Surveying I.
Lecture 11.
Setting out straight lines, angles, points in
given elevation, center line of roadworks and
curves.
Sz. Rózsa
Setting out points with geometric criteria:
• straight lines: the points must be on a straight line, which is defined by
two marked points;
• horizontal angles: one side of the angle is already set out, the other
side should be set out;
Koordinátákkal adott pontok kitűzése:
• setting out points with defined horizontal coordinates in a local or
national coordinate system;
• setting out points with defined elevation (local or national reference
system)
Setting out straight lines
Alignment from the endpoint
Alignment (AC’ distance is observable)
c  a tan ε
Alignment (AC’ distance is not observable)

1 c
c 
1  
1 2

2 c
c 
2  
1 2
c c c
1 2
Alignment (C is located on the extension of AB line)
Set out the extension of the line in Face Left!
Set out the extension of the line in Face Right!
Setting out straight lines
Alignment on the unknown point
Setting out straight lines
(AC’ and BC’ distance is observable)
c  a
c   b
   
ab  
c

a  b  
Setting out straight lines
(AC’ and BC’ distance is NOT observable)
Let’s use the formula of the previous case for c1 and c2!
c  ab 
1 a b 1

1 c
c 
1  
1 2
c  ab 
2 a b 2

2 c
c 
2  
1 2
c 
1 1
c 
2 2
c c c
1 2
Setting out straight lines through obstacles
BB
DD 
 DA
BA
BB
E E 
 E A
BA
Setting out horizontal angles
   
c  a tan 
Feladat:
iránnyal
tetszőleges
the
szöget
bezáró
Compute
 and
measure
distance
a. irány
Tűzzük
ki a az
C’AB
pont
helyét
(pl.
I. távcsőállásban
a kitűzésével),
kitűzése.
The linear
c can
be computed
 and a.
majd correction
mérjük meg
a BAC’
szöget (using
’)
Setting out coordinated points
Setting out coordinated points
1. Tape surveying (offset surveys)
2. Setting out with polar coordinates (radiation)
Offset surveys
The optical square
Top view
Offset surveys – computation of chainage and offset

cosWCB

WCB   N
 N
,,
 sinsin
 cosWCB
aai a E
EEi
WCB
iN

i

1
1
,
i
AB

1
,
i
AB
P  P A
AB  P
A
AB

cos
WCB  N
N  N sin
. ,
 WCB
 sin WCB
bbi biE
EEi1,cos
WCB
1
i
AB
i

1
,
i
AB

P  P A
AB  P
A
AB
Offset surveys – computation of coordinates
a  a  a
i i i1
b  b  b
i i i1
Y Y
r  B A
 sin 

AB
 a

 AB 
X X
m  B A  cos
AB
 a

 AB 
EE EE  a sin

a AB
 r bPbcos m
Pi Ai1P
i
i AB
cos
b  r 
asin m
NNi NNi
a
b
i AB P i AB
P
A 1P
Setting out with polar coordinates (radiation)
Given: A, B and P
2nd fundamental task of surveying:


AB
P
,

,t
AP AP
AP

AB
Setting out points with given elevation
lset  HoC  H Plan  H A  l A  H Plan
VI. Setting out the centerline of roadworks
1. Preparations:
- Given: S , E, T1, T2, … Tn, and r1, r2, …rn,
- 2nd fundamental task:
d
, d ,..., d
nV
K1 12

,  ,...,
nV
K 1 12
.
 
i
 
i
i ,i1
i1,i


i1,i
i ,i1
(in case of right curves – facing to increasing
stationing)
(in case of left curves – facing to increasing
stationing)

Tangent-length:
Length of arc:
i
t  r tan
i
i
2
i
A  2r π 
i
i 360
2. Stationing (computation of chainages)
• The station of S:
0+00
• Round stations between S and CS1
• CS1 station:
d
t
K1 1
• CE1 station = CS1 Station + Length of Arc
• CE1…CS2 first round station is S1, the station of CE1
should be rounded upwards (amount of rounding is 1);
• CS2 station = CE1 station + d12 – (t1 + t2)
• between CE1 and CS2 round stations should be computed
• CEn…E section: first station is Sn, the value is the upward
rounded station of CEn
• Station of E = Cen + (dnV – tn)
• Round stations between CEn és E
3. Computing the coordinates of CL points (stations) – along the straight lines
• Coordinates can be computed based on the distance between the traverse points (Ti)
and the WCB between the traverse points.
4. Setting out the CL points:
• Using polar setting out (radiation) from the traverse points.
5. The setting out of principal points on the curves:
Measure the tangent length
from T! Thus the CS and CE
points can be found:
t  r tan

2
With the distance c the
points A and and B can be
found:
c  r tan

4
CM is exactly between A
and B.
5. The setting out of principal points on the curves:
The point CM can be set
out from the chord CSCE:
y  r sin

2
x  r  r cos

2
5. The setting out of principal points on the curves:
When T is not suitable for
observations, then the points A and
B are set out.
The distance
e  AB is measured,
And the complementer angle of  and .
The distances AT and Bare computed
(sine-theorem)
The a’ and b’ distances are computed, and the points CS and CE are computed.
6. Setting out the detail points on the curves
Detail points with equal distance:
 

n
Detail points with equal y diff.:
y
y 
IV  r sin 
n
n
y  r sin k 
k
y  k  y
k
x  r  r cos k 
k
2
2
x r r y
k
k