. In such systems, the digital computer controlled the analog computer, providing initial set-up, initiating multiple analog runs, and automatically feeding and collecting data. The digital computer may also participate to the calculation itself using analog-to-digital and digital-to-analog converters.

The largest manufacturer of hybrid computers was Electronics Associates. Their hybrid computer model 8900 was made of a digital computer and one or more analog consoles. These systems were mainly dedicated to large projects such as the Apollo program and Space Shuttle at NASA, or Ariane in Europe, especially during the integration step where at the beginning everything is simulated, and progressively real components replace their simulated part.

Only one company was known as offering general commercial computing services on its hybrid computers, CISI of France, in the 1970s.

The best reference in this field is the 100,000 simulation runs for each certification of the automatic landing systems of Airbus and Concorde aircraft.

After 1980, purely digital computers progressed more and more rapidly and were fast enough to compete with analog computers. One key to the speed of analog computers was their fully parallel computation, but this was also a limitation. The more equations required for a problem, the more analog components were needed, even when the problem wasn't time critical. "Programming" a problem meant interconnecting the analog operators; even with a removable wiring panel this was not very versatile. Today there are no more big hybrid computers, but only hybrid components.

Implementations

Mechanical analog computers

Main article: Mechanical computer

 

William Ferrel's tide-predicting machine of 1881–1882

While a wide variety of mechanisms have been developed throughout history, some stand out because of their theoretical importance, or because they were manufactured in significant quantities.

Most practical mechanical analog computers of any significant complexity used rotating shafts to carry variables from one mechanism to another. Cables and pulleys were used in a Fourier synthesizer, a tide-predicting machine, which summed the individual harmonic components. Another category, not nearly as well known, used rotating shafts only for input and output, with precision racks and pinions. The racks were connected to linkages that performed the computation. At least one U.S. Naval sonar fire control computer of the later 1950s, made by Librascope, was of this type, as was the principal computer in the Mk. 56 Gun Fire Control System.

Online, there is a remarkably clear illustrated reference (OP 1140) that describes the fire control computer mechanisms. For adding and subtracting, precision miter-gear differentials were in common use in some computers; the Ford Instrument Mark I Fire Control Computer contained about 160 of them.

Integration with respect to another variable was done by a rotating disc driven by one variable. Output came from a pick-off device (such as a wheel) positioned at a radius on the disc proportional to the second variable. (A carrier with a pair of steel balls supported by small rollers worked especially well. A roller, its axis parallel to the disc's surface, provided the output. It was held against the pair of balls by a spring.)

Arbitrary functions of one variable were provided by cams, with gearing to convert follower movement to shaft rotation.

Functions of two variables were provided by three-dimensional cams. In one good design, one of the variables rotated the cam. A hemispherical follower moved its carrier on a pivot axis parallel to that of the cam's rotating axis. Pivoting motion was the output. The second variable moved the follower along the axis of the cam. One practical application was ballistics in gunnery.

Coordinate conversion from polar to rectangular was done by a mechanical resolver (called a "component solver" in US Navy fire control computers). Two discs on a common axis positioned a sliding block with pin (stubby shaft) on it. One disc was a face cam, and a follower on the block in the face cam's groove set the radius. The other disc, closer to the pin, contained a straight slot in which the block moved. The input angle rotated the latter disc (the face cam disc, for an unchanging radius, rotated with the other (angle) disc; a differential and a few gears did this correction).

Referring to the mechanism's frame, the location of the pin corresponded to the tip of the vector represented by the angle and magnitude inputs. Mounted on that pin was a square block.

Rectilinear-coordinate outputs (both sine and cosine, typically) came from two slotted plates, each slot fitting on the block just mentioned. The plates moved in straight lines, the movement of one plate at right angles to that of the other. The slots were at right angles to the direction of movement. Each plate, by itself, was like a Scotch yoke, known to steam engine enthusiasts.

During World War II, a similar mechanism converted rectilinear to polar coordinates, but it was not particularly successful and was eliminated in a significant redesign (USN, Mk. 1 to Mk. 1A).

Multiplication was done by mechanisms based on the geometry of similar right triangles. Using the trigonometric terms for a right triangle, specifically opposite, adjacent, and hypotenuse, the adjacent side was fixed by construction. One variable changed the magnitude of the opposite side. In many cases, this variable changed sign; the hypotenuse could coincide with the adjacent side (a zero input), or move beyond the adjacent side, representing a sign change.

Typically, a pinion-operated rack moving parallel to the (trig.-defined) opposite side would position a slide with a slot coincident with the hypotenuse. A pivot on the rack let the slide's angle change freely. At the other end of the slide (the angle, in trig. terms), a block on a pin fixed to the frame defined the vertex between the hypotenuse and the adjacent side.

At any distance along the adjacent side, a line perpendicular to it intersects the hypotenuse at a particular point. The distance between that point and the adjacent side is some fraction that is the product of 1 the distance from the vertex, and 2 the magnitude of the opposite side.

The second input variable in this type of multiplier positions a slotted plate perpendicular to the adjacent side. That slot contains a block, and that block's position in its slot is determined by another block right next to it. The latter slides along the hypotenuse, so the two blocks are positioned at a distance from the (trig.) adjacent side by an amount proportional to the product.

To provide the product as an output, a third element, another slotted plate, also moves parallel to the (trig.) opposite side of the theoretical triangle. As usual, the slot is perpendicular to the direction of movement. A block in its slot, pivoted to the hypotenuse block positions it.

A special type of integrator, used at a point where only moderate accuracy was needed, was based on a steel ball, instead of a disc. It had two inputs, one to rotate the ball, and the other to define the angle of the ball's rotating axis. That axis was always in a plane that contained the axes of two movement pick-off rollers, quite similar to the mechanism of a rolling-ball computer mouse (in that mechanism, the pick-off rollers were roughly the same diameter as the ball). The pick-off roller axes were at right angles.

A pair of rollers "above" and "below" the pick-off plane were mounted in rotating holders that were geared together. That gearing was driven by the angle input, and established the rotating axis of the ball. The other input rotated the "bottom" roller to make the ball rotate.

Essentially, the whole mechanism, called a component integrator, was a variable-speed drive with one motion input and two outputs, as well as an angle input. The angle input varied the ratio (and direction) of coupling between the "motion" input and the outputs according to the sine and cosine of the input angle.

Although they did not accomplish any computation, electromechanical position servos were essential in mechanical analog computers of the "rotating-shaft" type for providing operating torque to the inputs of subsequent computing mechanisms, as well as driving output data-transmission devices such as large torque-transmitter synchros in naval computers.

Other readout mechanisms, not directly part of the computation, included internal odometer-like counters with interpolating drum dials for indicating internal variables, and mechanical multi-turn limit stops.

Considering that accurately controlled rotational speed in analog fire-control computers was a basic element of their accuracy, there was a motor with its average speed controlled by a balance wheel, hairspring, jeweled-bearing differential, a twin-lobe cam, and spring-loaded contacts (ship's AC power frequency was not necessarily accurate, nor dependable enough, when these computers were designed).

Electronic analog computers

Switching board of EAI 8800 analog computer (front view)

Electronic analog computers typically have front panels with numerous jacks (single-contact sockets) that permit patch cords (flexible wires with plugs at both ends) to create the interconnections that define the problem setup. In addition, there are precision high-resolution potentiometers (variable resistors) for setting up (and, when needed, varying) scale factors. In addition, there is usually a zero-center analog pointer-type meter for modest-accuracy voltage measurement. Stable, accurate voltage sources provide known magnitudes.

Typical electronic analog computers contain anywhere from a few to a hundred or more operational amplifiers ("op amps"), named because they perform mathematical operations. Op amps are a particular type of feedback amplifier with very high gain and stable input (low and stable offset). They are always used with precision feedback components that, in operation, all but cancel out the currents arriving from input components. The majority of op amps in a representative setup are summing amplifiers, which add and subtract analog voltages, providing the result at their output jacks. As well, op amps with capacitor feedback are usually included in a setup; they integrate the sum of their inputs with respect to time.

Integrating with respect to another variable is the nearly exclusive province of mechanical analog integrators; it is almost never done in electronic analog computers. However, given that a problem solution does not change with time, time can serve as one of the variables.

Other computing elements include analog multipliers, nonlinear function generators, and analog comparators.

Electrical elements such as inductors and capacitors used in electrical analog computers had to be carefully manufactured to reduce non-ideal effects. For example, in the construction of AC power network analyzers, one motive for using higher frequencies for the calculator (instead of the actual power frequency) was that higher-quality inductors could be more easily made. Many general-purpose analog computers avoided the use of inductors entirely, re-casting the problem in a form that could be solved using only resistive and capacitive elements, since high-quality capacitors are relatively easy to make.

The use of electrical properties in analog computers means that calculations are normally performed in real time (or faster), at a speed determined mostly by the frequency response of the operational amplifiers and other computing elements. In the history of electronic analog computers, there were some special high-speed types.

Nonlinear functions and calculations can be constructed to a limited precision (three or four digits) by designing function generators—special circuits of various combinations of resistors and diodes to provide the nonlinearity. Typically, as the input voltage increases, progressively more diodes conduct.

When compensated for temperature, the forward voltage drop of a transistor's base-emitter junction can provide a usably accurate logarithmic or exponential function. Op amps scale the output voltage so that it is usable with the rest of the computer.

Any physical process that models some computation can be interpreted as an analog computer. Some examples, invented for the purpose of illustrating the concept of analog computation, include using a bundle of spaghetti as a model of sorting numbers; a board, a set of nails, and a rubber band as a model of finding the convex hull of a set of points; and strings tied together as a model of finding the shortest path in a network. These are all described in Dewdney (1984).

Components

A 1960 Newmark analogue computer, made up of five units. This computer was used to solve differential equations and is currently housed at the Cambridge Museum of Technology.

Analog computers often have a complicated framework, but they have, at their core, a set of key components that perform the calculations. The operator manipulates these through the computer's framework.

Key hydraulic components might include pipes, valves and containers.

Key mechanical components might include rotating shafts for carrying data within the computer, miter gear differentials, disc/ball/roller integrators, cams (2-D and 3-D), mechanical resolvers and multipliers, and torque servos.

Key electrical/electronic components might include:

• precision resistors and capacitors
• operational amplifiers
• multipliers
• potentiometers
• fixed-function generators

The core mathematical operations used in an electric analog computer are:

• addition
• integration with respect to time
• inversion
• multiplication
• exponentiation
• logarithm
• division

In some analog computer designs, multiplication is much preferred to division. Division is carried out with a multiplier in the feedback path of an Operational Amplifier.

Differentiation with respect to time is not frequently used, and in practice is avoided by redefining the problem when possible. It corresponds in the frequency domain to a high-pass filter, which means that high-frequency noise is amplified; differentiation also risks instability.

Limitations

In general, analog computers are limited by non-ideal effects. An analog signal is composed of four basic components: DC and AC magnitudes, frequency, and phase. The real limits of range on these characteristics limit analog computers. Some of these limits include the operational amplifier offset, finite gain, and frequency response, noise floor, non-linearities, temperature coefficient, and parasitic effects within semiconductor devices. For commercially available electronic components, ranges of these aspects of input and output signals are always figures of merit.

Decline

In the 1950s to 1970s, digital computers based on first vacuum tubes, transistors, integrated circuits and then micro-processors became more economical and precise. This led digital computers to largely replace analog computers. Even so, some research in analog computation is still being done. A few universities still use analog computers to teach control system theory. The American company Comdyna manufactured small analog computers. At Indiana University Bloomington, Jonathan Mills has developed the Extended Analog Computer based on sampling voltages in a foam sheet. At the Harvard Robotics Laboratory, analog computation is a research topic. Lyric Semiconductor's error correction circuits use analog probabilistic signals. Slide rules are still popular among aircraft personnel.

Resurgence

With the development of very-large-scale integration (VLSI) technology, Yannis Tsividis' group at Columbia University has been revisiting analog/hybrid computers design in standard CMOS process. Two VLSI chips have been developed, an 80th-order analog computer (250 nm) by Glenn Cowan in 2005 and a 4th-order hybrid computer (65 nm) developed by Ning Guo in 2015, both targeting at energy-efficient ODE/PDE applications. Glenn's chip contains 16 macros, in which there are 25 analog computing blocks, namely integrators, multipliers, fanouts, few nonlinear blocks. Ning's chip contains one macro block, in which there are 26 computing blocks including integrators, multipliers, fanouts, ADCs, SRAMs and DACs. Arbitrary nonlinear function generation is made possible by the ADC+SRAM+DAC chain, where the SRAM block stores the nonlinear function data. The experiments from the related publications revealed that VLSI analog/hybrid computers demonstrated about 1–2 orders magnitude of advantage in both solution time and energy while achieving accuracy within 5%, which points to the promise of using analog/hybrid computing techniques in the area of energy-efficient approximate computing. In 2016, a team of researchers developed a compiler to solve differential equations using analog circuits.

Analog computers are also used in neuromorphic computing, and in 2021 a group of researchers have shown that a specific type of artificial neural network called a spiking neural network was able to work with analog neuromorphic computers.

Practical examples

X-15 simulator analog computer

These are examples of analog computers that have been constructed or practically used:

• Boeing B-29 Superfortress Central Fire Control System
• Deltar
• E6B flight computer
• Kerrison Predictor
• Leonardo Torres y Quevedo's Analogue Calculating Machines based on "fusee sans fin"
• Librascope, aircraft weight and balance computer
• Mechanical computer
• Mechanical integrators, for example, the planimeter
• Nomogram
• Norden bombsight
• Rangekeeper, and related fire control computers
• Scanimate
• Torpedo Data Computer
• Torquetum
• Water integrator
• MONIAC, economic modelling
• Ishiguro Storm Surge Computer

Analog (audio) synthesizers can also be viewed as a form of analog computer, and their technology was originally based in part on electronic analog computer technology. The ARP 2600's Ring Modulator was actually a moderate-accuracy analog multiplier.

The Simulation Council (or Simulations Council) was an association of analog computer users in US. It is now known as The Society for Modeling and Simulation International. The Simulation Council newsletters from 1952 to 1963 are available online and show the concerns and technologies at the time, and the common use of analog computers for missilry.