Surveying is a process that involves observations and measurements with a wide range of electronic, optical and mechanical equipment some of which are very sophisticated. Despite the best equipment and methods used, it is still impossible to take observations that are completely free of small variations caused by errors which must be guided against or their effects corrected.
Mistakes and Errors
No measurement can be perfect or exact because of the physical limitations of the measuring instrument as well as limits in human perception. The difference between a measured distance or angle and its true value may be due to mistakes and/or errors. These are two distinct terms. It is necessary to eliminate all mistakes and to minimize all errors when conducting a survey of any type.
Blunders
A blunder is a significant mistake caused by human errors. It may also be called a gross error. Generally, it is due to the inattention or carelessness of the surveyor and it usually results in a large difference between the observed or recorded quantity and the actual or the true value. Mistakes may be caused by sighting on a wrong target with the theodolite when measuring an angle and by tapping to an incorrect station. They also may be caused by omitting a vital piece of information such as the fact that a certain measurement was made on a steep slope instead of horizontally. The possibilities for mistakes are almost endless. However, they are only caused by occasional lapses of attention.
Errors
An error is the difference between a measured quantity and its true value, caused by imperfection in the measuring instrument, by the method of measurement, by natural factors such as temperature or by random variation in human observation. It is not a mistake due to carelessness. Errors can never be completely eliminated, but they can be minimized by using certain instruments and field procedures and by applying computed correction factors. Following are a few common mistakes in chain surveying.
- Once an arrow is withdrawn from the ground during chaining it may not be replaced in proper position, if required due to some reason.
- A full chain length may be omitted or added. This happen when arrows are lost or wrongly counted.
- The number may be read from the wrong direction; for instance, a 6 may be read as a 9.
- Some number may be called wrongly. For example, 50.2 may be called as fifty-two without the decimal point being mentioned.
Types of errors
1) Gross Errors
These are referred to mistakes or blunders by either the surveyor or his assistants due to carelessness or incompetence. On construction sites, mistakes are frequently made by in – experienced Engineers or surveyors who are unfamiliar with the equipment and method they are using. These types of errors include miscounting the number of tapes length, wrong booking, sighting wrong target, measuring anticlockwise reading, turning instruments incorrectly, displacement of arrows or station marks etc. Gross errors can occur at any stage of survey when observing, booking, computing or plotting and they would have a damaging effect on the results if left uncorrected. Gross errors can be eliminated only by careful methods of observing booking and constantly checking both operations.
2) Systematic or Cumulative Errors
Errors, which may occur in the same direction and which finally tend to accumulate are said to be cumulative. They seriously affect the accuracy of the work and are proportional to the length of the line (L). The errors may be positive or negative. The errors, that occur always in the same direction are called cumulative errors.
- Bad ranging
- Bad straightening
- Erroneous length of chain
- Temperature variation
- Variation in applied pull
- Non-horizontality
- Sag in the chain.
These are repetitive errors and cumulative in effect and are caused by badly adjusted instrument and the physical condition at the time of measurement must be considered in this respect. Expansion of steel, frequently changes in electromagnetic distance (EDM) measuring instrument, etc. are just some of these errors. Systematic errors have the same magnitude and sign in a series of measurements that are repeated under the same condition, thus contributing negatively or positively to the reading hence, makes the readings shorter or longer. This type of error can be eliminated from a measurement using corrections (e.g. effect of tension and temperature on steel tape). Another method of removing systematic errors is to calibrate the observing equipment and quantify the error allowing corrections to be made to further observations. Observational procedures by re-measuring the quantity with an entirely different method using different instrument can also be used to eliminate the effect of systematic errors.
Under the same conditions of measurement, systematic errors are constant in magnitude and direction or sign (either plus or minus). They usually have no tendency to cancel if corrections are not made. For example, suppose that a 30-m steel tape is the correct length at 200c and that it is used in a survey when the outdoor air temperature is, say 350c. Since steel expands with increase in temperatures, the tape will actually be longer than it was at 200c. Theodolites and even EDM are also subjected to systematic errors. The horizontal axis of rotation of the theodolite, for instance, may not be exactly perpendicular to the vertical axis.
a) Positive Cumulative Error
The error, which make the measured length more than the actual is known as positive cumulative error.
Sources
i) The length of chain / tape is shorter than its standard length due to
- Bending of links
- Removal of too many rings due to adjustment of its length.
- Knots in connecting links
- The field temperature is lower than that at which the tape was calibrated
- Shrinkage of tape when moist
- Clogging of rings with mud
ii) The slope correction is ignored while measuring along slopping ground
iii) The sag correction, if not applied when chain / tape is suspended at its ends
iv) Incorrect alignment
b) Negative Cumulative Error
The error, which make the measured length less than the actual is known as negative cumulative error.
Sources
a) The length of chain / tape is longer than its standard length due to
- Flattening of connecting rings
- Opening of the ring joints
- The field temperature is higher than that at which the tape was calibrated
3) Random or Accidental Error or Compensating Error
Errors, which may occur in both directions (that is both positive and negative) and which finally tend to compensate are known as compensating errors. Although every precaution may be taken certain unavoidable errors always exist in any measurement caused usually by human limitation in reading/handling of instruments. Random errors cannot be removed from observation but methods can be adopted to ensure that they are kept within acceptable limits. In order to analyse random errors or variable, statistical principles must be used and in surveying their effects may be reduced by increasing the number of observations and finding their mean. It is therefore important to assume those random variables are normally distributed. Some compensating errors includes the following.
- Incorrect marking of the end of a chain.
- Graduations in tape may not be exactly same throughout.
An accidental or random error is the difference between a true quantity and a measurement of that quantity that is free from blunders or systematic errors. Accidental errors always occur in every measurement. They are the relatively small, unavoidable errors in observation that are generally beyond the control of the surveyor. These random errors, as the name implies, are not constant in magnitude or direction. One example of a source of accidental errors is the slight motion of a plumb bob string, which occurs when using a tape to measure a distance. The tape is generally held above the ground and the plumb bob is used to transfer the measurement from the ground to the tape.
4) Personal errors
Wrong reading, wrong recording, reading from wrong end of chain etc., are personal errors. These errors are serious errors and cannot be detected easily. Care should be taken to avoid such errors.
Precautions against Errors and Mistakes
- The point where the arrow is fixed on the ground should be marked with a cross (×).
- The zero end of the chain or tape should be properly held.
- During chaining the number of arrows carried by the follower and leader should always tally with the total number of arrows taken.
- The chainman should call the measurement loudly and distinctly and the surveyor should repeat them while booking.
- Ranging should be done accurately.
- No measurement should be taken with the chain in suspension.
Adjustment of Chain
Chains are adjusted in the following ways.
i) When the chain is too long, it is adjusted by
a) Closing up the joints of the rings
b) Hammering the elongated rings
c) Replacing some old rings by new rings
ii) When the chain is too short, it is adjusted by
a) Straightening the bent links
b) Opening the joints of the rings
c) Replacing the old rings by some larger rings
Most Probable Value
If two or more measurements of the same quantity are made, random errors usually cause different values to be obtained. As long as each measurement is equally reliable, the average value of the different measurements is taken to be the true or the most probable value. The average (the arithmetic mean) is computed simply by summing all the individual measurements and then dividing the sum by the number of measurements.
The 90 Percent Errors
Using appropriate statistical formulas, it is possible to test and determine the probability of different ranges of random errors occurring for a variety of surveying instruments and procedures. The most probable error is that which has an equal chance (50 percent) of either being exceeded or not being exceeded in a particular measurement. It is sometimes designated as E90.
In surveying, the 90 percent error is a useful criterion for rating surveying methods. For example, suppose a distance of 100.00 ft is measured. If it is said that the 90 percent error in one taping operation, using a 100 ft tape, is ± 0.01 ft, it means that the likelihood is 90 percent that the actual distance is within the range of 100.00 ± 0.01 ft. Likewise, there will remain a 10 percent chance that the error will exceed 0.01 ft. It is sometimes called maximum anticipated errors. The 90 percent error can be estimated from surveying data, using the following formula from statistics.
Δ = Delta, the difference between each individual measurement and the average of n measurements.
n = the number of measurements
To measure the distance, we have to use the tape several times; there would be nine separate measurements for 900ft distance, each with a maximum probable error of ± 0.01 ft. It is tempting simply to say that the total error will be 9 × (±0.01) = ± 0.09 ft. But this would be incorrect. Since some of the errors would be plus or some would be minus, they would tend to cancel each other out. It would be very unlikely that errors would completely cancel and so there still be a remaining error at 900 ft. A fundamental property of accidental or random errors is that they tend to accumulate or add up, in proportion to the square root of the number of measurements in which they occur. This relationship, called the law of compensation, can be expressed mathematically in the following equation.
E = the total error in n measurements
E1 = the error for one measurement
n = the number of measurements
From the above example, E = ± 0.01√9 = ± 0.01 × 3 = ± 0.03 ft. In other word, we can expect the total accidental error when measuring a distance of 900 ft to be within a range of ± 0.030 ft, with a confidence of 90 percent. It must be kept in mind that this type of analysis assumes that the series of measurements are made with the same instruments and procedures as for the single measurement for which the maximum probable error is known.
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