surveying i. lecture 9. plane surveying. fundamental tasks of surveying. intersections. orientation

25
Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation.

Upload: sharlene-webb

Post on 31-Dec-2015

429 views

Category:

Documents


12 download

TRANSCRIPT

Page 1: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Surveying I.

Lecture 9.

Plane surveying. Fundamental tasks of surveying. Intersections.

Orientation.

Page 2: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

The coordinate system

N

E

Nort

hin

g

Easting

Northing axis is the projection of the starting meridian of the projection system, while the Easting axis is defined as the northing axis rotated by 90° clockwise.

Page 3: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

The whole circle bearing

How could the direction of a target from the station be defined?

E

||NN

AA

B

WCBAB

Whole circle bearing: the local north is rotated clockwise to the direction of the target. The angle which is swept is called the whole circle bearing.

3600 ABWCB

Page 4: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Transferring Whole Circle Bearings

E

||NN

AA

BWCBAB

C

WCBAC

180ABBA WCBWCB

WCB of reverse direction:

Transferring WCBs: WCBAB is known, is measured, how much is WCBAC?

ACAB

ABAC

WCBWCB

or

WCBWCB

Page 5: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

1st fundamental task of surveying

E

||NN

A

BWCBAB

d AB

E

N

A(EA, NA), WCBAB and dAB is known, B(EB,NB)=?

.cos

,sin

cos

sin

ABABAB

ABABAB

ABABABAB

ABABABAB

WCBdNN

WCBdEE

WCBdNNN

WCBdEEE

Page 6: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

2nd fundamental task of surveying

E

||NN

A

BWCBAB

d AB

E-EB A

N-N B

A

A(EA, NA), B(EB,NB) is known, WCBAB=? and dAB=?

cWCB

NNEE

NNEEd

AB

AB

AB

ABABAB

,arctan

22

Page 7: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

cWCB

NNEE

NNEEd

AB

AB

AB

ABABAB

,arctan

22

A

WCBAB

||N

A

B

WCBAB

WCBAB

WCBAB

B

B

B

A

A

>00

0

2nd fundamental task of surveying

Quadrant EB-EA NB-NA c

I. + + 0

II. + - +180°

III. - - +180°

IV. - + +360°

Page 8: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Intersections

Aim: the coordinates of an unknown point should be computed. Measurements are taken from two different stations to the unknown point, and the so formed triangle should be solved.

A B

P

dAB

Page 9: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Foresection with inner angles

A (EA,NA)B (EB,NB) are known, are observed

1. Compute WCBAB, dAB using the 2nd fundamental task of surveying.

2. Using the sine theorem compute dAP and dBP!

A B

P

dAB

WCBAB

d=

?AP

d=

?BP

WCBAP

WCBBP

WCBBA

sinsin

sinsin

ABBPABAP dddd

3. Compute WCBAP and WCBBP:

BABPABAP WCBWCBWCBWCB

Page 10: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Foresection with inner angles

A B

P

dAB

WCBAB

d=

?AP

d=

?BP

WCBAP

WCBBP

WCBBA

4. Compute the coordinates of P:

22

,cossin

:

,cossin

:

BP

AP

P

BP

AP

P

BPBPBBPBPBPB

BP

APAPAAPAPAPA

AP

NNN

EEE

WCBdNNWCBdEE

BFrom

WCBdNNWCBdEE

AFrom

Page 11: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Foresection with WCBs

What happens, when B is not observable from A?

A B

P

dAB

WCBAB

d=

?AP

d=

?BP

WCB’AP

WCB’BP

WCBBA

CD

A,B,C and D are known points, and are measured.

Page 12: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Foresection with WCBs

A B

P

dAB

WCBAB

d=

?AP

d=

?BP

WCB’AP

WCB’BP

WCBBA

CD

BDBP

ACAP

WCBBWC

WCBBWC

BPBB

APAA

WCBEENN

WCBEENN

cot

cot

2

1

The equations of the lines AP and BP:

Page 13: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Foresection with WCBs

APAPAP

BPAP

BPBAPAABP

BPBAPAABBPAP

WCBEENN

WCBWCBWCBEWCBENN

E

WCBEWCBENNWCBWCBE

NN

cot

cotcotcotcot

cotcotcotcot21

A B

P

dAB

WCBAB

d=

?AP

d=

?BP

WCB’AP

WCB’BP

WCBBA

CD

Let’s compute the intersection of the lines AP and BP:

Page 14: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Different types of intersections

How can we use intersections, when A or B is not suitable for setting up the instrument:

A B

P

dAB

WCBAB

d=

?AP

d=

?BP

WCB’AP

WCB’BP

WCBBA

can be computed by =180°--. => Foresection.

Page 15: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Resection

A

B

C

P

T2

T1

O1

O2

E-EB A

E -ET1 A

N -NB A

N -NA T1

A,B,C are known control points and are observed angles

Aim: compute the coordinates of P (the station)

Page 16: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Resection

A

B

C

P

T2

T1

O1

O2

E-EB A

E -ET1 A

N -NB A

N -NA T1

.cot

cot

,cot

cot

cot

1

1

11

AABT

AABT

AT

AB

TA

AB

ENNE

NEEN

EENN

NNEE

Compute the coordinates of T1 and T2!

Page 17: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Resection

A

B

C

P

T2

T1

O1

O2

WCBT1P

WCBBP

Since T1, P and T2 are on a straight line:

9021

211

TTBP

TTPT

WCBWCB

WCBWCB

Foresection with WCBs

Page 18: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Resection – the dangerous circle

What happens, if all the four points are on one circumscribed circle?

P

A

B

C

P

A

B

C

P

Page 19: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Arcsection

A, B are known control points,DAP and DBP are measured.

Aim: compute the coordinates of P!

A

B

P

dAB

DBP

D AP

Using the cosine theorem, compute the angle :

.2

arccos

cos2

222

222

ABAP

BPABAP

ABAPABAPBP

dDDdD

dDdDD

Page 20: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Arcsection

A

B

P

dAB

DBPD AP

WCBAB

WCBAP

Compute WCBAB from the coordinates of A and B,

WCBAP = WCBAB-

1st fundamental task of surveying

Page 21: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Orientation

How can the WCB be determined from observations?

Recall the definition of mean direction:

A

0

P

MDAP

All the angular observations refer to the index of the horizontal circle, but they should refer to the Northing instead!

Orientation

A

0

P

MDAP

ZA

zA – orientation angle

Page 22: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Orientation

How to find the orientation angle?

A

0

P

MDAP

ZA

WCB’AP

B

MDAB

WCBAP

A,B are known points,MDAP and MDAB are observed.

Aim: Compute WCB’AP

Compute the orientation angle:

zA=WCBAB-MDAB

Computing the WCB’AP:

WCBAB=zA+MDAB

Page 23: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Computing the mean orientation angle

In case of more orientations, as many orientation angles can be computed as many control points are sighted:

zAB=WCBAB-MDAB

zAC=WCBAC-MDAC

zAD=WCBAD-MDAD

zAB, zA

C and zAD are usually slightly different

due observation and coordinate error.

However, the orientation angle is constant for a station and a set of observations.

Mean orientation angle:

ADACAB

ADDAAC

CAAB

BA

A ddddzdzdz

z

Page 24: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

WCB vs provisional WCB

Whole circle bearing (WCBAB): computed from coordinates, between two points, which coordinates are known.

Provisional whole circle bearing (WCB’AB): an angular quantity, which is similar to the whole circle bearing. However it is computed from observations, by summing up the (mean) orientation angle and the mean direction.

E

||NN

AA

B

WCBAB

Page 25: Surveying I. Lecture 9. Plane surveying. Fundamental tasks of surveying. Intersections. Orientation

Thank You for Your Attention!