Introduction & methodology
The task of this exercise was to carry out a looped levelling survey using the rise and fall booking method
around the CSM building. Our group consisted of Christopher Crabb, Alex Levantis and Robin Watson. The
weather conditions were overcast with a fairly pervasive mist throughout.
We chose the corner of a drain cover closest to the campus buildings to act as our first Backsight (BS) and
last Foresight (FS), the level we determined for this point with a handheld GPS was 124m AOD. From here
we proceeded to take one Intermediate Sight (IS) for each setup of the level, before taking a FS onto our
first Change Point (CP) where the staff remained whilst the instrument was moved to its next setup
position. The difference between each sight and the previous IS or BS was then worked out and applied
to the RL level of the last point as either a rise or fall. This was repeated for 11 different set-ups.
As can be seen on Fig 1., where practicable we kept our sights to the magnitude of 20-25m to reduce
collimation error, with an IS on a memorable location between these two CPs. Each of us took turns to
read the level, book the results and hold the staff.
Results
Fig 1 showing the location of our survey stations, change points and intermediate sights.
Point Name
1
Back Site
2
Corner of wall ESI
Building
White wall below
3 camera
Surveyors Mark
4 "JLI" by Mast
Survey mark "TI"
5 by disabled
Above 'FH' on
6 yellow drain
Lampost side by
7 triangle key
Left corner of
8 drain
Corner of lower
9 curb by reception
"00" in 2008 on
10 plaque
Base of double
11 lampost
12 Drain by bike rail
Drain Kite Mark,
13 by designated
North corner of
14 drain
Drain SE shipping
15 container
16
BS (M)
IS (M)
Rise (M)
Fall (M)
Reduced Level (M)
1.856
Remark
124.000 BM
1.551
0.045
0.305
1.611
2.364
0.893
2.718
2.139
0.513
3.005
2.983
1.999
3.874
1.625
0.602
2.513
3.985
2.715
2.435
3.060
0.509
0.714
4.380
0.659
0.402
1.969
1.687
Σ BS - Σ FS =
Σ Rises – Σ Falls =
Last initial RL –
First RL
0.060
124.245 CP
2.319
121.926 IS
0.354
121.572 CP
1.246
120.326 IS
0.866
119.460 CP
2.470
116.990 IS
0.891
116.099 CP
116.473 IS
0.888
115.585 CP
2.018
113.567 IS
0.095
113.472 CP
1.550
115.022 IS
1.926
116.948 CP
2.346
119.294 IS
0.055
119.349 CP
3.978
123.327 IS
0.624
19.302
124.305 IS
0.374
2.620
2nd pipe west of car
registration sign
17 Curb Corner
Drain by Nitrogen
18 Tank
Driain by
19 Nitrogen
Base of private
20 property sign
Return to initial
21 BS
Sum of the
recordings:
FS (M)
0.222
123.105 CP
0.282
123.387 IS
1.078
0.609
123.996 FS
19.306
11.425
11.429
0.004
-0.004
-0.004
0.004
Fig 2. Booking sheet with arithmetic checks.
On completing our survey we originally calculated our final error to be 0.051m, on examining the booking
sheet, it was noticed that one fall (point 3) had been treated as a rise and this was responsible for 0.047m
of the error. The booking sheet shown at Fig 2. is the revised version. Our final error was then -0.004m;
well within the allowable misclosure where m=5mm
m√11= 0.0165…
Likely sources of error include wind buffeting the staff, especially at its fullest extension. The mist
certainly made sighting onto the staff difficult at certain points. Changing the position of the staff on the
CP is another possible source of error.
Use of sights of unequal lengths along steep slopes may have exacerbated any collimation error present
in the instrument, other calibration issues may also have affected our results.
Reading errors, or inconsistencies in the method of estimating to the nearest 1mm between the three
people taking those readings may also contribute; booking errors would certainly have caused an error
outside the allowable misclosure (0.051m) had this not been identified during our arithmetic checks
(Uren & Price, 2010: 43, 54-55).
Contouring exercise
The next part of the assignment involved the recording of a series of levels in a rough grid across a slop.
The position of these spot heights was then to be worked out using the Stadia Tachometry method. For
each point a bearing was recorded, along with the upper and lower stadia readings, and a reading from
the central crosshair. The difference between these points multiplied by 100 gave a horizontal distance to
the point being levelled.
A=100d,
where d = the difference between the upper and lower stadia. These coordinates and their heights are
shown in Fig 3.
Our coordinates were then calculated with the sin/cosine rule and plotted in fig 3.
ΔN =cosθ°A, ΔE = sinθ°A
where θ=the bearing of the point and A=the distance to the point calculated by the stadia tachometry
method above;
Results
Fig 3. Location of spot heights with Point 19’s adjusted position in red.
POI Point Name
Back sight taken
from 'FH' on
yellow drain
levelling point
1
BS (M)
IS (M)
1.801
First row (near
CSM)
2
3
4
FS (M)
HPC (M)
122.082
Level (M)
Angle (Deg)
Angle (RAD) Upper Stadia Lower Stadia Distance
Easting
Northing
120.281
33
0.576
1.895
1.706
18.900 10.2936778 15.8508737
1.953
120.129
103
1.798
1.978
1.926
5.200 5.06672434 -1.1697455
1.872
120.210
91
1.588
1.897
1.847
5.000 4.99923848
1.813
120.269
79
1.379
1.838
1.787
5.100 5.00629864 0.97312588
-0.087262
1.756
120.326
68
1.187
1.783
1.729
5.400 5.00679281
5
First row (ending
at tree)
1.721
120.361
59
1.030
1.749
1.693
5.600 4.80013688 2.88421322
6
Second row (at
Tree)
1.876
120.206
65
1.134
1.908
1.844
6.400 5.80036984 2.70475688
1.974
120.108
74
1.292
2.004
1.943
6.100 5.86369635 1.68138787
2.014
120.068
84
1.466
2.043
1.983
6.000 5.96713137 0.62717078
2.064
120.018
92
1.606
2.093
2.034
5.900 5.89640588
2.183
119.899
101
1.763
2.214
2.153
6.100 5.98792582 -1.1639349
2.413
119.669
100
1.745
2.448
2.378
7.000 6.89365427 -1.2155372
2.359
119.723
91
1.588
2.394
2.324
7.000 6.99893387 -0.1221668
2.339
119.743
81
1.414
2.377
2.301
7.600 7.50643139 1.18890193
2.318
119.764
72
1.257
2.357
2.280
7.700 7.32313518 2.37943086
2.269
119.813
64
1.117
2.310
2.227
8.300 7.45999058 3.63848052
2.535
119.547
70
1.222
2.579
2.491
8.800 8.26929506 3.00977726
2.718
119.364
77
1.344
2.763
2.675
8.800 8.57445657 1.97956928
2.859
119.223
84
1.466
2.904
2.816
8.800 8.75179268 0.91985048
2.938
119.144
91
1.588
2.993
2.892
10.100 10.0984617 -0.1762693
2.996
119.086
100
1.745
3.040
2.951
7
8
9
10 Second row
(ending at CSM)
11 Third Row
(starting at CSM)
12
13
14
15 Third Row
(ending at tree)
16 Fourth Row
(starting at CSM)
17
18
19
20 Fourth row
(ending at Tree)
8.900
2.0228756
-0.205907
8.764789 -1.5454688
Fig 4. Stadia Tachometry booking sheet with outlying result highlighted. Note conversion to radians for
use in Excel.
An obvious outlier in the results appears to be due to a reading/booking error, as the IS does not lie in the
middle of the upper and lower stadia readings as it should do. The IS for point 19 should be equidistant
between the upper and lower stadia; 2.9425 rather than 2.938 as booked.
Lower Stadia = 2.892 IS = 2.938 Upper Stadia = 2.993
Lower Stadia – IS = -0.044, and IS – Upper Stadia = -0.055
We would expect these two differences to be equal. If we adjust the upper stadia by the difference
between these two differences and recalculate the coordinates, then we can now mark the point at 9m
from the level, 8.998629256 -0.157071658.
2.993 – 0.011 = 2.982
so 100(2.982 – 2.892) = 9m
so cos91x9 = -0.157071658 and sin91x9 = 8.998629256
As shown in Fig 3. this point is far closer to the actual progression of points across the slope. Of course
the exact booking error cannot be known, but it seems reasonable that an extra 0.010m was added,
probably by reading the wrong 0.010m block on the E type staff used.
Alternative levelling methods
An electronic laser level would have eliminated our booking error of 0.047m and any other potential
errors from booking or reading the staff, laser levels can also be used accurately over greater distances
(up to 100m). Poor light or weather would affect the ability of the electronic level to sight on the
barcoded staff but these conditions affect all methods of levelling. Perhaps the only significant
disadvantage of the electronic level is the increase in price compared to the advantages it affords;
competent surveyors with a systematic approach to reading and booking can complete a survey in a
comparable period of time with an automatic level (Uren and Price, 2010: 41).
Levels can be calculated trigonometrically using a theodolite. Trigonometric levelling can be prone to
error as gravity is not used as a control element; sighting and reading of vertical angles must be
absolutely precise or errors in calculation become exacerbated as the slope distance increases (Uren and
Price 2010, p175). Another limitation is that the horizontal distance between the survey station and the
point being levelled must be known or calculated, again increasing the possibility for errors due to
inaccurate sighting. A survey of this kind involves far more calculation than direct levelling with an
automatic level, with the corresponding time required and increased chances of booking error. However,
the trigonometric method is useful (and indeed may be the only possible method) in circumstances
where the points to be levelled are inaccessible, such as mountaintops, or overheard power cables.
Levelling with an EDM or total station is entails using the same calculations involved with trigonometric
levelling, only carried out automatically by the instrument itself. The EDM allows this method to be used
where the distance to a point is not known by accurately measuring the slope distance. The same errors
resulting from inaccurate sighting still remain however, the instrument must be sighted exactly in the
centre of the prism, and it is advised that numerous readings be taken and any anomalies discarded, thus
adding to the length of the survey. Total stations are far more sensitive than automatic levels and
atmospheric conditions require that the instrument be given a chance to acclimatise to the ambient
temperature, and low and high levels of light or ground shimmer can require mathematical adjustments
to be made to the readings . Levelling with a total station is an effective way of obtaining heights for a
topographical or walkover survey (Uren & Price 2010: 174).
Alternative methods for a contouring survey could involve carrying out a detail survey with other
methods (i.e., total station, GPS or even chain survey), then simply adding spot heights with an automatic
level and the height of collimation method. Indeed this is the most common method within the
archaeological profession and one I have some experience of.
As can be seen there are advantages to using survey equipment other than an automatic dumpy level,
but these all have the potential for errors and a greater complexity than the direct levelling method. An
automatic level is economical, simple and robust where other methods may be complicated, delicate or
expensive.
Bibliography
Uren, J and Price, B. 2010, Surveying for Engineers, Fifth Edition, Palgrave Macmillan, Basingstoke.