Surveying - traverse - web - Memphis

CIVL 1112

Surveying - Traverse Calculations

Surveying - Traverse

1/13

Surveying - Traverse

Introduction

? Almost all surveying requires some calculations to

reduce measurements into a more useful form for

determining distance, earthwork volumes, land areas,

etc.

? A traverse is developed by measuring the distance and

angles between points that found the boundary of a site

? We will learn several different techniques to compute the

area inside a traverse

Surveying - Traverse

Distance - Traverse

Methods of Computing Area

? A simple method that is useful for rough area estimates

is a graphical method

? In this method, the

traverse is plotted to scale

on graph paper, and the

number of squares inside

the traverse are counted

B

A

C

D

Distance - Traverse

Methods of Computing Area

B

a

A

Distance - Traverse

Methods of Computing Area

B

1

Area ABC ? ac sin ?

2

b

?

a

A

c

C

b

?

Area ABD ?

1

ad sin ?

2

Area BCD ?

1

bc sin ?

2

?

C

d

c

D

Area ABCD ? Area ABD ? Area BCD

CIVL 1112

Surveying - Traverse Calculations

Distance - Traverse

Surveying - Traverse

Methods of Computing Area

B

b

A

Area ABE ?

c

?

Balancing Angles

C

a

?

D

e

2/13

Area CDE ?

d

1

ae sin ?

2

? Before the areas of a piece of land can be computed, it is

necessary to have a closed traverse

? The interior angles of a closed traverse should total:

1

cd sin ?

2

(n - 2)(180¡ã)

where n is the number of sides of the traverse

E

? To compute Area BCD more data is required

Surveying - Traverse

Surveying - Traverse

Balancing Angles

Balancing Angles

A

Error of closure

B

D

? A surveying heuristic is that the total angle should not

vary from the correct value by more than the square root

of the number of angles measured times the precision of

the instrument

? For example an eight-sided traverse using a 1¡¯ transit,

the maximum error is:

?1' 8 ? ?2.83 ' ? ?3'

C

Angle containing mistake

Surveying - Traverse

Surveying - Traverse

Balancing Angles

Latitudes and Departures

? If the angles do not close by a reasonable amount,

mistakes in measuring have been made

? The closure of a traverse is checked by computing the

latitudes and departures of each of it sides

? If an error of 1¡¯ is made, the surveyor may correct one

angle by 1¡¯

? If an error of 2¡¯ is made, the surveyor may correct two

angles by 1¡¯ each

? If an error of 3¡¯ is made in a 12 sided traverse, the

surveyor may correct each angle by 3¡¯/12 or 15¡±

N

N

B

Latitude AB

Bearing ?

E

W

Bearing ?

A

W

C

Departure AB

Latitude CD

S

Departure CD

D

S

E

CIVL 1112

Surveying - Traverse Calculations

Surveying - Traverse

3/13

Surveying - Traverse

Latitudes and Departures

Error of Closure

? The latitude of a line is its projection on the north¨Csouth

meridian

? Consider the following statement:

N

? The departure of a line is

its projection on the east¨C

west line

B

Latitude AB

E

W

Bearing ?

A

¡°If start at one corner of a closed traverse and walk its lines

until you return to your starting point, you will have walked as

far north as you walked south and as far east as you have

walked west¡±

Departure AB

? A northeasterly bearing has:

+ latitude and

+ departure

? latitudes = 0

? Therefore

and

? departures = 0

S

Surveying - Traverse

Surveying - Traverse

Error of Closure

Error of Closure

? When latitudes are added together, the resulting error is

called the error in latitudes (EL)

? If the measured bearings and distances are plotted on a

sheet of paper, the figure will not close because of EL

and ED

? The error resulting from adding departures together is

called the error in departures (ED)

Error of closure

B ED

EL

A

C

Latitudes and Departures - Example

? EL ?

Precision ?

2

? ? ED ?

2

Eclosure

perimeter

Typical precision: 1/5,000 for rural land, 1/7,500 for

suburban land, and 1/10,000 for urban land

D

Surveying - Traverse

Eclosure ?

Surveying - Traverse

Latitudes and Departures - Example

A

N

Departure AB

S 6¡ã 15¡¯ W

N 42¡ã 59¡¯ E

189.53¡¯

234.58¡¯

B

?W ? ?(189.53 ft.)sin(6?15') ? ?20.63 ft.

A

W

E

E

142.39¡¯

175.18¡¯

S 29¡ã 38¡¯ E

S 6¡ã 15¡¯ W

Latitude AB

189.53 ft.

N 12¡ã 24¡¯ W

?S ? ?(189.53 ft.)cos(6?15 ') ? ?188.40 ft.

197.78¡¯

D

N 81¡ã 18¡¯ W

C

B

S

CIVL 1112

Surveying - Traverse Calculations

Surveying - Traverse

Surveying - Traverse

Latitudes and Departures - Example

Latitudes and Departures - Example

Bearing

Side

N

Departure BC

?E ? (175.18 ft.)sin(29?38 ') ? 86.62 ft.

B

W

4/13

AB

BC

CD

DE

EA

degree

m inutes

6

29

81

12

42

15

38

18

24

59

S

S

N

N

N

Length (ft.)

Latitude

Departure

189.53

175.18

197.78

142.39

234.58

939.46

-188.403

-152.268

29.916

139.068

171.607

-0.079

-20.634

86.617

-195.504

-30.576

159.933

-0.163

W

E

W

W

E

E

175.18 ft.

Latitude BC

S 29¡ã 38¡¯ E

?S ? ?(175.18 ft.)cos(29?38 ') ? ?152.27 ft.

C

S

Surveying - Traverse

Surveying - Traverse

Latitudes and Departures - Example

Bearing

Side

AB

BC

CD

DE

EA

Eclosure ?

S

S

N

N

N

? EL ?

Precision ?

2

degree

m inutes

6

29

81

12

42

15

38

18

24

59

? ? ED ? ?

2

Group Example Problem 1

Length (ft.)

Latitude

Departure

189.53

175.18

197.78

142.39

234.58

939.46

-188.403

-152.268

29.916

139.068

171.607

-0.079

-20.634

86.617

-195.504

-30.576

159.933

-0.163

A

S 77¡ã 10¡¯ E

W

E

W

W

E

? ?0.079 ?

2

? ? ?0.163 ? ? 0.182 ft.

0.182 ft.

Eclosure

?

?

939.46 ft.

perimeter

651.2 ft.

660.5 ft.

826.7 ft.

2

1

5,176

B

N 29¡ã 16¡¯ E

D

S 38¡ã 43¡¯ W

491.0 ft.

N 64¡ã 09¡¯ W

C

Surveying - Traverse

Surveying - Traverse

Balancing Latitudes and Departures

Group Example Problem 1

? Balancing the latitudes and departures of a traverse

attempts to obtain more probable values for the locations

of the corners of the traverse

Side

AB

BC

CD

DE

Length (ft.)

Bearing

S

S

N

N

degree

minutes

77

38

64

29

10

43

9

16

E

W

W

E

651.2

826.7

491.0

660.5

Latitude

Departure

? A popular method for balancing errors is called the

compass or the Bowditch rule

? The ¡°Bowditch rule¡± as devised by Nathaniel

Bowditch, surveyor, navigator and mathematician, as

a proposed solution to the problem of compass

traverse adjustment, which was posed in the

American journal The Analyst in 1807.

CIVL 1112

Surveying - Traverse Calculations

5/13

Surveying - Traverse

Surveying - Traverse

Balancing Latitudes and Departures

Balancing Latitudes and Departures

A

? The compass method assumes:

1) angles and distances have same error

2) errors are accidental

S 6¡ã 15¡¯ W

N 42¡ã 59¡¯ E

189.53¡¯

234.58¡¯

? The rule states:

B

E

¡°The error in latitude (departure) of a line is to the

total error in latitude (departure) as the length of the

line is the perimeter of the traverse¡±

142.39¡¯

175.18¡¯

S 29¡ã 38¡¯ E

N 12¡ã 24¡¯ W

197.78¡¯

D

Surveying - Traverse

N 81¡ã 18¡¯ W

C

Surveying - Traverse

Latitudes and Departures - Example

Latitudes and Departures - Example

Recall the results of our example problem

Recall the results of our example problem

Bearing

Side

AB

BC

CD

DE

EA

S

S

N

N

N

Length (ft)

degree

m inutes

6

29

81

12

42

15

38

18

24

59

W

E

W

W

E

Latitude

Departure

Bearing

Side

189.53

175.18

197.78

142.39

234.58

AB

BC

CD

DE

EA

S

S

N

N

N

degree

m inutes

6

29

81

12

42

15

38

18

24

59

W

E

W

W

E

Length (ft)

Latitude

Departure

189.53

175.18

197.78

142.39

234.58

939.46

-188.403

-152.268

29.916

139.068

171.607

-0.079

-20.634

86.617

-195.504

-30.576

159.933

-0.163

Surveying - Traverse

Surveying - Traverse

Balancing Latitudes and Departures

Balancing Latitudes and Departures

N

N

Latitude AB

Departure AB

?S ? ?(189.53 ft.)cos(6 15 ') ? ?188.40 ft.

?

A

W

E

Correction in Lat AB

LAB

?

EL

perimeter

S 6¡ã 15¡¯ W

189.53 ft.

B

?W ? ?(189.53 ft.)sin(6?15 ') ? ?20.63 ft.

A

W

Correction in Lat AB ?

EL ? LAB ?

189.53 ft.

B

Correction in Lat AB ?

939.46 ft.

Correction in Dep AB

LAB

?

ED

perimeter

S 6¡ã 15¡¯ W

Correction in Dep AB ?

perimeter

S

?0.079 ft. ?189.53 ft.?

E

?

? 0.016 ft.

ED ? LAB ?

perimeter

S

Correction in Dep AB ?

?0.163 ft. ?189.53 ft.?

939.46 ft.

?

? 0.033 ft.

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