5.5 Surveying

What Surveying Tests on the FE

Surveying contributes about 4 to 6 questions: leveling arithmetic, traverse closure, coordinate geometry, curve layout, and a few GPS/GIS and earthwork concepts. All formulas are in the NCEES FE Reference Handbook.

Distance, Angle, and Leveling

Horizontal distance can be measured by taping, electronic distance measurement (EDM), or stadia (distance = K·s + C, where K ≈ 100 is the stadia interval factor and s is the rod intercept). Angles are read with a total station; an azimuth is measured clockwise from north (0°-360°), while a bearing is an acute angle from north or south.

Differential leveling transfers elevation from a known benchmark:

• Height of instrument: HI = elevation of benchmark + backsight (BS)
• New point elevation: Elev = HI − foresight (FS)

Combined: Elev_new = Elev_BM + BS − FS. A backsight is taken on a point of known elevation; a foresight on the point being established.

Traverse and Closure

A closed traverse is a series of connected courses returning to the start. For each course of length L and azimuth α:

• Departure = L · sin α (east-west component)
• Latitude = L · cos α (north-south component)

A perfectly closed traverse has ΣLatitudes = 0 and ΣDepartures = 0. The compass (Bowditch) rule distributes misclosure to each course in proportion to its length.

Coordinate Geometry and Area

With adjusted latitudes and departures, accumulate coordinates (N, E) around the traverse. Compute enclosed area with the coordinate (shoelace) method:

Area = ½ · | Σ ( X_i · (Y_{i+1} − Y_{i−1}) ) |

The DMD (double meridian distance) method is the classical equivalent and also appears in the Reference Handbook.

Curve Layout

Horizontal circular curves are laid out from the point of curvature (PC):

• Length: L = R·Δ (Δ in radians) = R·Δ·(π/180) with Δ in degrees
• Tangent: T = R·tan(Δ/2)
• Long chord: C = 2R·sin(Δ/2)

Deflection-angle staking sets points along the curve from the PC using half the subtended central angle.

GPS and GIS Basics

GPS (Global Positioning System) uses trilateration from at least four satellites; surveying-grade work uses differential or real-time kinematic (RTK) corrections for centimeter accuracy. A Geographic Information System (GIS) stores layered spatial data (vector and raster) referenced to a datum such as NAD83 and a projection such as State Plane.

Earthwork Volumes

Volume between cross-sections uses the average-end-area method:

V = (A₁ + A₂) / 2 · d

where A₁ and A₂ are end cross-sectional areas and d is the distance between them. The prismoidal formula V = d·(A₁ + 4A_m + A₂)/6 is more accurate when a mid-area A_m is given. Remember 1 yd³ = 27 ft³ when converting cut/fill quantities.

Reference Handbook Tip

Leveling, latitude/departure, and curve formulas are under 'Surveying.' Watch units: azimuths are clockwise from north, and the area equation needs consistent sign on coordinates.