Sample questions for surveying I

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,
For Office use only Submission Date:……………………….
Question Paper Verified by: Name:………………………………………… Signature:………………………………………
PART - A
UNIT - I
Q.N
o
Questions Answer key with marking scheme
1 Why not "part to whole"? Give reason. Whole to part prevents accumulation of
errors and helps to control and localise
minor errors. part to whole makes work
uncontrollable at the end.
(2 marks)
2 The true length of a line is known to be 500 meters. The line
was again measured with a 20m tape and found to be 502m.
What is the correct length of the 20m tape? l
19.92m
(2 marks)
3 Map conventional signs for benchmark and contours.
(1 x 2 = 2 marks)
4 State the object of running a tie line. To take the details of nearby objects and
also serves as check line.
(2 marks)
UNIT - II
Q.N
o
Questions
Answer key with marking scheme
5 Define the term Bearing of a line. How will you measure
arbitrary bearing?
Bearing of a line: its direction relative to
a given meridian. (1 mark)

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Measured using a theodolite or sextant.
(1 mark)
6 At a place the bearing of sun is measured at local noon and
found to be 175°
15' .What is the magnitude and direction of
magnetic declination at the place?
4° 45'E
(2 marks)
7 When do you recommend plane tabling? i. for filling-in of the details between the
stations previously fixed by triangulation
or theodolite traversing.
ii. for small-scale or medium scale
mapping in which great accuracy in
detail is not required as for
topographical surveys.
(2 x 1 = 2 marks)
8 Give the methods of orienting a plane table. i. by magnetic needle
ii. by back sighting
iii. two point problem
iv. three point problem
(any 2 x 1 = 2 marks)
UNIT - III
Q.N
o
Questions Answer key with marking scheme
9 The observed reading on a staff held at point A is 3.894. If the
error of verticality is 16cm in a length of 4m, find the error in
staff reading.
0.156m
(2 marks)
10 Find the combined correction for curvature and refraction for
a distance of 4.0km
Combined correction = 0.0673D2
= 1.077m
(2 marks)
11 How a hill and depression can be differentiated using
contouring?
Hill: a closed contour with one or more
higher ones inside.
Depression: a closed contour line with
one or more lower ones inside.
(2 x 1 = 2 marks)
12 Give the limitations of Simpson's rule. The rule is applicable only when the
total number of ordinates is odd.

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If there are even number of ordinates,
the area of last division must be
calculated separately and added to
equation.
(1x 2 = 2 marks)
UNIT - IV
Q.No Questions Answer key with marking scheme
13 What are the fundamental lines of a transit theodolite? i. the vertical axis
ii. the horizontal or trunnion or
transit axis
iii. the line of collimation or line of
sight
iv. Axis of plate level
v. Axis of altitude level
vi. Axis of striding level, if provided.
(2 marks)
14 Define error of closure. If a closed traverse is plotted
according to the field measurements,
the end point of the traverse will not
coincide exactly with the starting point,
owing to the errors in the field
measurements of angles and distances.
such error is known as closing error.
(2 marks)
15 What is the use of Gale's traverse table? Traverse computations are usually done
in a tabular form known as Gale's table.
It is used to balance the traverse and also
used to find the area of the closed
traverse.
(2 marks)
16 What is northing and southing? Northing: The latitude of a line is
positive when measured northward and
is termed as northing.
southing: The latitude of a line is

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negative when measured northward and
is termed as southing.
(1x2 = 2 marks)
UNIT - V
Q.No Questions Answer key with marking scheme
17 The preliminary survey should be carried out with great
precision. Give reason.
Preliminary survey decides the final route
and recommends only one route in
preference to other alternative routes.
18 What is the versed sine of a curve? Express it
mathematically.
The mid-ordinate of the curve is also
known as versed sine of the curve.
(1 mark)
M = R versin /2
(1 mark)
19 Why are vertical curves provided? When the slopes or grades intersect or
meet, the vertical curves are provided in
the vertical plane to join them so as to
avoid an abrupt change in the rate of grade.
(2 marks)
20 List the requirements of hydrographic survey. i. Bed profile
ii. Horizontal control
iii.Shore details
iv.Vertical control
(4 x 0.5 = 2 marks)
PART - B
UNIT - I
Q.No Questions Answer key with marking scheme
21(a) Classify survey based on its objective. i. Engineering survey: for
determination of quantities for
designing engineering works such
as roads, reservoirs and sewage
disposal or water supply.
ii. Military survey: for determining

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points of strategic importance.
iii. Mine survey: for exploring
mineral wealth.
iv. Geological survey: for
determining different strata in
earth's crust.
v. Archeological survey: for
unearthing relics of anquity.
(4 marks)
21(b) Write the difference between a map and plan. Give the
designation and representative fraction for a line 135
meters long represented by 22.5cm on plan.
If the representation scale is small,
then called as map while it is called as
plan if the scale is large.
(2 marks)
6m and RF = 1/600
(2x1 =2 marks)
22(a) A chain line ABC crosses a river. B and C being on the near
and distant banks respectively. The respective bearings of C
and A taken at D, a point 60m measured at right angles to
AB from B are 280° and 190°, AB being 32m, Find the
width of the river.
112.5m
(4 marks)
22(b) Explain the basic principle of cross staff survey. The whole plot is divided into right-
angled triangles and trapeziums. The
area of individual triangles and
trapeziums are worked out and added to
get the area of the whole plot.
Geometric relations for computing area:
Area of triangle = ½ x base x
perpendicular offset
= base x mean offset
Area of trapezium = base x (sum of
perpendicular offsets)/2
= base x mean offset
(4 marks)
UNIT - II

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Q.No Questions Answer key with marking scheme
23(a) Give the rules to calculate R.B from W.C.B for all the quadrants.
W.C.B between
Rule for R.B
Quadrant
0°and90°
R.B = W.C.B
NE
90° and 180°
R.B = 180° - W.C.B
SE
180° and 270°
R.B = W.C.B - 180°
SW
270° and 360°
R.B = 360° - W.C.B
NW
(4 x 1 = 4 marks)
23(b) Categorize the errors in compass survey with any three of
their causes.
i. Instrumental errors
· needle not straight
· pivot bent
· sluggish needle
· blunt pivot
· improper balancing weight
· plane of sight not vertical
· line of sight not passing through
center
ii. personal errors
· inaccurate levelling of compass box
· inaccurate centering
· inaccurate bisection of signals

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· carelessness in reading and
recording
iii. natural errors
· variation in declination
· local attraction
· magnetic changes in atmosphere
· magnetic storms.
(4 marks)
24(a) Describe concisely the components of a plane table outfit. i. the drawing board
· made of well seasoned wood like
teak or pine
· size: 40cm x 30cm to 75cm x 60cm
or 50 t0 60cm square
· mounted on tripod
ii. the alidade
· consists of metal or box wood
straight edge.
· may be plane or telescopic.
· accessories to plane table: circular
box compass, plumbing fork, water-
proof cover.
iii. Paper
· Should be tinted in faint green or
grey.
· Zinc or celluloid sheets used to work
in damp climates.
( 4 marks )
24(b) Brief the method of resection. For what purpose it is
chiefly used?
Method of resection:
· select a base line PQ on the ground.
· set the table at P.
· place the alidade along pq and orient
till Q is bisected.
· with the alidade sight R to be
resected.
· shift the table to R and backsight P.

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· sight the station Q and draw a ray.
· point of intersection of this ray and
previously drawn gives required
point r. (3 marks)
purpose:
used for establishing the instrument
stations only.
(1 mark)
UNIT - III
Q.No Questions Answer key with marking scheme
25(a)
Categorize levelling staves and summarize the relative
merits of them.
Categories:
· self-reading staff
· Target staff
(1 mark)
Merits:
i. Fineness of reading taken by
target staff is greater than self
-reading staff.
ii. Level man records readings in
case of self- reading. Staff
holder takes reading in case
of target staff.
iii. Readings from self-reading
staff can be taken easily and
speedily compared to target
staff.
(3 marks)
25(b) For a certain observation, the bubble was out of center by 4
divisions. The error in staff reading held at a distance of
60m was found to b e0.03m. if the length of one division of
the bubble is 2mm, find out the radius of curvature and
sensitiveness of the bubble tube.
R = (4 x 1 60)/ (500 x 0.03) = 16m
(2 marks)
α1 = 25.78 seconds.
(2 marks)
26(a)
An observer standing on the bridge of a ship just sees the
mast of another ship. If the height of the observer’s eye
50.47km.
(4 marks)

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above sea level is 38m, and that of the mast of the other
ship 48m, what is the distance between the two ships.
26(b) The areas within the contour lines at the site of reservoir and the face of the proposed dam are as
follows:
Contour in
m
100
103
106
109
112
115
118
Area
enclosed in
m2
1000
12800
16600
18800
24400
30600
38400
Assuming 100m as the bottom level of the reservoir and 118m as the water level, calculate the capacity
of the reservoir by Prismoidal formula.
370200m3
(4 marks)
UNIT - IV
Q.No Questions Answer key with marking scheme
27(a) Explain in brief about micrometer theodolites. · Micrometer theodolites are
provided with a micrometer fitted
with a microscope.
· Gives accurate results in short
time.
· Diametrically opposite readings

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are made visible at one position
with the help of optical
arrangements.
· Microscope is in the the form of
miniature telescope, With eye
piece, object glass and diaphragm.
· The object glass pointed to
horizontal circle throws the image
of a portion of the graduated arc
on it, in the plane of the
diaphragm.
· The box has window openings
both at top and bottom.
· This box also has fixed index
mark either in the form of an
arrow or a V-notch and a movable
slide carrying a pair of vertical
parallel hair-lines placed very
close together. A drum when
turned by the fine-pitched screw
operates the movable slide.
(4 marks)
27(b) How will you eliminate parallax in a theodolite? i. The eyepiece is focused, so that the
cross-hairs are seen clearly and
distinctly. The telescope is pointed
towards the sky or white paper is
held in front of the object glass. The
eye piece is moved in and out till the
cross hairs are seen clearly.
ii. The object glass is focused so that
the image of object is brought in the
plane of cross hairs and there is no
apparent movement of the image
when the observer moves his eye.
For this purpose, the telescope is
directed towards the object and the

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focusing screw is turned until the
image appears to be sharp and clear.
(4 marks)
28(a) How you would measure magnetic bearing of a line using
theodolite?
The theodolite should be provided with
either tubular compass or trough compass.
Set the instrument at P and level.
Set vernier to zero.
Loose clamp. Release the needle of the
compass. Rotate the instrument till
magnetic needle points north.
Using the lower tangent screw, bring the
needle exactly against the mark so that it
is in magnetic meridian.
Loose the upper clamp and point the
telescope towards Q. Bisect Q using
upper tangent screw. Read verniers A
and B.
Change the face and repeat steps 2, 3 and
4. The average of the two will give the
correct bearing of the line PQ.
(4 marks)
28(b) Write a short note on Bowditch's rule. · Also referred to as compass rule.
· Adopted when angular and linear
measurements are taken with equal
precision.
· As per rule, total error in latitude and
departure is distributed in proportion
to the lengths of the sides.
· Used in traverse adjustment and
expressed as follows:
CL = ΣLe (l/ Σl) and
CD = ΣDe (l/ Σl)
Where,
CL = correction to latitude of any side
CD = correction to departure of any side
ΣLe = total error in latitude

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ΣDe = total error in departure
l = length of any side
Σl = Length of the perimeter.
(4 marks)
UNIT - V
Q.No Questions Answer key with marking scheme
29(a) Differentiate Reconnaissance survey and Location survey. Reconnaissance survey:
Carried out to study the details of the
proposed project or scheme.
Information collected is useful during
execution of work.
Depends on the personal qualities of the
engineer
Should be conducted according to
guiding principles than fixed rules.
Location survey:
Carries out the detailed survey along the
route which has been found and fixed as
the most economical route from the data
of the preliminary survey.
After location survey, construction work
is started.
End of location survey proves to be the
starting point of the construction
activities of the proposed project.
(4 marks)
29(b) Differentiate between M.B.M and T.B.M. MBM:
For a large project, a master bench mark
is established near the structure. The
existing BM in the vicinity of the
structure may be selected as a MBM. But
if no such existing BM is available, the
MBM is established by running levels
from the nearby BM.
TBM:

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Depending on the size and shape of the
structure, required numbers of TBMs are
established near the structures. Existing
permanent structures are selected as
TBM. Concrete or masonry pillars can be
constructed to serve as TBM.
(4 marks)
30(a) Draw the typical shapes of the lemniscate curves for the
deflection angles of 60̊and 120̊.
(2 x 2 = 4marks)
30(b) Give reason: The setting out process of tunnels demands a
high degree of precision throughout the process.
The procedure in setting out tunnels
naturally varies according to local
conditions and it demands a high degree
of precision throughout the process. This
is due to the fact that the survey results
will not be available for checking unless
and until the bore is holed through and if

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something wrong is found at this stage, it
proves to be too difficult for any
correction.
Hence the job of tunnel surveying should
be entrusted only to experienced
surveyors in that field.
(4 marks)
PART - C
UNIT - I
Q.No Questions Answer key with marking scheme
31(a) Explain the sources of errors in chaining. i. Erroneous length of chain or tape.
ii. Bad ranging
iii. Careless holding and marking
iv. Bad straightening
v. Non-horizontality
vi. Sag in chain
vii. Variation in temperature
viii. Variation in pull
ix. Personal mistakes
(12 marks)
31(b) Explain the different methods of chaining on sloping
ground.
Methods:
1. Direct method
2. Indirect method
· Angle measured
· Difference in level
measured
· Hypotenusal allowance
(12 marks)
32(a) i. Describe the method of reciprocal ranging.
ii. A 20m chain used for a survey was found to be 20.10m
at the beginning and 20.12m at the end of the work.
The area of the plan drawn to a scale of 1cm = 6m was
measured with the help of a planimeter and found to be
50.4sq.cm. Find the true area of the field in sq.m. .
i. Reciprocal ranging
· Used when both the ends of the
survey lines are not intervisible.
· Two persons station at P1 and Q1
with ranging rods.
· The person at Q1 directs the
person at P1 to move a new

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position P2 in line with A and Q1.
· The person at point P2 directs the
person at point Q1 in such a way
that he occupies the position Q2 in
line with P2 and B.
· the position is repeated until the
intermediate stations P and Q are
established.
(6 marks)
ii. Area = 1825sq.m
(6 marks)
32(b) i. What is well conditional triangle? Why is it necessary
to use well-conditioned triangles?
ii. What are the points to be observed while entering the
contents of a field book?
i. A well conditioned triangle has no
angle greater than 120 or smaller
than 30 .
The triangles are plotted by the method
of intersection of arcs. The
displacement of a point from its true
position is minimum, if it is
established by the intersection of two
arcs which intersect each other at 90̊.
(4 marks)
ii. Points to be observed:
· All entries should be made in neat
hand-writing and all figures should
be legible.
· Each chain line should be written
on a separate page.
· References to other pages should
be clearly mentioned.
· Position of tie line should be
specified in the beginning and at
the end.
· Entries should be made in pencil.
· Date of survey work, name of

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project, index of chain lines and
stations, north line etc should be
written on the field work.
· Entries should not be crowded.
· Line showing object should not
cross the column of the field book.
· Measurements should be recorded
as soon as they are taken.
· Sketch of the object should not be
shown in advance.
· Stations should be indicated by
triangle and tie stations by circle or
an oval round.
· Writing in the field book should be
commenced from bottom to the top.
(8 marks)
UNIT - II
Q.No Questions Answer key with marking scheme
33(a) The following bearings were taken in running a compass traverse.
Line
F.B
B.B
AB
124°30'
304°30'
BC
68°15'
246°0'
CD
310°30'
135°15'
DA
200°15'
17°45'

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At what stations do you suspect local attraction? Find the correct bearings of the lines and also
compute the included angles.
Local attraction: stations C and D.(1 mark)
Line
F.B
B.B
AB
124°30'
304°30'
BC
68°15'
248°15'
CD
312°45'
132°45'
DA
197°45'
17°45'
(5 marks)
Angle A = 106°45', Angle B = 123°45', Angle C = 64°30', Angle D = 65° (6 marks)
33(b) Draw a neat sectional elevation of a Prismatic compass. Give, in a tabular form, the difference between
prismatic compass and surveyor's compass.

18. Page | 17
( 6 marks)
Item
Prismatic
compass
Surveyor's
compass
Magnetic
needle
Broad needle
type. needle
does not act as
index.
Edge bar type
needle. acts as
index also.
Graduated card
· graduat
ions are in
WCB
· graduat

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ions are
inverted
· graduat
ions are in RB
· graduat
ions are erect
Sighting vanes
· object
vane has metal
vane with
vertical hair.
· eye
vane has small
metal vane
with slit
· object
vane has metal
vane with
vertical hair.
· eye
vane has small
metal vane
with fine slit
Reading
· reading
taken with the
help of prism.
· sightin
g and reading
taking done
simultaneously.
· reading
taken directly
seeing through
the top of glass
· sightin
g and reading
(6 marks)
34(a) What is three point problem? How is it solved by Bessel's
method?
Three point problem:
Location of the position on the plan of
the station occupied by plane table by
means of observations to 3 well-defined
points whose positions have been
previously plotted on the plan.(2 marks)
Bessel's method:
· set the table at station P. keep alidade
on b a and rotate, A is bisected.
clamp the table.
· pivot alidade about b. sight C and
draw x y along edge of alidade.

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· keep the alidade along a b and bisect
B.
· pivot alidade about a and sight C.
draw along alidade edge to intersect
ray x y in c'. join cc'.
· keep alidade along c'c and rotate till
C is bisected.
· pivot the alidade about b and sight B.
Draw the ray to intersect cc' in p.
· the points a,b,c and p form a
quadrilateral and all 4 points lie on
the circumference of the circle. hence
known as Bessel's method of
inscribed quadrilateral.
(10 marks)
34(b) What is meant by plane tabling? State the merits and
demerits of plane tabling.
i. Plane tabling:
A graphical method of surveying in
which the field work and plotting are
done simultaneously. (2 marks)
ii.
Merits :

21. Page | 20
· suitable for preparing small scale
maps.
· rapid
· field book not necessary
· comparison of plotted work with
actual features is possible.
· no omission of measurements.
· error in measurement and plotting
detected by check lines readily.
· useful in areas where compass
survey is not possible.
· contours and irregular objects
represented accurately.
· less costly than theodolite survey
· no skill is required.
Demerits:
· a tropical instrument
· not suitable for wet climate
· heavy, cumbersome and awkward
to carry.
· several accessories carried and
therefore tend to be lost.
· not intended for accurate work.
· if survey to be replotted, it is a
great inconvenience in the
absence of survey notes.
(10 marks)
UNIT - III
Q.No Questions Answer key with marking scheme
35(a) During construction, the bottom of the slab was taken as a
temporary BM with RL as 32.752. Following notes were
recorded in the field book:
Reading of inverted staff on temporary BM = 2.630
Reading on a staff held on peg A on the ground = 1.725
The instrument is now shifted and the reading taken again
RL of B = 33.907
(12 marks)

22. Page | 21
on the staff held on peg A is 1.840 and the reading on
inverted staff at B is 3.670.
Calculate RL of B and enter the readings in level book form.
35(b) The following consecutive readings were taken with a
level and 4m staff on continuously sloping ground at a
common interval of 30m.
0.780, 1.535, 1.955, 2.430, 2.985, 3.480, 1.155, 1.960,
2.365, 3.640, 0.935, 1.045, 1.630 and 2.545.
The reduced level of the first point was 180.750. Rule out a
page of a level field book and enter the above readings.
Calculate the reduced levels of the points by the rise and
fall method, and also the gradient of the line joining the
first and last points.
179.995, 179.575, 179.100, 179.545,
178.050, 177.245, 176.840, 175.565,
175.455, 174.870, 173.955
(8 marks)
1 in 48.7 falling
(4 marks)
36(a) i. What is reciprocal leveling?
ii. Two points P and Q are situated on the opposite banks
of a river. When the instrument was near P, the
readings observed were 1.365 and 2.550 respectively.
When the instrument was near Q, the readings observed
on P and Q were 1.055 and 1.960 respectively.
Calculate a.) the true difference in level between P and
Q b) true RL of Q, if RL of P is 112.695 and c) the
total error due to curvature, refraction and imperfect
collimation adjustment.
i.When it is necessary to carry leveling
across a river, ravine or any obstacle
requiring a long sight betweentwo points
so situated that no place for the level can
be found from which the lengths of
foresight and backsight will be even
approximately equal, special method i.e,
reciprocal leveling must be used.
(3 marks)
ii.
a) 1.045m
b)111.65m
c)0.28m
(9 marks)
36 (b) Discuss various methods of interpolating the contours. Methods:
i. By estimation
Position of contour points
between guide points are located
by estimation.
ii. By arithmetic calculations
Time consuming.
iii. By graphical method
Done with the help of a tracing

23. P age | 22
paper or tracing cloth.
2 methods for graphical
interpolation.
(12 marks)
UNIT - IV
Q.No Questions Answer key with marking scheme
37(a) Describe in brief the permanent adjustments of a theodolite. i. To adjust the plate level
ii. To adjust the line of
collimation
iii. To adjust the horizontal axis
iv. To adjust the axis of the
altitude bubble
v. To adjust the vertical circle
vi. To adjust the striding level.
(12 marks)
37(b) How will you set out horizontal angle by repetition method?
State what errors are eliminated by repetition method.
To measure angle PQR:
· set the instrument at Q. set 00
reading on vernier A. note vernier B
reading.
· loose the telescope and direct
telescope towards P. Clamp and
bisect point P.
· unclamp upper and turn instrument
clockwise towards R.
· note the readings in both verniers A
and B to get angle PQR.
· unclamp lower and turn telescope
clockwise to sight P.
· unclamp upper, turn clockwise and
sight R.
· repeat until the angle is repeated for
3 times.
· the average angle with face left will
be equal to final reading divided by
3.

24. P age | 23
· change face and make three more
repetitions. find the average angle.
· average horizontal angle = average
of the angles taken with face left and
face right.
(8 marks)
Elimination of errors:
· due to eccentricity of verniers and
centers
· due to inadjustments of line of
collimation and trunnion axis
· due to inaccurate graduations
· due to inaccurate bisection of the
object, eccentric centering etc.
(4 marks)
38(a) Following are the latitudes and departures of lines AB, BC, CD and DA in a theodolite traverse:
Line
Latitude
Departure
AB
123.35
35.68
BC
93.82
205.86
CD
-177.44

25. Page | 24
70.11
DA
-39.21
-312.25
Adjust the traverse by applying the transit rule.
Line
Latitude
Correctio
n(-ve)
Correcte
d latitude
Departur
e
Correctio
n(+ve)
Correcte
d
departure
AB
123.35
0.15
123.20
35.68
0.03
35.71
BC
93.82
0.11
93.71
205.86
0.20
206.06
CD
-177.44
0.21
-177.65

26. Page | 25
70.11
0.07
70.18
DA
-39.21
0.05
-39.26
-312.25
0.30
-311.95
(12 marks)
38(b) A closed traverse was conducted round an obstacle and the
following observations were made. Work out the missing
quantities.
Side
Length(m)
Azimuth
AB
500
98̊30’
BC
620
30̊20’
CD
468
298̊30’
DE
?
230̊0’
EA
?
150̊10’
DE = 695.27m
EA = 273.99m
(12 marks)

27. Page | 26
UNIT –V
Q.No Questions Answer key with marking scheme
39(a) Describe any six methods of location of the soundings. By cross rope
i. By intersecting ranges
ii. By one angle from the shore and
one from the boat
iii. By range and one angle from the
boat.
iv. By range and one angle from the
shore.
v. By range and time intervals.
vi. By tacheometry
vii. By two angles from the boat.
viii. By twor angles from the
shore.
(12 marks)
39(b) What is ground tracing? Explain in detail the setting out of
foundation trenches for buildings.
Ground tracing is the process of laying
down the excavation lines and center
lines etc on the ground, before
excavation is started.
(2 marks)
Setting out foundation using pegs:
· longest outer wall of the building is
first marked on ground with a string
between wooden pegs driven.
· this is reference line.
· two pegs each on either side of the
central pegs are driven at each end of
line.
· the distance between outer pegs
correspond to the width of foundation
trench to be excavated.
· Peg projects 25 to 50m above GL and
may be driven at a distance 5m from
the edge of excavation.
· The boundary is marked on the

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ground with dry lime powder.
· A right angle can be set out forming a
triangle with 3, 4 and 5 units long
sides.
· A theodolite or prismatic compass
may be used for setting out right
angles.
Setting out foundation using masonry
pillars:
· reference pillars of masonry are
constructed of 20cm thick, 15cm
wider than the width of the
foundation trench.
· pillars are plastered and set at
plinth level.
· pegs are embedded in pillars to
represent center line and outer
lines.
· additional nails are provided to
represent plinth lines.
(10 marks)
40(a) Where is serpentine curve? Derive an expression for the
tangent of a serpentine curve between parallel straights.
Serpentine or reverse curve:
A compound curve having two circular
arcs of same or different radii, but
curving in opposite directions with a
common tangent.
(2 marks)
Expression:
T1T2 = 2(R1 +R2) sin(α/2)-------------(i)
X = (R1 +R2)versinα-----------(ii)
γ= (R1 +R2)sinα--------(iii)

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sin (α/2) = (X/( T1T2))-----(iv)
T1T2 = √(2X(R1+R2)----(v)
γ= 2Rsinα--------(vi)
T1T2 = 2√(RX)
(10 marks)
40(b) Derive the intrinsic equation of an ideal transition curve. Equation of a clothoid or Euler spiral
or True spiral:
Inclination of the tangent to the
transition curve α= L1
2
/ 2RL radians
Spiral angle of transition curve α1=
L/(2R)
(12 marks)

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