This document discusses the strength of figure formula used to determine the reliability of survey networks. It defines the strength of figure factor F as the ratio of the number of stations P to the number of lines L. Several examples are provided of calculating F for different survey networks. It also covers using the distance angle method to solve for unknown sides within a quadrilateral using different combinations of triangles formed by the stations. Formulas are provided for calculating distances based on the respective differences of sines from the distance angles.

1. 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 Services
1
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

2. 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

3. STRENGTH of FIGURE
FACTOR (F)

4. STRENGTH OF FIGURE FACTOR
A B
C
D
P = number of stations
L = number of lines
P = 4
L = 6
F = 0.6
Where:

5. P = number of stations
L = number of lines
L = 3
F = 0.75
Where:
P = 3
. .
.A
BC
STRENGTH OF FIGURE FACTOR

6. A B
C
D
P = number of stations
L = number of lines
.
L = 8
F = 0.64
Where:
P = 5
STRENGTH OF FIGURE FACTOR

7. A B
C
D
P = number of stations
L = number of lines
P = 6
L = 10
F = 0.67
Where:
E
.
.
.
.
.
.
F
STRENGTH OF FIGURE FACTOR

8. A
B
C
D
P = number of stations
L = number of lines
P = 8
L = 14
F = 0.69
Where:
G
.
.
.
.
..
.
.F
E
H
STRENGTH OF FIGURE FACTOR

9. DIFFERENT ROUTES WITHIN A QUADRILATERAL
C
D
BA Known side
C
D
BA Known side
C
D
BA Known side
C
D
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 AB
CD=1.650 AB

10. 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
C
D
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°

11. 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
C
D
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°

12. 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
C
D
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°

13. 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
C
D
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°

14. A B
C
D
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

15. Using ABD and ADC with AD as the common side.
R = F
= 44.65
F = 0.60
R = 26.78

16. A B
C
D
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.

17. Using ABC and ADC with AC as the common side.
R = F
= 22.86
F = 0.60
R = 13.72

18. DIFFERENT ROUTES WITHIN A QUADRILATERAL
C
D
BA Known side
C
D
BA Known side
C
D
BA Known side
C
D
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 AB
CD=1.650 AB
R = 13.72R = 26.78
R = 6.39 R = 18.92