Principles and Practice of Surveying Exam (PS) Plats, Plans, Subdivisions, and Spatial Data Systems Syllabus

Using the arc definition, relate the degree of curve $D$ to the radius $R$ (US, 100 ft arc).

$$R = \frac{100 \times 180^{\circ}}{\pi D} = \frac{5729.58}{D}\ \text{ft}$$ The degree of curve $D$ is the central angle subtended by a 100 ft arc.

What essential graphic and textual content must appear on a recordable plat?

Title/name of subdivision, north arrow and scale, bearings and distances of all lines, lot and block numbers, dimensions and areas, streets and ROW widths, easements, monuments found/set, legal description, dedications, surveyor's certificate and seal, owner's acknowledgment, and approval/recording blocks.

What is monumentation on a plat, and why are monuments set at controlling points?

Monumentation is the placement of physical markers (iron pins, concrete monuments, etc.) at block corners, lot corners, points of curvature, and angle points. They provide permanent, recoverable physical evidence of the boundaries created, controlling future retracement.

What does 'recording' a plat accomplish legally?

Recording files the approved final plat in the public land records (county recorder's office), giving constructive notice of the new lots, dedications of streets/easements to the public, and creating the legal lots that can then be conveyed by lot-and-block description.

In GIS, distinguish the vector data model from the raster data model.

The vector model represents features as points, lines, and polygons with explicit coordinates and attributes—ideal for discrete features like parcels. The raster model represents space as a grid of cells (pixels), each with a value—ideal for continuous data like elevation or imagery.

What is topology in a GIS vector data model?

Topology defines and stores the spatial relationships between features—adjacency, connectivity, and containment—independent of exact coordinates. It enforces rules (e.g., polygons must not overlap, lines must connect at nodes) ensuring data integrity for parcels and networks.

What is the surveyor's role in a GIS / land information system?

Surveyors provide the geometrically accurate, properly georeferenced parcel and control data (the 'authoritative' spatial framework), define datums/coordinate systems, supply metadata and accuracy statements, and ensure legal boundary integrity—the foundation upon which other GIS layers are registered.

What is metadata in a spatial dataset, and name three components it typically documents.

Metadata is 'data about data' describing a dataset's content and quality. Components include: source/lineage, coordinate system/datum, positional accuracy, resolution/scale, collection date, attribute definitions, and responsible party/contact.

Differentiate accuracy from precision in spatial data.

Accuracy is the closeness of a measurement to the true (or accepted) value. Precision is the closeness of repeated measurements to one another (repeatability). Data can be precise but inaccurate (consistently biased).

What does the National Standard for Spatial Data Accuracy (NSSDA) report, and at what confidence level?

NSSDA reports positional accuracy as a root-mean-square error statistic expressed at the 95% confidence level (e.g., 'tested X meters horizontal accuracy at 95% confidence'). It replaced the older National Map Accuracy Standards' pass/fail approach.

Give the horizontal RMSE formula used to assess positional accuracy from $n$ checkpoints with errors in $x$ and $y$.

$$RMSE_r = \sqrt{RMSE_x^{2} + RMSE_y^{2}}, \quad RMSE_x = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i - x_{i,\text{check}})^{2}}$$

Differentiate active and passive remote sensing systems with examples.

Passive systems detect natural energy (reflected sunlight or emitted thermal), e.g., aerial photography and most satellite multispectral imagers. Active systems emit their own energy and measure the return, e.g., LiDAR and radar (SAR).

In photogrammetry, what is the relationship between photo scale, camera focal length $f$, flying height above ground $H$?

$$\text{Scale} = \frac{f}{H} = \frac{1}{S}$$ where $H$ is the flying height above the mean ground (terrain) and $f$ is the focal length, in consistent units.

Define stereoscopic parallax and its use in photogrammetry.

Parallax is the apparent shift in position of an object between two overlapping photographs taken from different camera stations, measured parallel to the flight line. The difference in parallax between points is used to compute elevations/heights (relief).

What are typical end lap (forward overlap) and side lap percentages for aerial photogrammetric coverage?

End lap (forward overlap) is typically about 60% along the flight line, and side lap between adjacent flight lines is typically about 30%. The overlap enables stereoscopic viewing and continuous stereo coverage.

What is LiDAR and what does the acronym stand for?

LiDAR (Light Detection and Ranging) is an active remote-sensing technology that emits laser pulses and measures their round-trip travel time to determine range, producing dense 3D point clouds of terrain and surface features.

For a LiDAR pulse, give the equation relating range $R$ to the round-trip travel time $t$ and the speed of light $c$.

$$R = \frac{c\,t}{2}$$ The factor of $\tfrac{1}{2}$ accounts for the two-way (out-and-back) travel of the pulse.

Differentiate a Digital Elevation Model (DEM/DTM) from a Digital Surface Model (DSM).

A DTM/DEM represents the bare-earth ground surface with vegetation and buildings removed. A DSM represents the top reflective surface including buildings, trees, and other above-ground features. LiDAR first returns build a DSM; last/ground returns build a DTM.

What are LiDAR 'first return' and 'last return,' and what does each typically capture?

A single laser pulse can produce multiple returns. The first return reflects from the highest object (tree canopy, rooftop); the last return often reaches the bare ground beneath vegetation. Multiple returns enable separating surface (DSM) from terrain (DTM).

What are the two types of vertical curves, and how are they defined?

Crest curves (where the grade transitions from positive to negative, i.e., over a hill) and sag curves (negative to positive, i.e., through a valley). Both are typically equal-tangent parabolic curves connecting two grades.

For an equal-tangent parabolic vertical curve, give the elevation equation along the curve in terms of station $x$ from the BVC.

$$y = y_{BVC} + g_1 x + \frac{(g_2 - g_1)}{2L}x^{2}$$ where $g_1, g_2$ are grades (decimal), $L$ is curve length (same units as $x$), and $x$ is distance from the BVC.

Give the formula for the rate of grade change $r$ on a parabolic vertical curve and its use.

$$r = \frac{g_2 - g_1}{L}$$ where $r$ is the rate of change of grade per station (or per unit length). It is used to compute elevations, locate the high/low point, and check for adequate sight distance.

How do you locate the station of the high or low point of a vertical curve from the BVC?

$$x = -\frac{g_1}{r} = \frac{g_1\,L}{g_1 - g_2}$$ Distance $x$ from the BVC to the turning point, where the slope (first derivative) equals zero.

State the average-end-area formula for earthwork volume between two cross sections.

$$V = \frac{L}{2}\,(A_1 + A_2)$$ where $A_1, A_2$ are the end cross-sectional areas and $L$ is the distance between them. Volume is typically converted to cubic yards by dividing by 27.

Give the prismoidal formula for earthwork volume and state when it is preferred.

$$V = \frac{L}{6}\,(A_1 + 4A_m + A_2)$$ where $A_m$ is the area of the middle section. It is more accurate than average-end-area for curved or warped (prismoidal) shapes; average-end-area generally overestimates volume.

What is the difference between cut, fill, and a balance point (grade line balancing) in earthwork?

Cut is material excavated (existing ground above grade); fill is material placed (grade above existing ground). A balance point is a station where cumulative cut equals cumulative fill (mass-haul curve crosses zero), minimizing haul/borrow/waste.

What is a shrinkage (or swell) factor in earthwork computation?

Excavated soil changes volume when handled. A swell factor accounts for bulking of loose excavated material; a shrinkage factor accounts for compacted fill occupying less volume than in-situ bank material. Example: 1.1 (10%) shrinkage means 1.1 yd³ of cut yields 1.0 yd³ of compacted fill.

What is construction staking, and name two common types of stakes set.

Construction staking transfers design plan information to the ground so contractors can build to line and grade. Common stakes include slope stakes (limits of cut/fill at the daylight line), offset/hub stakes, grade stakes, and centerline alignment stakes.

What is an as-built (record) survey and why is it performed?

An as-built survey measures and documents the actual horizontal and vertical locations of constructed improvements after building. It verifies conformance to design, records deviations, and provides a permanent record for owners, agencies, and future utility/maintenance work.

What is a FEMA Elevation Certificate, and what key elevations does it record?

It is a FEMA form documenting a building's elevation relative to flood risk for floodplain management and flood insurance rating. It records the Base Flood Elevation (BFE), lowest floor elevation, lowest adjacent grade, and the structure's flood zone, certified by a licensed surveyor or engineer.

Define Base Flood Elevation (BFE) and the 100-year flood it represents.

The BFE is the computed water-surface elevation of the base flood—the flood having a 1% chance of being equaled or exceeded in any given year (the '100-year flood'). It is the regulatory standard used in the Special Flood Hazard Area (SFHA) for floodplain management.