Second theodolite

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In geodesy, a second theodolite is a particularly precise but still handy theodolite . It is a development from the first third of the 20th century, but the term did not appear until 1950 - among other things due to the pioneering developments of the brilliant mechanic Heinrich Wild .

The instrument type arose from the further development of the large (still openly built) triangulation theodolite, which, like its successor, which was built with a closed housing, had a measurement accuracy of ± 1 ″ .

Second theodolite DKM2-A from Kern-Aarau (year of construction ~ 1980)

To the success story of the second theodolite

The following factors, among others, were decisive for the same accuracy at around a third of the mass (e.g. DKM2-A only around 5 kg):

Decisive improvements from 1900 to 1950

  1. The closed envelope, which greatly reduced the thermal influences on the alidade , the telescope axes and the metal components of the reading .
  2. The better attachment of the dragonflies (even good dragonflies migrate by about a pars (about 10–30 ″) to the side when one of their ends warms up by 1 ° compared to the other due to solar radiation )
  3. better constructions of the vertical axis and the tilt axis
  4. mechanically and thermally more stable mounted rectification screws, e.g. B. for the optical axis ( collimation or target axis error )
  5. Pitch circles of glass (instead of metal with silver inlay ), which is also less cyclical and random errors had
  6. Replacement of the open, with vernier equipped Ablesemikroskope and measuring spindles -. The so-called micrometers - by covered, partially optically operating Ablesefernrohre
  7. the double circle principle for the direction to be read, invented by H. Wild around 1930 (first realized with the DKM1 , which could then be constructed as small as a travel theodolite . It was precisely for this reason that it was not a great market success, because many geodesists doubted its accuracy).

Forerunner astronomical instruments: fixed and cooled

The forerunners of the triangulation and astronomical theodolites used in the middle of the 19th century were essentially the large universal instruments , which in turn had borrowed constructively from the passage instruments and the meridian circles of the observatories. But since an astronomical instrument i. A. is not exposed to large fluctuations in temperature (the domes of the observatories remain relatively cool during the day ) and are only rarely transported, the thermal disadvantages of the first triangulation theodolites (around 1850) are all too understandable. After all, almost all of the famous geodesists (e.g. Gauss, Bouguer, Cassini, Lambert and the “stars” of the Paris Academy ) came from the circle of astronomers or mathematicians.

In addition to some optically well-versed precision mechanics , the experience with the geodetic field service use of small instruments also contributed to technical innovations , for example through some perfectly designed components of the diopters of the time and the tilting rule , through further developments of the azimuthal quadrant (prototype as early as 1500), the board ashes Instruments and some special designs that have now been completely forgotten. At about the same time as the "seconds-capable" , but now portable universal measuring devices, repetition theodolites were also developed, with which the measuring accuracy could be increased two to three times by adding angles.

Optical and electronic distance measurement

Until the beginning of the 20th century, theodolites were only suitable for measuring angles, but not for measuring distances . However, with the establishment of modern machine and construction techniques , which gave instrument making powerful impulses, geodetic instruments came onto the market that were equipped with accessories for optical distance measurement. They worked by measuring the parallactic angle on a two-meter base rod and soon split into those with a horizontal and vertical rod : the former achieved greater accuracy and were used for land surveying , the latter in building surveying and engineering geodesy . Today these devices - although they still function without complaint after 50 years - have become pure collector's items or museum pieces, because they were able to compete against the electronic " distancers " that emerged in the 1960s (based on microwaves, infrared and soon also lasers ) do not maintain long.

You can find out more at the Dortmund Museum of Surveying Technology (Förderkreis Vermessungstechnisches Museum e.V., D-44137 City of Dortmund), on whose website some of the constructions mentioned are documented in good photos. Precise universal instruments were built for triangulation and astronomy from 1850 onwards.

Construction of a second theodolite

Today's second theodolite

Substructure and superstructure

A modern second theodolite basically has almost the same structure as the "screw steamers" (a nickname coined by TU students) that were sold until around 1950. However, the closed design makes it 1) more accurate, 2) more thermally stable and 3) less prone to impact. In the 1970s, the “star” of a geodesy fair was a Wild T2 , which in its metal bomb had “survived” a fall over a 100 meter high rock face . It only had to be readjusted slightly by Wild Heerbrugg . The container, however, looked like an accordion.

The theodolite substructure or limbus (usually somewhat conical) contains the horizontal circle (1) and the vertical standing axis (S). The alidade is rotatably mounted on it - the so-called superstructure, between whose supports (2) the measuring telescope (3) can be rotated around the horizontal tilting axis (K). There is a clamping and a fine movement for both axes . The latter is often designed with two threads in order to enable very fine adjustments. The reading of the angle set for the respective target point takes place optically with 2 × 2 plane plates and associated micrometers, which are located at the points with (4) and (5).
The telescope has an aperture of around 40 mm, a magnification of 30–35 times and a thread network that is actually a microphotographically produced or electronically etched reticle . This extremely precise glass plate ( reticule ) is located in the common focal point of objective and eyepiece for optically infinitely distant targets . If the target point (whether detail or polygon point , measuring stick or ground point , optically does not matter) is closer than about 100 meters, it must be brought into focus by means of an internal focus. For this purpose, a focusing lens is built into the rear quarter of the telescope , which can be moved precisely along the target axis (Z) with an extremely precisely manufactured inner cylinder . The focusing screw is usually located on the upper edge of the telescope or is designed as a non -slip knurled ring that is easy to find even at night . It no longer shifts the eyepiece part with the reticle (as was the case with theodolites before 1950), but changes the focal length of the lens.

Note on the potential measurement accuracy

The displacement of the inner focusing lens cannot be completely linear. Therefore a comment that is superfluous for experienced observers: Although all these mechanical-optical components are manufactured with tolerances below about one µm , there is always a slight deviation from the optical axis (see also alignment ) or a backlash. In order to be able to maintain the 1 ″ accuracy, the geodesist must always do the last fine rotation of the focusing in the same direction (usually clockwise). Otherwise there will be systematic target errors that can reach around 3–5 ″. Frequent focusing between measuring points at different distances is also unfavorable if you want to achieve ultimate accuracy (about 0.5 mm at 100–200 meters). It is better to accept a slight blurring and to keep the measuring eye exactly in the optical axis (easily recognizable by the symmetrical field of view ). In the case of glare from strong sunshine or poor contrast of the targeted points, etc., this method of working is of course more difficult.

Another method to circumvent this optically inevitable small source of error would be to measure the detail points in a kind of ring-shaped sequence (i.e. the figurant does not place the yardstick on the points to be measured spatially one behind the other , but rather circles the theodolite set up above the polygon or fixed point 1–3 ring ways ). However, the sequencing of the measurements, which is to be striven for, speaks against this , and that the remaining circle division errors and slip effects could become somewhat more effective.

Because the sequence of points usually has to be coded (roadside, fixtures, corners of houses, etc.) or at least put in good order on the field sketch so that nothing is forgotten. It is best - also in terms of economic efficiency - if the engineer explores the choice of the most suitable measuring equipment and measuring methods long before the start of the measurements and if necessary familiarizes himself with alternative programs in the theodolite system. Nor does it always have to be the tried and tested polygon course with subsequent polar imaging : Sometimes the free stationing of the measuring device is preferable, or two instead of simple checks with restricted dimensions , or network balancing for particularly sensitive projects . Assuming the appropriate experience, many modern digital theodolites allow a certain change in the procedure in between.

Tripod and installation

The substructure of the theodolite is seated on the base plate, the at tripod mounted and three leveling screws and the vial exactly on the alidade (between the two telescope supports) leveled is.

If this happens too quickly, in strong solar radiation or with vibrations (e.g. on a bridge), a noticeable error in the standing axis remains . It has a similar effect to a deviation from the perpendicular (which, however, only plays an important role in steep terrain). If this inevitable setup error z. B. δ = 10 ″ (typical for an alidaden vial with par value 20 ″), the imprecise vertical axis causes a measurement error that increases with the tangent of the elevation angle h . At 10 ″, because of δ · tan h <1 ″, something of the accuracy of a second theodolite is “given away” from an elevation angle of h = 5.7 °.

In addition to the horizontal installation, the exact centering over the polygon or measurement point is essential. In addition, every modern theodolite and every total station has an optical plummet - a small telescopic sight that looks exactly in the plumb direction when the substructure is correctly set up . There are several methods for setting up the theodolite on level ground or even on a steep slope , which are listed in the university scripts of the geodesy institutes (see e.g. web link no. 2).

Other types of theodolites

As can be seen from the above, a second theodolite or tacheometer is suitable for the majority of surveying projects . However, sometimes it is better to choose a less precise instrument if the work with it is sufficiently precise but a little faster. For high-precision networks in large-scale technical projects or in a machine hall to be measured to <0.1 mm, an even more precise measuring device may be required. Hence the following small list:

Typical size of the instrument defects

For every theodolite, 4 types of precision mechanical or operational errors play a role, which can only be partially reduced:

Further increases in measurement accuracy are possible through

  • repeated measurements, especially with different partial circle positions
  • If there are several sentences; halfway turn the theodolite on the tripod plate by 180 ° (reducing the wobble of the standing axis)
  • or (after a prior analysis of the axis errors) by subsequent reduction.

Observation and accuracy : To eliminate errors, the targets are measured in a so-called sentence or in (sometimes also in half-sentences , for example when measuring the sun ). One set consists of two series of measurements (two half-sentences), whereby for the second series of measurements the telescope is knocked through (rotated around the tilting axis to the other side of the device), the superstructure is rotated by 180 ° and the targets are aimed again. As a result, the target directions are read off at opposite points of the partial circles (i.e. with a difference of about 180 ° = 200 gons), so that the geodesistcan eliminatesome of the small systematic errors that are always presentin the angle calculation. Some others can bereducedby experienced observers, for example certain error influences of the circle division , the telescope bending and various thermal errors.

As for the object of observation, one distinguishes

Theodolites, one also electronic distance measurement allow (abbreviated EDM, hot tachymeter or - if equipped with GIS modules or with GPS - even total stations ).

Well-known manufacturers

Web links