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Figure 4. Diagram showing key areas and dimensions 
As can be seen from Figure 4, each of the areas concerned is 
circular in nature and the centre point and radius of each was of 
prime concern. The vertical axis of the hopper is defined by the 
upper and lower circles designated 1 and 2 in Figure 4, whilst 
the origin of the design system is defined as an offset below the 
centre of circle 2. The flange, designated as circle 3 in Figure 4, 
defines the horizontal orientation of the design system and is 
specified to be at a design distance and angle from the origin. 
Clearly, each circle would have to be targeted appropriately to 
allow the computation of the plane of best fit and circle of best 
fit, then the centre and radius. The measurement task here was 
the coordinate determination of approximately 50 target points. 
The location of these targets is shown in Figure 5. Additional 
targets shown on the sides of the hopper are necessary for 
photogrammetric measurement only, in order to strengthen the 
self-calibrating network. 
    
Plan view of target array 
Figure 5. Target locations in principle planes 
THEODOLITE TRIANGULATION 
Initially the use of an on-line triangulation system, comprising 
of three total stations and PC based software was considered. 
The advantage of the online system is that it provides 
coordinates with a quality measure for every intersection 
measurement as it is taken, and measurements can be repeated 
immediately as required. The online capability of theodolite 
triangulation initially proved to be very enticing. 
Based on an object diameter of 6 metres and a minimum 
instrument set back of 5 metres, it was calculated that 
approximately ten instrument stations would be required to 
adequately cover the object. This ideal configuration and a 
configuration which accounts for the proximity of the wall and 
other obstructions along one side of the object are shown in 
Figure 6. 
  
  
  
  
  
  
Figure 6. Ten station coverage with and without obstructions 
Points adjacent to the obstructions will no doubt suffer a 
degradation of accuracy due to fewer, sharper intersection 
angles. The number of instrument stations can be reduced by 
increasing the minimum set back to effectively improve the 
angular coverage. This improvement will of course be at the 
expense of target coordinate precision due to the increase in 
target range. The level of coordinate precision degradation can 
of course be estimated through network simulations. Naturally 
enough, even a six or seven station network would be 
complicated by the need to “leap-frog” instruments around the 
object. The establishment of a three head triangulation system 
requires 1-2 hours depending on the determination of control. 
Once established, approximately 30 minutes is required to shift 
and reintegrate a new instrument station into the system. Based 
on the following parameters it is possible to estimate the time 
taken to complete the measurement phase using theodolite 
triangulation : 
Three instrument initial establishment 1.5 hr 
Seven station re-establishments (30 minutes each) 3 hr 
Target measurement (50 targets @ approx. 2min. each) 1.5hr 
Total measurement time 6 hr 
These figures do not take into account object targeting which is 
a requirement regardless of the measurement method selected. 
The height of the object poses other issues which must be 
addressed. The hopper stands to a height of 2.5 metres and for 
easy work access was supported on a tooling jig, giving an 
additional 1 metre of height. Sighting to points on the top of 
the hopper would therefore require the purchase or manufacture 
of an offset rod which could be placed flush against the edge of 
the top circle surface. The number of measurements for offsets 
is doubled or tripled, as offset rods have multiple targets which 
provide the information necessary to locate the point of interest, 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996 
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