distance adjustment

step measurement

step measurement is the process of breaking the overall distance down into manageable short sections each much less than a whole tape length . The tape is stretched horizontally and a plumb-bob suspended from the elevated end of the tape . this method of measurement over sloping ground should be avoided if hogh accuracy is required 

The main source of error lies in attempting to accurately locate the suspended end of the tape .

The steps should be kept short enough to minimize sag in the tape , Thus the sum of steps equals the horizontal distance required .

To eliminate or minimize the systematic errors of taping , it is necessary to adjust each measured to its final horizontal equivalent as follows .

STANDARDIZATION :

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 end industry (DTI) for stel tapes , or by comparing it with a 70 N tension , or as 30 m exactly at a temperature other standard .

WORKED EXAMPLES :

Example 4.1  A distance of 220.450 m was measured with a steel band of nominal legth 30 m . On  standardization the tape was found to be 30.003 m . Calculate the correct measured distance , assuming the error is evely distributed throughout the tape .

Error per 30 m =  3 mm

                            220.450

 ∴Correction for total length =  (  _________ )   ×  3 mm  =  22  mm

                             30

∴ Correct length is 220.450 +  0.022  =   220,472  m

Note that :

(1)  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 rule in (1) are reversed .

(3) It  is better to compute Example 4.1 on the basic of the correction (as shown ) , rather than the total corrected length .

in this way fewer significant figures are required .

Temperature 

Tapes are usually standardized at 20ًC Any varion above or below this value will cause the tape to expand or contract , givivg rise to systematic errors . Difficulty of obtaining true temperatures of the tapes lead to the use 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 = KL ⋴⧍ t

where ∆ t  = difference between the standard  and field temperatures ( ُC) = ( ts - t a)

The sign of the correction is in accordance with the rule specified in note (1) above .


Tension 

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 Hook's law :

stress = stain × a constant 


This constant is same for a given material and is called the modulus of elasticity (E) since strain is a non-dimensional quanitity , E has the same dimensions as strees , i ,e N/mm₂

                  ⩟ T
∴ Ct = L × ____
                AE

⩟ T  is normally the total 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 compatiblity with the other units used in the formula ,i,e  1 kgf  = 9.80665 N

E is modulus of elasticity in N/mm₂ : L is measured lenfth in m : and Ct is the extension and thus correction to the tape length in m . As the tape is stretched under the extra tension . the correction is positive .