TOPIC 1 : TACHIMETRY

DEFINATION OF TACHIMETRY Tacheometry is an optical solution to the measurement of distance. The word is derived from the Greek Tacus, meaning 'swift', and metrot, meaning 'a measure'.

Tacheometry /tachemetry /telemetry is a branch of angular surveying in which the horizontal and Vertical distances of points are obtained by optical means as propposed to the ordinary slower process of measurements by tape or chain.

WHY USING THIS METHOD

The method is very rapid and convenient. It is best adapted in obstacles such as steep and broken ground, deep ravines, stretches of water or swamp and so on, which make chaining difficult or impossible, The primary object of tachimetry is the preparation of contoured maps or plans requiring both the horizontal as well as Vertical control. Also, on surveys of higher accuracy, it provides a check on distances measured with the tape.

USES OF TACHEOMETRY The direct methods of measurement of horizontal distances and differences in elevations

Preparation of topographic maps which require both elevations and horizontal distances. Survey work in difficult terrain where direct methods are inconvenient Detail fillingReconnaissance surveys for highways, railways, etc.Checking of already measured distancesHydrographic surveys andEstablishing secondary control.

Vertical axis(distance VBearing (horizontal angle)-HrHorizontal distance(H)Figure 1.0 : Three dimensional data where x = horizontal distance, y = bearing and z = elevation(vertical distance)DATA NEEDS TO PLOTTING TOPOGRAPHY MAP

STEPS IN TACHIMETRY WORKRECONAISSANCEfor a good planning and selecting the appropriate SURVEY station.

MAKE SURE total of survey station suitable with the plan area.

Tachimetry 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(refer to existing plan), often established by traversing. STEPS IN TACHIMETRY WORKHORIZONTAL CONTROL

13Figure 1.1 : Traverse controlStation 1 is reference object/datum (bearing 2-1 is refer to existing plan )Known bearing 2-12STEPS IN TACHIMETRY WORKHORIZONTAL CONTROL

Making a traverse control for the final bearing of each traverse line.

survey stations or line traverse can be determined using theodolite traverse measurement. HORIZONTAL CONTROL

STEPS IN TACHIMETRY WORKVERTICAL CONTROLThis is required to transfer reduced level from bench mark to each traverse station.

Vertical control are carried out using a second-class levelling.

132Known Reduce Level at point 1.Example, RL point 1 = 100.00mVERTICAL CONTROLBSFS

STEPS IN TACHIMETRY WORKDETAILINGDetails measurement is observation of all ground information either natural or non natural details.

Can be conduct using total station, the level or EDM, staff or mini prism with pole.

For the example building(edges), drainage(invert and top), road, contour(ground level), parking lot etc.

The following information of details needs to observe and booking:

Height of instrument (Hi)) Bearing (horizontal angle-Hr) Vertical angle(Vr) Stadia readings top, middle, lower

5

1-5 horizontal angle/bering

234DETAILING1

buildingDETAILING213Line traverseLine detailPoint station201202204203205301302303304305105104103102101204,102,105Point detail which are where it can consist of items such as roads, edges of buildings, drains45401402403404405501502503504505

DATA OBSERVATIONObservation of data devided into several method/system :

Stadia System The theodolite is directed at the level staff and the distance is measured by reading the top and bottom stadia hairs on the telescope view.

Handle with two situation. Its depends on terrain.

Observation of point will be conduct either HORIZONTAL SIGHTING or INCLINED SIGHTING.

Stadia System

HORIZONTAL SIGHTINCLINE SIGHTBased on principe distance-elevation stadia formulae derived for the horizontal sights.As height differences between staff positions and instrument increase, it will become impossible to use the horizontal line of sight which so far has only been considered.

Stadia System HORIZONTAL SIGHTIt is principe stadia system.

Where Principe stadia system is derived from distance and elevation formulae for horizontal sight

Diafragma instrument axisa

bxObject lensFocal pointcfdDxBAi

Stadia System HORIZONTAL SIGHT

Stadia System HORIZONTAL SIGHTFrom the figure given, look at the similar triangle AOB and AOBVertical dist AB = OC AB OC equation 1equation 2stadia Formula is :Insert the equation 2 to the equation 1f/i is stadia constant and f+c is additive constantSo, stadia formula is:D = Ks+c

Stadia System INCLINED SIGHTHANDLE WITH TWO SITUATION

VERTICAL STAFFStadia System INCLINED SIGHTstaff vertical(angle of elevation) Staff vertical(Angle of depression) From figure S = stadia intercepth = middle stadia readingsV = Vertical distanceH = horizontal distanceD = Slope distance = vertical angle

VERTICAL STAFF FORMULAStadia System INCLINED SIGHTH = Ks cos2 + C cos D = Ks cos + C V = Ks sin 2 + C sin H = 100s (cos)V = (100/2) s sin 2D = Ks cos where the additive constant is zero and K = 100, these formulae are simplified as follows:where the additive constant is zero and K not = 100 and c not = 0, these formulae are simplified as follows:

VERTICAL STAFF FORMULAReduced Level of instrument = Reduced Level TBM + Hi V - hReduced Level of point = Reduced Level of instrument + Hi V - hTBMInstrumentTBMInstrumentPoint station

NORMAL/INCLINE STAFFStadia System INCLINED SIGHTStaff held normal (90 with line of sight)line of sight

D = Ks + CStadia System INCLINED SIGHTNORMAL/INCLINE STAFF FORMULAH = (Ks + C) cos h sin V = (Ks + C) sin C is zero, K = 100 and the value of is less than 10 (the assumption is generally made that the term h sin is zero), these formulae can be simplified as :H = 100 s cos V = 100 s sin

Stadia System INCLINED SIGHTNORMAL/INCLINE STAFF FORMULAReduced Level of instrument = Reduced Level TBM + Hi V h cos Reduced Level of point = Reduced Level of instrument + Hi V - h cos

EDM (ELECTRONIC DISTANCE MEASUREMENT) The term EDM is used to describe a category of instruments that measure distance using an electronic signal. The instrument broadcasts a focused signal that is returned by a prism or reflection from the object.

Therefore, if the speed of the signal is known (speed of light), and the time for the signal to travel to the target and back is known, the distance can be calculated.Advantages of EDMsPrecise measurement of distance.Line of sight instrumentCapable of measuring long distancesReflectorless are single person operationDisadvantages of EDMsElectronic = batterersAccuracy affected by atmospheric conditions.Can be expensiveEDM

Distances can be measured in two ways:Horizontal distanceSlope (surface) distanceThe horizontal distance between two points is the distance between those points measured on a horizontal plane.The slope distance between two points is a distanced measured along the surface of the earth.(either instrument point higher or lower than station observe)When should horizontal distance be used?When should slope distance be used?EDM

H distanceSlope distance(D) H distanceV distanceSituation 1Situation 2Formula :H = D kos V = D tan RL point = RL instrument + Hi V prism reading

Formula :H = D distanceV = 0 = 90/0

When the measurements require horizontal distance, the individual has two choices.Use equipment and techniques to record horizontal distance.Record slope distance and collect the additional information required to calculate horizontal distance.EDM

Example 1:(Find out the constant value of instrument-theodolite)A levelling staff is held vertical at distance of 100 m and 300m from the axis of a tachimetry and the staff intercept for horizontal sights are 0.99m and 3.00m respectively. Find the constants of the instrument.

The instrument is set up at station A and the staff is held vertical at a point B. With the telescope inclined at an angle depression of 10 to the horizontal. The readings on the staff are 2.670, 1.835 and 1.000m. calculate te R.L of B and its horizontal distance from A. The H.I is 1.42 m and R.L is 450.5m.

D = Ks +CGiven D1 = 100m, D2 = 300m, s1 = 0.99, s2 = 3.00D1 = Ks1 + C .. equation 1D2 = Ks2 + C ..equation 2 100 = 0.99K + C (1)300 = 3.00K + C ..(2)Equation 1 equation 2200 = 2.01 K + C .equation 3Find K value, assumed c value = 0200 = 2.01 K + 0 K = 99.502K = 99.052, find c value using equation 3200 = 2.01(99.502) + C C = 1Solution :

Example 2:(vertical staff problem distance)It was required to determine the distance between two points A and B by a tachimeter fitted with an analatic lens. Given k = 100and c = 0. instrument set up at point A and staff at point B. the observation made were a vertical angle = 946 and staff intercept = 1.915m.

What is the horizontal distance AB.

Later on its founds that the constant of the instrument were 100 and 0.5. What would be the percentage error in the horizontal distance computed?

K= 100, c = 0H = Ks cos2 + C cos = 100x1.915 (cos 946) + 0 = 185.9893And K= 100, c = 0.5H = Ks cos2 + c cos = 100x1.915 (cos 946) + 0.5 cos 946 = 185.9893 + 0.4927 = 186.482Solution:Actual distance = 185.9893Error = 186.482 185.9893 = 0.4927Percentage of error= 0.4927 x100 = 0.2649% 185.9893

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