3

/ Measurements

-

-

5

Differential LevelingDifferential Leveling

=___ft

Ghilani, C.D. and Wolf, P.R., 2012, Elementary Surveying An Introduction to Geomatics 13th edition

6

figure 4.5, page 79.

Differential LevelingDifferential LevelingFSBS

HI = ElevBM + BSElevX = HI FSHI = ElevBM + BSElevX = HI FS= ElevBM + BS - FS= ElevBM + BS - FS

Ghilani, C.D. and Wolf, P.R., 2012, Elementary Surveying An Introduction to Geomatics 13th edition ElevX = 820.00 + 8.42 1.20 = 827.22 ftElevX = 820.00 + 8.42 1.20 = 827.22 ft

7

figure 4.5, page 79.

2

1. Direct measurement 1 D rect measurement

2 I di t t 2. Indirect measurement

8

differential leveling differential leveling Direct measurement Indirect measurementDirect measurement

Indirect measurement

,

9

Q

Q

(blunders)

( i )(mistake)

Bell, S., 2001, A Beginners Guide to Uncertainty of Measurement, https://www.wmo.int/pages/prog/gcos/documents/gruanmanuals/UK_NPL/mgpg11.pdf.

AR d dRedundancy

n no

n > nn > no

R d d Redundancy, r

r = n no

d dRedundancyy

Repeated measurementsRepeated measurements

1 10 1.10 .

1.00 .n, no, r

n = 1no = 1

A B C D B,C,D d

n, n , r , o,

Ghil ni C D nd W lf P R 2012 El m nt r Surv in An Intr ducti n t G m tics 13th diti n Ghilani, C.D. and Wolf, P.R., 2012, Elementary Surveying An Introduction to Geomatics 13th edition figure 5.8, page 114.

Closure error / Misclosure

= dAB + dBC + dCD + dDA= 10.60 + 5.42 8.47 7.31

= 16 02 15 78 = 0 26 ft 16.02 15.78 0.26 ft

n = 3no = 3n = 4n = 4r = 1r = 1

24

(km.) (Lb,m),

1 BMR.5 S.8424 14.726 7.37670 S 4 4 S 4 45 S.8424 S.15525 46.657 -10.00747

6 S.12088-1 BMR.5 52.520 3.40324 7 S.15525 S.12088-1 11.222 -0.74562

misclosure = 7.377 10.007 + 3.403 0.746 = 0.027 m

25

misclosure 7.377 10.007 + 3.403 0.746 0.027 m

n n r n,no,r

n = 98no = 98n = 58n = 58r = 40r = 40

Mi t kMistake

- (blunders)-

ERRORS

ERRORSERRORS

= y -

30

Ghilani, C.D. and Wolf, P.R., 2006, Adjustment computations : spatial data analysis.

(.)

1.065

1.066

1 0671.067

1.068

Ghilani, C.D. and Wolf, P.R., 2006, Adjustment computations : spatial data analysis, figure 1.2, page 6.

ErrorsErrors

Systematic Error

Random Error

Blunders

Systematic Errors (Bias)

Random Errors

Adjustment Computation

A B C D B,C,D d

n, n , r , o,

Ghil ni C D nd W lf P R 2012 El m nt r Surv in An Intr ducti n t G m tics 13th diti n Ghilani, C.D. and Wolf, P.R., 2012, Elementary Surveying An Introduction to Geomatics 13th edition figure 5.8, page 114.

most probable valuemost probable value

residualr s ua

40

2

2

41

2

3 2

2

42

3

A + B + C = 180o 2 2

A = A B = B A1 = A2, B1 = B2

3 A + B + C 180o

2 2

A1 A2, B1 B2

43

3 A + B + C 180o

o180 =++ CBA

AvAA +=B

vCC

vBB

++=

vA,vB,vC (residuals)

CvCC +=(residuals)

44

1. 100%2.

3. ()4 4.

46

- -

()

- -

( redundancy)

(Most probable value)

48

, 2555, 1,

Bell, S., 2001, A Beginners Guide to Uncertainty of Measurement, https://www.wmo.int/pages/prog/gcos/documents/gruanmanuals/UK_NPL/mgpg11.pdf.

Ghilani, C.D. and Wolf, P.R., 2012, Elementary Surveying An Introduction to Geomatics 13th edition, Pearson n ntro uct on to G omat cs t on, arson Education, Inc.