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

 Problem 

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 

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.