3. Principles
The Tangential System of Tachymetry
β
s
V
= the staff intercept AB
= the vertical component XY, the height of the centre hair reading above
(or below) the instrument axis
θ ,β = vertical angle (variable)
H = the horizontal distance required.
hi = instrument height
4. Publication formula
AY
= H tan θ
BY
= H tan β
AY –BY = s
= H ( tan θ – tan β)
H =
s
tan θ – tan β
Horizontal
distance
If used θ,
If used β,
Vertical
distance
Vθ = H tan θ
Vβ = H tan β
Difference
height
dH = hi ± Vθ – hθ
dH = hi ± Vβ – hβ
Reduced level RL1 = RLTBM + hi ± Vθ – hθ
RL1 = RLTBM + hi ± Vβ – hβ
5. Where
S = staff intercept
H = horizontal distance
V = vertical distance
θ = zenith angle (θ > β)
hi = the height of instrument (always positive)
h = the centre hair reading (θ @ β)
RL= Reduced level
RL
6. Work procedure
EXAMPLE RESULT PRACTICAL 3 - TACHEOMETRY BOOKING
FORM
(The Tangential System )
Inst. Stn. Staff
and Ht. of stn
inst. axis
Horizontal
angle, HL
Horizontal
angle, HR
SETTING
SETTING
A
B
105015’30” 285015’30”
(1.455 m)
C
155010’36” 335012’30”
C
A
335 11’33” 155011’33”
(1.305 m)
D
45020’26”
SETTING
SETTING
0
225032’30”
Average
horizontal
angle
Vertical angle,
V
α =95011’25”
β = 92010’20”
α =90012’20”
335011’33”
β = 90010’10”
α =83020’25”
β = 85016’25”
α =88018’10”
225026’28”
β = 89028’00”
Stadia
hα =1.205
hβ =1.525
hα =1.050
hβ =1.450
hα =1.345
hβ =1.205
hα =1.250
hβ =1.205
Remarks
GIVEN REFERENCE
BERING AB =
105015’30”
7. Practical 3
• GIVEN THE TBM (Temporary bench mark) – Stn A & B
• DETERMINING THE NUMBER OF STATIONS
• READING VERTICAL ANGLE BELONG THE SITUATION
• TRAVERSE METHOD
• TAKE TOPOGRAPHY ITEMS (Tree, Building, Pedestrian)
8. Sketches topography
B Tree 1
H=
Vα =
Sα=
Vβ =
Sβ=
A b1
H=
Vα =
Sα=
Vβ =
Sβ=
A P2
H=
Vα =
Sα=
Vβ =
Sβ=
B b2
H=
Vα =
Sα=
Vβ =
Sβ=
E Tree 2
H=
Vα =
Sα=
Vβ =
Sβ=
A P4
H=
Vα =
Sα=
Vβ =
Sβ=
Ped
e str
ia n
A P6
H=
Vα =
Sα=
Vβ =
Sβ=
C B3
H=
Vα =
Sα=
Vβ =
Sβ=
C P1
H=
Vα =
Sα=
Vβ =
Sβ=
C P3
H=
Vα =
Sα=
Vβ =
Sβ=
C P5
H=
Vα =
Sα=
Vβ =
Sβ=
9. Example for field book - topography
Inst. Stn.
and Ht.
of inst.
axis
Staff
stn.
Horizontal
angle, HL
Horizontal
angle, HR
Average
horizontal
angle
Vertical angle,
V
Stadia
Remarks
B
α =
β =
Sα =
Sβ =
GIVEN REFERENCE
BERING AB =
b1
α =
β =
Sα =
Sβ =
Building 1
P2
α =
β =
Sα =
Sβ =
Pedestrian 2
α =
β =
Sα =
Sβ =
Pedestrian 4
P6
α =
β =
Sα =
Sβ =
Pedestrian 6
C
α =
β =
Sα =
Sβ =
A
α =
β =
Sα =
Sβ =
T1
α =
β =
Sα =
Sβ =
Tree 1
α =
β =
Sα =
Sβ =
Building 2
α =
β =
Sα =
Sβ =
A
(155 ) P4
B
(155 ) b2
E
10. EXAMPLE CALCULATION
Inst.
Stn.
and Ht.
of inst.
axis
Staff
stn.
Horizontal
angle
Vertical angle
Zenith angle, θ
Stadia
77° 00’ 00”
A
(1.5m)
B
+13° 00’ 00”
+5° 00’ 00”
Vertical
distance
V (m)
Difference
height,
dH (m)
R.L. at R.L. at Remarks
stn.
staff
3.50
85° 00’ 00”
Horizontal
distance
H (m)
1.50
Take the
first RL =
50 m
27° 30’ 00”
H
=
s
=
tan θ – tan β
(3.50 – 1.50)
= 13.94 m
tan +13° – tan +5°
If used θ,
If used β,
Vθ = H tan θ
= 13.94 . Tan +13°
= 3.22 m
Vβ =
=
=
dH =
dH = hi ± Vθ – hθ
= 1.5 +3.22 – 3.50
= 1.22 m
RL1 = RLTBM + hi ± Vθ – hθ
= 50 + 1.5 +3.22 – 3.50 = 51.22 m
H tan β
13.94 . Tan +5°
1.22 m
hi ± Vβ – hβ
= 1.5 + 1.22 -1.50 = 1.22 m
RL1 = RLTBM + hi ± Vβ – hβ
= 50 + 1.5 + 1.22 -1.50 = 51.22 m
