Bihar Special Survey Amin cheat sheet

Surveying is classified as plane when the area is under about 250 km²; curvature effects are then negligible for horizontal distances and elevations.

Geodetic surveying accounts for earth curvature and is used for areas larger than roughly 250 km² or for high-precision control networks.

1 chain (Gunter's) = 66 ft = 20.1168 m = 100 links; 1 link = 0.66 ft = 0.201168 m; 10 chains = 1 furlong; 80 chains = 1 mile.

1 acre = 4840 sq yd = 43,560 sq ft = 4046.86 m² = 0.404686 hectare; 1 hectare = 10,000 m² = 2.47105 acres.

1 mile = 1.609344 km = 1760 yd = 80 chains; 1 nautic mile = 1.852 km; 1 m = 3.28084 ft = 39.3701 in.

Scale: RF = map distance / ground distance; a 1:2500 scale means 1 cm on map = 25 m on ground; 1:50000 means 1 cm = 500 m.

Errors: systematic (cumulative, correctable by calibration), accidental (random, reduced by repetition), gross (mistakes, detected by checks).

Precision vs accuracy: precision is repeatability; accuracy is closeness to true value; a survey can be precise but biased.

Scale of a survey map is chosen by purpose: 1:1000 to 1:2500 for cadastral detail; 1:10000 to 1:50000 for topographical reconnaissance.

Metric chain: 20 m or 30 m, links of 0.2 m or 0.3 m; tallies at every 5 m; brass handle at each end; chain length measured between outside of handles.

Chain testing: compare with a standard steel tape on level ground; correction per chain = (L − L')/L' × measured length (L' true, L nominal).

Ranging rods: 2 m or 3 m, painted in 0.2 m bands alternating red/white/black; used for ranging and line marking.

Cross-staff / optical square: sets out 90° offsets; optical square uses double reflection and gives 90° between lines of sight.

Prismatic compass: graduated in quadrantal bearings (0–90° from N or S toward E or W); magnetic needle points magnetic north; local attraction detected by FB−BB difference of 180°.

Total station: integrates EDM and electronic theodolite; measures slope distance, zenith angle, and computes horizontal distance and reduced level; needs prism constant and atmospheric correction.

Dumpy level: fixed telescope with bubble tube; tilting level allows small tilting of telescope for quick bubble centring; automatic level uses a compensator in place of the bubble tube.

Levelling staff: self-reading staff with E-pattern graduations in 5 mm or 10 mm; reading to 1 mm with a micrometer staff.

GPS/GNSS for control: static mode for high precision (cm), RTK for real-time cm accuracy; needs at least 4 satellites for a 3D fix.

Chain survey: base line is the longest line, measured most carefully; check lines (tie lines) verify the framework; offsets are perpendicular distances from chain line to objects.

Offset limits: for a 20 m chain offsets up to 15 m may be measured by eye or with an offset rod; beyond that use a cross-staff or optical square.

Well-conditioned triangle: angles between 30° and 120° preferred; no angle less than 30°; base line should be the longest side.

Plane table methods: radiation (single station, radial rays), intersection (two stations, no measuring), traversing (successive stations), and resection (three-point problem).

Orientation of plane table: by magnetic needle (trough compass) or by backsight; backsight is more accurate and is preferred when a fixed station is visible.

Three-point problem: locate table position from three known points; solution by trial and error, mechanical (tracing paper), or graphical (Bessel's) method.

Two-point problem: table position fixed using two known points plus a third auxiliary point; used when the third known point is inaccessible.

Chain surveying is suited to small, open, fairly level areas; it is unsuitable for wooded, hilly, or built-up areas where offsets are obstructed.

Plane table is unsuitable for rainy or windy weather and for very large areas because errors accumulate in orientation.

Reduced level (RL) of a point = HI − staff reading; Height of Instrument (HI) = RL of benchmark + backsight reading.

Rise and fall method: rise if next reading is smaller than previous, fall if larger; arithmetic check: ΣBS − ΣFS = ΣRise − ΣFall = last RL − first RL.

HPC (collimation) method: HI = RL + BS; RL of point = HI − FS or IS; check: ΣBS − ΣFS = last RL − first RL.

Curvature correction = 0.0785 d² m (d in km); refraction correction = 1/7 of curvature correction; combined correction = −0.0673 d² m.

Sensitiveness of a level bubble: angle per division = (length of one division)/(radius of curvature); expressed in seconds of arc.

Contour interval: vertical distance between successive contours; small interval for flat ground and detailed work, large interval for steep or reconnaissance surveys.

Characteristics of contours: contours of different elevations never cross (except overhanging cliff), closed contours indicate a hill or depression, spacing indicates slope steepness.

Reciprocal levelling eliminates errors due to curvature, refraction, and instrument adjustment when a river or valley must be crossed.

Benchmark: a fixed reference of known RL; GTS benchmark is the most precise, followed by permanent and temporary benchmarks.

Theodolite parts: telescope, vertical circle, horizontal circle, upper and lower plates, levelling head (three foot screws), trunnion axis, vertical axis, tangent and clamp screws.

Transit theodolite: telescope can be revolved in the vertical plane through 180°; non-transit cannot; transit is the common Indian field type.

Face left (direct) and face right (reversed) observations: mean of both faces eliminates errors of collimation, trunnion axis, and vertical axis.

Fundamental lines: vertical axis, horizontal axis (trunnion), line of collimation, axis of bubble tube; they must be mutually perpendicular in adjustment.

Temporary adjustments: setting, levelling with foot screws, focusing the eyepiece (for cross hairs) and objective (for object), and eliminating parallax.

Permanent adjustments: plate level axis perpendicular to vertical axis; line of collimation perpendicular to horizontal axis; horizontal axis perpendicular to vertical axis; altitude bubble axis parallel to line of collimation.

Measurement of horizontal angle: by repetition (for precision, using the repeating method) or by direction method; mean of face left and face right reduces errors.

Vertical angle measurement: with the vertical circle; zenith angle + altitude = 90°; index error detected by face left/face right readings.

Traversing with a theodolite: measure deflection or included angles; closed traverse angle check: sum of interior angles = (2n − 4) × 90°.

Latitude = L cos θ (northing positive, southing negative); Departure = L sin θ (easting positive, westing negative); θ is the reduced bearing.

Closed traverse check: Σlatitude = 0 and Σdeparture = 0; misclosure = √(ΣL² + ΣD²).

Bowditch (compass) rule: correction to latitude = −(ΣL / Σperimeter) × length of side; correction to departure = −(ΣD / Σperimeter) × length of side.

Transit rule: correction to latitude = −ΣL × (latitude of side / Σ|latitude|); used when linear measurement is more precise than angular.

Interior angle check: Σ interior angles = (2n − 4) × 90°; exterior = (2n + 4) × 90°; deflection angles sum = 360° for a closed traverse.

Included angle = back bearing of previous line − fore bearing of next line (measured clockwise); FB − BB = 180° for the same line.

Conversion: RB to WCB - NE: WCB = RB; SE: WCB = 180° − RB; SW: WCB = 180° + RB; NW: WCB = 360° − RB.

Traverse area by coordinates: 2A = Σ(Xᵢ × Yᵢ₊₁ − Xᵢ₊₁ × Yᵢ); area is half the absolute value; independent of the starting point.

Omitted measurements: a single omitted length or bearing can be computed from the closing conditions ΣL = 0 and ΣD = 0; two omitted quantities need two equations.

Cadastral survey maps each parcel with a unique plot number (khasra/khata), owner, area, and boundary; it forms the basis of land revenue records.

Bihar land records are maintained by the Department of Revenue and Land Reforms; key records include the Jamabandi (record of rights), Khatiyan (record of rights), and Register II.

Khatiyan (record of rights) records the tenant, landlord, nature of right, and area; Jamabandi is the working account of rents and dues.

Survey settlement operations in Bihar historically followed the Bengal system; the current resurvey uses total station and GNSS for parcel coordinates.

Plot area computation: regular parcels by geometric formulas; irregular parcels by dividing into triangles or by the coordinate (shoelace) method.

Boundary disputes: cadastral maps and field books (khatian and field measurement book) are primary evidence; demarcation uses permanent boundary marks (stone or concrete pillars).

Scale for cadastral maps in India typically 1:1000, 1:2000, or 1:4000 depending on parcel density; urban areas use larger scales.

Chain of measurement in cadastral work: control traverse first, then parcel boundaries tied to control; every parcel must close on the control network.

Amin duties: field measurement, preparation of field book and maps, demarcation of boundaries, and reporting to the revenue authority.

Field book: record of chainages, offsets, and remarks; entries in pencil, no erasures; errors struck through and rewritten with initials.

Conventional signs: contours as brown lines, water bodies blue, roads red or double lines, buildings black blocks, boundaries as chain-dotted lines.

Plotting: choose scale so the survey fits the sheet with a north arrow, title block, scale bar, and legend; use a graphical scale for reproduction.

Contour maps show relief; a hachure or spot height supplements contours where the terrain is flat.

Traverse plot: plot by coordinates or by bearings and distances; close the traverse graphically and check against the computed misclosure.

Field records must be contemporaneous; the field book and level book are legal documents in revenue and engineering disputes.

Reduction of levels: enter BS, IS, FS in the level book; compute HI or rise/fall; apply arithmetic checks before leaving the field.

Map projection for large areas: transverse Mercator (used in Indian topographic maps) and Lambert conformal conic; small cadastral sheets use plane coordinates.

Digital records: total station data files, CAD drawings, and GIS layers now supplement the traditional field book; backup and metadata are mandatory.

Area of triangle: ½ × base × height; Heron's formula A = √(s(s−a)(s−b)(s−c)) with s = (a+b+c)/2.

Trapezoidal rule for area: A = h[(y₀ + yₙ)/2 + y₁ + y₂ + … + yₙ₋₁]; Simpson's rule (odd number of ordinates): A = h/3[(y₀ + yₙ) + 4(sum of odd) + 2(sum of even)].

Volume by prismoidal formula: V = h/6(A₁ + 4Aₘ + A₂); by end areas: V = h(A₁ + A₂)/2.

Trigonometric ratios: sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse; tan θ = opposite/adjacent; sin²θ + cos²θ = 1.

Sine rule: a/sin A = b/sin B = c/sin C; cosine rule: c² = a² + b² − 2ab cos C.

Pythagoras: c² = a² + b²; used for offset and diagonal checks in chain surveying.

Mean, median, mode: mean = Σx/n; median is the middle value of ordered data; mode is the most frequent value.

Percentage error = (measured − true)/true × 100; relative error expressed as 1 in n.

Slope correction: correction = −h²/(2L) for small height difference h over length L; exact correction = L(1 − cos θ).

Bihar shares boundaries with Uttar Pradesh (west), Nepal (north), West Bengal (east), and Jharkhand (south).

Capital: Patna; Bihar Day is celebrated on 22 March, marking the separation of Bihar from Bengal in 1912.

Major rivers: Ganga (flows east–west through the middle), Gandak, Kosi, Son, Punpun, Bagmati, and Ghaghara (border with UP).

Kosi is known as the 'Sorrow of Bihar' for its shifting course and floods; the Gandak and Bagmati also cause flooding.

Bihar's physiographic divisions: Shivalik foothills (north-west), Gangetic plain (central), and the southern plateau (Chotanagpur fringe).

Bihar has three main agro-climatic zones: Zone I (north-west alluvial plain), Zone II (north-east alluvial plain), and Zone III (south Bihar alluvial plain).

Nalanda, Bodh Gaya, Rajgir, Vaishali, and Vikramshila are major historical and Buddhist heritage sites in Bihar.

Bihar's land revenue administration is headed by the Board of Revenue; the Divisional Commissioner and District Magistrate supervise survey and settlement.

Bihar Diwas, Rajgir Mahotsav, and Sonepur Mela are prominent state cultural events; Sonepur hosts Asia's largest cattle fair.

Number series: check differences, ratios, squares/cubes, and alternating patterns before assuming a simple progression.

Coding-decoding: apply the letter-shift rule consistently; A=1 … Z=26 for positional arithmetic.

Blood relations: draw a family tree; vertical lines for generations, horizontal for siblings, and mark gender explicitly.

Direction sense: track net displacement using north/south and east/west components; use Pythagoras for straight-line distance.

Ranking: total = (rank from top + rank from bottom) − 1; for a person between two ranks, number between = difference of ranks − 1.

Calendar: odd days - ordinary year 1, leap year 2, century 400 years 0; day of week shifts by the number of odd days.

Clock: angle between hands = |30H − 5.5M| degrees; hands coincide 11 times in 12 hours.

Syllogism: use Venn diagrams; a conclusion is valid only if it holds in every possible diagram consistent with the premises.

Data interpretation: read units and scale carefully; compute percentage change as (new − old)/old × 100.