1. General Principles of Surveying.
The main principles to
be observed in surveying are to "work
from the whole to the
part ", and to use methods which are accurate enough for the object in view
but which, since increased accuracy means greater labour and cost, are no more accurate
than the necessity of the case demands. These principles are best exemplified in
the case
of a large national
survey. Here the first thing that is done is the establishment of a number of fairly
widely separated points fixed with the most refined apparatus and methods. Next,
the wide gaps between these primary points are filled in with a number of
secondary points at much closer intervals
than the primary points,
and surveyed by methods which are rigorous and accurate, but not so rigorous or
so accurate as those used in fixing the positions of the primary points. This still
leaves rather wide gaps between fixed points, so a number of tertiary points
are fixed to fill in the gaps, the positions of these tertiary points not being
so accurately surveyed as are those of the secondary and primary points. The result
is a network of points, fairly thickly spaced, which can be used by the
ordinary surveyor who is engaged in surveying the detail on the ground as fixed
points whose positions he can accept and use to control his own work, his work not
being nearly so accurate as any that has gone before. In this way, the work has
proceeded from the whole to the part, and each stage is of no greater accuracy than
is necessary for the purpose for which it was designed. It is to be noted that,
if the final object of the survey is merely to produce a map or plan, the
accuracy of the last stage of the work, i.e. the survey of the detail, need only
be such that the errors in this stage are too small to be plotted, but the accuracy
of the fixings of the original primary, secondary, and tertiary points will need
to be greater than this, that of the fixings of the primary points being very much
greater. The reason for this is that all survey work, even the most refined, is
subject to error, and errors are very quickly propagated and generally very much
magnified as the work proceeds. Hence, if the primary work were not of the utmost
possible accuracy, and the secondary work only slightly less so, very small errors
at the beginning would soon become very large errors as the work was extended over
a large area. In the above example, the primary points control the secondary, the
secondary the tertiary, and the tertiary the detail survey. Errors in the primary
can lead to large errors in the secondary, and so on. Much the same principle is
observed even in simple surveys. Thus, in a chain survey of a small estate, lines
are first run round the perimeter, with a number of clear cross lines between, or
else the outer perimeter is surveyed with a theodolite traverse, and lines are then
run across the interior. These lines are fairly accurately measured and are the
first to be plotted to see that they all fit in properly. Minor chain lines, which
may be of lesser accuracy, are then run between the main lines until the area is
split up into convenient blocks for the survey of the detail. We shall see later
on how this process works in practice. In none of these cases do we start with the
survey of detail and build up from block to block or from detail to tertiary points
and then to primary points: in all cases, the points first laid down are the most.
2. Methods used in Surveying.
Nearly every operation
in surveying is based ultimately on fixing on a horizontal plane the position of
one or more points with relation to the position of one or more others, or/and determining
the elevation or vertical height of one or more points above a definite horizontal
datum plane, which is very often taken as Mean Sea Level. There are four main methods
used in fixing the position of a point on the horizontal plane.
1. By triangulation
from two points whose positions are already fixed and known.
2. By bearing
and distance from a single fixed point.
3. By offset
from a chain line.
4. By resection.
In fig.1, A and B are two points whose positions
are known.
This means that we
know (or can compute) the distance between the two points, and the direction of
one from the other. C is a point whose position is required. If now (a) two of the
angles of the triangle ABC are observed, or (6) the distances AC and BC are measured,
the size and shape of the triangle can be fully determined, either by drawing
Fig. 1
In practical triangulation involving angular observations, the three angles of every triangle are measured wherever possible, as this not only acts as a check, but it also serves to add considerably to accuracy.
Fig. 2
If the angles BAC and ABC only in fig.1 are observed, the point C is said
to be fixed by intersection. In fixing a point by bearing and distance, we measure
the distance AB, fig.2, where A is the
fixed point and B the point to be fixed, and also measure the bearing or direction
of the line AB. For certain purposes, when very great accuracy is not needed, we
can measure bearings or directions directly by means of a magnetic compass.
This will give the bearing or direction of the line with reference to a fixed
direction known as magnetic north, which
is shown as the line AC in the figure. For more accurate work, the bearing must
be obtained by sextant or theodolite by observing the angle DAB between a fixed
point, say D in fig.2, whose bearing
or direction from A is known, and the point B. When this angle is known, we can
compute the bearing of AB and this, combined with the measured distance, enables
us to fix the position of B.
Fig. 3
This principle is used in traversing, a process
also extensively used in surveying. A traverse consists of a series of zigzag lines
whose bearings and distances are measured. Thus, in fig.3, starting from the fixed point B we measure the distances BC,
CD, DE, EF and FG, and also either the bearings of BC, CD, DE, EF, FG or else the
angles ABC, BCD, CDE, DBF, EFG, where in the latter case the bearing
or direction of the
point A from B is known, and the bearing of BC is obtained by calculation from it
and the measured angle ABC. Then, knowing the bearing and distance BC, we can fix
the position of C, and after that, knowing the bearing and distance CD, we can fix
the position of D, and so on, the bearing of CD, if not observed directly from
compass observations, being obtained from the bearing of BC, which we have already
found, and the observed angle BCD.
The term offset in surveying is applied to a line
laid out at right angles to a chain line to fix some point of detail. In fig.4, AB is part of a chain line and c
is a point on it whose distance from A, the beginning of the line, is noted and
recorded, d is a point of detail whose position is to be plotted. The point c is
chosen so that the line cd is perpendicular to the line AB, and the distance cd
is measured. When the line AB is plotted on paper, and the line cd laid out the
correct distance from the plotted position of c, so that dc is perpendicular to
AB, the position of the point d is at once plotted. It will be seen that an offset
is really a special case of fixing by bearing and distance.
Fig. 4
Offsets are mainly
used in the survey of detail in chain surveying and their length is generally
limited to something less than 100 metre. Offsets much longer than this are very
seldom used, except perhaps for fixing the positions of spot heights in connection
with contouring.
 |
|||
 |
|||
Fig. 5
It sometimes happens that the fixed points from which it
is desired to fix the position
of a new point are inaccessible,
or are in positions which
are inconvenient to use as observing
points, but, provided all
four points do not lie on or near a single circle, it is possible to fix a point
by angular observations taken at it to three fixed points. Thus, in fig.5, A, B and C are three points whose
exact positions are known or are plotted on a plan. Then the position of the
point can be fixed if the angles AOB and BOG are measured. Alternatively, if the
work is being done by plane-table, there is a method which, by suitable
pointings of the alidade or sight rule in the directions of A, B and C, enables
the position of to be determined graphically in the field. This method of fixing
the position of a point by observations to three fixed points is known as resection,
but it breaks down
if a circle drawn through
the three fixed points passes through, or near, the point to be fixed.
If prismatic compass fixings only are
required, the point in fig.5 can be fixed
from two fixed points only by observing magnetic bearings to them from the
point to be fixed. In addition, a fixing can be obtained from two fixed points only
if a subsidiary station is chosen suitably placed with regard to the station to
be fixed, and angular observations at each of these stations are taken to the
other one and to the two fixed points.
In determining differences of elevation between
points, several
methods are available.
These are:
1. By observing vertical
angles between points when the lengths of the lines joining them are known.
2. By ordinary spirit
levelling.
3. By readings on a
barometer or aneroid.
4. By readings with the
hypsometer or boiling-point thermometer.
Of these methods, (1) and
(2) are, in general, more accurate than(3) and (4), good spirit levelling being
the most accurate of all.
3. Errors in Surveying.
All survey operations are subject to errors of
observation, but
certain types of error
are more serious than others.
The first type of
error is a gross error or mistake. This means a serious mistake in reading an instrument:
for instance, reading 130 instead of 150 when reading the circle of a theodolite,
or booking a reading of 80 on a chain when it is really 60. Every care must be
taken to avoid making mistakes of this kind, since the results may naturally be
very serious.
The second kind of error is a constant error which
has the same
value and sign for every
single observation. For example, an index error in a sextant will affect every
angle measured with that sextant by the same amount. Sometimes constant errors cancel
out. Suppose the first graduation on a level staff is marked 1 metre. instead
of zero. Then every single sight taken on the staff will be one foot longer than
it should be, and hence the apparent reading will be one foot too high. But, since
a level is used to measure differences of elevation, and these differences are obtained
by subtracting one staff reading from another, the error will cancel out and the
true difference of elevation will be obtained. Nevertheless, constant errors are
to be avoided as much as possible.
Systematic
error is an error which has always the same sign, not necessarily always the
same magnitude, at every observation. Thus, a chain may be uniformly stretched
so that the error in apparent length of any part of it is proportional to the length.
If a line is measured with this chain, the apparent length will be too short by
an amount equal to the length of the line multiplied by the amount of the error
per unit length.
If we knew the amounts and signs of constant or
systematic errors we could allow for them by applying calculated corrections. This
is often done, but sometimes, although systematic error is suspected, neither its
magnitude nor its sign is known, and consequently no correction
is possible.
Accidental errors of observation are the small
errors of observation that vary in magnitude and in sign with every single observation.
Their occurrence depends on the laws of chance and, their magnitudes and signs being
unknown, their effects cannot be calculated and allowed for. Small errors are more
likely to occur than large ones. The small errors in reading a levelling staff due
to" shimmer" in the atmosphere or to temperature changes, small errors
in reading an angle, etc., are of this type.
It should be noted that, in the case of systematic
error, the total error in a measurement which is dependent on the sum of a series
of repeated readings of
the same quantity, is directly proportional to the total measurement, but, in the
case of accidental errors of observation, the total error is proportional to the
square root of the total measurement, or rather to the square root of the number
of repetitions of readings. Thus, if there is a systematic error of k units per
unit length in the reading of a chain, the total error from this cause in the length
L of a line measured with that chain will be k X L. On the other hand, errors of
ordinary levelling tend on the whole to be of the accidental type, so that the total
error in the measurement of a difference of elevation between two points L units
of length apart will be K√L, where
K is the “probable” accidental error per unit length of line. Hence, since the effects
of systematic and constant errors tend to be propagated according to a linear law,
and the effects of accidental errors according to a square root law, it is more
important to reduce or eliminate constant and systematic errors than it is to reduce
or eliminate the small purely accidental errors.
In many cases, but not in all, constant and systematic
errors can be reduced or eliminated by using suitable methods of observation. Thus,
errors of vertical collimation in a theodolite may be entirely eliminated by observing
angles “face right” and “face left” and taking the mean of the two sets of readings.
Similarly, errors of horizontal collimation in levelling may be eliminated by keeping
“Backsights” and “Foresights” equal in length.
No comments:
Post a Comment