Horizontal distance measurement

 Types
 Gross errors (blunders or mistakes)
 Systematic errors
 Random and accidental errors
 Gross errors are results of mistakes due
to carelessness of observer. Examples
pointing on wrong survey target,
incorrect reading on the scale, recording
wrong reading.
 Careful checking all the points on survey targets.
 Taking multiple reading on scale and checking for
 Taking repeated measurement independently and checking
for consistency
 Using simple geometric and algebraic checks, such as sum
of all the angles taken at a station is 360 ⁰, sum of three
angles in a plane triangle is 180⁰
 Systematic errors: These are the errors which occur from
well-understood causes and can be reduced by adopting
suitable method. These errors follow same pattern. Example
sag of tape supported at the end can be calculated and
subtracted from each measurement. However the tape can
be supported through out its length at short intervals and
the sag errors may be reduced to a negligible quantity.
 A systematic error follows a definite
mathematical or physical law and therefore,
a correction can always be determined and
applied. Also known as cumulative error.
 Random error/ accidental error: after all
mistakes are detected and removed and the
measurements are corrected for all known
errors, there will still remain some errors
due to combination of various causes and
are beyond the control of surveyor. It can be
plus or minus. These are probabilistic errors
and can not be calculated using standard
functional relationship. Human eye has
limitation of distinguishing between two
close readings.
 Method of horizontal distance measurements
 Direct: using chain (chaining) or tape (taping)
 Low precision work: chaining
 High precision work: taping or bars
 Engineer’s chain: 100 ft long, 100 links each 1 ft,
at every 10 links brass tags are fastened.
Notches on the tag indicates the number of 10
link segment between th tag and the end of the
 Gunter’s chain: 66 ft long, 100 links, each 0.66
 distances are recorded in chains and links.
 Indirect: the distances are not measured directly
on the field but are computed indirectly using
observed quantities.
Metric chain
 Ranging and chaining
 Taping on flat ground: length of the line is
less than length of the tape easily measure
the line with tape. If length of the line is
greater than length of the tape subdivide the
line to lengths less than tape length.
 Taping on sloping or uneven ground
 Direct method
 Indirect method
 Errors in tapping and tape correction
 Gross errors
 Systematic errors
 Ranging if the points are intervisible
 Ranging when points are not visible
 Horizontal distance measurement by on
moderately flat ground
 Horizontal distance measurement on
slopping ground
1. Correction for absolute length: Before
using a tape, the actual length is ascertained by
comparing it with a standard tape of known
length. If the actual tape length is not equal to
the standard value, a correction will have to be
applied to the measured length of the line.
Ca = correction for absolute length
C = correction per tape length
l = the designated or nominal length of the tape
L= measured length of the line
2. Correction for temperature
 Ct = temperature correction
 α = the coefficient of linear expansion of tape material
 tm = mean temperature during the measurement
 to= standard temperature
 3.Correction for pull: if the pull applied to the tape during
the measurement is more than the standard pull at which the
tape was standardized, its length increases. Hence the distance
measured will become less than the actual. Correction is +ve if
applied pull is greater than standard pull and its is –Ve if applied
pull is less than standard pull
 Cp = the pull correction
 P = pull applied in the field during measurement,
 Po = the standard pull
 A= Cross sectional are of the tape
 E = the modulus of elasticity 2.1 X 105 N/mm2 for steel
 1.54 X 105 N/mm2 for invar
4. Correction for the sag
 When the measurements is made by stretching the tape
above the ground, supports are needed at the end of the
tape. Consequently the tape sags under its own weight,
with the maximum dip occurring at the middle of the tape,
and the tape takes the shape of a catenary. This necessitate
the correction known as sag correction.
 Cg= sag correction
 W= weight of the tape per span length
 P=pull applied during the measurement
 If both the ends of line are not at the same
level, a further correction to Cg is required
 α= angle of slope between the end support
5. Corrections for the slope: If the two
ends of the tape are at different
elevations, the measured length needs a
correction known as correction for slope
 Correction for alignment
 If the intermidiate points are not in correct
alignment with the ends of the line, or they
are not on the line to be measured, a
correction known for alignment has to be
applied to the measured length.
 d= distance by which the other end of the
tape is out of alignment
Cm is always negative
 Reduction to mean sea level
 The length of the line measured at an
altitude of h meteres above mean sea
level is always more compared to length
measured on mean sea level surface. The
necessity of reducing distances to a
common datum arises when the survey
are to be connected to national grid.
R= radius of the earth
 The pull which, when applied to a tape
suspended in the air, equalizes the
correction due to pull and sag is known
as normal tension
 The value of P may be calculated by trial
and error
 A steel tape of nominal length 30 m was
suspended between supports to measure
the length of a line. The measured length
of the line on a slope of angle 3⁰ 50’ is
29.859 m. The mean temperature during
the measurement was 12 ⁰C and the pull
was 100 N. If standard length of the tape
is 30.005 m at 20 ⁰C, and the standard
pull is 45.0 N, calculate the corrected
horizontal length. Take the weight of the
tape 0.15 N/m, its cross-sectional area =
2.5 mm2, α=1.15 X10-5 per ⁰C, and E= 2.0
X 105 N/mm2.
The measured distance between two points is 615 m. If
the angle of slope between the points is 7⁰, what is the
horizontal distance between the points.
The distance between two points A and B, is measured
along the slope as 435 m. The difference in elevation of
these points is 49 m. Determine the horizontal distance
between A and B.
If the slope of the ground is 1 in 5, and the measured
distance between two points is 503 m, what is the
horizontal equivalent of the measures distance.
What slope distance must be laid out along a line that rises
5 m/100 m in order to establish a horizontal distance of
830 m.
5. A measurement is made along a line that is
inclined by a vertical angle of 2 26. the measured
slope distance is 4035.46 m. to what accuracy
must the slope angle be measured if the relative
accuracy of the horizontal distance is to be
1/25000? Also compute the horizontal distance.
6. To what accuracy must the slope angle of
example 3.5, be measured if the horizontal
distance is to be accurate to 0.005 m.
7. What is the correct length of a line which is
measured as 350 m with 20 m tape, 10 cm too
8. At the end of a survey of a parcel land, a tape of length
was found to be 10 cm short. The area of the plan drawn
with the measurements taken with this tape is found to be
135 cm2. if the scale of the plan is 1/1000, what is the
true area of the field assuming that the chain was exact 30
m at commencement of survey?
9. A line was measured with a steel tape which was exactly
30 m at 25 C at a pull of 10 kg, the measured length being
1700.00 m. the temperature during measurement was 34
C and the pull applied was 18 kg. compute the length of
the line if the cross sectional area of the tape is 0.025 cm2.
take α = 3.5 X 10-6 per 1 C and E= 2.1 X 106 kg/cm2 for
the material of the tape.

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