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MODERN SURVEYING HEIGHT DETERMINATION
Heights of surface features above sea level are determined in four main ways: by spirit leveling, by measuring vertical angles and distances, by measuring differences in atmospheric pressure, and, since the late 20th century, by using three-dimensional satellite or inertial systems. Of these the first is the most accurate; the second is next in accuracy but faster; the third is least accurate but can be fastest if heights are to be measured at well-separated points. The last two techniques require sophisticated equipment that is still very expensive
In spirit leveling the surveyor has for centuries used a surveying level, which consists of a horizontal telescope fitted with cross hairs, rotating around a vertical axis on a tripod, with a very sensitive spirit level fixed to it; the instrument is adjusted until the bubble is exactly centred. The reading on a graduated vertical staff is observed through the telescope. If such staffs are placed on successive ground points, and the telescope is truly level, the difference between the readings at the cross hairs will equal that between the heights of the points. By moving the level and the staffs alternately along a path or road and repeating this procedure, differences in height can be accurately measured over long horizontal distances
In the most precise work, over a distance of 100 kilometres the error may be kept to less than a centimeter. To achieve this accuracy great care has to be taken. The instrument must have a high-magnification telescope and a very sensitive bubble, and the graduated scale on the staff must be made of a strip of invar (an alloy with a very small coefficient of thermal expansion). Moreover, the staffs must be placed on pegs or special heavy steel plates, and the distance between them and the level must always be the same to cancel the effects of aerial refraction of the light
In less precise work a single wooden staff can be used; for detailed leveling of a small area, the staff is moved from one point to another without moving the level so that heights can be measured with a radius of about 100 metres. The distances of these points from the instrument can be measured by tape or more commonly, by recording not only the reading at the central cross hair in the field of view of the telescope but also those at the stadia hairs, that is by tachymetry. The bearing of each point is observed by compass or on the horizontal circle of the level so that it can be plotted or drawn on the map
Since the 1950s levels have been introduced in which the line of sight is automatically leveled by passage through a system of prisms in a pendulum, thus removing the need to check the bubble. The disadvantage of spirit leveling is the large number of times the instrument has to be moved and realigned, particularly on steep hills; it is used primarily along practically flat stretches of ground.
For faster work in hilly areas, where lower accuracies usually are acceptable, trigonometric height determination is employed using a theodolite to measure vertical angles and measuring or calculating the distances by triangulation. This procedure is particularly useful in obtaining heights throughout a major framework of triangulation or traverse where most of the points are on hilltops. To increase precision, the observations are made 23 simultaneously in both directions so that aerial refraction is eliminated; this is done preferably around noon, when the air is well mixed.
The third method of height determination depends on measurements of atmospheric pressure differences with a sensitive aneroid barometer, which can respond to pressure differences small enough to correspond to a foot or two in height. The air pressure changes constantly, however, and to obtain reliable results it is necessary to use at least two barometers; one at reference point of known height is read at regular intervals while the surveyor proceeds throughout the area, recording locations, times, and barometer readings. Comparison of readings made at the same time then gives the height differences.
An alternative to the barometer for pressure measurement is an apparatus for measuring the boiling point of a liquid, because this temperature depends on the atmospheric pressure. Early explorers determined heights in this way, but the results were very rough; this technique was not accurate enough for surveyors until sensitive methods for temperature measurement were developed. The airborne profile recorder is a combination of this refined apparatus with a radar altimeter to measure the distance to the ground below an aircraft.
Analysis of the signals received simultaneously from several satellites gives heights as accurately as positions. Heights determined in this way are useful in previously unmapped areas as a check on results obtained by faster relative methods, but they are not accurate enough for mapping developed areas or for engineering projects. All-terrain vehicles or helicopters can carry inertial systems accurate enough to provide approximate heights suitable for aerial surveys of large areas within a framework of points established more accurately by spirit leveling.
MODERN SURVEYING AERIAL SURVEYING
Aviation and photography have revolutionized detailed mapping of features visible from the air. An aerial photograph, however, is not a map. In the case of the House of Parliament and Westminster Bridge, London, for example, the tops of the towers would coincide with the corners of the foundations when mapped. In an aerial photograph, however, they would not, being displaced radially from the centre. An important property of vertical aerial photographs is that angles are correctly represented at their centres, but only there. Similar distortions are present in photographs of hilly ground. This problem may be dealt with in two principal ways, depending on the relative scales of the map and the photographs and on whether contours are required on the map. The older method, adequate for planimetric maps at scales smaller than the photographs, was used extensively during and after World War II to map large areas of desert and thinly populated country; mountainous area could be sketched in, but the relief was not accurately shown.
As in ground survey, a framework of identified points is necessary before detailed mapping can be carried out from the air. The photographs are ordinarily taken by a vertically aligned camera in a series of strips in which each picture overlaps about 60 percent of the preceding one; adjacent strips overlap only slightly. The overlaps make it possible to assemble a low-order framework or control system based on small, recognizable features that appear in more than one photograph. In the simplest form of this procedure each photograph is replaced by a transparent template on which rays are drawn (or slots are cut) from the centre of the picture to the selected features. The angles between these rays or slots are correct, and slotted templates can be fitted together by inserting studs, which represent the features, into the appropriate slots and sliding the templates so that each stud engages the slots in all the pictures showing the corresponding feature. This operation ensures that the centres of the pictures and the selected features are in the correct relationship. The array of overlapping photographs can be expanded or contracted by sliding them about on the work surface as long as the studs remain engaged in the slots, so the assemblage can be positioned, oriented, and scaled by fitting it to at least two – preferably several –groundcontrol points identified on different photographs.
This technique may be extended by using two additional cameras, one on each side, aimed at right angles to the line of flight and 30 degrees belowthe horizontal. The photographs taken by the side cameras overlap those taken by the vertical one and also include the horizon; the effect is to widen the strip of ground covered and thus to reduce the amount of flying required. Points in the backgrounds of the oblique photographs can be incorporated in the overlapping array as before to tie the adjacent flight paths together. Photography from high-flying jet aircraft and satellites has rendered this technique obsolete, but before those advances took place it greatly facilitated the mapping of underdeveloped areas.
For the production of maps with accurate contours at scales five or six times that of the photographs, a more sophisticated approach is necessary. The ground-survey effort must be expanded to provide the heights as well as the positions of all the features employed to establish the framework.
In this technique the details within each segment of the map are based not on individual photographs but on the overlap between two successive ones in the same strip, proceeding from the positions and heights of features in the corners of each area. A three-dimensional model can be created by viewing each pair of consecutive photographs in a stereoscope; by manipulation of a specially designed plotting instrument, the overlapping area can be correctly positioned, scaled, and oriented, and elevations of points within it can be derived from those of the four corner points. These photogrammetric plotting instruments can take several forms. In projection instruments the photographs are projected onto a table in different colours so that, through spectacles with lenses of complementary colours, each eye sees only one image, and the operator visualizes a three-dimensional model of the ground. A table or platen, with a lighted spot in the middle, can be moved around the model and raised or lowered so that the spot appears to touch the ground while the operator scans any feature, even if it is located on a steep hillside. A pencil directly beneath the spot then plots the exact shape and position of the feature on the map. For contouring the platen is fixed at the selected height (at a scale adjusted to that of the model), and the spot is permitted to touch the model surface wherever it will; the pencil then draws the contour.
With more complex mechanical devices, rays of the light reaching the aircraft taking the two photographs are represented by rods meeting at a point that represents the position of the feature of the model being viewed. With a complicated system of prisms and lenses the operator, as with projection instruments, sees a spot that can be moved anywhere in the overlap and up or down to touch the model surface. A mechanical or electronic system moves a pencil into the corresponding position on a plotting table to which the map manuscript is fixed.
With computerized analytic instruments the mechanical operation is limited to measuring coordinates on the two photographs, and the conversion to a three-dimensional model is performed entirely by the computer. It is possible with the most precise plotting instruments of either type to draw a map at four to six times the scale of the photographs and to plot contours accurately at a vertical interval of about one one-thousandth of the height from which the photographs were taken. With such analytic instruments the record can be stored in digital as well as graphic form to be plotted later at any convenient scale.
All these methods produce a line or drawn map; some of them also create a data file on disk or tape, containing the coordinates of all the lines and other features on the map. On the other hand, aerial photographs can be combined and printed directly to form a photomap. For flat areas this operation requires simply cutting and pasting the photographs together into a mosaic. For greater accuracy the centres of the photographs may be aligned by the use of slotted templates to produce a photomap called a controlled mosaic.
A much more precise technique is based on the use of an orthophotoscope. With this device, overlapping photographs are employed just as in the stereoscopic plotter, but the instrument, rather than the manual tracing of the features and contours, scans the overlap and produces an orthophotograph by dividing the area into small sections, each of which is correctly scaled. This procedure is best applied to areas of low relief without tall buildings; the resulting maps can then be substituted for line maps in rural areas where they are practically useful in planning resettlement in agricultural projects. Because no fair drawing is required, the final printed map can be produced much more quickly and cheaply than would otherwise be possible.
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СОВРЕМЕННОЕ ОПРЕДЕЛЕНИЕ ВЫСОТЫ СЪЕМКИ
Высота рельефа над уровнем моря определяется четырьмя основными способами: геометрическим нивелированием, измерением вертикальных углов и расстояний, измерением разности атмосферного давления, а с конца 20 в. - с помощью трехмерных спутниковых или инерциальных систем. Из них первое является наиболее точным; второй следующий по точности, но быстрее; третий наименее точен, но может быть самым быстрым, если необходимо измерить высоту в хорошо удаленных точках. Последние два метода требуют сложного оборудования, которое все еще очень дорогие.
При геометрическом нивелировании геодезист на протяжении веков использовал геодезический уровень, который состоит из горизонтального телескопа с перекрестием нитей, вращающегося вокруг вертикальной оси на треноге, с прикрепленным к нему очень чувствительным спиртовым уровнем; прибор регулируется до тех пор, пока пузырек не окажется точно по центру. Показания на градуированной вертикальной рейке наблюдают через зрительную трубу. Если такие вехи размещены на последовательных наземных точках, и зрительная труба действительно выровнена, разница между показаниями на перекрестии нитей будет равна разнице между высотами точек. Перемещая уровень и рейки попеременно вдоль пути или дороги и повторяя эту процедуру, можно точно измерить разницу в высоте на больших горизонтальных расстояниях.
При самой точной работе на расстоянии 100 километров погрешность может составлять менее сантиметра. Для достижения такой точности необходимо соблюдать большую осторожность. Прибор должен иметь линзы с большим увеличением и очень чувствительный куполом, а градуированная шкала на рейке должна быть сделана из полоски инвара (сплав с очень малым коэффициентом теплового расширения). Кроме того, рейки должны быть размещены на колышках или специальных тяжелых стальных пластинах, а расстояние между ними и уровнем всегда должно быть одинаковым, чтобы исключить влияние воздушного преломления света.
При менее точной работе можно использовать один деревянный стержень; для детального выравнивания небольшой площади рейку перемещают из одной точки в другую, не перемещая нивелир, так что можно измерять высоты в радиусе около 100 метров. Расстояния от этих точек до инструмента можно измерить рулеткой или, что чаще, путем записи не только показаний на центральном перекрестии в поле зрения зрительной трубы, но и на дальномерных нитях, т. е. с помощью тахиметрии. Пеленг каждой точки наблюдается по компасу или по горизонтальному кругу уровня, чтобы его можно было нанести или нарисовать на карте.
С 1950-х годов были введены уровни, в которых линия обзора автоматически выравнивается путем прохождения через систему призм в маятнике, что устраняет необходимость проверять пузырь. Недостатком геометрического нивелирования является необходимость большого количества перемещений и повторной юстировки инструмента, особенно на крутых склонах; он используется в основном на практически плоских участках земли.
Для более быстрой работы в холмистой местности, где обычно приемлема более низкая точность, используется тригонометрическое определение высоты с использованием теодолита для измерения вертикальных углов и измерения или расчета расстояний с помощью триангуляции. Эта процедура особенно удобна для получения высот на основной схеме триангуляции или маршрута, где большинство точек находится на вершинах холмов. Для повышения точности наблюдения производятся одновременно в обоих направлениях, чтобы исключить воздушную рефракцию; это делается предпочтительно около полудня, когда воздух хорошо перемешан.
Третий метод определения высоты зависит от измерения перепадов атмосферного давления с помощью чувствительного барометра-анероида, который может реагировать на перепады давления, достаточно малые, чтобы соответствовать одному или двум футам роста. Однако давление воздуха постоянно меняется, и для получения надежных результатов необходимо использовать по крайней мере два барометра; один в контрольной точке известной высоты считывается через равные промежутки времени, в то время как геодезист перемещается по территории, записывая местоположения, время и показания барометра. Сравнение показаний, сделанных в одно и то же время, дает разницу в высоте.
Альтернативой барометру для измерения давления является прибор для измерения температуры кипения жидкости, так как эта температура зависит от атмосферного давления. Таким способом ранние исследователи определяли высоту, но результаты были очень приблизительными; этот метод не был достаточно точным для геодезистов, пока не были разработаны чувствительные методы измерения температуры. Бортовой регистратор профилей представляет собой комбинацию этого усовершенствованного устройства с радиолокационным высотомером для измерения расстояния до земли под самолетом.