Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line...
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![Page 1: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/1.jpg)
Surveying I.
Lecture 11.
Setting out straight lines, angles, points in given elevation, center line of roadworks and
curves.
Sz. Rózsa
![Page 2: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/2.jpg)
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)
![Page 3: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/3.jpg)
Alignment from the endpoint
Setting out straight lines
![Page 4: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/4.jpg)
Alignment (AC’ distance is observable)
εac tan
![Page 5: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/5.jpg)
cc
21
11
cc
21
22
ccc
21
Alignment (AC’ distance is not observable)
![Page 6: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/6.jpg)
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!
![Page 7: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/7.jpg)
Alignment on the unknown point
Setting out straight lines
![Page 8: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/8.jpg)
ba
abc
ac bc
Setting out straight lines (AC’ and BC’ distance is observable)
![Page 9: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/9.jpg)
Let’s use the formula of the previous case for c1 and c2!
cc
21
11
cc
21
22
ccc
21
11
baabc
22
baabc
2
1
2
1
c
c
Setting out straight lines (AC’ and BC’ distance is NOT observable)
![Page 10: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/10.jpg)
ADABBB
DD
AEABBB
EE
Setting out straight lines through obstacles
![Page 11: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/11.jpg)
Feladat: az AB iránnyal tetszőleges szöget bezáró irány kitűzése.
Tűzzük ki a C’ pont helyét (pl. I. távcsőállásban a kitűzésével), majd mérjük meg a BAC’ szöget (’)
tanac
Compute and measure the distance a. The linear correction c can be computed using and a.
Setting out horizontal angles
![Page 12: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/12.jpg)
Setting out coordinated points
1. Tape surveying (offset surveys)
2. Setting out with polar coordinates (radiation)
Setting out coordinated points
![Page 13: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/13.jpg)
Offset surveys
![Page 14: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/14.jpg)
The optical square
Top view
![Page 15: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/15.jpg)
Offset surveys – computation of chainage and offset
,sincos
,cossin
ABWCB
AN
PN
ABWCB
AE
PE
Pb
ABWCB
AN
PN
ABWCB
AE
PE
Pa
.sin
,1cos
,11
,cos,1
sin,11
ABWCB
iiN
ABWCB
iiE
ibib
ABWCB
iiN
ABWCB
iiE
iaia
![Page 16: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/16.jpg)
Offset surveys – computation of coordinates
1i
aiaia
1i
bibib
ABAB
aA
YB
Yr sin
ABAB
aA
XB
Xm cos
ABPb
ABPa
AN
PN
ABPb
ABPa
AE
PE
sincos
cossin
mibriai
EiE 1
miaribi
NiN 1
![Page 17: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/17.jpg)
Given: A, B and P
2nd fundamental task of surveying:
APt
APAB,,
ABAPP
Setting out with polar coordinates (radiation)
![Page 18: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/18.jpg)
Setting out points with given elevation
PlanAAPlanset HlHHHoCl
![Page 19: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/19.jpg)
VI. Setting out the centerline of roadworks
- Given: S , E, T1, T2, … Tn, and r1, r2, …rn,
- 2nd fundamental task: nVdd
Kd ,...,
12,
1 nVK ,...,
12,
1
1. Preparations:
![Page 20: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/20.jpg)
(in case of right curves – facing to increasing stationing)iiiii ,11,
1,,1
iiiii (in case of left curves – facing to increasing
stationing)
.
![Page 21: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/21.jpg)
2tan i
ir
it
Tangent-length:
Length of arc:
360π2 i
iriA
![Page 22: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/22.jpg)
2. Stationing (computation of chainages)
• The station of S: 0+00
• Round stations between S and CS1
• CS1 station:11t
Kd
![Page 23: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/23.jpg)
• 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
![Page 24: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/24.jpg)
• 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
![Page 25: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/25.jpg)
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.
![Page 26: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/26.jpg)
4. Setting out the CL points:
• Using polar setting out (radiation) from the traverse points.
![Page 27: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/27.jpg)
5. The setting out of principal points on the curves:
2tan
rt
Measure the tangent length from T! Thus the CS and CE points can be found:
4tan
rc
With the distance c the points A and and B can be found:
CM is exactly between A and B.
![Page 28: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/28.jpg)
The point CM can be set out from the chord CS-CE:
2sin
ry
2cos
rrx
5. The setting out of principal points on the curves:
![Page 29: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/29.jpg)
When T is not suitable for observations, then the points A and B are set out.
The distance is measured, BAe And the complementer angle of and .
The distances AT and Bare computed (sine-theorem)
The a’ and b’ distances are computed, and the points CS and CE are computed.
5. The setting out of principal points on the curves:
![Page 30: Surveying I. Lecture 11. Setting out straight lines, angles, points in given elevation, center line of roadworks and curves. Sz. Rózsa.](https://reader035.fdocuments.us/reader035/viewer/2022070407/56649e3b5503460f94b2d963/html5/thumbnails/30.jpg)
6. Setting out the detail points on the curves
n
krk
y sin
krrk
x cos
Detail points with equal distance: Detail points with equal y diff.:
n
r
n
IVy
ysin
ykk
y
22
kyrr
kx