Kinds of error
1.
Mistakes
> Mistakes are errors which
occur due to inattention, inexperience, carelessness and poor judgment
or confusion in the mind of
observer.
> These may by displacement
of arrows, miscounting of number of chain, mis reading, erroneous
booking, etc.
> Mistakes are blunders can’t
be rectified.
> Hence, every observation
made should be checked by some independent field observations.
2.
Systematic errors (cumulative errors)
> A systematic error is one
which occurs in the same direction and tends to accumulate.
> This error under the same
conditions will of same size and sign, regarded as positive or negative as
they make the result too great or
too small and are proportional to the length of line.
> Can be rectified /
corrected.
3.
Accidental errors (compensating errors)
> These errors occurs in both directions hence tends
to accumulate or balance in the final result. > These errors remain there
after the mistakes and systematic errors have been eliminated, since they are
caused due to uncontrollable reasons.
> These errors are proportional to the square root
of length of line.
> Cannot be corrected as nature ofthe error is not
known clearly.
|
Errors
|
Type
|
|
1)
Incorrect length of tape
|
Cumulative + ve or –
ve
|
|
2) Bad ranging
|
Cumulative + ve
|
|
3)
Careless holding and marking
|
Compensative + or
|
|
4)
Sag in chain
|
Cumulative + ve
|
|
5)
Variation in pull
|
Compensating + or
|
|
6)
Variation in temperature
|
Cumulative + ve or –
ve
|
|
7)
Bad straightening
|
Cumulative + ve
|
|
8)
Non-horizontality
|
Cumulative + ve
|
|
9)
Error in marking tape lengths
|
Compensating + or
|
|
10) Disturbing arrous
after they are set
|
Blunder
|
|
11) Errors in reading
the tape
|
Mistake
|
|
12) Incorrect counting
of tape length
|
Blunder
|
Tape Corrections
Correction is positive, when the erroneous length or
incorrect length is more than the designated length.
Correction is negative, when the erroneous length or
incorrect length is lesser than the designated length.
1.
Correction
for absolute length or correction for standardization (+ve or -ve) If the absolute length (or actual length)
of tape or wire is not equal to its nominal or designated length the correction
is need to be applied.
|
Ca c
= x
|
L
|
l
Ca = correction for absolute
length =
EAL
L = measured length of
line l
=
l = designated (or actual)length
of the tape L
=
C = correction per tape
length L
= A
If tape is too long –
error is negative – correction is positive.
If tape is too short
– error is positive – correction is negative.
2.
Correction for slope (- ve)
The distance measured along the slope is always
greater than the horizontal distance and hence the correction to be applied is
always negative.
Slope correction,
CS = L — L — h
2 2
CS =L—L cos = L(1— cos ) = 2 L sin2 ( j= L Vers sin
2
ApproximatelyCS = h2 / 2L
3.
Correction for temperature (+ve or -ve)
> Tapes are standardized at a particular temperature.
Ifthe temperature on the field during measurement is more than the standard
temperature, the length of tape increases, measured distance becomes less
(negative error), so correction is positive or additive.
>
Similarly, ifthe temperature is less than the standard temperature, the length
of tape decreases, measured distance becomes more (positive error), so
correction is negative.
> The temperature correction
is given by,
C t L (Tm–To)
α = Coefficient of thermal
expansion,
To = Standard
temperature,
Tm = mean temperature
during measurement.
Ct will be
positive if Tm > To
Ct will be
negative if Tm < To
4.
Correction for pull or tension (+ve or -ve)
Ifpull applied during
measurement is more than the pull at which tape is standardized, the length of
the tape increases, measured distance becomes less (negative error), and
correction will be positive. Similarly, vice versa.
Pull correction is given by,
|
CP
|
|
( 0 )
P P
|
L
|
|
AE
|
|
Cp will be positive, if P > Po
Cp will be negative, if P <
Po.
Where,
P = Pull applied during
measurement (N or Kg),
Po = Standard pull (N or
Kg),
L = Length of tape (m or cm),
A = c/s area of tape or chain,
E = young’s modulus of
elasticity of material of tape or chain (N/m2 or Kg/cm2)
5. Correction for sag (always -ve):-
> When the tape is stretched on supports between two
points, it takes the form ofa horizontal
catenaries (curve).
> Horizontal distance (actual
distance) will be less than the distance along the curve.
> Thus, the difference
between horizontal distance and the measured length along the catenaries is
called sag correction.
a. When the ends of the chain / tape are
at the same level
> The curve is assumed as
parabola.
> Sag correction is given as,
W2l
C =_________ For n number of bays (correction for all nbays)
S 24 p
S 24 p
n 2 2
2 For single
tape length
where
W = total weight of tape in kg. =
w l,
w = wt. of tape in kg/m run,
l = total length of tape or
chain,
Cs = sag correction for total
number of bays or for one tape length.
b. When the ends of the tape / chain are
not at the same level
For chain CS' CSCos2 (1wl
sin )
p
+ ve, when tension applied at the
higher end - ve , when tension applied at lower end.
For steel tape CS CSCos2
Where θ = inclination with the
horizontal.
6.
Normal tension (Pn)
It is the pull applied to the tape, which will
neutralize the effect ofpull and sag and no correction is required.
Normal tension is given by,
7.
Correction for mis - alignment (Cm) (always
-ve)
When the survey line is not ranged properly, error
occurs. The measured distance will be more than the actual distance. Thus, the
error is positive and correction is negative.
Cm L1 –L1
cos 1 L 2 –L2
cos2 L1 1– cos 1 L2 1– cos 2
d d
2 2
C ____ ____ ( approximately)
m 2 2
L L
1 2
|
Correction C
, S
|
L h L h
_
R h R |
8.
Reduction
of length to mean sea level:
Where,
L = measured length,
R = radius of earth,
h = height above msl
The correction is negative if measured distance is
above msl.
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