Tachymetry lesson 4 normal staff
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Transcript of Tachymetry lesson 4 normal staff
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TACHYMETRY TACHYMETRY LESSON 4
Incline Sights With
the Staff NormalStaff Normal
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ContentsContents
PRINCIPLES1
2 CALCULATION3
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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
PrinciplesPrinciples
dH
hi
Incline Sight With The Staff NormalIncline Sight With The Staff Normal
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Formula staff normal Formula staff normal
Horizontal Distance;Horizontal Distance; H = (Ks + C) cos θ ± h sin θ
Vertical DistanceVertical Distance ; V = (Ks + C) sin θ
First Reduced Level Station First Reduced Level Station ; RLRL1 1 = RL= RLTBMTBM – hi – hi V – V – h cos θ
Difference HeightDifference Height ; dH = hi . ± V – h cos θ
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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 depression)
hihi = the height of instrument (always positive)
hh = the centre hair reading (always negative)
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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(1.64m
)
B 97 30’ 00” 81 30’ 00” +8 30’ 00”2.025 1.515 1.000
Take the first RL = 42.353 m
HH = (Ks + C) cos θ ± h sin θ = ((((100 . (2.025 – 1.000)100 . (2.025 – 1.000))) + 0.65 + 0.65)) . (Cos . (Cos +8+800 30’ ))) + (1.515 . Cos + (1.515 . Cos +8+800 30’ )) = (103.150. (Cos . (Cos +8+800 30’ ))) ) + + 0.2240.224 = 102.240 m= 102.240 m
VV = (Ks + C) sin θ = = ((100 . (2.025 – 1.000) + 0.65100 . (2.025 – 1.000) + 0.65) ) . (Sin . (Sin +8+800 30’ )) = = (103.150. (Sin . (Sin +8+800 30’ ))) ) = 15.250 m= 15.250 m
dH = hi dH = hi V – h kos V – h kos θ = 1.64 + 15.25 - 1.515 kos= 1.64 + 15.25 - 1.515 kos +8 +800 30’ = 15.387 m= 15.387 m
RLRLA A = RL= RLTBMTBM – hi – hi V – h V – h = RL= RLTBMTBM – – dHdH = 42.353 + 15.387= 42.353 + 15.387 = 57.740 m= 57.740 m
Given K = 100 and C = 0.65
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