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TACHYMETRY TACHYMETRY LESSON 2 The stadia system Incline Sights With the Staff Vertical

ContentsContents

PRINCIPLES1

WORK PROCEDURE

2 CALCULATION

3 PRACTICAL 2

4

hi

dH

s = the staff intercept ABh = the length of the centre hair reading from the staff baseV = the vertical component XY, the height of the centre hair reading above (or below) the instrument axisD = the length of the line of sight IXH = the horizontal distance required.hi = instrument height

Incline Sight With The Staff Vertical Incline Sight With The Staff Vertical

PrinciplesPrinciples

Publication formulaPublication formulaTo obtain Slope distanceSlope distance;So, D = Ks + C

= K(A’B’) + CBut, A’B = ABCos atau sCos So D = KABCos + C D = Ks.Cos + CTo obtain Horizontal DistanceHorizontal Distance and Vertical DistanceVertical Distance ;

H H = DCos = Ks.CosKs.Cos22 + C.Cos + C.Cos

VV = Dsin = Ks.Cos .Sin + C.Sin = ½ (Ks.Sin 2½ (Ks.Sin 2) + C.Sin ) + C.Sin Determination First Reduced Level Station First Reduced Level Station ;RLRLstnstn= RL= RLTBMTBM – hi – hi V – h V – hDetermination Difference HeightDifference Height ;dH = hi dH = hi V – h V – hThe reduced level of the instrument position I plus the difference in height

equal the reduced level of the staff position S. Therefore:

R.L.R.L.ss = R.L. = R.L.II + hi ± + hi ±

V – V – hh

Cycle Diagram Cycle Diagram

Where

DD = Distance

K & CK & C = constant (if not given assume K = 100 & C = 0)

S = staff intercept

HH = horizontal distance

VV = vertical distance

= zenith angle (positive for angles of the elevation, negative for angles of the depression)

hihi = the height of instrument (always positive)

hh = the centre hair reading (always negative)

Work procedure - Work procedure -

Text

Text

Text

Text

Text

Inst. Stn. and

Ht. of inst. axis

Staff stn

Horizontal angle,

HL

Horizontal angle,

HR

Average horizonta

l angle

Vertical angle, V

Upper stadia

Middle stadia

Lower stadia

Remarks

A BSETTING

105015’30”

SETTING285015’30

”

95011’25”

1.205 1.080 0.950

GIVEN REFERENCE

BERING AB = 105015’30”

(25m)(1.455

m)C

155010’36”

335012’30”

335011’33”

90012’20”

1.050 1.030 1.010

C ASETTING

335011’33”

SETTING155011’33

”

85016’25”

1.345 1.145 0.945

(1.305 m)

D45020’26

”225032’3

0”225026’28

”88018’1

0”1.250 1.100 0.950

D CSETTING

225026’28”

SETTING45026’28”

90010’20”

1.530 1.230 0.930

(1.250 m)

E345005’2

6”165002’3

0”165003’58

”92045’0

0”0.855 0.755 0.655

E DSETTING

165003’58”

SETTING345003’58

”

89035’00”

1.855 1.605 1.355

(1.256 m)

B265045’5

5”85040’05

”85043’00”

85025’40”

1.055 0.755 0.455

B ESETTING

85043’00”

SETTING265043’00

”

90016’35”

1.355 1.055 0.755

(1.355 m)

A285015’2

6”105012’3

0”105013’58

”90015’5

0”1.555 1.305 1.055

EXAMPLE RESULT PRACTICAL 2 - TACHEOMETRY BOOKING FORM (The stadia system Incline Sights With The Staff Vertical)

• GIVEN THE TBM (Temporary bench mark) – Stn A & BStn A & B• READING VERTICAL ANGLE BELONG THE SITUATION• TRAVERSE METHOD• TAKE TOPOGRAPHY ITEMS (Tree, Building)

Refer the planABABH =V =S upper=S middle=S lower =

BABAH =V =S upper=S middle=S lower =

ACACH =V =S upper=S middle=S lower =

CACAH =V =S upper=S middle=S lower =

CDCDH =V =S upper=S middle=S lower =

DCDCH =V =S upper=S middle=S lower =

EDEDH =V =S upper=S middle=S lower =

DEDEH =V =S upper=S middle=S lower =

BEBEH =V =S upper=S middle=S lower =

EBEBH =V =S upper=S middle=S lower =

Practical 2Practical 2D Tree 1D Tree 1H =V =S upper=S middle=S lower =

E Tree 2E Tree 2H =V =S upper=S middle=S lower =

C Tree 3C Tree 3H =V =S upper=S middle=S lower =

A Building 1A Building 1H =V =S upper=S middle=S lower =

A Building 2A Building 2H =V =S upper=S middle=S lower =

C Building 3C Building 3H =V =S upper=S middle=S lower =

C Building 4C Building 4H =V =S upper=S middle=S lower =

Calculation – example for field book Calculation – example for field book Inst. Stn.

and Ht. of inst.

axis

Staff stn.

Horizontal angle,

HL

Horizontal angle,

HR

Average horizontal

angle

Vertical angle, V

Upper stadia

Middle stadia

Lower stadia

Remarks

AA(155 m)

BBGIVEN REFERENCE BERING AB =

b1b1 Building 1

b2b2 Building 2

CC

CC(155 m)

AA

b3b3 Building 3

b4b4 Building 4

treetree33 Tree 3Tree 3

DD

DiagramDiagram

TRAVERSEREADING

TOPOGRAPHYREADING

CORRECTION

EXAMPLE CALCULATION EXAMPLE CALCULATION Inst

. Stn. and Ht. of

inst.

axis

Staff

stn.

Horizontal angle

Vertical angle

Zenith angle,

Upper stadia

Middle

stadia

Lower stadia

Horizontal

distanceH (m)

Vertical distanc

eV (m)

Difference height,dH (m)

R.L. at

stn.

R.L. at

staff

Remarks

A(1.25m

)

B 27 30’ 00” 82 00’ 00” +8 00’ 00”2.025 1.515 1.000

Take the first RL = 50 mHH = Ks.CosKs.Cos22 + C.Cos + C.Cos

= 100 (2.025 -1.000) . (Cos100 (2.025 -1.000) . (Cos+8+800))22 + (0.Cos + (0.Cos +8+800)) = 100 (2.025 -1.000) . (Cos100 (2.025 -1.000) . (Cos+8+800))22 + + 00 = =

VV = ½ (Ks.Sin 2½ (Ks.Sin 2) + C.Sin ) + C.Sin = (½ (100 .= (½ (100 .(2.025 -1.000) (2.025 -1.000) .Sin (2 . .Sin (2 . +8+800)) + )) + (0.Sin (0.Sin +8+800)) = (½ (100 .= (½ (100 .(2.025 -1.000) (2.025 -1.000) .Sin (2 . .Sin (2 . +8+800)) + )) + 00 = 14.126 m= 14.126 m

dH = hi dH = hi V – h V – h = 1.25 + 14.126 - 1.515= 1.25 + 14.126 - 1.515 = 13.861m= 13.861m

RLRLA A = RL= RLTBMTBM – hi – hi V – h V – h = RL= RLTBMTBM – – dHdH = 50 – 13.861= 50 – 13.861 = 36.139 m= 36.139 m

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