ENGR. BRODDETT B. ABATAYO, GE, REA

Part-time Lecturer – GE division, CEIT, CSU, Ampayon, Butuan City

Research Assistant – Phil-LiDAR 2 Project, CSU, Ampayon, Butuan City

Proprietor – BPA ABATAYO Land Surveying Services1

with CASIO fx-991 es plus Calculator Technique

Lecture 5

Caraga State University

College of Engineering and Information Technology

Ampayon, Butuan City 8600

STRENGTH OF FIGURE

GE 105 – Theory of Errors and Adjustments

STRENGTH OF FIGURE FORMULA

STRENGTH OF FIGURE

STRENGTH OF FIGURE FACTOR

δA and δB are the logarithmic differences

corresponding to 1″ for the distance-angles A and B

STRENGTH of FIGURE

FACTOR (F)

STRENGTH OF FIGURE FACTOR

A B

CD

P = number of stationsL = number of lines

P = 4

L = 6

F = 0.6

Where:

P = number of stationsL = number of lines

L = 3

F = 0.75

Where:

P = 3

. .

.A

BC

STRENGTH OF FIGURE FACTOR

A B

CD

P = number of stationsL = number of lines

.

L = 8

F = 0.64

Where:

P = 5

STRENGTH OF FIGURE FACTOR

A B

C

D

P = number of stationsL = number of lines

P = 6

L = 10

F = 0.67

Where:

E

.

.

.

..

.

F

STRENGTH OF FIGURE FACTOR

A

B

C

D

P = number of stationsL = number of lines

P = 8

L = 14

F = 0.69

Where:

G

..

..

..

.

.F

E

H

STRENGTH OF FIGURE FACTOR

DIFFERENT ROUTES WITHIN A QUADRILATERAL

CD

BA Known side

CD

BA Known side

CD

BA Known side

CD

BA Known side

Using ABC and ADC with AC as the common side.

Using ABC and BCD with BC as the common side.Using ABD and BCD with BD as the common side.

Using ABD and ADC with AD as the common side.

44°56°

26°

30°68°

44°

38°

54° 44°56°

26°

30°68°

44°

38°

54°

44°56°

26°

30°68°

44°

38°

54° 44°56°

26°

30°68°

44°

38°

54°

CD=1.231 AB CD=1.492 AB

CD=1.439 ABCD=1.650 AB

DISTANCE ANGLE

Distance Angle – is the angle opposite to the known and common side of the first triangle and angle opposite to the common and required side of the second triangle.

Known side

Required side

A B

CD

44°

56°

26°

30°68°

44°

38°

Using ABC and ADC with AC as the common side.

For triangle ABC:26⁰ and 100⁰

For triangle ADC:112⁰ and 38⁰

54°

DISTANCE ANGLE

Distance Angle – is the angle opposite to the known and common side of the first triangle and angle opposite to the common and required side of the second triangle.

Known side

Required side

A B

CD

44°

56°

26°

30°68°

44°

38°

Using ABD and ADC with AD as the common side.

For triangle ABD:44⁰ and 44⁰

For triangle ADC:30⁰ and 38⁰

54°

DISTANCE ANGLE

Distance Angle – is the angle opposite to the known and common side of the first triangle and angle opposite to the common and required side of the second triangle.

Known side

Required side

A B

CD

44°

56°

26°

30°68°

44°

38°

Using ABD and BCD with BD as the common side.

For triangle ABD:44⁰ and 92⁰

For triangle BCD:56⁰ and 56⁰

54°

DISTANCE ANGLE

Distance Angle – is the angle opposite to the known and common side of the first triangle and angle opposite to the common and required side of the second triangle.

Known side

Required side

A B

CD

44°

56°

26°

30°68°

44°

38°

Using ABC and BCD with BC as the common side.

For triangle ABC:26⁰ and 54⁰

For triangle BCD:68⁰ and 56⁰

54°

A B

CD

Using ABD and ACD with AD as the common side.

ABC

distance angle of AB = 44°

distance angle of AD = 44°44°

30°68°

44°

38°

distance angle of AD = 30°

distance angle of DC = 38°

ADC

= 14.26

= 30.39

Known side

Required side

54°

= 14.26 + 30.39 = 44.65

Using ABD and ADC with AD as the common side.

R = F

= 44.65

F = 0.60

R = 26.78

A B

CD

Respective differences of sines

ABC

distance angle of AB = 26°

distance angle of AC = 100°

44°

56°

26°

30°68°

44°

38°

distance angle of AC = 112°

distance angle of DC = 38°

ADC

= 17.17

= 5.69

= 17.17 + 5.69 = 22.86

Known side

Required side

54°

Using ABC and ADC with AC as the common side.

Using ABC and ADC with AC as the common side.

R = F

= 22.86

F = 0.60

R = 13.72

DIFFERENT ROUTES WITHIN A QUADRILATERAL

CD

BA Known side

CD

BA Known side

CD

BA Known side

CD

BA Known side

Using ABC and ADC with AC as the common side.

Using ABC and BCD with BC as the common side.Using ABD and BCD with BD as the common side.

Using ABD and ADC with AD as the common side.

44°56°

26°

30°68°

44°

38°

54° 44°56°

26°

30°68°

44°

38°

54°

44°56°

26°

30°68°

44°

38°

54° 44°56°

26°

30°68°

44°

38°

54°

CD=1.231 AB CD=1.492AB

CD=1.439 ABCD=1.650 AB

R = 13.72R = 26.78

R = 6.39 R = 18.92