THE SCALE OF WOODEN LEVELLING STAFFS AT AMBIENT TEMPERATURES
4th Year Thesis
by
George C.Y. Leung
School of Geomatic Engineering
University of New South Wales
Supervised by
Assoc. Prof. J.M. Rüeger
 

Aim
The purpose of this thesis was to find out the magnitude of the errors of normal levelling staffs. Only the major errors affecting the scale of the measured height difference were considered. These are the staffs graduations. The project included laboratory and field experiments. Least Square adjustments were used for the processing of the data, and the estimation of the scale corrections.

Laboratory Experiment
Initially, the wooden staffs of the School of Geomatic Engineering, UNSW, were calibrated in a horizontal position against a steel tape. See Fig. 1 below. Ten graduation marks on each wooden staff were measured. This was being done by placing the staff on wooden supports, positioning the steel tape over it, and clamping it at the zero end the of staff. The steel tape was being tensioned with a 5 kg weight, using a roller-grip and hook for this purpose.

Figure 1
Figure 1 ~ Set-up of the Laboratory Experiment in the Surveying Measurement Laboratory, School of Geomatic Engineering, UNSW
 

Field Experiment
After the laboratory experiment, the wooden staffs of the School of Geomatic Engineering, UNSW, were calibrated against a invar staff in a vertical position. (The invar staff was assumed to be of true length at 20°C.) Two precise levels were set-up: one of these levels took the readings to the lower end of the staff (at 0.050 m) while another level took the readings to the top end of the staff (at 2.990 m) (see Fig. 2 below).

Figure 2
Figure 2 ~ Setting up of the field experiment
 

Joint Errors
These are errors of the graduations at the hinges of folding staffs, or between the sections of extension staffs. It cannot be cancelled or eliminated during the levelling run unless all staff readings occur on the upper part or the lower part of the staff. Normally, a cumulative error is introduced into the observations of a levelling run (see Figs. 3 and 4). For a pure scale error, the deviation will be linear, at a constant gradient to the graduation axis (see Fig. 4). The joint error manifests itself by a jump between the two deviations at the joint. In this case, the deviations form two separate lines of best fit with same gradient on both sides of the joint.

Figure 3
Figure 3 ~ Joint error shown on the plot of the differences between tape and staff readings versus staff reading for Staff No.3 (Wild GNLE4). ("1" = 0.050 m, "10" = 3.830 m; spacing 0.420 m.)
Figure 4 ~ Differences between tape and staff readings versusstaff readings for Staff No.3 (Wild GNLE4) after the correction of joint error. ("1" = 0.050 m, "10" = 3.830 m; spacing 0.420 m.)
 

Estimated Scale Corrections
The scale corrections (at 20°C) of the 21 staffs of the School of Geomatic Engineering, UNSW, are listed in the table below together with their associated standard deviations and uncertainty at 95% level of confidence.  The scale correction of Staff No.2 is statistically not significant.  All scale corrections are based on the invar staff Wild GPLE3 (s/n 6820A) being of true length at 20°C and having a coefficient of expansion of 0.92 ppm/°C.
 

Staff Staff Number Scale Correction    
(ppm)
Standard Deviation    
(ppm)
Uncertainty at 95%    
(ppm)
Wild GNLE4 1 1
14.67
6.87
13.47
2 2
9.87
7.60
14.89
3 3
53.10
10.85
21.26
4 4
53.40
9.44
18.51
"Orange" 5 5
378.07
3.90
7.65
6 6
216.70
3.01
5.90
7 7
457.98
2.87
5.62
8 8
429.14
6.86
13.45
9 9
336.19
4.37
8.57
Wild GNLE4 FM-71-57 10
-71.19
6.40
12.55
Nedo Green 1 11
380.98
4.60
9.02
Green 2 12
202.53
6.41
12.56
Myzog 01 13
47.44
8.28
16.22
02 14
103.97
19.44
38.10
03 15
-255.23
2.88
5.64
04 16
-162.82
4.58
8.98
05 17
-46.26
2.81
5.51
06 18
-218.59
5.01
9.82
07 19
-73.59
9.53
18.68
08 20
-77.68
5.76
11.30
09 21
-186.63
9.85
19.32
Figure 5 ~ Summary of scale corrections of 4 m wooden folding staffs
 

Conclusion and Recommendations
According to the Australian Standard (AS1290.8 - 1995), the permissible error in length between any two points on a staff at 20°C (Standard Temperature), with the staff in a vertical position, shall not exceed 1.5 mm over 4 m at an ambient temperature of 20°C.  Staffs No. 5, 7, 8 and 11 do not meet these requirements.  The precision of graduations of the Wild staffs were the smallest.  The precisions of the Myzog staffs were about three times than those of the Wild staffs.

Out of the 21 staffs tested, 12 (57%) have a scale correction that exceeds 1 mm / 10 m height difference (or 100 ppm).  In these cases, a correction should be applied if millimetre accuracy is to be achieved. (Rüeger, J.M. 1997. Staff Errors in and the Adjustment of Ordinary Levelling Runs. The Australian Surveyor, Vol. 42, No.1, pp. 16-24).
 


Last modified: 3rd Dec 1997 by EGM