FUNDAMENTALS OF SURVEYING
MODULE 2 - DISTANCE CORRECTION








Types of Correction
Incorrect Tape Length
Temperature Variations
Slope Corrections
Sag and Tension Corrections
Combined Taping Corrections
Errors in Taping
Taping Precision
recall: TYPES OF ERRORS
1. SYSTEMATIC / COMMULATIVE ERROR
 The error which remains the same with the conditions remaining unchanged.
2. ACCIDENTAL / COMPENSATING ERROR
 Error which is likely to be positive as well as negative with the conditions remaining the same.
TYPES OF CORRECTION
1. Incorrect tape length
2. Slope
3. Alignment
4. Temperature variations
5. Pull / Tension
6. Sag
7. Wind
8. Combined correction
TYPES OF CORRECTION
I. ERRONEOUS LENGTH OF TAPE
•
CASE I:
𝑒=𝑙−𝐿
where:
 L – standard length of the tape (indicated at the tape)
 l – actual length of the tape
 e – error
•
CASE II: (too short) e(-)
𝑒=𝑙−𝐿
𝑒 = 49.95 − 50
𝑒 = −0.05 𝑚 (too short)
a. Measuring a Line
𝑻=𝑴−
𝑴
𝒆
𝑴
𝒆
(𝒆) or 𝑻 = 𝑴 (𝟏 − )
𝑳
𝑳
b. Laying out a Line
𝑻=𝑴+




(𝒆) or 𝑻 = 𝑴 (𝟏 + )
𝑳
𝑳
where:
M – distance measured with erroneous tape
L – standard length of the tape
e – error per tape length
T – correct length measured
Prepared by:
Engr. ROSELLA C. ALGADO
Engr. PATRICK LOUIE JAY FEDERIZO
FUNDAMENTALS OF SURVEYING
•
CASE III: (too long) e(+)
𝑒=𝑙−𝐿
𝑒 = 50.008 − 50
𝑒 = +0.008 𝑚 (too long)
a. Measuring a Line
𝑻=𝑴+
𝑴
𝑳
𝒆
(𝒆) or 𝑻 = 𝑴 (𝟏 + )
𝑳
a. Laying out a Line
𝑻=𝑴−




𝑴
𝑳
𝒆
(𝒆) or 𝑻 = 𝑴 (𝟏 − )
𝑳
where:
M – distance measured with erroneous tape
L – standard length of the tape
e – error per tape length
T – correct length measured
II. CORRECTION DUE TO SLOPE
where:
 s – measured slope distance between A & B
 h – difference in elevation of A & B
 d – equivalent horizontal distance AC
 Ch – slope correction or the difference between the slope length and the horizontal distance
𝑪𝒉 = 𝒔 − 𝒅
𝒔𝒍𝒐𝒑𝒆 =
𝒉
× (𝟏𝟎𝟎%)
𝒅
Slope Correction Formulas (Ch)
1. Gentle Slope (𝑠 < 20%)
𝒉𝟐
𝑪𝒉 =
𝟐𝒔
2. Steep Slope (20% ≤ 𝑠 ≤ 30%)
𝑪𝒉 =
𝒉𝟐 𝒉𝟒
+
𝟐𝒔 𝟖𝒔𝟑
3. Very Steep Slope(𝑠 > 30%)
𝑪𝒉 = 𝒔(𝟏 − 𝒄𝒐𝒔 𝜽)
III. CORRECTION DUE TO ALIGNMENT
It is usually difficult to keep the tape in perfect alignment with the end marks when taping through grass or when a
strong wind is blowing.
The linear error due to inaccuracy in alignment of tape is similar to the effect of a slope and can be computed in
the same manner.
Prepared by:
Engr. ROSELLA C. ALGADO
Engr. PATRICK LOUIE JAY FEDERIZO
FUNDAMENTALS OF SURVEYING
IV. CORRECTION DUE TO TEMPERATURE
Due to changes in temperature a tape used in measuring or laying-out distances may become either too short or
too long. The effect of temperature is usually considered in most taping operation such as taping in taping a baseline
for triangulation system.
In ordinary taping of short distances, it is usually considered since the amount involved is usually small.
Steel tape is standard when the temperature is 20°C or 68°F. Thermal coefficient (k) is 11.6 x 10-6/°C or
6.45 x 10-6/°F
𝑪𝒕 = 𝒌𝑳 (𝑻 − 𝑻𝒐)
▪
▪
▪
▪
▪
▪
where:
Ct – error due to temperature

(-) Ct (too short)

(+) Ct (too long)
k – thermal coefficient
L – length of tape
To – temperature of tape @ standard length
T – temperature of tape during taping
STEEL TAPE – standard temp. 20°C / 68°F
V. CORRECTION DUE TO PULL / TENSION
When steel tape is pulled with a tension greater or less than the standard pull, it elongates or shortens
according in an elastic manner.
The standard tension for a steel tape usually varies from 4.5 kg – 5.5 kg (10-12 lbs) unit weight (Uw) of
steel tape 7.866 x 10-3 kg/cm3 or (490 lbs/ft3)
𝑪𝒑 =
(𝑷 − 𝑷𝒐 )
𝑳
𝑨𝑬
where:
▪
Cp – error due to pull / tension

(-) Ct (too short)

(+) Ct (too long)
▪
L – length of tape
▪
▪
▪
Po – tension for which tape is standardized
P – applied tension
A – area of the steel tape
𝑨=
▪
𝑾
𝑳(𝑼𝒘 )
E – Modulus of elasticity (N/mm2) (2.0 x 106 kg/cm2 – average modulus of elasticity for steel tape)
VI. CORRECTION DUE TO SAG
A tape attains its correct length when it is fully supported.
due to the weight of the steel tape, there’s a tendency to sag even if the standard pull is maintained.
Sag shortens the horizontal distance between end graduations since the tape length remains.
𝑪𝒔 =
𝒘𝟐 𝑳𝟑
or
𝟐𝟒𝑷𝟐
𝑪𝒔 =
𝑾𝟐 𝑳
𝟐𝟒𝑷𝟐
where:
▪
Cs – error due to sag
▪
w – weight of tape per unit length (kg/m)
▪
W – total weight of tape between supports (kg)
▪
L – interval between support or the unsupported length
of tape (m)
▪
P –tension or pull applied on the tape (kg)
Prepared by:
Engr. ROSELLA C. ALGADO
Engr. PATRICK LOUIE JAY FEDERIZO
FUNDAMENTALS OF SURVEYING
VII. CORRECTION DUE TO WIND
Similar with the effects of sag but is usually much less.
To eliminate the error, it is preferably not to undertake any taping work during windy days.
𝑷𝑵 =
𝟎. 𝟐𝟎𝟒𝑾√𝑨𝑬
√𝑷𝑵 − 𝑷𝑺
Type equation here.
where:
▪
PN – normal tension or pull which will eliminate the effect of sag (kg)
▪
▪
▪
▪
W – total weight of tape between supports (kg)
A – cross sectional area of tape (cm2)
E – modulus of elasticity of tape material (kg/cm2)
Ps – standard pull for the tape (kg) 4.5-5.5 kg
Prepared by:
Engr. ROSELLA C. ALGADO
FEDERIZO
Engr. PATRICK LOUIE JAY