tachymetry lesson 3 vertical staff
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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 -
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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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