To eliminate or minimize the systematic errors of taping, it is necessary to adjust each measured bay to its final horizontal equivalent as follows.
During a period of use, a tape will gradually alter in length for a variety of reasons. The amount of change can be found by having the tape standardized at either the National Physical Laboratory (NPL) for invar tapes or the Department of Trade and Industry (DTI) for steel tapes, or by comparing it with a reference tape kept purely for this purpose. The tape may then be specified as being 30.003 m at 20◦C and 70 N tension, or as 30 m exactly at a temperature other than standard.
Example A distance of 220.450 m was measured with a steel band of nominal length 30 m. On standardization the tape was found to be 30.003 m. Calculate the correct measured distance, assuming the error is evenly distributed throughout the tape.
Error per 30 m = 3mm
Correct length is 220.450 0.022 = 220.472 m
(1) Figure shows that when the tape is too long, the distance measured appears too short, and the correction is therefore positive. The reverse is the case when the tape is too short.
(2) When setting out a distance with a tape the rules in (1) are reversed.
(3) It is better to compute Example 4.1 on the basis of the correction (as shown), rather than the total corrected length. In this way fewer significant figures are required.
Tapes are usually standardized at 20◦C. Any variation above or below this value will cause the tape to expand or contract, giving rise to systematic errors. Difficulty of obtaining true temperatures of the tapes lead to the use of invar tapes. Invar is a nickel-steel alloy with a very low coefficient of expansioN.
Coefficient of expansion of steel K = 11.2 × 10−6 per ◦C
Coefficient of expansion of invar K = 0.5 × 10−6 per ◦C
Temperature correction Ct = KLt
where t = difference between the standard and field temperatures (◦C) = (ts − ta). The sign of the correction is in accordance with the rule specified in note (1) above.
Generally the tape is used under standard tension, in which case there is no correction. It may, however, be necessary in certain instances to apply a tension greater than standard. From Hooke’s law:
stress = strain × a constant
This constant is the same for a given material and is called the modulus of elasticity (E). Since strain is a non-dimensional quantity, E has the same dimensions as stress, i.e. N/mm2:
∴ CT = L × T /AE
T is normally the total stress acting on the cross-section, but as the tape would be standardized under tension, T in this case is the amount of stress greater than standard. Therefore T is the difference between field and standard tension. This value may be measured in the field in kilograms and should be converted to newtons (N) for compatibility with the other units used in the formula, i.e. 1 kgf= 9.806 65N.