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Surveying – Complete Study Notes

GATE ESE / IES SSC JE State PSC RRB JE

Comprehensive chapter-wise notes covering every topic of Surveying — classification, chain and compass surveying, levelling methods, theodolite and traversing, tacheometry, field astronomy, GPS, map preparation, photogrammetry, remote sensing, layout surveys for civil structures, and setting out of curves. All formulae, IS code references, SVG diagrams, worked examples and exam-angle tables for GATE, ESE & SSC JE.

Ch 1 · Classification & Chain Surveying Ch 2 · Compass Surveying Ch 3 · Levelling Ch 4 · Theodolite & Traversing Ch 5 · Tacheometry Ch 6 · Field Astronomy & GPS Ch 7 · Map Preparation Ch 8 · Photogrammetry Ch 9 · Remote Sensing Ch 10 · Layout Surveys Ch 11 · Setting Out of Curves ★ Quick Revision

1Classification of Surveys & Chain Surveying►

1.1 Classification of Surveys

Basis	Types	Description
Nature of field	Land, Hydrographic, Astronomical, Aerial	Based on where survey is conducted
Object / Purpose	Topographic, Cadastral, City, Engineering, Mine, Military, Geological	Based on what is being surveyed
Instruments used	Chain, Compass, Plane Table, Theodolite, Tacheometric, Photographic, EDM/GPS	Based on primary measuring tool
Methods employed	Triangulation, Traversing, Radiation, Intersection	Based on geometric technique
Earth's curvature	Plane surveying (area <260 km²); Geodetic surveying (larger areas)	Plane: earth treated as flat; Geodetic: accounts for curvature

ℹ️ Plane vs Geodetic Surveying: For areas up to 260 km² (radius ~9.12 km), the difference between plane and spherical earth is within 1/1,000,000 — negligible for engineering. For larger areas (national surveys, geodesy), earth's shape must be accounted for.

1.2 Principles of Surveying

Working from whole to part: Establish large framework first, then fill in detail — prevents error accumulation
Locating a point by two measurements: Any point fixed by minimum 2 independent measurements (angles, distances, offsets)
Check: Always check measurements; use redundant observations

1.3 Chain Surveying — Instruments

Instrument	Standard Length	Least Count / Accuracy	Use
Gunter's chain	20.12 m (66 ft); 100 links	1 link = 0.2012 m	Land surveying (historical)
Engineer's chain	30.48 m (100 ft); 100 links	1 link = 0.3048 m	Engineering surveys
Metric chain	20 m or 30 m; 100 or 150 links	20 m: 1 link = 0.2 m; 30 m: 1 link = 0.2 m	Standard in India (IS 1492)
Steel tape	10, 20, 30, 50 m	±2 mm in 30 m	Precise distance measurement
Invar tape	30, 50, 100 m	Very high (low thermal expansion)	Precise base line measurement

1.4 Errors in Chain Surveying and Corrections

Correction for incorrect chain length:
Corrected distance = Measured distance × (True length of chain / Nominal length)
L_true = L_measured × (L_actual / L_nominal)

Correction for slope (horizontal distance from sloped measurement):
D_horizontal = L × cos θ (θ = angle of slope)
OR: D = L − h²/(2L) [approximate when h/L < 0.1; h = vertical difference]

Correction for temperature:
C_t = α × L × (T − T₀) (α = coefficient of thermal expansion)
For steel: α = 11.2 × 10⁻⁶ /°C

Correction for pull (tension):
C_p = (P − P₀) × L / (AE)
P = applied pull, P₀ = standard pull, A = cross-section of tape, E = modulus

Correction for sag (catenary):
C_s = −w² × l³ / (24P²) per span (negative; tape sags down)
w = weight per unit length, l = unsupported length, P = applied tension

Normal tension (makes pull correction = sag correction):
P_n = 0.204 × W × √(AE / (P_n − P₀)) [iterative]

1.5 Offsets — Perpendicular and Oblique

Perpendicular offset: e_perp = x² / (2L) [error in offset due to angular error δ]
where x = offset length, L = chain line (spacing between offsets)

Maximum length of offset for given error e_perp:
x = √(2eL) → limits offset length in accurate work

For oblique offset (from two chain points A and B to object O):
AO = √(AB² + BO² − 2AB × BO × cos(∠ABO)) [cosine rule]

1.6 Triangulation and Trilateration

Triangulation: angles measured; one baseline measured
Trilateration: all sides (distances) measured; no angles
Combined: most modern surveys use both (with EDM or GPS)

Strength of figure — well-conditioned triangle: all angles 30°–120°
Ideal angle for triangulation: 60° (equilateral triangle)
Avoid angles < 30° (elongated; error propagates rapidly)

📝 GATE Tip: Correction for incorrect chain = L × (L_actual/L_nominal). Slope correction: D = L·cosθ or L − h²/(2L). Sag correction always negative. Normal tension = tension making pull correction equal to sag correction. These corrections are favourite GATE numerical questions.

2Compass Surveying – Bearings & Traversing►

2.1 Bearings

Whole Circle Bearing (WCB): measured clockwise from N; range 0°–360°
Quadrantal / Reduced Bearing (QB/RB): measured from N or S toward E or W; 0°–90°

Conversion WCB → QB:
0°–90°: QB = N(WCB)E
90°–180°: QB = S(180°−WCB)E
180°–270°: QB = S(WCB−180°)W
270°–360°: QB = N(360°−WCB)W

Back bearing: BB = FB ± 180° (add if FB < 180°; subtract if FB > 180°)
Declination (δ): angle between magnetic N and true N
True bearing = Magnetic bearing + δ (if E declination)
True bearing = Magnetic bearing − δ (if W declination)

2.2 Local Attraction

Local attraction is disturbance of the magnetic needle by local magnetic influences (iron, electric cables, steel structures). It affects all compass readings at a station equally.

Detection: If (FB − BB) ≠ 180°, local attraction exists at one or both stations

Correction procedure:
1. Find station(s) free from local attraction (FB − BB = 180° exactly)
2. Start correction from that station
3. Error at each station = (BB of previous line) − (FB of previous line + 180°)
4. Corrected bearing = observed bearing ± error at that station

2.3 Traversing with Compass

Consecutive coordinates (latitude and departure):
Latitude L = d × cos θ (N positive, S negative)
Departure D = d × sin θ (E positive, W negative)
θ = bearing of line, d = length of line

Closing error:
e_L = ΣL (algebraic sum of latitudes; should be 0 for closed traverse)
e_D = ΣD (algebraic sum of departures; should be 0 for closed traverse)
Linear closing error: e = √(e_L² + e_D²)
Accuracy ratio (Precision) = 1 : (Σd / e) [e.g., 1:500 means error = 1/500 of total distance]

2.4 Adjustments of Traverse

Bowditch's (Compass) Rule

Correction to latitude of any line = −e_L × (length of that line / total length of traverse)
Correction to departure of any line = −e_D × (length of that line / total length of traverse)
Use when: angular and linear accuracy are comparable (angular error ∝ √n)

Transit Rule

Correction to latitude = −e_L × |L of that line| / Σ|L|
Correction to departure = −e_D × |D of that line| / Σ|D|
Use when: angular accuracy >> linear accuracy (theodolite traverse)

2.5 Gale's Traverse Table and Area Calculation

After adjustment, calculate independent coordinates (Northing N_i, Easting E_i) from
consecutive coordinates and starting point.

Area by coordinate method (double area):
2A = Σ(N_i × E_{i+1} − N_{i+1} × E_i) [for vertices in order]
A = |2A| / 2

Alternatively — mid-ordinate rule, trapezoidal rule, Simpson's 1/3 rule:
Trapezoidal: A = d × [(h₁+h_n)/2 + h₂+h₃+...+h_{n-1}]
Simpson's 1/3: A = d/3 × [(h₁+h_n) + 4(h₂+h₄+...) + 2(h₃+h₅+...)]
(Simpson's needs even number of equal divisions; more accurate than trapezoidal)

📝 GATE Tip: Bowditch rule: correction proportional to length. Transit rule: correction proportional to coordinate magnitude. For GATE numericals, remember latitude = d·cosθ and departure = d·sinθ with correct signs. 2A = Σ(N_i × E_{i+1} − N_{i+1} × E_i) is the key area formula.

3Levelling – Methods, Instruments & Corrections►

3.1 Basic Terms

Term	Definition
Datum	Reference surface for elevation; MSL (Mean Sea Level) is standard in India (GTS Benchmark)
RL (Reduced Level)	Elevation of a point above the datum
BS (Back Sight)	First staff reading taken on a point of known RL (BM or CP) after instrument is set up
FS (Fore Sight)	Last staff reading taken before shifting the instrument; on TP or BM
IS (Intermediate Sight)	Any reading taken between BS and FS from the same instrument position
HI (Height of Instrument)	Elevation of line of collimation = RL of BM + BS reading
Turning Point (TP)	Intermediate point where both BS and FS are taken (instrument moved here)
Benchmark (BM)	Fixed reference point of known RL; GTS BMs by Survey of India

3.2 Methods of Levelling Reduction

Height of Instrument (HI) Method

HI = RL of BM + BS
RL of any point = HI − Staff reading (IS or FS)

Arithmetic check: ΣBS − ΣFS = Last RL − First RL
(This check does NOT detect errors in IS readings — major limitation)

Rise and Fall Method

Rise = previous reading − current reading (if positive = rise)
Fall = current reading − previous reading (if positive = fall)
RL_n = RL_{n-1} + Rise (or − Fall)

Arithmetic check: ΣBS − ΣFS = ΣRise − ΣFall = Last RL − First RL
(Three-way check — detects all errors including IS; preferred for precise work)

Fig. 3.1 — Differential levelling: BS taken on BM; IS taken on intermediate points; FS taken on TP before shifting; HI is horizontal line of sight

3.3 Types of Levelling

Type	Purpose	Method
Simple levelling	Determine difference in elevation between 2 nearby points	One instrument position
Differential levelling	Determine RL of distant points through TPs	Multiple instrument positions; most common
Fly levelling	Rapid transfer of RL over long distance; less accurate	Long sight lines; no IS readings
Profile levelling	RL along a route (road, canal, pipeline centreline)	Differential levelling along centreline with IS at stations
Cross-section levelling	RL across width of route for earthwork calculation	IS taken at measured offsets from centreline
Reciprocal levelling	Determine accurate elevation across wide obstacle (river)	Instrument on each bank; mean of two results eliminates curvature + refraction
Trigonometric levelling	RL from vertical angles and distances	Theodolite; used in hilly terrain

3.4 Curvature and Refraction Corrections

Correction for curvature (C_c): Staff reading appears too large (distant point looks higher):
C_c = +D² / (2R) [adds to staff reading; makes level line curve away]
For earth R = 6370 km: C_c = 0.0785 × D² (D in km, C_c in m)

Correction for refraction (C_r): Atmospheric bending makes ray curve downward ≈ 1/7 of C_c:
C_r = −D² / (14R) = −C_c / 7 = −0.0112 × D²

Combined correction:
C = C_c + C_r = D²/(2R) − D²/(14R) = D² × (6/(14R)) = 0.0673 × D² (D in km, m units)
Net effect: distant staff reads 0.0673D² metres too high → subtract from reading

Distance of visible horizon: D = √(2Rh) ≈ 3.855√h [D in km, h in metres]

3.5 Errors and Permanent Adjustments of Level

Two-peg test (finding error in line of collimation):
1. Instrument at C (midway between A and B, distance d each side)
2. h_true = (a₁ − b₁) [true difference, no collimation error when instrument is midway]
3. Move instrument to A; read staff at A (a₂) and B (b₂)
4. Error in collimation = (a₂ − b₂) − h_true
5. Correct reading at B = b₂ ± error; adjust cross-hair to match

Sensitiveness of bubble tube:
Angular value of one division = s / R (radians) = s × (ρ/R) seconds
s = length of one division, R = radius of curvature of bubble tube

3.6 Precise Levelling and Trigonometric Levelling

Precise levelling (geodetic): invar staff; parallel plate micrometer; short sights (<50m); balanced BS/FS
Accuracy: ±1–3 mm/km (first-order); ±5 mm/km (second-order)

Trigonometric levelling:
For near object: h = D × tan α (no curvature/refraction correction needed for short distances)
For distant object (D in km):
h = D × tan α + D²×(1/2R − 1/7×1/2R) = D × tan α + 0.0673D²
h = S × sin α (if slope distance S measured with EDM; α = vertical angle)

4Theodolite & Traversing►

4.1 Theodolite — Components and Types

A theodolite is a precision optical instrument for measuring horizontal and vertical angles. Modern total stations combine a theodolite with an EDM (electronic distance measurement) in one unit.

Feature	Vernier Theodolite	Optical (Micrometer) Theodolite	Total Station (Electronic)
Angle reading	Vernier scale; least count 20″	Optical scale; least count 1″	Electronic encoder; least count 1″ or less
Distance	Not measured	Not measured (tacheometry only)	Built-in EDM; ±(2mm + 2ppm)
Data storage	Manual booking	Manual booking	On-board data collector; downloads to PC
Use	Older; exam reference standard	Precise surveys; triangulation	Modern construction, setting out, control surveys

4.2 Temporary Adjustments of Theodolite

Setting up: Centring over station (plumb bob / optical plummet); approximate levelling
Levelling: Using plate bubble; two screws bring bubble to centre; rotate 90°; third screw; repeat
Elimination of parallax: Focus eyepiece on cross-hairs; focus objective on signal

4.3 Measurement of Horizontal Angles

Method of repetition:
- n repetitions accumulate the angle; read once (R × angle ≈ final reading)
- Average angle = Final reading / n
- Advantage: eliminates graduation errors; increases precision by √n factor

Method of reiteration (directions method):
- Direct and reverse readings taken on all signals
- Average of Face Left (FL) and Face Right (FR) eliminates instrument errors
- Most systematic method for triangulation

Face Left and Face Right mean:
FL: vertical circle is on left of observer; FR: on right
Mean of FL+FR eliminates: (1) line of collimation error; (2) trunnion axis error; (3) eccentricity

4.4 Measurement of Vertical Angles

Vertical angle = (FL + FR − 360°) / 2 [if FL and FR are both supplementary]
Or: Vertical angle = (FL − FR) / 2

Zenith angle Z = 90° − vertical angle α (ZA measured from vertical, not horizontal)

Index error: average of FL and FR zenith angles; should sum to 360° exactly
Index error e = (ZA_FL + ZA_FR − 360°) / 2
Corrected angle = ZA − e

4.5 Theodolite Traversing

Included angle method: measure interior (or exterior) angle at each traverse station
Check: Sum of interior angles = (n−2) × 180° [n = number of sides]
For exterior angles: Sum = (n+2) × 180°

Deflection angle method: measure angle between prolongation of back line and forward line
Check: Σ Left deflections − Σ Right deflections = 0 (for closed traverse)
OR each bearing check directly

Omitted measurements in a traverse:
If length of one line is missing: l = √(e_L² + e_D²) [using closing error = missing side]
If bearing is missing: θ = arctan(e_D / e_L)

4.6 Electronic Distance Measurement (EDM)

Principle: electro-magnetic wave (microwave, infrared, laser) sent to retroreflector
Measured: phase difference of outgoing and return signals
D = nλ/2 + φλ/4π (n = integer wavelengths, φ = fractional phase difference, λ = wavelength)

Errors in EDM:
Additive (prism constant): fixed offset at reflector; calibrated
Scale error (ppm): proportional to distance; due to atmospheric refraction

Atmospheric correction:
K_ppm = 79.661 × P/T − 11.27 × e/T − 26.578 (P = pressure mbar, T = temp K, e = vapour pressure)
Corrected distance = observed × (1 + K/10⁶)

5Tacheometry – Stadia & Tangential Methods►

5.1 Principle of Tacheometry

Tacheometry allows simultaneous determination of horizontal distance and elevation difference using a theodolite and graduated staff, without tape measurement. It is rapid but less accurate than chaining — suitable for topographic surveys, contour mapping, and detail surveys.

5.2 Stadia Method

Fig. 5.1 — Stadia tacheometry: staff intercept s between upper and lower stadia hairs; D = ks + c = 100s for internal focusing

Fig. 5.2 — Inclined sight: horizontal dist D = ks·cos²α; vertical component V = ks·sinα·cosα = D·tanα

5.3 Stadia Formulae

Horizontal sight (α = 0°):
D = ks + c (k = multiplying constant = 100; c = additive constant ≈ 0 for internal focus)

Inclined upward sight (elevation angle α):
Horizontal distance: D = ks × cos²α + c × cosα
Vertical distance: V = ks × sin2α/2 + c × sinα = D × tanα

Reduced level of staff station B:
RL_B = RL_A + h_i + V − m
where: h_i = height of instrument above A, m = central hair reading on staff, V = vertical distance
(V positive if angle of elevation; negative if depression)

Staff intercept: s = upper hair reading − lower hair reading
Central hair reading: m = (upper + lower) / 2 (or direct reading)

5.4 Tangential Method (No Stadia Hairs)

Two vertical angles α₁ (to top) and α₂ (to foot) of staff of known height S:

Case 1: Both angles of elevation:
D = S × tan α₁ × tan α₂ / (tan α₁ − tan α₂)
h = D × tan α₁ + h_i − reading at lower target

Case 2: One elevation, one depression:
D = S × tan α₁ × tan α₂ / (tan α₁ + tan α₂)

5.5 Subtense Bar

Horizontal distance: D = b / (2 × tan β/2) ≈ b / β (for small β in radians)
b = length of subtense bar (typically 2 m); β = horizontal angle subtended at instrument
Accuracy: ~1 in 1000 for distances up to 200 m; better with precise theodolite

📝 GATE Tip: Stadia constants k=100, c=0 (internal focus). Horizontal: D=100s. Inclined: D=100s·cos²α. RL = RL_A + hi + V − m. Tangential method: D = S·tanα₁·tanα₂/(tanα₁ − tanα₂). Subtense bar: D = b/β. These formulae are the most tested in this chapter.

6Field Astronomy & Global Positioning System (GPS)►

6.1 Celestial Sphere Concepts

Term	Definition
Celestial sphere	Imaginary sphere of infinite radius centred at observer; all celestial bodies appear on its surface
Zenith (Z)	Point on celestial sphere directly above observer; opposite = Nadir
Celestial meridian	Great circle through Z, N pole, S pole, and Nadir
Declination (δ)	Angular distance of celestial body N or S of celestial equator (like latitude for stars)
Right Ascension (RA)	Angular distance E of vernal equinox (like longitude for stars)
Hour Angle (HA)	Angle at pole between observer's meridian and star's meridian; measured W; 0–24 hours
Altitude (a)	Vertical angle above horizon to celestial body (0°–90°)
Azimuth (A)	Horizontal angle from North (or South) to the vertical circle through the body
Zenith Distance (z)	90° − altitude; angular distance from zenith to body

6.2 Astronomical Triangle and Formulae

Astronomical (PZS) triangle: P = Pole, Z = Zenith, S = Star
Sides: PZ = co-latitude = (90° − φ), ZS = zenith distance z = (90° − a), PS = co-declination = (90° − δ)
Angle at P = Hour angle H; Angle at Z = Azimuth A; Angle at S = parallactic angle

Cosine rule: cos(ZS) = cos(PZ)cos(PS) + sin(PZ)sin(PS)cos(H)
Simplified: sin(a) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(H) [altitude formula]

Azimuth from altitude:
cos(A) = [sin(δ) − sin(φ)sin(a)] / [cos(φ)cos(a)]

Azimuth by ex-meridian observation of Polaris:
A_Polaris = (ρ/15) × sin(ρ) / [cos(φ) × sin(H)] [ρ = polar distance]

6.3 Determination of True North

By observation of Polaris (North Star): Most accurate in N hemisphere; observe at elongation (greatest E or W) when azimuth correction is maximum and rate of change is minimum
By solar observation: Measure altitude and time; compute azimuth from formulae
By equal altitudes of sun: Sun observed in AM and PM at equal altitudes; bisect angle = true N direction
By magnetic bearing + declination: Least accurate; uses compass

6.4 Global Positioning System (GPS)

ℹ️ GPS (USA), GLONASS (Russia), Galileo (EU), and India's NavIC (IRNSS) are satellite-based positioning systems collectively called GNSS (Global Navigation Satellite Systems).

GPS constellation: 24+ satellites in 6 orbital planes; MEO at ~20,200 km altitude
Orbital period: ~12 hours; each satellite sends signals on L1 (1575.42 MHz) and L2 (1227.60 MHz)

Positioning principle: trilateration (NOT triangulation)
Range to satellite i: ρ_i = c × Δt_i (c = speed of light, Δt = signal travel time)
Pseudorange (with receiver clock error b): ρ_i = R_i + c × b
4 satellites needed for 3D position (X,Y,Z) + receiver clock error (4 unknowns)

Position accuracy (standard GPS without differential correction):
Horizontal: ~10–15 m (SA off since 2000); currently ~3–5 m
DGPS (Differential GPS): 0.5–3 m horizontal
RTK GPS: ±1–2 cm horizontal; ±2–3 cm vertical
Network RTK / PPP: cm-level accuracy

Dilution of Precision (DOP):
PDOP (Position DOP) = HDOP² + VDOP²; ideal PDOP < 6; poor if > 8

6.5 GPS Error Sources

Error Source	Magnitude	Remedy
Ionospheric delay	1–10 m (dominant)	Dual-frequency receiver (L1+L2); ionospheric model
Tropospheric delay	0.5–2 m	Elevation mask >15°; tropospheric model (Hopfield, Saastamoinen)
Satellite clock error	<1 m	Broadcast corrections in navigation message
Receiver clock error	Eliminated by	Using 4th satellite (clock solution)
Multipath	1–5 m	Site selection; choke ring antennas; RAIM
Ephemeris error	<1 m	Precise ephemerides from IGS

6.6 NavIC (Navigation with Indian Constellation)

India's own regional navigation system:
7 satellites (3 GEO + 4 IGSO); covers Indian subcontinent and 1500 km surrounding region
Accuracy: <20 m (standard service); <10 m with correction
Signals: L5 (1176.45 MHz) and S-band (2492.028 MHz)
Operational since: 2018 (IRNSS, rebranded as NavIC)

📝 GATE Tip: GPS needs 4 satellites for 3D position + clock error. Altitude formula: sin a = sinφ·sinδ + cosφ·cosδ·cosH. PDOP < 6 is good. DGPS accuracy: 0.5–3 m; RTK: 1–2 cm. NavIC = Indian regional system (7 satellites).

7Map Preparation – Plane Table & Contours►

7.1 Plane Table Surveying

Plane table surveying is a graphical method where the map is drawn in the field simultaneously with the survey — eliminating the need for office calculations. The alidade (sighting rule with telescope) is used to take directions, and distances are measured by tacheometry or tape.

Methods of Plane Table Surveying

Method	Principle	Use
Radiation	From a single station, rays drawn to all detail points; distances measured	Open ground; small areas; detail survey
Intersection (Graphic triangulation)	Rays from two known stations intersect to locate unknown point	Locating inaccessible points; rivers; hills
Traversing	Table moved and oriented at each station; check provided	Large areas; roads, rivers
Resection	Location of instrument station from rays to known plotted points	When instrument station is unknown; three-point problem

Three-Point Problem (Resection)

Given: Three control points A, B, C plotted on the sheet
Find: Location P of the instrument on the sheet
Methods: (1) Bessel's method (graphical); (2) Trial and error (Lehmann's rules); (3) Analytical

Lehmann's rules (for iterative solution):
1. If instrument is outside triangle ABC, P is outside the triangle of error
2. P lies in the same sector (angle) as the intersection point of the three rays

7.2 Contour Lines

A contour line is an imaginary line on the ground joining all points of equal elevation. Contour maps provide a two-dimensional representation of three-dimensional terrain.

Contour interval (CI): vertical difference between successive contours
CI = H / n (H = total height difference; n = desired number of contours)
Recommended CI: 1:50,000 map → 20 m; 1:25,000 → 10 m; detailed engineering → 0.5–2 m

Horizontal Equivalent (HE): horizontal distance between two contours
Scale of slope = tan(slope angle) = CI / HE

Gradient: g = CI / HE_actual (HE from map × map scale)

Characteristics of Contours

Contour lines never cross or branch (except for overhanging cliffs)
Every contour line closes on itself, either within or outside the map
Closely spaced contours → steep slope; widely spaced → gentle slope
Contours crossing a valley form V-shapes pointing upstream (uphill)
Contours crossing a ridge form V-shapes pointing downhill
Uniformly spaced = uniform slope; concave up = slope flattens upward
Circular contours with decreasing values outward → hill; increasing → depression

7.3 Methods of Contouring

Method	Procedure	Accuracy	Use
Direct method	Physically locate points of equal elevation on the ground; connect on plan	High	Slow; used when high accuracy needed; hilly terrain
Indirect method (cross-section)	Spot heights taken at grid or cross-section points; contours interpolated	Moderate	Open ground; most common; faster
Tacheometric	Spot heights with tacheometer; interpolated	Moderate	Hilly or wooded terrain
Aerial photogrammetry	Stereo photographs; contours drawn by photogrammetric methods	High (large areas)	Large area mapping; fastest

7.4 Uses of Contour Maps

Determine slope of land at any point
Draw profile/section along any line
Locate a route of a given gradient between two points
Estimate volume of earthwork (for roads, embankments, reservoirs)
Delineate catchment area of a watershed
Determine intervisibility of two points (line of sight)

📝 GATE Tip: Contours cross valleys as V (pointing uphill). Closest contours = steepest slope. Direct method is most accurate; indirect grid method is most common. Scale of slope = CI/HE. These are the commonly tested qualitative facts.

8Photogrammetry►

8.1 Introduction and Types

Photogrammetry is the science and art of obtaining reliable measurements from photographs. It extracts geometric and spatial information from images.

Type	Camera Position	Application
Terrestrial (close-range)	Camera on ground or tripod	Architectural, industrial, archaeological measurement
Aerial photogrammetry	Camera in aircraft pointing vertically down (near-vertical)	Topographic mapping, cadastral survey, DEM generation
UAV / drone photogrammetry	Camera on drone; overlapping photos	Site surveys, 3D models, construction monitoring
Satellite photogrammetry	Stereo satellite imagery	Global mapping; Google Earth level; Cartosat-2

8.2 Aerial Camera and Photo Geometry

Scale of vertical aerial photograph:
S = f / H (f = focal length; H = flying height above ground)
For undulating ground: S = f / (H − h) (h = elevation of point above datum)

Photo scale: 1/S = H/f; if H = 3000 m, f = 150 mm → scale = 1/20,000

Relief displacement (radial distortion due to height of object):
d = h × r / H
r = radial distance from principal point to image of top of object
h = height of object; H = flying height
Object leans outward from the centre in vertical photo

Length of object on ground (from shadow or by stereo): L = l × H / f = l / S
l = length on photo

Flying height H: H = f / S for required scale S

8.3 Overlap and Coverage

Forward overlap (end overlap): typically 60% (min 55–65%)
Side overlap (lateral overlap): typically 30% (for mapping); 60% for urban 3D models

Ground coverage per photo: A = (p × f / S) each side (p = photo dimension)
For photo size 230 mm × 230 mm, scale 1:10,000:
Ground coverage = 230 × 10,000 mm = 2300 m → 2.3 km square

Number of photos (approximate) for an area A_total:
n = A_total / [(1−p₁)(1−p₂) × A_photo] (p₁ = forward overlap, p₂ = side overlap)

Base-to-height ratio (B/H):
B = air base (distance between exposure stations)
B/H = (1 − forward overlap fraction) × photo width / f
Optimal B/H = 0.5–0.6 (good stereoscopic measurement)

8.4 Stereoscopy and DEM Generation

Parallax difference (for elevation determination):
h = H × Δp / (p_b + Δp) ≈ H × Δp / p_b (for small Δp)
h = elevation of object above datum
Δp = parallax difference = p_top − p_base (stereoscopic parallax)
p_b = absolute stereoscopic parallax of datum point

Absolute stereoscopic parallax: p_b = f × B / H (B = air base, f = focal length, H = flying height)

Height of building / tree from parallax:
h = (H × Δp) / p_b = (H × Δp) / (B × f / H)

8.5 Orthophoto and Digital Elevation Model (DEM)

Orthophoto: Aerial photo corrected for relief displacement and tilt — like a true planimetric map; scale is uniform throughout
DEM (Digital Elevation Model): Grid of elevation values; generated from stereo pairs
DSM (Digital Surface Model): Elevations include buildings, trees (first return lidar)
DTM (Digital Terrain Model): Bare earth elevations (filtered lidar ground returns)
LiDAR: Light Detection and Ranging; airborne laser scanning; point cloud; density 1–30 pts/m²; accuracy ±5–15 cm

📝 GATE/ESE Tip: Photo scale = f/H. Relief displacement d = hr/H (objects lean outward). Parallax height formula: h = H·Δp/p_b. Standard overlap: 60% forward, 30% side. B/H ratio = 0.5–0.6. These are the quantitative formula facts most tested.

9Remote Sensing►

9.1 Principles of Remote Sensing

Remote sensing is the acquisition of information about an object or area from a distance — typically using sensors onboard satellites or aircraft — without physical contact. It exploits electromagnetic radiation (EMR) reflected or emitted by the Earth's surface.

Electromagnetic spectrum bands used in remote sensing:
Visible: 0.4–0.7 µm (B, G, R channels; human eye range)
Near IR: 0.7–1.3 µm (NIR; vegetation health; Landsat Band 4)
Short-wave IR: 1.3–3 µm (SWIR; minerals, moisture content)
Mid IR: 3–8 µm (thermal emission begins)
Thermal IR: 8–14 µm (Earth's emitted radiation; temperature mapping)
Microwave: 1 mm–1 m (SAR — Synthetic Aperture Radar; cloud penetration)

9.2 Types of Remote Sensing Systems

Parameter	Passive RS	Active RS
Energy source	Sun (reflected solar radiation) or Earth's thermal emission	Own source (radar, lidar, sonar)
Day/night operation	Daytime only (visible/NIR); thermal works at night	Day and night (own illumination)
Cloud penetration	Cannot (visible/NIR cloud-blocked)	SAR: penetrates clouds and rain
Examples	Landsat, SPOT, IKONOS, Cartosat	SAR (ERS, Sentinel-1, RISAT); LiDAR; RADAR altimeter

9.3 Image Resolution Types

Resolution Type	Definition	Example
Spatial	Smallest ground feature distinguishable; ground pixel size	0.3 m (WorldView-3); 30 m (Landsat); 23.5 m (Cartosat-1)
Spectral	Number and width of spectral bands; ability to distinguish features by colour	Pan: 1 band; MS: 4–8 bands; Hyperspectral: 100–200+ bands
Temporal	Revisit time (how often same area is imaged)	MODIS: daily; Landsat: 16 days; Cartosat-2: 4 days
Radiometric	Number of digital levels (bits) for intensity; sensitivity to brightness difference	8-bit = 256 levels; 11-bit = 2048; 16-bit = 65536 levels

9.4 Indian Remote Sensing Satellites

Satellite	Resolution	Application
Cartosat-1	2.5 m (PAN); stereo pair (fore + aft)	Large-scale mapping; DEM generation; cadastral
Cartosat-2 series	0.65–1 m (PAN)	Urban planning, infrastructure mapping
LISS-IV (ResourceSat)	5.8 m (MS)	Crop monitoring, land use mapping
RISAT-1	1–3 m (C-band SAR)	All-weather mapping; flood, oil spill
Oceansat-2	360 m	Ocean colour, wind speed, fisheries
INSAT-3D	1–4 km	Weather, cyclone, fog monitoring

9.5 Image Interpretation and Spectral Indices

NDVI (Normalized Difference Vegetation Index):
NDVI = (NIR − Red) / (NIR + Red) range −1 to +1
>0.6: Dense healthy vegetation; 0.2–0.6: Sparse/moderate vegetation
<0.1: Bare soil, water, snow

NDWI (Normalized Difference Water Index):
NDWI = (Green − NIR) / (Green + NIR) [McFeeters, for water bodies]

NDBI (Built-up Index): NDBI = (SWIR − NIR) / (SWIR + NIR)

Supervised classification: Training sites defined; algorithm assigns remaining pixels
Unsupervised classification: ISODATA, k-means clustering; no training sites; classes defined post-hoc

9.6 GIS (Geographic Information System)

ℹ️ GIS integrates spatial data (maps, satellite images) with attribute data (population, soil type, land use) for analysis. It enables overlay, buffer analysis, spatial query, network analysis, and 3D modelling. Common platforms: ArcGIS, QGIS (open source), Bhuvan (ISRO India).

Vector data: Points, lines, polygons; precise boundaries; smaller files
Raster data: Grid of cells (pixels); each cell has one value; satellite images, DEMs
Map projection: Converts spherical earth to flat map; India uses Polyconic projection (SOI toposheets) and UTM (WGS-84 for GPS)
Datum: Everest 1830 (old SOI maps); WGS-84 (GPS, modern); transformation needed

📝 GATE Tip: NDVI = (NIR−Red)/(NIR+Red); >0.6 = dense vegetation; <0.1 = bare/water. Cartosat-1 = 2.5 m stereo; Cartosat-2 = 0.65 m. Passive RS: sun-powered; Active RS: own energy source (SAR). SAR penetrates clouds. These are common ESE and GATE MCQ topics.

10Survey Layout for Civil Structures►

10.1 Road / Highway Alignment Survey

Preliminary survey (reconnaissance): walk the route; identify obstacles; select alternatives
Preliminary survey: traverse + levels along each alternative; longitudinal section drawn
Location survey: detailed survey of chosen alignment; cross-sections; volume estimates
Setting out: centre line pegged at 20–30 m intervals (tangents) and 10 m (curves)

Gradient computation from profile:
Grade G = (RL_B − RL_A) / (horizontal distance A to B) × 100%
Ruling gradient (IRC:73): 3.3% for NH; 5% for other roads; 1:20 to 1:30

Limiting gradient: steepest permitted; exceptional gradient = short steep section
Compensated gradient on curves: gradient reduced by 30/R + 75/R on horizontal curves
(R = radius in metres; avoid compound effects of curve + grade)

10.2 Railway Alignment Survey

Ruling gradient (IRS): 1:150 for BG plains; 1:100 for hills; 1:80 exceptional
Compensation for curvature on railways: G_comp = G − 0.04 × (degree of curve)
OR: G_comp = G − 1/R × compensation factor

Track geometry (IRS standards for BG):
Gauge: 1676 mm (Broad Gauge); 1000 mm (Metre Gauge); 762 mm (Narrow Gauge)
Maximum superelevation: 165 mm (BG); 100 mm (MG)
Transition length: L_t = V²/(R × 3.6²) × ca (ca = rate of change of cant)

Level crossing layout: survey 60 m each side of track; gradient ≤ 1:40 for road approach

10.3 Canal Alignment Survey

Canal alignment: trace a contour or follow natural watershed
Full Supply Level (FSL) and Bed Level (BL):
BL = FSL − d (d = canal depth at full supply; typically 1.5–4 m)
Freeboard: FSL to top of bank (0.5–1.0 m depending on canal capacity)

Longitudinal section of canal route:
RL of FSL must follow hydraulic gradient; BL ≥ 0 (canal must not flow uphill)
Canal bed slope: 1:5000 to 1:10,000 typical for main canals

Cross-section for earthwork:
Cut section (FSL below ground): V_cut = cross-section area × distance between sections
Fill section (FSL above ground): V_fill = cross-section area × distance
Total earthwork V = Σ [(A₁+A₂)/2 × L] (prismoidal formula more accurate)

10.4 Bridge Survey

Hydrological survey: stream cross-section; flood levels; bed profile upstream/downstream
High Flood Level (HFL): maximum observed flood level; from records or calculation
Afflux: rise in backwater level due to bridge piers — should be <0.3 m (IRC:5)

Triangulation for bridge alignment (short spans, wire sighting or electronic):
Two base lines on each bank; triangulate to locate pier positions

Setting out pier positions:
From control points on each bank using intersection method (two theodolites)
Or total station on one bank

Scour depth: D_s = 1.33 × (HFL − foundation level); Lacey's formula for scour

10.5 Building Layout

Setting out a building from a plan:
1. Fix baseline (road edge or property boundary)
2. Offset from baseline to building corner A
3. Set out right angle at A (3-4-5 or optical square)
4. Measure along perpendicular to get B
5. Repeat for other corners; check diagonal AC = BD (rectangle check)

Optical square (cross-staff): uses two mirrors at 45° to set perpendicular direction
Right angle by 3-4-5 method: a=3, b=4, c=5 (or any multiple); angle between 3 and 4 = 90°

Column and pile foundation layout:
Grid lines (column lines) established by total station
Column centres marked with offset pegs clear of excavation
Check: sum of diagonals equal for rectangular grid

10.6 Culvert Survey and Layout

Culvert site selection: where road/railway crosses a drainage channel at minimum angle
Preferred crossing angle: 90° (square culvert); but skew culvert may be needed to follow drainage
Skew angle β: angle between road centreline and normal to culvert axis

Minimum RL of road at culvert: FSL of stream + afflux + freeboard + carriage way thickness

Setting out: measure stream centreline direction; set perpendicular for culvert axis
Profile of stream bed: levels at 3–5 m intervals for 50 m each side

📝 GATE/ESE Tip: Ruling gradient for NH = 3.3%; Railways BG = 1:150. Prismoidal formula for earthwork volume. Compensation gradient on curves = reduce by 30/R (roads) or 0.04×degree (railways). Optical square sets right angles without calculation.

11Setting Out of Curves►

11.1 Types of Curves

Curve Type	Profile / Plan	Use
Simple circular curve	Circular arc; constant radius R	Change in direction of route (horizontal)
Compound curve	Two or more simple curves of different radii	Difficult terrain where single radius insufficient
Reverse curve	Two simple curves turning in opposite directions	Railway junctions; avoid if possible (no transition)
Transition (easement) curve	Curvature increases gradually from 0 to 1/R; Euler's spiral or clothoid	Roads and railways between tangent and circular curve
Summit curve (vertical)	Convex parabolic curve; crest	At hilltop; visibility requirement governs
Valley (sag) curve	Concave parabolic curve	At valley; headlight sight distance governs at night

11.2 Simple Circular Curve — Geometry

Fig. 11.1 — Simple circular curve elements: PI = vertex; PC = point of curvature (T₁); PT = point of tangency (T₂); T = tangent length; L = arc length; Δ = deflection angle

11.3 Elements of Simple Circular Curve

Tangent length: T = R × tan(Δ/2)
Length of curve: L = πRΔ/180° = RΔ [Δ in radians]
Long chord: L_c = 2R × sin(Δ/2)
Mid-ordinate: M = R × (1 − cos(Δ/2))
External distance: E = R × (sec(Δ/2) − 1)
Apex distance: U = E (same as external distance)

Degree of curve (chord definition):
D = 2 × arcsin(C / 2R) C = chord length (usually 20 m or 30 m)
D ≈ 1718.87 / R [D in degrees; R in metres; arc definition]

Note: R in metres; Δ in degrees for formula (convert to radians for arc length)

11.4 Methods of Setting Out Circular Curves

Method 1 — Offsets from Long Chord

y_x = √(R² − x²) − √(R² − (L_c/2)²)
y_x = ordinate at distance x from midpoint of chord
L_c = long chord length
Fast for small curves; no theodolite needed

Method 2 — Successive Offsets from Chord Produced (Rankine)

Offset from chord produced for each peg:
O_n = C²/(2R) for first sub-chord C₁
O_n = C(C_n + C_{n-1}) / (2R) for subsequent sub-chords of equal length
Where C = chord length (equal peg interval), R = radius

Method 3 — Deflection Angle (Rankine's Method) — Most Used

Deflection angle for chord C from PC (Rankine's method):
δ = C / (2R) radians = (C × 90) / (πR) degrees
Cumulative deflection to peg n:
Δ_n = n × δ (for equal chord intervals)

Check: Total deflection from PC to PT = Δ/2 (half the intersection angle)

Procedure: Set up theodolite at PC; orient to PI (zero reading); deflect each chord angle
successively and chain distance C each time from previous peg

Method 4 — Two Theodolite Method (No Chaining)

Theodolite at PC: deflect angle δ_n = n×C/(2R) × (180°/π)
Theodolite at PT: deflect same cumulative angle from PT
Intersection of both rays = curve point n (no distance measurement needed)
Useful: across ravines, rivers, inaccessible ground

11.5 Transition Curves

Purpose: gradually introduce curvature so centrifugal force builds up smoothly
Used: railways (mandatory), highways (recommended)

Clothoid (Euler's spiral / Cornu's spiral):
l × R = L × R₀ = constant = A²
l = length along transition, R = radius at that point
L = total transition curve length, R₀ = radius of circular curve

Minimum transition length:
L = V³ / (47 R) [L in m, V in km/hr, R in m] (for roads, IRC:38)
L = 0.01e_s × V / C (e_s = superelevation, V km/h, C = rate of change of cant = 35–55 mm/s)

Shift (s): amount main circular curve is shifted inward to accommodate transition:
s = L² / (24R) (for small angles)

Superelevation (cant) e: rotates road cross-section inward to balance centrifugal force
e = V² / (gR) = V² / (127R) [e = fraction; V in km/hr, R in m; g = 9.81]
Maximum e = 0.07 (7%) for highways; 165 mm BG railways

11.6 Vertical Curves

Vertical curve: parabolic arc connecting two grades at a VPI (Vertical Point of Intersection)
Grade 1 = g₁ %; Grade 2 = g₂ %;
Rate of change of grade = (g₂ − g₁) / L_v (L_v = length of vertical curve in m)

Elevation at any point x from VPC (Vertical Point of Curvature):
y = y_VPC + g₁x + (g₂ − g₁) × x² / (2L_v)

High/low point on vertical curve (crest or sag):
x = g₁ × L_v / (g₁ − g₂) [distance from VPC to highest/lowest point]

Summit curve — minimum length for sight distance (IRC:66):
L_v = S² × (g₁−g₂) / (h₁^0.5 + h₂^0.5)² [if S < L_v]
h₁ = 1.2 m (eye height); h₂ = 0.15 m (object height for SSD on summits)

📝 GATE Tip: T = R·tan(Δ/2); L_c = 2R·sin(Δ/2); Degree of curve D ≈ 1718.87/R. Rankine's deflection angle δ = C/(2R) radians. Transition curve length L = V³/(47R) for roads. Superelevation e = V²/(127R). These eight formulae are the core of this chapter.

★Quick Revision – All Formulae, Tables & Mnemonics►

Chain Surveying Corrections

Wrong chain: L_true = L_meas × (L_actual/L_nominal)
Slope: D = L·cosθ or D = L − h²/(2L)
Temperature: C_t = αL(T−T₀); α = 11.2×10⁻⁶/°C for steel
Sag correction: C_s = −w²l³/(24P²) (always negative)
Pull: C_p = (P−P₀)L/(AE)

Compass / Traverse

L = d·cosθ (lat); D = d·sinθ (dep); Closing error = √(ΣL² + ΣD²)
Bowditch: correction ∝ line length / total length
Transit: correction ∝ coordinate / sum of coordinates
2A = Σ(N_i·E_{i+1} − N_{i+1}·E_i) (area by coordinates)
Simpson: A = d/3[(h₁+h_n) + 4(even terms) + 2(odd middle terms)]

Levelling

HI = RL_BM + BS; RL = HI − staff reading
Rise & fall check: ΣBS−ΣFS = ΣRise−ΣFall = Last RL − First RL
Curvature: C_c = 0.0785D² (D km); Refraction: C_r = −0.0112D²
Combined: C = 0.0673D² (D km, m units)
Sensitiveness: angular value = s/R radians per division

Tacheometry

Horizontal: D = ks + c = 100s + 0
Inclined: D = 100s·cos²α; V = 100s·sinα·cosα = D·tanα
RL_B = RL_A + hi + V − m (V pos for elevation; neg for depression)
Tangential: D = S·tanα₁·tanα₂/(tanα₁−tanα₂) [both angles elevation]
Subtense: D = b/β (b = bar length, β = subtended angle radians)

Field Astronomy

sin(a) = sinφ·sinδ + cosφ·cosδ·cosH (altitude formula)
cos(A) = [sinδ − sinφ·sin(a)] / [cosφ·cos(a)] (azimuth)
GPS: 4 satellites for 3D position + clock; PDOP < 6 ideal
DGPS: 0.5–3 m; RTK: ±1–2 cm

Photogrammetry

Scale: S = f/H; Relief displacement: d = hr/H
Parallax height: h = H·Δp/p_b
B/H ratio = 0.5–0.6; Forward overlap 60%; Side overlap 30%
Absolute parallax: p_b = f·B/H

Remote Sensing

NDVI = (NIR−Red)/(NIR+Red); >0.6 dense veg; <0.1 bare/water
NDWI = (Green−NIR)/(Green+NIR) [water bodies]
Visible: 0.4–0.7µm; NIR: 0.7–1.3µm; TIR: 8–14µm; Microwave: 1mm–1m
SAR = active RS; penetrates clouds; NDVI = passive (solar)

Circular Curves

T = R·tan(Δ/2); L = πRΔ/180°; L_c = 2R·sin(Δ/2)
M = R(1−cosΔ/2); E = R(secΔ/2 − 1); D ≈ 1718.87/R (deg/m)
Rankine deflection: δ = C/(2R) rad = 1718.87·C/R minutes
Transition: L = V³/(47R); Superelevation: e = V²/(127R)

Key Tables At-a-Glance

Topic	Key Number / Value	Significance
Metric chain	20 m or 30 m; 100 links	Standard in India
Steel tape α	11.2 × 10⁻⁶ /°C	Temperature correction
Stadia constants	k=100, c=0	Internal focusing tacheometer
Curvature correction	0.0785D² (D in km, m)	Long sights correction
Combined curvature + refraction	0.0673D²	Net correction; subtract from reading
Degree of curve	D = 1718.87/R	Arc definition; D deg, R metres
Min transition length (roads)	L = V³/(47R)	V km/h; R metres
Max superelevation (highway)	7% (0.07)	IRC standard
GPS satellites needed	4 (minimum for 3D + clock)	3D positioning
NDVI range	−1 to +1; >0.6 = dense veg	Vegetation index
Aerial photo overlap	60% forward; 30% side	Standard mapping
Ruling gradient NH	3.3% (1:30)	IRC:73
Ruling gradient BG railway	1:150 (plains)	IRS standard

Mnemonics

Levelling check: "BFS = LF − LI" (Bowditch's Final Sanity check)
ΣBS − ΣFS = Last RL − First RL — works for both HI and Rise/Fall methods

Bowditch vs Transit:
"Bowditch uses Blocks (lengths); Transit uses Tally (coordinates)"
Bowditch correction ∝ line length; Transit correction ∝ coordinate magnitude

Sag correction is always Sad (negative):
"Sag → tape sags → measures too long → subtract the sag correction from measured length"

Contour V-shapes:
"Valleys → V points upstream (uphill); Ridges → V points downstream (downhill)"
OR: "Valley V-shape is like a V pointing to the Vantage (high ground)"

Curve elements: "TLLME"
Tangent = R·tanΔ/2 | Length of curve = RΔ | Long chord = 2R·sinΔ/2 |
Mid-ordinate = R(1−cosΔ/2) | External = R(secΔ/2−1)

GPS accuracy hierarchy (best to worst):
RTK (±2 cm) → DGPS (±1 m) → Standard GPS (±5 m) → SA-on (±100 m; now off)
"Really Terrific Kid — Decent GPS — Standard — Scrambled Awful"

Photogrammetry scales:
"Scale = Focal / Height" — S = f/H; to get larger scale, fly lower or use longer focal length

Remote sensing wavelengths (mnemonic: "V–N–S–M–T"):
Visible (0.4–0.7) → NIR (0.7–1.3) → SWIR (1.3–3) → Mid-IR (3–8) → Thermal (8–14) µm

Exam-Angle Comparison

Topic	GATE Focus	ESE Focus	SSC JE Focus
Chain surveying	Tape corrections numerical; sag correction formula	All corrections combined; Tellurometer; baseline measurement	Chain types; correction names and direction
Compass surveying	Bowditch vs Transit rule; area by coordinates	Local attraction correction procedure; Gale's table; traverse closure	WCB to QB conversion; back bearing; declination
Levelling	HI method vs R&F; curvature+refraction; two-peg test	Precise levelling; profile levelling; reciprocal levelling; bubble sensitiveness	Basic terms; RL computation; types of levelling
Theodolite / Traversing	Angle measurement method; traverse closure; omitted measurements	Permanent adjustments; triangulation; EDM errors; total station	Temporary adjustments; face left/right concept
Tacheometry	Stadia formulae (horizontal and inclined); RL computation	Anallactic lens; subtense bar; tangential method; stadia constants	Stadia constant k=100; basic formula D=100s
Field astronomy / GPS	GPS satellite number; PDOP; DGPS vs RTK accuracy	Altitude/azimuth formulae; astronomical triangle; NavIC details	GPS principle; satellite number; NDVI and RS concepts
Photogrammetry	Scale=f/H; relief displacement; parallax height formula	Overlap calculations; B/H ratio; orthophoto; LiDAR	Types of RS; photo scale concept; overlap values
Remote sensing	NDVI formula; SAR vs passive; resolution types	Band combinations; classification methods; Indian satellites; GIS basics	Active vs passive; NDVI concept; satellite names
Curves	T, L, L_c formulae; Rankine deflection; degree of curve	Compound curves; transition length; vertical curve design; superelevation	Elements of simple curve; tangent length; deflection angle concept

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Surveying – Complete Study Notes

1.1 Classification of Surveys

1.2 Principles of Surveying

1.3 Chain Surveying — Instruments

1.4 Errors in Chain Surveying and Corrections

1.5 Offsets — Perpendicular and Oblique

1.6 Triangulation and Trilateration

2.1 Bearings

2.2 Local Attraction

2.3 Traversing with Compass

2.4 Adjustments of Traverse

Bowditch's (Compass) Rule

Transit Rule

2.5 Gale's Traverse Table and Area Calculation

3.1 Basic Terms

3.2 Methods of Levelling Reduction

Height of Instrument (HI) Method

Rise and Fall Method

3.3 Types of Levelling

3.4 Curvature and Refraction Corrections

3.5 Errors and Permanent Adjustments of Level

3.6 Precise Levelling and Trigonometric Levelling

4.1 Theodolite — Components and Types

4.2 Temporary Adjustments of Theodolite

4.3 Measurement of Horizontal Angles

4.4 Measurement of Vertical Angles

4.5 Theodolite Traversing

4.6 Electronic Distance Measurement (EDM)

5.1 Principle of Tacheometry

5.2 Stadia Method

5.3 Stadia Formulae

5.4 Tangential Method (No Stadia Hairs)

5.5 Subtense Bar

6.1 Celestial Sphere Concepts

6.2 Astronomical Triangle and Formulae

6.3 Determination of True North

6.4 Global Positioning System (GPS)

6.5 GPS Error Sources

6.6 NavIC (Navigation with Indian Constellation)

7.1 Plane Table Surveying

Methods of Plane Table Surveying

Three-Point Problem (Resection)

7.2 Contour Lines

Characteristics of Contours

7.3 Methods of Contouring

7.4 Uses of Contour Maps

8.1 Introduction and Types

8.2 Aerial Camera and Photo Geometry

8.3 Overlap and Coverage

8.4 Stereoscopy and DEM Generation

8.5 Orthophoto and Digital Elevation Model (DEM)

9.1 Principles of Remote Sensing

9.2 Types of Remote Sensing Systems

9.3 Image Resolution Types

9.4 Indian Remote Sensing Satellites

9.5 Image Interpretation and Spectral Indices

9.6 GIS (Geographic Information System)

10.1 Road / Highway Alignment Survey

10.2 Railway Alignment Survey

10.3 Canal Alignment Survey

10.4 Bridge Survey

10.5 Building Layout

10.6 Culvert Survey and Layout

11.1 Types of Curves

11.2 Simple Circular Curve — Geometry

11.3 Elements of Simple Circular Curve

11.4 Methods of Setting Out Circular Curves

Method 1 — Offsets from Long Chord

Method 2 — Successive Offsets from Chord Produced (Rankine)

Method 3 — Deflection Angle (Rankine's Method) — Most Used

Method 4 — Two Theodolite Method (No Chaining)

11.5 Transition Curves

11.6 Vertical Curves

Chain Surveying Corrections

Compass / Traverse

Levelling

Tacheometry

Field Astronomy

Photogrammetry