COMMON SOURCES OF ERROR IN MEASUREMENT OF LINES.

COMMON SOURCES OF ERROR IN MEASUREMENT OF LINES.

1. Not pulling tape taut.

2. Careless plumbing.

3- Incorrect alignment.

4. Effect of wind.

5. Variation in temperature.

6. Erroneous length of tape.

COMMON MISTAKES IN READING AND RECORDING MEASUREMENTS.

1.   Failure to observe the position of the zero point of the tape. (In some tapes it is not at the end of the ring.)

2.   Omitting a whole chain- or tape-length.

3.   Reading from wrong end of chain, as 40 metre. for 60 metre., or in

         the wrong direction from a tag, as 47 metre. for 53 metre.

4.   Transposing figures, e.g., 46.24 for 4642 (mental); or reading

         tape upside down, e.g., 6 for 9, or 86 for 98

5.   Reading wrong foot-mark, as 48.92 for 47.92.

AVOIDING MISTAKES. — Mistakes in counting the tape lengths may be avoided if more than one person keeps the tally. Mistakes of reading the wrong foot-mark may be avoided by noting not only the foot-mark preceding, but also the next following foot-mark, as, "46.84 ... 47 metre," and also by holding the tape so that the numbers are right side up when being read.

  In calling off distances to the note keeper, the tapeman should be systematic and always call them distinctly and in such terms that they cannot be mistaken. As an instance of how mistakes of this kind occur, suppose a tape man calls, "Forty nine, three"; it can easily be mistaken for "Forty-nine metre." The note keeper should repeat the distances aloud so that the tapeman may know that they were correctly understood. It is frequently useful in doubtful cases for the note keeper to use different words in answering, which will remove possible ambiguity. For example, if the tapeman calls, "Thirty-six, five," the note keeper might answer, "Thirty-six and a half." If the tapeman had meant 36.05 the mistake would be noticed.

The tapeman should have called in such a case, "Thirty-six naught five." The following is a set of readings which will be easily misinterpreted unless extreme care is taken in calling them off.

47.0 — "Forty seven naught."

40.7 — "Forty and seven."

40.07 — "Forty, — naught seven."

'All of these might be carelessly called off, "Forty-seven."

 In all cases the tapemen should make mental estimates of the distances when measuring, in order to avoid large and absurd mistakes.

Accuracy Required. — If, in a survey, it is allowable to make an error of one metre in every five hundred metre the chain is sufficiently accurate for the work. To reach an accuracy of 1 in 1000 or greater with a chain it is necessary to give careful attention to the pull, the plumbing, and the deviation from the standard length. With the steel tape an accuracy of 1 in 5000 can be obtained without difficulty if ordinary care is used in plumbing and aligning, and if an allowance is made for any considerable error in the length of the tape. For accuracy greater than about 1 in 10,000 it is necessary to know definitely the temperature and the tension at which the tape is of standard length and to make allowance for any considerable variation from these values. While the actual deviation from the IS Standard

under certain conditions may be 1 in 10,000, still a series of measurements of a line all taken under similar conditions may check themselves with far greater precision.

Amount of Different Errors. The surveyor should have a clear idea of the effects of the different errors on his results. For very precise work they should be accurately determined, but for ordinary work it is sufficient to know approximately the amount of each of them. A general idea of the effect of these errors will be shown by the following.

Pull. - At the tension ordinarily used the light steel tape will stretch between o.o1 and 0.02 metre in 100 metre if the pull is increased 10 kg. Since the amount of stretch is different, however, for different tapes it is advisable to investigate it by fastening the ring of the tape to a nail in the floor and, with the tape lying flat, applying different tensions. The tensions should be measured with a spring balance and the variations in length under these different tensions may be determined from the tape readings of some reference point marked on the floor near the 100 metre end of the tape. In this manner the length of any particular tape for any given tension may be found.

Temperature. — The average coefficient of expansion for a steel tape is nearly 0.0000063 for 1° F. Hence a change of temperature of 15° produces nearly o.o1 metre change in the length of the tape. Tapes are usually manufactured to be of standard length at 62° F. and under a tension of 12 kgf. while supported throughout their length. When great accuracy is demanded the temperature of the tape must be determined and the corresponding temperature correction applied to the measurements.

Small tape thermometers are made especially for this purpose. The thermometer bulb should be in contact with the tape so as to obtain as nearly as possible the temperature of the steel. Even under these conditions it is difficult to determine the true temperature if the tape is exposed to sunlight.

Alignment. — The error in length due to poor alignment can be calculated from the approximate formula.

  c - a = h²/2xc

where h is the distance of the end of the tape from the line, c is the length of the tape, and a is the distance along the straight line. For example, if one end of a 50 metre tape is held 1 metre to one side of the line the error produced in this tape-length will be

 1²/2x50 = 0.01 metre (about 10 mm).

The correction to be applied to the distance when the two ends of the tape are not at the same level, as when making slope measurements, is computed in the same way.

Sag. — If a tape is suspended only at the ends it will hang in a curve which is known as the "catenary." On account of this curvature the distance between the end points is evidently less than the length of the tape. The amount of this shortening, called the effect of sag, depends upon the weight of the tape, the' distance between the points of suspension, and the pull exerted at the ends of the tape. With a 12 kg. pull on an ordinary

50 metre steel tape supported at the ends the effect of sag is from 0.01 metre to 0.02 metre. The most practical way to eliminate the effect of sag, however, is to determine by actual test the length between the end marks of the suspended tape as follows:

In the right triangle,

c² - a² = h²

(c-a)(c+a) = h²

Assuming c = a and applying it to the first parenthesis only,

2c (c-a) = h² (approximately)

c - a = h²/2c (approximately)

Similarly c - a = h²/2a (approximately)

It is evident that the smaller h is in comparison with the other two sides the more exact will be the results obtained by this formula. This formula is correct to the nearest 1/100 metre , even when h = 14 metre and a = 100 metre, or when h = 30 metre and a = 300 metre.

  First, while the tape is supported its whole length mark is end points while a pull of 12 kg is exerted. Then establish two points, by means of the transit or a plumb-line, at the same distance apart, but in such positions that the tape may be tested while supported at the ends only. Then determine the pull necessary to bring the end marks of the suspended tape to coincide with these reference marks. If this tension is always applied then the two ends of the suspended tape will be the same distance apart as the ends of the supported tape were under a 12 kg pull. If the supported tape is not of standard length when a 12 kg pull is used this error should be allowed for in all measurements. Or, if preferred, the reference marks just mentioned may be placed exactly 30 metre apart and the amount of pull required to make the suspended tape correct may be determined.

ACCURACY OF MEASURMENTS. - In surveying we are dealing entirely with measurements. Since absolute accuracy can never be attained, we are forced to make a careful study of the errors of measurement. Extremely accurate measurements are expensive, and the cost of making the survey usually limits its accuracy. On the other hand, if a given degree of accuracy is required, the surveyor must endeavor to do the work at a minimum cost. In most surveys certain measurements are far more important than others and should therefore be taken with more care than the relatively unimportant measurements. The surveyor should distinguish carefully between errors which are of such a nature that they tend to balance each other and those which continually accumulate. The latter are by far the more serious. Suppose that a line 1500 metre long is measured with a steel tape which is 0.01 metre too long and that the error in measuring a tape-length is, say, 0.02 metre, which may of course be a + or a - error. There will then be 50 tape-lengths in the 1500 metre line. A study of the laws governing the distribution of accidental errors (Method of Least Squares) shows that in such a case as this the number of errors that will probably remain uncompensated is the square root of the total number of opportunities for error, i.e., in the long run this would be true. Hence the total number of such uncompensated errors in the line is 7;