# What are the Corrections Applied in Surveying?

Posted in Surveying | Email This Post |For surveying, we need to have some prerequisite conditions. If these conditions are not met we can have a huge variation in result. Therefore we have to apply corrections to get the true result.

**Ideal Conditions**

1) A tape accurate to 0.00305m or 0.01 ft should be used.

2) Tension of the tape should be about 66.7N or 15 lb.

3) Temperature should be determined within 5.56°C or 10°F

4) The slope of the ground, should be within 2 percent

On ground these are nearly impossible to achieve and thus corrections need to be applied.

**Corrections Applied for Temperature**

The correction applied on steel tape is C_{t}=0.0000065s(T-T_{0})

where

C_{t}= temperature correction to measured length, ft (m)

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

T_{0}= temperature at which tape is standardized, F ( C)

s= measured length, ft (m)

**Correction Applied to Measurements on Slope**

C_{h}= s (1-cos@) [exact]

or = 0.00015s@^{2}[approximate]

or = h^{2}/2s

where

C_{h}= correction to be subtracted from slope distance, ft (m)

s= measured length, ft (m)

@ =slope angle, degree

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

**Correction Applied for Tension **

C_{p}=s[P_{m}-P_{s}]/SE

**Correction Applied for Sag when not Fully Supported**

C_{s}=w^{2}L^{3}/24P_{m}^{2}

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, in^{2} (mm^{2})

E= modulus of elasticity of tape, lb/in^{2} (MPa) (29 million lb/in^{2}(MPa) for steel) (199,955 MPa)

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

L= unsupported length, ft (m)

**What are Slope Corrections?**

We know that the horizontal distance H= Lcos@, where L slope distance and @=vertical angle, measured from the horizontal.

For slopes of 10 percent or less

C_{s}=d^{2}/2L

For a slope greater than 10 percent

C_{s}=d^{2}/2L+d^{4}/8Ld^{3}

**What are Temperature Corrections in terms of 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, in^{2} (mm^{2})

E=modulus of elasticity29,000,00 lb / in^{2} for steel (199,955 MPa).

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

C= -w^{2}L^{3}_{s}/24P^{2}

where

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

L_{s}= unsupported length of tape, ft (m)

P=pull on tape, lb (N)

I hope this is more useful..

For a slope greater than 10 percent

Cs=d2/2L+d4/8Ld3

remove d3 from the above formula

corrected one is as below

Cs=d2/2L+d4/8L3