8/15/2019 Lecture 10B--Area Computation Techniques and Omitted Measurements

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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I 1

OMITTED

MEASUREMENTS

8/15/2019 Lecture 10B--Area Computation Techniques and Omitted Measurements

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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I 2

Omitted Measurements

• When it is not practical or possible to determinethe length or direction of a line by field

observation

•

Missing quantities should not exceed 2 in number •  Assumption is that observed values are without

error 

8/15/2019 Lecture 10B--Area Computation Techniques and Omitted Measurements

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Common Types

of Omitted Measurements

2. Omitted measurements involving 2 adjoining sides

1st CASE: Length of 1 side & direction of another side

unknown2nd CASE: Lengths of 2 sides unknown

3rd CASE: Directions of 2 sides unknown

1. Length and direction of 1 side unknown

3. Omitted measurements involving 2 Non-

adjoining sides

1st CASE: Length of 1 side & direction ofanother side unknown

2nd CASE: Lengths of 2 sides unknown

3rd CASE: Directions of 2 sides unknown

8/15/2019 Lecture 10B--Area Computation Techniques and Omitted Measurements

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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I 4

Common Types

of Omitted Measurements

2. Omitted measurements involving 2 adjoining sides

1st CASE: Length of 1 side & direction of another side

unknown2nd CASE: Lengths of 2 sides unknown

3rd CASE: Directions of 2 sides unknown

1. Length and direction of 1 side unknown

3. Omitted measurements involving 2 Non-

adjoining sides

1st CASE: Length of 1 side & direction ofanother side unknown

2nd CASE: Lengths of 2 sides unknown

3rd CASE: Directions of 2 sides unknown

8/15/2019 Lecture 10B--Area Computation Techniques and Omitted Measurements

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Example:Given the ff sketch and data for a closed traverse, determine the

length and bearing of unknown side FA

LINE LENGTH BEARING AB 733.75 N 76-18 E

BC 598.23 N 23-20 W

CD 415.05 S 61-35 W

DE 511.38 N 57-00 W

EF 395.06 S 32-45 WFA ________ ________  710.88 S 48-25 E

A

B

C

D

E

F

Omitted Measurements

Length and direction of 1 side unknown (TYPE 1)

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Omitted Measurements

Involving 2 Adjoining Sides (TYPE 2)

1

st

CASE: Length of 1 side & direction of another side unknownExample:

Given the ff sketch and data for a closed traverse, determine the

omitted measurements of lines DE and EA

LINE LENGTH BEARING

AB 1084.32 S 75-48 E

BC 1590.51 S 15-18 W

CD 1294.74 S 68-06 W

DE  _________ N 28-39 WEA 1738.96 _________ 

A

B

C

D

E

8/15/2019 Lecture 10B--Area Computation Techniques and Omitted Measurements

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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I 7

A

B

C

D

E

Omitted Measurements Involving 2 Adjoining Sides1st CASE: Length of 1 side & direction of another side unknown

Solving for the closing line:

Lda = 2353.48m

 da = N 14-01 E

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Omitted Measurements Involving 2 Adjoining Sides1st CASE: Length of 1 side & direction of another side unknown

Determining the bearing of line DE and length of line EA:

Unknown Length

Summation of Angles at D:

 Angle D = 42-40

By Sine Law:

 Angle E = 66-31

Since of angles = 180o :

 Angle A = 70-49

About station E:

bEA = N 84-50 E

By Sine Law:

DE = 2423.52m

A

D

E

B

C

A

D

E

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Omitted MeasurementsInvolving 2 Non-adjoining Sides (TYPE 3)

2

nd

CASE: Lengths of 2 sides unknownExample:

Given the ff sketch and data for a closed traverse, determine the

omitted measurements of non-adjoining sides BC and EF

LINE LENGTH BEARINGAB 620.06 S 87-30 E

BC ________   N 30-30 E

CD 691.56 S 42-45 E

DE 688.48 S 60-40 W

EF ________   N 74-05 W

FA 412.35 N 07-02 E

C

BA

D

E

F

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Omitted Measurements Involving 2 Non-adjoining Sides2nd CASE: Lengths of 2 sides unknown

C

D

E

bc

ef 

Draw an equivalent transformed figure!

abC

BA

D

E

F

fa

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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I 11

C

D

E

bc

ef 

Side BC

(Unknown Length)

Side EF

(Unknown Length)

Omitted Measurements Involving 2 Non-adjoining Sides2nd CASE: Lengths of 2 sides unknown

ab

Determining the length and bearing of the closing line CL

DepCL= -Sdep = -539.18m

LatCL= -Slat = +462.91m

Therefore, dCL=710.63 m and bCL = N 49-21 W

fa

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Omitted Measurements Involving 2 Non-adjoining Sides2nd CASE: Lengths of 2 sides unknown

Determining lengths of sides BC and EF

1

3

2

bc

Side BC

(Unknown Length)

ef 

Side EF

(Unknown Length)

710.63 m

Closing Line

 Angle 1= bBC+bCL=79-51

 Angle 2= bEF - bCL=24-44

 Angle 3=

180-(angle1+angle2)=75-25

By Sine Law:

BC = 307.22 m (length of side BC)

EF = 722.80 m (length of side EF)

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For the other cases of Types 2 &3 of Omitted Measurements, consult

Elementary Surveying, 3rd Ed by Juny Pilapil La Putt, pp. 431-458

The said cases can be solved by following the procedures we have

discussed in this lecture.

WHAT ABOUT THE OTHER CASES OF TYPES 2 & 3?

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