Ge 105 lecture 4 (TRIANGULATION ADJUSTMENT) by: Broddett B. Abatayo

ENGR. BRODDETT B. ABATAYO, GE, REA

Part-time Lecturer – GE division, CEIT, CSU, Ampayon, Butuan CityResearch Assistant – Phil-LiDAR 2 Project, CSU, Ampayon, Butuan City

Proprietor – BPA ABATAYO Land Surveying Services1

with CASIO fx-991 es plus Calculator Technique

Lecture 4

Caraga State University

College of Engineering and Information Technology

Ampayon, Butuan City 8600

TRIANGULATION

ADJUSTMENT

GE 105 – Theory of Errors and Adjustments

HORIZONTAL CONTROL SURVEY

TRAVERSE

TRILATERATION (SIDE)

TRIANGULATION (ANGLE)

TRIANGULATION FIGURES

CHAIN OF TRIANGLES

CHAIN OF QUADRILATERALS

CHAIN OF POLYGONS

TRIANGULATION FIGURES

Chain of Triangles

TRIANGULATION FIGURES

Chain of Quadrilaterals

TRIANGULATION FIGURES

Chain of Polygons

TRIANGULATION ADJUSTMENT

a. The sum of the angles about each station is equals to 360°.

CHAIN OF TRIANGLES

Step 1: STATION ADJUSTMENT

Step 2: FIGURE ADJUSTMENT

b. The sum of the interior angles of each triangle equals to 180°.

Angle Measured

Value Station

AdjustmentFigure

Adjustment

A 312°00‘24"

B 47°59‘40"

C 137°10‘29"D 57°02‘42"

E 100°40‘25"F 65°06‘20"

G 241°05‘13"H 66°53‘30"

I 52°10‘20"J 289°00‘30"K 70°59‘30"

L 280°43‘58"M 27°18‘12"

N 51°57‘53"

1. Adjust the angles by station adjustment method.

TRIANGULATION ADJUSTMENT

NM

L

K

J

I

H

G

F

ED

C

B

A

2. Adjust the angles by figure adjustment method.

Angle Measured

Value Station

AdjustmentFigure

Adjustment

A 312°00‘24" 312°00‘22"

B 47°59‘40" 47°59‘38"

C 137°10‘29" 137°10‘30"D 57°02‘42" 57°02‘43"

E 100°40‘25" 100°40‘26"F 65°06‘20" 65°06‘21"

G 241°05‘13" 241°02‘12"H 66°53‘30" 66°50’29"

I 52°10‘20" 52°07‘19"J 289°00‘30" 289°00‘30"K 70°59‘30" 70°59‘30"

L 280°43‘58" 280°43‘57"M 27°18‘12" 27°18‘11"

N 51°57‘53" 51°57‘52"

1. Adjust the angles by station adjustment method.

TRIANGULATION ADJUSTMENT

NM

L

K

J

I

H

G

F

ED

C

B

A

2. Adjust the angles by figure adjustment method.

Angle Measured

Value Station

AdjustmentFigure

Adjustment

A 312°00‘24" 312°00‘22"

B 47°59‘40" 47°59‘38" 48°00’48.67"

C 137°10‘29" 137°10‘30"D 57°02‘42" 57°02‘43" 57°02’41.33"

E 100°40‘25" 100°40‘26" 100°38’27.33"F 65°06‘20" 65°06‘21" 65°07’31.67"

G 241°05‘13" 241°02‘12"H 66°53‘30" 66°50’29" 66°51’39.67"

I 52°10‘20" 52°07‘19" 52°05’20.33"

J 289°00‘30" 289°00‘30"K 70°59‘30" 70°59‘30" 70°59’28.33"

L 280°43‘58" 280°43‘57"M 27°18‘12" 27°18‘11" 27°16’12.33"

N 51°57‘53" 51°57‘52" 51°57’50.33"

1. Adjust the angles by station adjustment method.

TRIANGULATION ADJUSTMENT

2. Adjust the angles by figure adjustment method.

NM

L

K

J

I

H

G

F

ED

C

B

A

TRIANGULATION ADJUSTMENT

a. Sum of angles about each station is equal to 360°.

CHAIN OF QUADRILATERAL

Step 1: STATION ADJUSTMENT

A: ANGLE CONDITION

Step 2: FIGURE ADJUSTMENT

a. The sine of each angle should be proportional to the length of the opposite side of that triangle.

B: SIDE CONDITION

a. Sum of interior angles equals to 360°.

b. Opposite angles at the intersection of diagonals should be equal.

1. Adjust the angles by simple adjustment method.

TRIANGULATION ADJUSTMENT

FG

HA B

C

DE

Angle Value

A 42°38‘36"

B 64°52‘28"

C 40°32‘57"

D 31°56‘07"

E 62°00‘46"

F 45°29‘58"

G 33°31‘32"

H 38°57‘40"

F

G

HA B

C

D

E

Angle Value

ANGLE CONDITION

SIDE CONDITIONFigure Adjustment(Step 2 a)

Figure Adjustment(Step 2 b)

A 42°38‘36"

B 64°52‘28"

C 40°32‘57"

D 31°56‘07"E 62°00‘46"

F 45°29‘58"G 33°31‘32"

H 38°57‘40"

F

G

HA B

C

D

E

Angle Value

ANGLE CONDITION

SIDE CONDITIONFigure Adjustment(Step 2 a)

Figure Adjustment(Step 2 b)

A 42°38‘36" 42°38’35.5"

B 64°52‘28" 64°52’27.5"

C 40°32‘57" 40°32’56.5"

D 31°56‘07" 31°56’06.5"E 62°00‘46" 62°00’45.5"

F 45°29‘58" 45°29’57.5"G 33°31‘32" 33°31’31.5"

H 38°57‘40" 38°57’39.5"

F

G

HA B

C

D

E

Angle Value

ANGLE CONDITION

SIDE CONDITIONFigure Adjustment(Step 2 a)

Figure Adjustment(Step 2 b)

A 42°38‘36" 42°38’35.5" 42°38’30.5"

B 64°52‘28" 64°52’27.5" 64°52’22.5"

C 40°32‘57" 40°32’56.5" 40°32’58.5"

D 31°56‘07" 31°56’06.5" 31°56’08.5"E 62°00‘46" 62°00’45.5" 62°00’50.5"

F 45°29‘58" 45°29’57.5" 45°30’02.5"G 33°31‘32" 33°31’31.5" 33°31’29.5"

H 38°57‘40" 38°57’39.5" 38°57’37.5"

F

G

HA B

C

D

E

Angle Value

ANGLE CONDITION

SIDE CONDITIONFigure Adjustment(Step 2 a)

Figure Adjustment(Step 2 b)

A 42°38‘36" 42°38’35.5" 42°38’30.5" 42°38’30.45"

B 64°52‘28" 64°52’27.5" 64°52’22.5" 64°52’22.55"

C 40°32‘57" 40°32’56.5" 40°32’58.5" 40°32’58.45"

D 31°56‘07" 31°56’06.5" 31°56’08.5" 31°56’08.55"E 62°00‘46" 62°00’45.5" 62°00’50.5" 62°00’50.45"

F 45°29‘58" 45°29’57.5" 45°30’02.5" 45°30’02.55"G 33°31‘32" 33°31’31.5" 33°31’29.5" 33°31’29.45"

H 38°57‘40" 38°57’39.5" 38°57’37.5" 38°57’37.55"