Chapter 3 is worth 15 points (5 points per problem PLUS 5 points for the field notes).
Problem 3.1
Determine the elevation of B.M. 2 from the following
notes. Check arithmetic by adding F.S.s and B.S.s.
|
Sta.
|
B.S.
|
H.I.
|
F.S.
|
Elevation
|
| B.M. 1 |
1.21
|
|
|
50.00
|
| T.P. 1 |
6.20
|
|
4.65
|
|
| T.P. 2 |
4.82
|
|
3.11
|
|
| T.P. 3 |
3.03
|
|
5.22
|
|
| B.M. 2 |
|
|
3.16
|
|
Solution to 3.1
|
Sta.
|
B.S.
|
H.I.
|
F.S.
|
Elevation
|
| B.M. 1 |
1.21
|
|
50.00
|
|
51.21 |
||||
| T.P.1 |
6.20
|
|
4.65
|
46.56
|
52.76 |
||||
| T.P. 2 |
4.82
|
|
3.11
|
49.65
|
54.47 |
||||
| T.P. 3 |
3.03
|
|
5.22
|
49.65
|
52.28 |
||||
| B.M. 2 |
3.16
|
49.12
|
||
| Sum |
15.26
|
16.14
|
OR
|
Sta.
|
B.S.
|
H.I.
|
F.S.
|
Elevation
|
| B.M. 1 |
1.21
|
51.21
|
50.00
|
|
| T.P.1 |
6.20
|
52.76
|
4.65
|
46.56
|
| T.P. 2 |
4.82
|
54.47
|
3.11
|
49.65
|
| T.P. 3 |
3.03
|
52.28
|
5.22
|
49.65
|
| B.M. 2 |
3.16
|
49.12
|
||
| Sum |
15.26
|
16.14
|
Sum (B.S.) - Sum (F.S.) = 15.26 - 16.14 = -0.88
Elev B.M. 2 - Elev B.M. 1 = 49.12 - 50.00 = -0.88
Arithmetic check: do these differences equal?
Sum (B.S.) - Sum (F.S.) = Elev B.M. 2 - Elev B.M. 1
Answer: yes, they do equal
Problem 3.7
From the survey in Fig. 3.16, check the arithmetic by
summing the B.S. and the F.S. Hint: Select only F.S. applicable to the differential
survey. What is the error?
|
Sta.
|
B.S.
|
H.I.
|
F.S.
|
Elevation
|
| B.M.1 |
4.38
|
100.00
|
||
|
104.38
|
||||
| 0 + 00 |
3.04
|
101.34
|
||
| 0 + 50 |
2.81
|
101.57
|
||
| 1 + 00 |
5.43
|
98.95
|
||
| 1 + 50 |
6.12
|
98.26
|
||
| 2 + 00 |
2.15
|
4.11
|
100.27
|
|
|
102.42
|
||||
| 2 + 50 |
7.16
|
95.26
|
||
| 3 + 00 |
5.01
|
97.41
|
||
| 3 + 50 |
7.15
|
1.29
|
101.13
|
|
|
108.28
|
||||
| 4 + 00 |
2.16
|
106.12
|
||
| 4 + 10 |
1.19
|
107.09
|
||
| B.M. 1 |
8.30
|
99.98
|
Solution to 3.7
|
Sta.
|
B.S.
|
H.I.
|
F.S.
|
Elevation
|
| B.M.1 |
4.38
|
100.00
|
||
|
104.38
|
||||
| 0 + 00 |
3.04
|
101.34
|
||
| 0 + 50 |
2.81
|
101.57
|
||
| 1 + 00 |
5.43
|
98.95
|
||
| 1 + 50 |
6.12
|
98.26
|
||
| 2 + 00 (T.P. 1) |
2.15
|
4.11
|
100.27
|
|
|
102.42
|
||||
| 2 + 50 |
7.16
|
95.26
|
||
| 3 + 00 |
5.01
|
97.41
|
||
| 3 + 50 (T.P. 2) |
7.15
|
1.29
|
101.13
|
|
|
108.28
|
||||
| 4 + 00 |
2.16
|
106.12
|
||
| 4 + 10 |
1.19
|
107.09
|
||
| B.M. 1 |
8.30
|
99.98
|
||
| Sum |
13.68
|
13.70
|
Sum (B.S.) - Sum (F.S.) = 13.68 - 13.70 = -0.02
Elev B.M. 1(calc) - Elev B.M. 1(given) = 99.98 - 100.00 = -0.02
Math check: Sum (B.S.) - Sum (F.S.) = Elev B.M. 1(calc)
- Elev B.M. 1(given)
differences are equal, therefore the math checks.
Accuracy of the work = error = Elev B.M. 1(given) - Elev B.M. 1(calc) = 100.00 - 99.98 = 0.02
Allowable error = 0.007[length of traverse, ft/100]**1/2 length of traverse, ft = 4 + 10 = 410 ft (from figure 3.16 field notes)
Allowable error = (0.007)[410 ft/100]**1/2 = 0.014
Therefore, the survey is not within reasonable accuracy because calculated error exceeds allowable error.