There are four direct reading instruments that are mainly used in measuring horizontal and vertical distance: 1. Beaman Stadia are 2. Jeffcot Direct Reading Tacheometer 3. Szepessy Direct Reading Tacheometer 4. Hammer Fennel Auto Reduction Tacheometer.
Instrument # 1. Beaman Stadia Are (Fig. 10.13):
It is a mechanical device fitted to the vertical circle of a theodolite or to the telescope alidade. It is used to determine horizontal and vertical distances by stadia without reading vertical angles and without the use of stadia tables, diagrams or slide rule.
It consists of two scales:
(i) The vertical scale marked V in the figure and
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(ii) The horizontal scale marked H.
The graduations not he vertical scale are marked by whole numbers in terms of 100 x ½sin 2θ. When the telescope is horizontal, the index I is opposite to the zero graduation.
The horizontal scale gives the percentage corrections to be deducted from the observed stadia distance:
To determine the vertical component (V);
(i) Set up the instrument and direct the telescope towards the staff.
(ii) Read the stadia wires and find the stadia intercept (S).
(iii) Raise or depress the telescope slowly by means of the vertical tangent screw until the index I coincides exactly with the nearest graduation on the vertical scale (V) and note the reading, the plus reading indicates elevation and a minus one depression.
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(iv) Observe the reading at the central wire.
(v) Multiply the stadia intercept by the whole number reading. This gives the vertical component (V).
(vi) Find the elevation of the staff point by the relation, Elevation of the staff point = Elevation of the instrument axis ± V – central wire reading.
Example:
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If, elevation of the instrument axis = 102.50
Vertical scale reading = + 20
Central wire reading = 1.95
Stadia intercept = 1.65
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Then, V = Stadia intercept * vertical scale reading
= 1.65 x 20 = 33.00 m
∴ Elevation of the staff point = 102.50 + 33.00- 1.95
= 133.55.
To determine the horizontal distance (D):
(i) Read horizontal scale simultaneously when the vertical scales is read and note the reading by means of the same index α 1.
(ii) Multiply the stadia intercept by the reading obtained in (i). This will give correction to be subtracted from the distance (100 S) obtained from the stadia intercept.
(iii) Add the value of the additive constant (f+d) to this distance. The result gives the horizontal distance (D).
Note:
The observations with the Beaman stadia are do not count for additive constant (f+d)
Example:
If the horizontal scale reading = 5
Stadia intercept =1.65
Additive constant (f+d) = 0.3
Then, the correction = 5 x 1.65 = 8.25 (-ve)
The horizontal distance, D = 165 – 8.25 + 0.3
= 157.05 m.
Instrument # 2. Jeffcott Direct Reading Tacheometer:
In this instrument, the diagram carries three points or pointers (Fig. 10.14) by means of which staff readings are taken. The middle point is fixed and the other two are movable, they are automatically set by a system of cams and levers when the telescope is raised or depressed.
The right hand movable pointer is called the distance pointer and the staff intercept between the fixed pointer and the distance pointer multiplied by 100 gives the horizontal distance (D). The left hand movable pointer is called the height pointer, and the staff intercept between the fixed pointer and the height pointer multiplied by 10 gives the vertical component (V). The staff readings are taken by first setting the fixed pointer at a metre or a decimeter mark and then reading the other two pointers.
Note:
The left hand pointer moves upwards from the fixed pointer for angles of elevation, while, it moves downwards for angles of depression.
Example:
If the staff readings are 1.70, 1.30, 0.95
Then, horizontal distance, D = 100 (1.70 – 1.30) = 40 m
Vertical component, V = 10 (1.30 – 0.95) = + 3.5 m
Instrument # 3. Szepessy Direct Reading Tacheometer:
In this type of the tacheometer, a scale of tangents of vertical angles is engraved on a glass are which is fixed to the vertical circle cover. The prisms are provided to bring the scale into the field of view of the eye-piece, and when the staff is sighted, the image of the staff is seen alongside that of the scale (Fig. 10.15). It is graduated to 0.005 and numbered at 0.01. Thus the graduation, say 14 corresponds to the angle whose tangent is 0.14.
To read the staff:
(i) Sight the staff and clamp the vertical circle close to some numbered division.
(ii) By means of vertical circle tangent screw, bring the numbered division, say 14, opposite the horizontal cross-hair and note the axial hair reading.
(iii) Read the staff intercept between the short 0.005 divisions immediately above and below the numbered division. Multiply this intercept with 100, which is the horizontal distance (D).
(iv)The vertical component (V) is found by multiplying the intercept by the number marking the division brought opposite the horizontal crosshair.
Example:
If staff intercept = 0.76
and number against axial hair = 14
The, horizontal distance, D = 0.76 x 100 = 76 m
Vertical component, V = 0.76 x 14 = 10.64 m.
Instrument # 4. Hammer Fennel Auto Reduction Tachemoter:
This type of the tacheometre is provided with a special auto-reduction device and gives both the horizontal and vertical distance by a single reading of a vertically held staff.
As shown in fig. 10.16, there are four curves marked by the letters N, E, D and d, which are visible in the field of view:
a. (N) curve is zero curve
b. (E) curve is for reading distance
c. (D) curve is for angles upto ± 14°
d. (d) curve is for angles upto ± 47°
Plus sign is for angles of elevation, and minus for angles of depression.
The multiplying constants are:
a. 100 for curve (E)
b. 10 for curve (D)
c. 20 for curve (d).
To take the reading:
(i) Bisect the zero curve N by the specially marked zero point of the staff.
(ii) Take the staff reading with the distance curve E and the height curve (d) or (D).
(iii) Multiply the distance curve reading by the respective multiplying constant 10 or 20 to find the vertical component (V).
