Traverses
 Fieldwork In Traversing
 Control By Traversing
 Angular Closure
 Linear Closure
 Adjustment Of Traverses
 Function Of Traverses
 Missing Data
 Bearing And Distance Of
    One Line
 Bearing Of One Line,
    Distance Of Another
 Lengths Or Bearings Of
    Two Lines

Linear Closure

The method of checking the distance component of the closed traverse is known as performing a linear closure. In its simplest form this consists of converting the corrected angles into bearing and then computing the partial Easting and Northing for each line.

D Easting = D . Sin q, D Northing = D . Cos q

These values are then summed, and any deviation from the expected value is assessed. In a traverse that starts and finishes on the same point the total change in position should be zero, and in a traverse that starts and finishes on points that have a known position the sum should equal the known displacement. An angular closure must be performed first, as these formuale contain two measured variables (direction and distance) the bearings must have their error eliminated so we can attribute the remaining error to the distances.

If the linear misclosure is acceptable, then this can be adjusted out of the network, but if the misclosure is too large then the fieldwork should be repeated (unless the source of the problem can be isolated). For example, consider the following traverse and traverse table:

The first task is to sum the internal angles and to distribute any misclosure (if and only if this amount is acceptable). If the angular misclosure is excessive then the work should be examined to determine the source of the the mistake, or repeated if necessary.

Sum of angles:

96° 107° 141° 87° 106° 539°

54' 32' 27' 15' 49' 59'

10" 30" 10" 40" 40" 10"

Sum of angles should equal (n - 2)p = 540° in this case. Therefore misclosure = 50" which is 10"/angle

The angles area adjusted for this misclosure amount, this case 10 seconds would be added to each angle to distribute the misclosure evenly throughout the traverse. Having done this a bearing is adopted for one of the lines (or a known bearing is used) and bearings for all the linees are computed. The bearing of a line is computed by adding 180° to the bearing of the line before, and then subtracting the included angle.

q_n = q_n-1 + 180° - a

These bearings may be to an arbitrary datum, they are sometimes calculated to perform a linear closure only and may bear no relationship to 'north' as such.

From the table, SDE = -0.029, and SDN = -0.026. This is then converted to a vector, expressing the misclosure in terms of a bearing and distance.

Distance = 0.039 metres, Bearing = 227° 30'

Conventionally the misclosure is expressed as a ratio of the total perimeter of the traverse and referred to as the 'accuracy'. In this case this is 1:13,795 which satisfies requirements under the Survey Coordination Act. If the misclosure was found to be large then it is likely that a mistake had occurred during the field process. The bearing of the misclosure vector can be used as an indication of the line in which the mistake occurred, however this is a guide only. Naturally if the misclosure was close to one physical length of the measuring device (say 50m) then it is likely that a chain length was omitted somewhere. If the source of the mistake cannot be isolated, then the work is repeated.