# Tacheometry

## Tacheometry

Tacheometry is defined as an optional distance measurement method. The other names given to tacheometry are Tachymetry or Telemetry.

As compared to chaining on flat grounds, the accuracy of tacheometric distances is low, but on rough and steep grounds the accuracy is more.

## Tacheometer

It is transit theodolite fitted with stadia diaphragm. The stadia diaphragm consists of two stadia hairs at equal distances, one above and the other below the horizontal hair of the crosshairs.

### Important Characteristics of Tacheometer

1. Value of the multiplying constant, k=100
2. Value of the additive constant, C=0
3. Telescope should be fitted with an anallactic lens.
4. Magnification power of the eyepiece is kept high.

It is a special convex lens, fitted in between the object glass and eyepiece, at a fixed distance from the object glass, inside the telescope of a tacheometer.

It is also called as vertical stove.

It is a 5-15m long rod, graduated in decimals of meter.

For small distances up to 100m, an ordinary levelling staff may be used but beyond this stadia rod is used, since the graduations of an ordinary levelling staff become indistinct.

The staff can be held either vertical or normal to the line of sight.

The staff is held normal to the line of sight can be judged when staff intercept is minimum.

## Methods of Tacheometry

There are three methods of measuring distances by optical means.

In a tacheometer the various wires, in addition to the cross-wires on the diaphragm, are known as Stadia wires and the vertical distances between these stadia wires is termed as Stadia interval.

When the parallactic angle α, defined with the help of stadia wires, is kept fixed and staff intercept is varied, e.g., AB and A’B’, the method is known as fixed hair method.

Another way used to make the observation is to keep the staff intercept fixed, e.g., AB, and A”B”, and vary the parallactic angle, e.g., α and α’.

In this case the stadia wires will have to be moved and is accordingly called as the movable hair or subtense method.

In both the above method a tacheometer and staff are used to take the observations.

### Tangential Method

In this method observations are made for vertical angles and staff intercepts are obtained with the cross-wires only.

Stadia wires are not used at all. This method of tacheometry is quite similar to the method of trigonometrical levelling.

#### Range Finding

This method is used to determine the horizontal distance and direction of a line without going to the far end of the line. The instrument used is called as Range Finder.

A fixed base is used to compute the ranges. The instruments and methods used are based on measurement of either the base angles or the angle of parallax.

By this method only horizontal distance can be measured but with the help of a level the vertical distances can also be measured.

A great care should be taken to observe the staff intercepts during tacheometric surveying.

## Movable-Hair Method

If the stadia hairs are fixed, the angle β between the ray along the upper stadia and that along the lower stadia is also fixed.

The staff intercept varies with the distance of the staff from the instrument if the stadia hairs are movable and the staff whereas intercept ‘s’ is kept fixed, the tacheometer angle β changes with the staff position.

The diaphragm has an arrangement for the measurement of the stadia interval i accurately.

Each hair of the stadia diaphragm can be moved independently by a separate sliding frame.

Each sliding frame is actuated by a micrometre screw with a large graduated head.

When both the stadia hairs coincide with the central mark on the comb, they are in the horizontal plane of the line of sight and reading on the graduated heads of the both the screws should be zero.

When an observation is made, the upper head is rotated till the upper stadia hair bisects the upper target. Similarly, the lower head is rotated till the lower stadia hair bisects the lower target.

The movable hair method is also known as the vertical base subtense method.

In this method S is fixed but i is variable where as in stadia method, S is variable but i is fixed.

The stadia interval is measured with the help of micrometre screws. If the pitch of screw is P and m revolution of the micrometre are made.

### Advantage of the Movable-hair Method

• As compound to the stadia method (fixed hair method), this method is more accurate for long sights which can be taken with great accuracy as only targets are to be bisected.

### Disadvantage of the Movable-hair Method

• The method is slow.
• It is very difficult to measure the stadia interval accurately.
• Computations are tedious as the factor m comes in the denominator.

## Tangential Method of Tacheometry

• The tangential method of tacheometry is generally used when the diaphragm doesn’t have stadia hairs, when the staff is too far from the instrument and it becomes difficult to read the staff.
• In this method, a staff fitted with two big targets spaced at a fixed vertical distance (s) of 2m or 3m is sighted.
• Vertical angle θ1 and θ2 are measured by sighting the two targets.
• Horizontal distance D and the vertical intercept V are computed from the values of s, θ1, and θ2.
• Depending upon whether the angles θ1 and θ2 are the angles of elevation or depression, the following three cases usually occur.

#### Case 2. Both angles at Depression

D= S/ (tan θ2-tan θ1)

V= D tan θ2

#### Case 3. One angle of elevation and one angle of depression

D= S/ (tan θ1-tan θ2)

V= D tan θ2

### Disadvantage of the Tangential Method

The tangential method is inferior to the stadia method. The method should be used only if the diaphragm doesn’t have stadia hairs. This method has the following disadvantage:

• As two vertical angles have to be measured, it takes more time in comparison the stadia method.
• Error will occur if the instrument gets disturbed between the two observations.
• There may be changes in atmospheric refraction in the period between the two observations which will cause error.
• Reading are not easily reduced to the horizontal distance and vertical intercept.

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