TACHEOMETRY

INTRODUCTION

• Tacheometry is an optical solution to the measurement of distance. The word is derived from the Greek Tacns, meaning 'swift', and metrot, meaning 'a measure'. It also can be describe as detail surveys.

TACHOMETRY SYSTEM

• Present day methods of tacheometry can be classified into four groups:-

1. Stadia System

2. Tangent System

3. Optical Wedge System

4. Range Finder System

TACHEOMETRY SYSTEM

• There are two types of instruments used for stadia surveying. In the first type the distance between the two stadia hairs in the theodolite telescope is fixed. In the second type of equipment the distance between the stadia hairs is variable, being measured by means of a micrometer.

• The most common method used involves the fixed hair tacheometer, or theodolite

BASIC PRINCIPLE OF TACHEOMETRY

A

B

C

D

α / 2

α / 2

BC = Base distance α = Top angle

STADIA SYSTEM

• The figure below shows the calculation of the distance (D) from the centre of the fixed hair theodolite to a target.

STADIA SYSTEM

• Where,

• f = Focal distance object lens• o = Outer focal point object lens• i = stadia interval ab• S = Staff intercept AB• c = Object lens distance to instrument axis• d = Outer focal point distance to staff• D = Horizontal distance

STADIA SYSTEM

d / S = f / iBut d = D – (f + c)Therefore [D – (f + c)] / S = f / i [D – (f + c)] = (f / i ). S Therefore D = (f / i) . S + (f + c) (Basic

Stadia Formula)

STADIA SYSTEM

• The reduction of this formula would be simplified considerably if the term f / i is made some convenient figure, and if the term (f + c) can be made to vanish.

D= Ks + C

• In practice, the multiplicative constant generally equals 100 and the additive constant equals zero. This is certainly the case with modern instruments by may not always be so with older theodolites.

MEASUREMENTS OF TACHEOMETRIC CONSTANTS

• The values are usually given by the makers but this is not always the case. It is sometimes necessary to measure them in an old or unfamiliar instrument. The simplest way, both for external and internal focusing instruments, is to regard the basic formula as being a linear one of the form:

D= Cs + K

a. On a fairly level site chain out a line 100 to 120m long, setting pegs at 25 to 30 meter intervals.

b. Set at up at one end and determine two distances using tacheometer or theodolite, one short and one long. hence C and K may be determined.

i.e. D1 (known) = Cs1 (known) + k

D2 (known) = Cs2 (known) + k

MEASUREMENTS OF TACHEOMETRIC CONSTANTS

D = Ks + C

30.00 = K * 0.300 + C

90.00 = K * 0.900 + C

therefore K = 100 & C = 0

STADIA SYSTEM• Generally a theodolite is sighted to a level staff held vertically

(by use of a staff bubble), which gives rise to the figure below.

STADIA SYSTEM

REDUCTION OF HORIZONTAL DISTANCE

From the basis formula D = KS Cos θ + C

The distance require is H.

H = D Cos θ (Look at IXY triangle)H = (KS Cos θ). Cos θ + C Cos θ

Therefore

H = KS Cos2 θ + C. Cos θ

STADIA SYSTEM

REDUCTION OF VERTICAL DISTANCE

From the IXY triangleV = D Sin θD = KS Cos θ + C

ThereforeV = KS Cos θ. Sin θ + C. Sin θ

ButCos θ. Sin θ = (Sin 2θ) / 2

Therefore

V = (KS Sin 2θ / 2) + (C. Sin θ)

STADIA SYSTEM

If K = 100 and C = 0Therefore the formulas of reduction can be simplified

by

H = 100S Cos2 θV = 50S Sin 2θ or V = H tan θ

STADIA SYSTEM

• The difference in height between the two points is given by:

ΔH =Hi ± V - h

• and the Relative Level (R.L.) of the point is given by

RL = RLA + Hi ± (50S Sin 2θ) – h

• The use of these formulae gives the three dimensional location of the point. It is quite easy to determine the coordinates of the point if the bearing is measured as well as the staff intercepts and vertical angle, which of course is the standard field procedure.

TACHEOMETRY CALCULATION

• Tacheometric surveys are usually performed to measure the three dimensional location of points on the landscape so as to produce contour and detail plans for further work, or to produce coordinates for area and volume calculations. Observations are usually performed from known survey stations, often established by traversing.

FIELDWORK OF TACHOMETRY• Traverse (Horizontal Control)

Traverse second classMisclosure 2’ 30” and 1: 4000Distance observation until 0.001mUse EDM or chainageFor angle, use teodolite or total station

• Levelling (Vertical Control)Second class levellingObserved from BM

• Detail ObservationDepends on detail to be observeAlso remarks information such as height instrument, bearing, uppper, mid and lower stadia.

• PlottingSuitable graphPlot only observe detailCan be plot using mathematic, graphic, scaleShow title of the plan.