Booking

1
Booking Calculations Rise Fall Method

• Staff readings usually recorded in level book /
  booking form printed for that purpose
• Readings have to be processed to find RLs
  (usually carried out in the same book)

2

• Recommended hand-held calculator / notebook
  computer with spreadsheet avoid hand
  calculations potential mistakes
• Rise fall method one of most common booking
  methods
• all rise/falls computed recorded on sheet
• RL of any new station add rise to (or subtract
  fall from) previous stations RL, starting from
  known BM.

3
Example 1. Rise fall method (staff readings in
Fig. 2.12) Table 2.2
3.729
2.518
0.556
4.153
4.212
0.718
B
CP2
Fig. 2.12
CP1
Table 2.2
BM
4
From (2.3), (2.4) (2.5),
Total rise total fall Last RL first RL

• Equalities checked in last row of Table 2.2.
• Any discrepancy ? existence of arithmetic
  mistake(s), but has nothing to do with accuracy
  of measurements.

5
Example 2. BS, FS ( IS) readings in Fig. 2.13
are booked as shown in Table
2.3
0.595
1.522
2.234
3.132
2.587
1.334
1.985
TBM
2.002
58.331m above MSL
B
A
C
D
Fig. 2.13 BS FS Observed at Stations A - D
Table 2.3
Using rise fall method, a spreadsheet can be
written to deduce RLs of points A through D as
shown in Table 2.4. (use IF MAX in Excel) you
are encouraged to reproduce Table 2.4 on Excel.
6
Table 2.4
Last row of Table 2.4
Total rise total fall Last RL first RL
no mistake with arithmetic.
7
Closure Error

• Definition of misclosure allowable values
• Whenever possible close on either starting
  benchmark or another benchmark to check accuracy
  detect blunders. Misclosure (evaluated at
  closing BM)
• ? measured RL of BM ?? correct RL of BM
  (2.9)
• If ? acceptable corrected for so that closing BM
  has correct known RL

8

• Max. acceptable misclosure (in mm)
• E ? C
• where K total distance of leveling route (in
  number of kilometers)
• C a constant typically between 2 mm (precise
  leveling work of highest standards) 12 mm
  (ordinary engineering leveling)

9

• Somewhat empirical values can be justified by
  statistical theory Bannister et al. (1998).
• Construction leveling often involves relatively
  short distances yet a large number (n) of
  instrument stations. In this case, an alternative
  criterion for E can be used
• E ? D (2.10)
• 5 mm 8 mm commonly adopted values for D.

10
LS Adjustment of Leveling Networks Using
Spreadsheets
Surveyors often include redundancy Fig. 2.15
leveling network associated data Arrowheads
direction of leveling e.g. Along line 1 rise
of 5.102 m from BM A to station X, i.e. RLX RLA
5.102, Along line 3 fall of 1.253 m from B
to Z, i.e. RLZ RLB 1.253. (unknown)
RLs of stations X, Y, Z lower-case letters x, y,
z.
Fig. 2.15
11

• Common practice in leveling adjustments
  observations assigned weights inversely
  proportional to (plan) sight distances L
• wi
  (2.11)
• i 1, 2, , 7.
• Objective determine x, y, z.
• Many different solutions
• (e.g. by loop A-X-Y-Z-A, or B-Z-Y-X-B),
• probably all differ slightly ? random errors
  in data.

12

• Utilize all available data weights least
  squares analysis.
• Note
• 7 observed elevation differences vector
• x 200.000, 207.500 x, z 207.500,
  200.000 z, y x, y 207.500, z yT

13
This vector can be decomposed into a matrix
product as follows
(2.12)

14

• Separate unknowns from constants ? re-write
  leveling information
• Ax k1
  k2
• where
• A coefficient matrix of 0s 1s on RHS of
  (2.12),
• k1 last vector in (2.12) containing benchmark
  values,
• k2 5.102, 2.345, -1.253, -6.132, -0.683,
  -3.002, 1.703T.
• Problem now in Ax k form,
• where k k2 k1,
• weight matrix W Diag 1/40,1/30,1/30,1/30,1/20,1
  /20,1/20

15

• Problem treated in Ch.1
• Solution (1.5) ?numerical matrix computations
• Spreadsheet method
• fast, easy to learn, highly portable
• instant, automatic recalc. if s in problem
  changed (common situation in surveying updating
  of control coordinates, discovery of mistakes,
  etc.).

16

• Spreadsheet shown in Table 2.6. Note
• computed s in Table 2.6 do not necessarily show
  all d.p. ? paper space limitations (all
  computations full accuracy).
• Format Cells Number Decimal places to
  display only desired number of d.p. (computations
  always carry full accuracy).
• Select any cell in matrix ? ctrl - ? whole
  matrix selected (matrix must be completely
  surrounded by blank border)
• See Table 2.6 steps to be carried out on
  spreadsheet

17
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18
Table 2.6 Performing LS Adjustment of Leveling
Network on a Spreadsheet
Most probable RLs for stations X, Y, Z 205.148
m, 204.482 m, 206.188 m, respectively.
19
Contours

• Contour lines best method to show height
  variations on a plan
• Contour line drawn on a plan
• a line joining equal altitudes
• Elevations indicated on plan
• tidemarks left by a flood that fell at a
  discrete contour interval.

20

• Fig. 2.16 plan section of an island
• contour line of 0 meter value tidemark left by
  the sea
• Ascending at 10 m contour intervals a series of
  imaginary horizontal planes passing through
  island ? contours with values of 10 m, 20 m, 30
  m, 40 m, at their points of contact with
  island.

21
Fig. 2.16
22

• Fig. 2.16 gradient of the ground between A C
• Gradient along AC
  1 in 6
• Similarly,
• Gradient along DE
  1 in 3
• regions where contours are more closely packed
  have steeper slopes
• a contour line is continuous closed on itself,
  although the plan may not have sufficient room to
  show.
• Height of any point unique ? two contour lines
  of different values cannot cross or meet, except
  for a cliff / overhang.

23

• Contouring laborious. One direct method
• BM (30.500 m above HKPD) sighted, back sight
  0.500 m ? height of instrument (HI) 31.000m.
• Staff reading 1.000 m ? staffs bottom at 30-m
  contour level
• Staff then taken throughout site, and at every
  1.000 m reading, point is pegged for subsequent
  determination of its E, N coordinates by another
  appropriate survey technique ? 30-m contour
  located.
• Similarly, a staff reading 2.000 m ? a point on
  9-m contour so on.
• Tedious uneconomical for large area
• Suitable in construction projects requiring
  excavation to a specific single contour line.

24
Trigonometric Leveling
Discussion so far differential leveling may not
be practical for large
elevations (e.g. tall buildings height)
trigonometric leveling ( heighting) basic
procedure
25

• rough estimate of h, e.g. residential buildings
  h ? (number of stories ? 3 m).
• Useful for checking result later, also a good
  separation (if possible) between instrument
  building (why?).
• If taping horizontal distance AB from instrument
  to building obtained directly. Alternatively EDM
  at A reflector at some point B directly above
  / below B slope distance AB zenith angle ? AB
  BB computed. Also, vertical distance BG (or
  prism height BG) to base of building by a staff
  / tape.

26

• Raise telescope to sight building top, measure ?v
  precisely.
• Note most theodolites give zenith angle ?z,
  vertical angle ?v 90? ?z.
• Height of building PG AB tan ?v BG (where BG
  BG BB if EDM was used).

27
Modern Instruments

• Many total stations built-in Remote Elevation
  Measurement (REM) mode expedites trigonometric
  leveling
• Sight point B (Fig. 2.17) once distance
  zenith angle measured stored.
• As one raises / lowers telescope ? corresponding
  height of new sighted point calculated
  displayed automatically.
• Reflector to be placed at B (usually
  prism on top of a held pole)

28

• Difficulties
• People walking outside base of building may block
  prism
• Reflectorless total station EDM laser beam can
  be reflected back from suitable building surfaces
  (e.g. white walls) w/o prism. Fig. 2.18(b) ? can
  sight any convenient point B along PG (see Fig.
  2.17) w/o prism,
• Only limitations lasers maximum range
  (typically 100 m) type of buildings surface
  (certain absorbing/ dark surfaces may not work).

29

• Sighting top of tall building ? steep vertical
  angles ? telescope points almost straight up ?
  reading eyepiece becomes difficult to view
• Diagonal eyepiece provides extension of eyepiece
  allows comfortable viewing from the side Fig.
  2.18(a).

(a) A Diagonal Eyepiece (b) Nikon NPL-820
Reflectorless Total Station
Fig. 2.18
Leveling fieldwork time-consuming error-prone,
especially for staff reading by eye.
30

• Digital levels (DL)
• capable of electronic image processing.
• Require specially made staffs with bar codes on
  one side conventional graduations on the other.
  
• Observer directs telescope onto staffs bar-coded
  side focuses on it, as done in conventional
  leveling.
• By pressing a key DL reads bar codes
  determines corresponding staff reading,
  displaying result on a panel.
• Eliminate booking errors expedite leveling work
• Can be used in conventional way also.

31
Standard error for DL typically sighting distance 100 m Observation
range typical upper limit 100 m, lower limit
2 m.

(a) Topcon DL-103 Digital Level (b)
Bar-coded side of a staff
Fig. 2.19