Surveying & Triangulation
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Surveying Equipment
When looking for surveying equipment there are a lot of different things you need to take into consideration. What kind of surveying are you going to be doing, do you want to use a total system or would you rather use a theodolite, and how much can you afford to spend on your surveying equipment. The surveying equipment that we sell is the highest quality surveying equipment around.
The History Of Surveying And Survey Equipment
Surveying is the technique and science of accurately determining the terrestrial or 3D space position of points and the distances and angles between them. These points are usually, but not exclusively, associated with positions on the surface of the Earth, and are often used to establish land maps and boundaries for ownership or governmental purposes. In order to accomplish their objective, surveyors use elements of geometry (Latin: measuring the Earth), of engineering, mathematics, physics, and law.
Surveying has been an essential element in the development of the human environment since the beginning of recorded history (ca. 5000 years ago) and it is a requirement in the planning and execution of nearly every form of construction. Its most familiar modern uses are in the fields of transport, building and construction, communications, mapping, and the definition of legal boundaries for land ownership.
Historically, angles and distances were measured using a variety of means, such as chains with links of a known length, for instance a Gunter’s Chain (see Edmund Gunter), or measuring tapes made of steel or invar. In order to measure horizontal distances, these chains or tapes would be pulled taut, to reduce sagging and slack. Additionally, attempts to hold the measuring instrument level would be made. In instances of measuring up a slope, the surveyor might have to “break” the measurement that is, raise the rear part of the tape upward, plumb from where the last measurement ended.
Historically, horizontal angles were historically measured using compasses, which would provide a magnetic bearing, from which deflections could be measured. This type of instrument was later improved upon, through more carefully scribed discs, providing better angular resolution, as well as through mounting telescopes with reticles for more precise sighting atop the disc (see theodolite). Additionally, levels and calibrated circles allowing measurement of vertical angles were added, along with verniers for measurement down to a fraction of a degree such as a turn-of-the-century Transit (surveying).
The simplest method for measuring height is with an altimeter (basically a barometer) using air pressure as an indication of height. But for surveying more precision is needed. Toward this end, a variety of means, such as precise levels have been developed, which are calibrated to provide a precise plane from which differentials in height between the instrument and the point in question, typically through the use of a vertical measuring rod.
The basic tool is a theodolite, set on a tripod, with which one can measure angles (horizontal and vertical), combined with triangulation. Starting from a benchmark, a position with known location and elevation, the distance and angles to the unknown point are measured. A more modern instrument is a total station, which is basically a theodolite with an electronic distance measurement device (EDM). Still more modern is the use of satellite positioning systems, such as a Global Positioning System (GPS). Though GPS systems have increased the speed of surveying, they are still only accurate to about 20 mm. As well GPS systems do not work in areas with dense tree cover. It is because of this that EDMs have not been completely phased out. Robotics allows surveyors to gather precise measurements without extra workers to look through and turn the telescope or record data. A faster way to measure (no obstacles) is with a helicopter with laser echolocation, combined with GPS to determine the height of the helicopter. To increase precision, beacons are placed on the ground (about 20 km apart). This method reaches a precision of about 5 cm.
With the triangulation method, first, one needs to know the horizontal distance to the object. If this is not known or cannot be measured directly, it is determined as explained in the triangulation article. Then the height of an object can be determined by measuring the angle between the horizontal plane and the line through that point at a known distance and the top of the object. In order to determine the height of a mountain, one should do this from sea level (the plane of reference), but here the distances can be too great and the mountain may not be visible. So it is done in steps, first determining the position of one point, then moving to that point and doing a relative measurement, and so on until the mountaintop is reached.
Triangulation
In trigonometry and elementary geometry, triangulation is the process of finding a distance to a point by calculating the length of one side of a triangle, given measurements of angles and sides of the triangle formed by that point and two other reference points.
Some identities often used (valid only in flat or euclidean geometry): The sum of the angles of a triangle is pi rad or 180 degrees. The law of sines - The law of cosines - The Pythagorean theorem Triangulation is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision and gun direction of weapons.
Many of these surveying problems involve the solution of large meshes of triangles, with hundreds or even thousands of observations. Complex triangulation problems involving real-world observations with errors require the solution of large systems of simultaneous equations to generate solutions.
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