WORLD FOR CIVIL

Measurement of distance with tapes

Reasonable precisions for different methods of measuring distances are

Pacing (ordinary terrain): 1 /50 to 1 /100
Taping (ordinary steel tape): 1 /1000 to 1 /10,000.
Baseline (invar tape): 1 /50,000 to 1/ 1,000,000
Stadia: 1 /300 to 1 /500
Subtense bar: 1 /1000 to 1/ 7000
Due to the technological upgradation and invention of Electronic distance measurement (EDM) devices,steel tapes are being largely replaced with them on large projects. But still knowledge of steeltaping errors and corrections remains important,

For ordinary taping, a tape accurate to 0.01 ft (0.00305 m) should be used. The tension of the tape should be about 15 lb (66.7 N). The temperature should be determined within
10°F (5.56°C); and the slope of the ground, within 2 per- cent; and the proper corrections, applied.

Corrections To Be Applied
1)The correction to be applied for temperature when using a steel tape is

C_t=0.0000065s(T-T_o)

2)The correction to be made to measurements on a slope is

C_h= s (1-cos ? ) [exact]
or 0.00015s?,sup> 2 [approximate]

where
C_t= temperature correction to measured length, ft (m)
C_h= correction to be subtracted from slope distance, ft (m)

s= measured length, ft (m)

T= temperature at which measurements are made, F ( C)

T_o= temperature at which tape is standardized, F ( C)

h= difference in elevation at ends of measured length, ft (m)

? =slope angle, degree

In more accurate taping, using a tape standardized when fully supported throughout, corrections should also be made for tension and for support conditions.

3)The correction for tension is

C_p=s[P_m-P_s]/SE

4)The correction for sag when not fully supported is

C_s=w²L³/24P_m²

where
C_p= tension correction to measured length, ft (m)

C_s = sag correction to measured length for each section of unsupported tape, ft (m)

P_m actual tension, lb (N)

P_s tension at which tape is standardized, lb (N)
(usually 10 lb) (44.4 N)
S= cross-sectional area of tape, in² (mm²)

E= modulus of elasticity of tape, lb/in² (MPa)
(29 million lb/in²(MPa) for steel) (199,955 MPa)

w= weight of tape, lb/ft (kg/m)

L= unsupported length, ft (m)

5)Slope Corrections

In slope measurements, the horizontal distance H= L cos x, where L =slope distance and x= vertical angle, measured from the horizontal. For slopes of 10 percent or less, the correction to be applied to L for a difference d in elevation between tape ends, or for a horizontal offset d between tape ends, may be computed from

C_s=d²/2L

For a slope greater than 10 percent, Cs may be determined from

C_s=d²/2L+d⁴/8Ld³

6)Temperature Corrections

For incorrect tape length:

C_t=(actual tape length-nominal tape length)L/nominal tape length

For nonstandard tension:

C_t(applied pull-standard tension)L/AE

where A= cross-sectional area of tape, in² (mm²); and
E =modulus of elasticity 29,000,00 lb / in² for steel
(199,955 MPa).

For sag correction between points of support, ft (m):

C= -w²L³_s/24P²

where
w = weight of tape per foot, lb (N)

L_s= unsupported length of tape, ft (m)

P =pull on tape, lb (N)

7)Orthometric Correction

This is a correction applied to preliminary elevations due to flattening of the earth in the polar direction. Its value is a function of the latitude and elevation of the level circuit. Curvature of the earth causes a horizontal line to depart from a level surface. The departure C_f , ft, or C_m, (m), may
be computed from

C_s= 0.667M²=0.0239F²

C_m =0.0785K ²

where M, F, and K are distances in miles, thousands of feet, and kilometers, respectively, from the point of tangency to the earth.
Refraction causes light rays that pass through the earth’s atmosphere to bend toward the earth’s surface. For horizontal sights, the average angular displacement (like the sun’s diameter) is about 32 min. The displacement R_f, ft, or R_m m, is given approximately by

R_f= 0.093M²= 0.0033F²

R_m =0.011K²

8)Vertical Control

Following formulaes are used to calculate vertical control:

First order: C= 0.5?K for Class I and 0.7?K for Class II
Second order: C = 1.0?K for Class I and 1.3?K for Class II
Third order: C= 2.0?K

where K is the distance between bench marks, km.