UNIT 2 TACHEOMETRIC SURVEYING

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1 UNIT 2 TACHEMETRIC SURVEYING Tacheometrc Surveyng Structure 2.1 Introducton bjectve 2.2 rncple of Tacheometry Advantage of Tacheometry Tacheometer Stada Rod Sytem of Tacheometrc Meaurement Bac rncple of Stada Method Movable Har Method Anallactc Len 2.3 Method of Tacheometry Varou Cae Inclned Sght wth Staff Vertcal and Staff Normal to the Lne of Sght Tangental Method Subtene Bar Method Tacheometrc Traverng 2.4 Summary 2.5 Anwer to SA 2.1 INTRUCTIN Generally, horzontal dtance are meaured by drect method,.e. layng of chan or tape on ground. Thee method are not alway convenent f the ground undulatng, rough, dffcult and nacceble. Under thee crcumtance, ndrect method are ued to obtan dtance. ne uch method Tacheometry. Ung tacheometrc method, elevaton can alo be determned. It n fact a branch of angular urveyng n whch both the horzontal and vertcal poton of pont are determned from the ntrumental obervaton, the chan urvey beng entrely elmnated. bjectve After tudyng th unt, you hould be able to explan the prncple of tacheometry, decrbe varou tacheometrc method, learn tada prncple, learn fxed har and movable har method, and carry out tacheometrcal urveyng. You wll alo be learnng prncple of anallactc len whch make the calculaton mple. Staff vertcal and taff normal cae are alo dcued. You wll alo undertand tangental tacheometry and ubtene bar method ncludng tacheometrcal traverng. 37

2 Advanced Survey 2.2 RINCILES F TACHEMETRY Advantage of Tacheometry Snce both the quantte vz., horzontal dtance and the dfference of elevaton are determned ndrectly n tacheometrc urveyng, t ha a number of advantage over the drect method of meaurement of thee quantte. In terran where drect method are not convenent, tacheometrc method can be ued. Tacheometrc method are convenent for reconnaance urvey of route, for hydrographc urveyng and for fllng n detal n a travere. There conderable avng n tme and money wth the ue of tacheometrc method Tacheometer A tacheometer mlar to an ordnary trant theodolte, generally a verner theodolte telf, ftted wth two tada wre n addton to the central cro-har. The tada daphragm ha three horzontal har vz., a central horzontal har and upper and lower tada har. The upper and lower tada har are equdtant from the central horzontal har. Stada har are ometme called tada lne. For the purpoe of tacheometry, even though an ordnary trant can be employed, accuracy and peed are ncreaed f the ntrument pecally degned for the work. The magnfcaton of the telecope n tacheometer hould be at leat 20 to 30 dameter, wth an aperture of at leat 40 mm for a uffcently brght mage. The magnfyng power of the eyepece alo greater than for an ordnary trant to produce a clearer mage of a taff held far away. Further, the alttude bubble made more entve, nce vertcal angle form an mportant part of the data for calculaton of elevaton dfference. Fgure 2.1 how a more commonly ued pattern of tada daphragm. 38 Fgure 2.1 : Stada aphragm Stada Rod For hort ght of about 100 m or le, an ordnary levellng taff may be ued. For long ght, pecal taff called tada rod generally ued. The graduaton are n bold type (face about 50 mm to 150 mm wde and 15 mm to 60 mm thck) and the tada rod 3 m to 5 m long. To keep the taff or tada rod vertcal, a mall crcular prt level ftted on t backde. It hnged to fold up Sytem of Tacheometrc Meaurement The underlyng prncple common to varou ytem of tacheometry that the horzontal dtance between an ntrument taton and a pont, a well a the elevaton of relatve to the ntrument, can be deduced from (a) the angle at ubtended by a known mall dtance at, and (b) the vertcal angle from to.

3 Th bac prncple appled n dfferent way n dfferent tacheometrc method. There are bacally three ytem of tacheometrc meaurement uch a tada ytem, tangental ytem, and ubtene bar ytem. Tacheometrc Surveyng Stada Sytem Th the more extenvely ued ytem of tacheometry partcularly for detaled work, uch a thoe requred n engneerng urvey. In th ytem, a tacheometer frt et up at a taton, ay, and a taff held at taton, a hown n Fgure 2.2. The dfference of upper har readng and lower har readng called taff ntercept. All the three har ncludng central cro har are read, and determned. Vertcal angle, θ, correpondng to the central har alo meaured. Thee meaurement enable determnaton of horzontal dtance between and and ther dfference n elevaton. There are two dfferent type of ytem n tada method. Thee are a follow : Fxed Har Method In th method, the dtance between the upper har and lower har,.e. tada nterval, on the daphragm of the len ytem fxed. The taff ntercept, therefore, change accordng to the dtance and vertcal angle θ. Movable Har Method In th method, the tada nterval can be changed. The tada har can be moved vertcally up and down by ung mcrometer crew. The taff ntercept, n th cae, kept fxed. Two vane (target) are fxed on the taff at a fxed nterval of 2 m or 3 m. The fxed har method the one whch commonly ued and, unle otherwe mentoned, tada method mean fxed har method. Movable har method not n common ue due to dffculte n determnng the value of accurately. θ h Fgure 2.2 : The Stada Sytem Tangental Sytem 39

4 Advanced Survey In th ytem, obervaton are not taken on tada har. Intead vertcal angle θ 1 and θ 2 to the two target fxed on a taff are recorded (Fgure 2.3). The target are at a fxed dtance. Vertcal angle θ 1, θ 2 and taff ntercept enable horzontal dtance and the dfference of elevaton to be determned. In Fgure 2.3, both the vertcal angle θ 1 and θ 2 are the angle of elevaton. There may be two more cae where ether both the angle may be angle of depreon or one of the angle angle of elevaton and another angle of depreon. θ 1 θ 2 h Subtene Bar Sytem Fgure 2.3 : Tangental Sytem Subtene bar a bar of fxed length generally 2 m ftted wth two target at the end. The target are at equal dtance apart from the centre. The ubtene bar can be fxed on a trpod tand and kept horzontal. A hown n Fgure 2.4, angle α ubtended by the two target at taton meaured by a theodolte. The dtance between the target and the angle α enable the dtance between taton and to be determned. α Fgure 2.4 : Subtene Bar Sytem (Shown n lan) Bac rncple of Stada Method We wll derve dtance and elevaton formulae for fxed har method aumng lne of ght a horzontal and conderng an external focung type telecope. In Fgure 2.5, the optcal centre of the object gla. The three tada har are a, 40

5 b and c and the correpondng readng on taff are A, B and C. Length of mage of AB ab. The other term ued n th fgure are f = focal length of the object gla, = tada har nterval = ab, = taff ntercept = AB, c = dtance from to the vertcal ax of the ntrument, d = dtance from to the taff, d = dtance from to the plane of the daphragm, and = horzontal dtance from the vertcal ax to the taff. Tacheometrc Surveyng A b c d' Focu bjectve d C a aphragm f c Intrument Ax B Staff From mlar Δ, AB and ab, we get And from len formula, Fgure 2.5 : rncple of Stada Method d = d' = + f d' d Combnng the two equaton, we get Addng c to both the de f d = + f f = + ( f + c)... (2.1) or = K + C,... (2.2) where the contant K equal to (f /). It called multplyng contant of the tacheometer and generally kept a 100. The contant C equal to (f + c). It called addtve contant whoe value range from 30 cm to 50 cm for external focung telecope and 10 cm to 20 cm for nternal focung telecope. For telecope ftted wth anallactc len, C equal zero. Elevaton of the taff taton can be determned a n mple levellng, ung the central har readng C and knowng the Reduced Level (RL) of the plane of collmaton. 41

6 Advanced Survey Movable Har Method In movable har method, the taff ntercept fxed, wherea the varable tada-har nterval adjuted by the ue of mcrometer crew. The upper and lower tada har hould multaneouly bect the target end on the taff. The nterval o meaured enable determnaton of horzontal dtance. The expreon f. = + ( f + c) become f. = ( f ) n. p + + c, where p = ptch of the crew, and n = number of ptche between the tada har or the number of turn neceary to move the tada har untl they ubtend on the taff. Th expreon nvolve the two ntrumental contant (f/p) and (f + c). A tacheometer wth movable tada har called a Subtene Theodolte Anallactc Len The bac formula for determnaton of horzontal dtance n tada tacheometry f. = + ( f + c ), or = K. + C ue to the preence of the addtve contant C, not drectly proportonal to. Th accomplhed by the ntroducton of an addtonal convex len n the telecope, called an anallactc len, placed between the eyepece and object gla, and at a fxed dtance from the latter. The anallactc len provded n external focung telecope. It ue mplfe the reducton of obervaton nce the addtve contant (f + c) made zero and the multplyng contant k made 100. However, there objecton to t ue alo a t ncreae the aborpton of lght n the telecope thereby caung reducton n brllancy of the mage. Anallactc len not ftted n nternal focung telecope. In nternal focung telecope, there a concave len between the objectve and the eyepece. Th not an anallactc len. However, the addtve contant C of an nternal focung telecope extremely mall. It uually n the range of 5 cm to 15 cm. It taken a zero n ome of the modern tacheometer. Neverthele, t may be aumed zero, unle pecfed. 2.3 METHS F TACHEMETRY Varou Cae Inclned Sght wth Staff Vertcal and Staff Normal to the Lne of Sght In tada tacheometry wth fxed har method, horzontal ght may not alway be avalable, partcularly n rough and hlly terran where dfference of elevaton between the ntrument and taff taton are large. The meaurement nvolve recordng of vertcal angle (elevaton or depreon) to the central tada har n

7 addton to the taff ntercept. There may be two cae one n whch taff held vertcal and another n whch taff held normal to the lne of ght. Generally, the former preferred. Staff Vertcal In Fgure 2.6, θ the angle of elevaton of the lne of ght. Let u draw an ntercept A B through C perpendcular to C. Now ACA = θ and AA C may be taken practcally equal to 90 o. A B may, therefore, be expreed a. co θ wth mall error, whch can be neglected. Now, dtance C = can be expreed a f. = co θ + (f + c) Smlar to the Eq. (2.1) and the requred horzontal dtance H wll be or H = co θ, f. 2 H = co θ + ( f + c) co θ... (2.3) Tacheometrc Surveyng A' A h C θ B co θ B' v b c Focu G c θ F a f Fgure 2.6 : Inclned Sght Staff Vertcal H For determnaton of elevaton dfference between and, t neceary to determne the value of V,.e. FC, whch the dfference of level between the collmaton plane and the pont C (.e. central har readng) on the taff. Now or V =. n θ or H. tan θ f. 1 V =. n 2 θ + ( f + c) n θ... (2.4) 2 enotng C, the central har readng a h, the level dfference between G and for an angle of elevaton gven by F = V h and f θ angle of depreon, F = V + h Now, f we expre the level of collmaton lne above datum by Heght of Intrument (HI), then RL of = HI + V h 43

8 Advanced Survey In cae of a depreed ght Staff Normal RL of = HI V h Fgure 2.7 how the tuaton when the taff held normal to the lne of ght. Some ghtng devce attached to the taff to enable the taffman to hold the taff normal to the lne of ght. If no ghtng devce attached, the nclnaton of the taff may be adjuted tll the taff ntercept mnmum. In th cae, but f. = + ( f + c) H = co θ + CC = co θ+ h n θ f. H = co θ+ ( f + c). co θ+ h. n θ (a) In cae of angle of depreon, h n θ term wll be ubtractve, nce the taff held away from the ntrument. Now, or For an angle of elevaton, and V = F C = n θ f. V = n θ+ ( f + c) n θ (b) F = V h. co θ, RL of = HI + V h co θ And for an angle of depreon, and F = V + h co θ, RL of = HI V h co θ where HI heght of ntrument at above datum A C C' B h θ v b c a G H θ F' F Tangental Method Fgure 2.7 : Inclned Sght Staff Normal

9 The method of tangental tacheometry can be ued when taff held much away from the ntrument makng t dffcult to read t. Th method ueful when the daphragm doe not have tada har. The taff ued n th method mlar to the one employed n movable har method. The dtance between the target vane may be 2 m or 3 m. Vertcal angle θ 1 and θ 2 to the top and bottom target are meaured from the ntrument taton. The horzontal dtance and the vertcal ntercept V are computed from the value of, θ 1 and θ 2. ependng upon the angle (.e., angle of elevaton or depreon), there can be three cae. Thee are decrbed below. Both the Angle beng Angle of Elevaton Fgure 2.8 how the mplet cae n whch the ground uch that the horzontal lne of ght poble. The readng at B oberved by keepng the telecope level at A. The readng of A noted and the angle θ 1 alo meaured. By knowng the taff ntercept, the horzontal dtance can be gven a, =. cot θ 1... (2.7) Tacheometrc Surveyng A θ 1 B Fgure 2.8 : Tangental Sytem The elevaton of determned from the readng obtaned at B a n ordnary levellng. When the ground doe not permt a horzontal ght, two vertcal angle θ 1 and θ 2 are meaured a hown n Fgure 2.9. A B v θ 1 θ 2 F Fgure 2.9 : Tangental Sytem Both Angle of Elevaton Now AF = tan θ 1 and BF = tan θ 2 = AF BF = (tan θ1 tan θ2) 45

10 Advanced Survey = tan θ tan θ 1 2.tanθ2 and V =.tanθ 2 = tan θ tan θ (2.8)... (2.9) Knowng HI,.e., the heght of the ax of the ntrument above datum, the elevaton of gven a, RL of = HI + FB B = HI +. tan θ 2 B Both the Angle beng Angle of epreon From Fgure 2.10 = BF AF = tan θ tan θ 2 1.tanθ1 and V =.tanθ 1 = tan θ tan θ 2 1 RL of = HI tan θ 1 B θ 1 θ 2 F... (2.10)... (2.11) A B v Fgure 2.10 : Tangental Sytem Both Angle of epreon ne Angle of Elevaton and Another Angle of epreon From Fgure 2.11 = AF + BF = tan θ 1 + tan θ 2 and V = tan θ 1... (2.12) RL of = HI. tan θ 2 B A θ 1 θ 2 F B v 46 Fgure 2.11 : Tangental Sytem ne Angle of Elevaton and Another epreon Subtene Bar Method

11 In the ubtene bar method, the horzontal angle ubtended by two target fxed on a horzontal bar at a known dtance apart meaured at ntrument taton by theodolte. A ubtene bar a hown n Fgure 2.12(a). The two target are at a dtance apart, and each at /2 from the centre,.e. vertcal ax. The bar can be mounted on a trpod tand and can be rotated about t vertcal ax. The ubtene bar hould be kept perpendcular to the lne of ght, whch et through a ght rule or a mall telecope ftted at the centre of the ubtene bar. The horzontal angle α, a hown n Fgure 2.12(b), meaured carefully by mean of a theodolte. Method of repetton of horzontal angle meaurement ued to meaure angle α. Tacheometrc Surveyng / 2 / 2 (a) / 2 α α/2 α/ 2 C / 2 From the geometry, where, A α mall where α n radan. or (b) Fgure 2.12 : Subtene Bar and t Theory 1 α =.cot... (2.13) 2 2 = the dtance between the target of ubtene bar, and α = apex angle ubtended by target at. α α tan = 2 2 = /α, = (α n econd) α 47

12 Advanced Survey If the vertcal angle to the centre of the bar meaured, elevaton dfference can be determned. The ubtene bar method can be ued for meaurng the length of travere lne n rough country. Th ytem can alo be ued for contourng Tacheometrc Traverng Stada tacheometry may be ued for control etablhment of traverng. Stada travere not a accurate a a theodolte travere but both are omewhat mlar. However, n tada travere, dtance are meaured ndrectly by tacheometrc method and not by drect method ung tape etc. Stada travere generally run to generate upplementary control between the taton already fxed by more accurate method. SA 1 (a) (b) (c) (d) (e) (f) (g) erve an expreon for the horzontal dtance of a vertcal taff from a tacheometer f the lne of ght of the telecope horzontal. What are the contant of a tacheometer and how are they determned? erve expreon for the horzontal dtance and the vertcal ntercept V when the taff (a) vertcal, and (b) normal. fferentate between the fxed-har method and the movable-har method. cu the advantage and dadvantage of each method. What tangental method of tacheometry? What are t advantage and dadvantage over the tada method? cu the ubtene bar method of tacheometrc urveyng. What are t advantage? The followng readng were taken wth a tacheometer on to a vertcal taff. Horzontal tance Stada Readng m 0.780; 1.010; m 1.860; 2.165; Calculate the tacheometrc contant. (h) () Stada readng were taken wth a theodolte on a vertcal taff wth the telecope nclned at an angle of depreon of 3 o 30. The taff readng were 2.990, and The reduced level of the taff taton m, and the heght of the ntrument 1.40 m. What the reduced level of the ground at the ntrument? Take contant a 100 and zero. A tacheometer etup at an ntermedate pont on a travere coure and the followng obervaton are made on a taff held vertcal. Staff Staton Vertcal Angle Staff Intercept Axal Har Readng + 9 o o The contant are 100 and 0. Compute the length and the reduced level of. RL of = m.

13 (j) Followng obervaton were taken wth a tacheometer ftted wth an anallactc len havng value of contant a 100. Tacheometrc Surveyng (k) (l) Int. Staton Staff Staton Reduced Bearng Vertcal Angle Staff Readng N 37 o W 4 o , 1.510, N 23 o E 5 o , 2.705, Calculate the horzontal dtance between and. The horzontal angle ubtended at the theodolte taton by a ubtene bar wth vane 3 m apart 0 o Calculate the horzontal dtance between the theodolte and the ubtene bar. The vertcal angle to vane fxed at 1 m and 3 m above the foot of the taff held vertcally at a taton were 1 o 45 and + 2 o 30, repectvely. Fnd the horzontal dtance and the reduced RL of f the RL of the ntrument ax m. (m) The followng note refer to a travere run by a tacheometer ftted wth an anallactc len, wth contant 100 and taff held vertcal. Lne Bearng Vertcal Angle Staff Intercept 30 o o R 300 o o RS 226 o 12 2 o Fnd the length and bearng of S. 2.4 SUMMARY In th unt, you have tuded detal of ndrect method of dtance meaurement ncludng determnaton of elevaton dfference through tacheometrc urveyng method. The horzontal and vertcal dtance can be obtaned by optcal mean a oppoed to the lower proce of meaurement by chan or tape. Th method of tacheometrc meaurement very rapd and convenent. The accuracy of tacheometry n general not a good a wth that of channg. 2.5 ANSWERS T SA SA 1 The anwer to theoretcal queton may be found out n varou ecton of th unt. For numercal problem, the anwer are a follow : (g) (h) () 100, 0.20 m m m; m (j) m (Hnt : Ue formula a 2 = b 2 + c 2 2 b c co A) (k) m 49

14 Advanced Survey (l) m, (m) m, 126 o or S 53 o E 50