The following are the main sources of error in levelling: 1. Instrumental Errors 2. Errors of Manipulation 3. Errors due to Settlement of Level and Staff 4. Errors due to Natural Causes 5. Common Mistake in Levelling.
Source # 1. Instrumental Errors:
(i) Imperfect adjustment:
The essential requirement in levelling is that the line of collimation must be horizontal when the instrument is levelled. If the level is in perfect adjustment, the line of collimation is parallel to the bubble axis so that it becomes horizontal when the bubble is centred.
If the adjustment is not correct, the line of collimation will be inclined even though the bubble is central. The error due to the inclination of the line of collimation is proportional to the distance of the staff from the instrument.
This is most common and serious source of error, it can be eliminated:
(a) Testing and adjusting the instrument, and
(b) By equalising the back sight foresight distances.
(ii) Defective level tube:
If the bubble is sluggish, it may remain in centre even though the bubble axis is not horizontal. And if it is over sensitive, much time is wasted in levelling the instrument. Therefore the level tube fitted with the level should be only of the required sensitiveness.
(iii) Shaky tripod:
A shaky tripod renders the instrument unstable and thus leads to erroneous readings. The tripod should therefore be examined and loose joints be tightened.
(iv) Incorrect graduations of the staff:
When the staff is new one, the graduations should be checked up with an invar tape as there is every possibility of error in graduating the staff. It is however negligible in ordinary work.
Source # 2. Errors of Manipulation:
(i) Careless levelling-up of the instrument:
The instrument should be accurately levelled and the hand should not rest on the telescope or tripod while taking the readings.
(ii) The bubble not being central at the time of taking reading:
This is the most serious and common source of error. The position of the bubble should be checked just before and after each reading is taken. The bubble should be brought in the centre of its run, if necessary, by means of a levelling screw most nearly in line with the telescope.
(iii) The parallax not removed properly:
This error is due to imperfect focussing of the eye-piece and of the object-glass. The parallax should be entirely elimination by proper focussing before taking any reading.
(iv) The staff not being held vertical:
If the staff is not held perfectly vertical, the reading obtained will always be too great. This error is much pronounced for greater readings of staff, the greater the staff reading, the greater is the error. Great care should, therefore, be taken when taking larger readings. This error can be avoided by keeping the staff vertical by having a spirit level or a pendulum plumb-bob attached to the staff or by waving the staff and noting the smallest reading.
Source # 3. Errors due to Settlement of Level and Staff:
(i) Settlement of level:
If the level is set up on soft ground it may gradually settle down in the interval between taking a back sight and the fore sight reading. It will make the fore sight reading smaller than it should be. The level should, therefore, be set up as far as possible on solid ground and the legs of tripod firmly pressed into the ground.
Also the fore sight reading should be taken as soon after taking the back sight reading as possible. In exceptionally soft ground, the legs of the tripod may be set over long wooden stakes driven firmly into the ground.
(ii) Settlement of staff:
At change points, if the staff is held on soft ground, the ground may settle down during the time the instrument is shifted and set up on the point. The back-sight will become greater than it should be. This is a serious source of error and can be eliminated by avoiding soft ground as change point. In case the soft ground being unavoidable, a long peg driven into ground or a steel four-plate should serve as a change point.
Source # 4. Error due to Natural Causes:
(i) Curvature and refraction:
The effect of curvature of the earth is to cause the objects sighted lower than they actually are while that of the refraction is to make them appear higher than they actually are. In ordinary levelling , the error due to curvature and refraction need not be taken into consideration, since it is very small and hence negligible (only 0.003 m for a 200 m sight-length). For long sights, the correction for curvature and refraction has to be applied.
It is difficult to perform accurate work in a wind storm because of the vibration of the instrument. If levelling is necessarily to be performed during wind , adequate arrangements should be made to shelter the instrument and larger readings should be avoided due to difficulty in holding the staff vertical.
On hot sunny days, during the mid-day hours, the staff appears trembling near the ground and taking the correct readings becomes impossible. The work should therefore be suspended during hot hours. If this is not possible, the line of sight should be kept as much above the ground as possible and the length of sight kept short . Also ray-shade should be used if the Sun shines on the object glass.
Source # 5. Common Mistakes in Levelling:
(i) The levelling -staff not being fully extended.
(ii) The staff held upside down.
(iii) Reading the staff upwards instead of downwards.
(iv) Taking reading coincident with one of the stadia-hairs (top or bottom) instead of central-hair.
(v) Omitting an entry.
(vi) Entering a reading in the wrong column.
(vii) Reading the wrong number of metres and decimetres.
Permissible limits of error in levelling:
the permissible closing error may be expressed as E = C √ Km
where, E = the error in metres.
C = the constant, the value of which depends upon the type of instrument, nature of the country, atmospheric conditions and care and judgement of the level man.
Km = the distance in Kilometres.
(i) Rough levelling: E = ± 0.100 √Km
(ii) Ordinary levelling: E = ± 0.025 √Km
(iii) Accurate levelling: E = ± 0.012 √Km
(iv) Precise Levelling: E = ± 0.006 √Km