Lecture 10B--Area Computation Techniques and Omitted Measurements

OMITTED MEASUREMENTS

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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Omitted Measurements • When it is not practical or possible to determine the 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

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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Common Types of Omitted Measurements 1. Length and direction of 1 side unknown

2. Omitted measurements involving 2 adjoining sides 1st CASE: Length of 1 side & direction of another side unknown 2nd CASE: Lengths of 2 sides unknown 3rd CASE: Directions of 2 sides unknown 3. Omitted measurements involving 2 Non-adjoining sides 1st CASE: Length of 1 side & direction of another side unknown 2nd CASE: Lengths of 2 sides unknown 3rd CASE: Directions of 2 sides unknown Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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Common Types of Omitted Measurements 1. Length and direction of 1 side unknown

2. Omitted measurements involving 2 adjoining sides 1st CASE: Length of 1 side & direction of another side unknown 2nd CASE: Lengths of 2 sides unknown 3rd CASE: Directions of 2 sides unknown 3. Omitted measurements involving 2 Non-adjoining sides 1st CASE: Length of 1 side & direction of another side unknown 2nd CASE: Lengths of 2 sides unknown 3rd CASE: Directions of 2 sides unknown Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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Omitted Measurements Length and direction of 1 side unknown (TYPE

1)

Example: Given the ff sketch and data for a closed traverse, determine the length and bearing of unknown side FA

LINE AB BC CD DE EF FA

LENGTH 733.75 598.23 415.05 511.38 395.06 710.88 ________

BEARING N 76-18 E N 23-20 W S 61-35 W N 57-00 W S 32-45 W S 48-25 E ________

E

C

D F

B

A Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

5

Omitted Measurements Involving 2 Adjoining Sides (TYPE 2) 1st CASE: Length of 1 side & direction of another side unknown Example: Given the ff sketch and data for a closed traverse, determine the omitted measurements of lines DE and EA A E

LINE AB BC CD DE EA

LENGTH 1084.32 1590.51 1294.74 _________ 1738.96

B

BEARING S 75-48 E S 15-18 W S 68-06 W N 28-39 W _________ C

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

D

GE 10 – General Surveying I

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

Solving for the closing line:

A

E B

Lda = 2353.48m bda = N 14-01 E

C

D

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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

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

E

B

Summation of Angles at D:

Angle D = 42-40 By Sine Law:

Angle E = 66-31 Since S of angles = 180o : Angle A = 70-49 Unknown Length

About station E: bEA = N 84-50 E C

By Sine Law: DE = 2423.52m D

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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Omitted Measurements Involving 2 Non-adjoining Sides (TYPE 3) 2nd CASE: Lengths of 2 sides unknown Example: Given the ff sketch and data for a closed traverse, determine the omitted measurements of non-adjoining sides BC and EF C

LINE AB BC CD DE EF FA

LENGTH 620.06 ________ 691.56 688.48 ________ 412.35

BEARING S 87-30 E N 30-30 E S 42-45 E S 60-40 W N 74-05 W N 07-02 E

A

F

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

B

D

GE 10 E– General Surveying I

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

Draw an equivalent transformed figure!

C

ab

C

bc A

B

ef

F

D D fa

E E Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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

Determining the length and bearing of the closing line CL ab

C

bc Side BC (Unknown Length)

ef

Side EF (Unknown Length)

D fa

DepCL= -Sdep = -539.18m LatCL= -Slat = +462.91m Therefore, dCL=710.63 m and bCL = N 49-21 W Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

E

GE 10 – General Surveying I

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

Determining lengths of sides BC and EF 1

Closing Line

Side BC (Unknown Length)

Angle 1= bBC+bCL=79-51 bc

Angle 2= bEF - bCL=24-44

710.63 m

Angle 3= 180-(angle1+angle2)=75-25 3

ef 2 Side EF (Unknown Length)

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

By Sine Law: BC = 307.22 m

(length of side BC)

EF = 722.80 m

(length of side EF) GE 10 – General Surveying I

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WHAT ABOUT THE OTHER CASES OF TYPES 2 & 3?

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.

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

13

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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