Principles and Practice of Surveying Exam (PS) Measurement, Field Data Acquisition, and Error Analysis Syllabus

What is the difference between the direction method and the repetition method of measuring horizontal angles?

Direction method: point to each target and read directions from a fixed circle; angles are differences of directions, good for multiple targets at one station. Repetition method: mechanically accumulate the same angle several times on the circle and divide the total by the number of repetitions to refine precision of a single angle.

In trigonometric leveling, write the formula for the elevation difference between instrument and target using slope distance $S$ and zenith angle $z$.

$$\Delta H = S\cos z + h_i - h_t$$ where $h_i$ is instrument (HI) height and $h_t$ is the target/reflector height. With vertical angle $\alpha$: $\Delta H = S\sin\alpha + h_i - h_t$.

Give the combined curvature-and-refraction correction for trigonometric/differential leveling over distance $D$ (in meters).

$$C_{CR}\approx 0.0675\,D^{2}\ \text{(m, with } D \text{ in km)}$$ Equivalently $C_{CR}=\frac{(1-k)D^2}{2R}$ where $R$ is Earth's radius and $k\approx 0.13$ is the refraction coefficient. Earth curvature lowers the apparent sight; refraction partly offsets it.

In differential leveling, define backsight (BS), foresight (FS), height of instrument (HI), and the basic equations.

BS: rod reading on a point of known elevation. FS: rod reading on a point of unknown elevation. $$HI = \text{Elev}_{known} + BS$$ $$\text{Elev}_{new} = HI - FS$$ Net elevation change over a circuit equals $\sum BS - \sum FS$.

What is the purpose of balancing backsight and foresight distances in differential leveling?

Equal BS and FS distances cancel systematic errors from Earth curvature, atmospheric refraction, and instrument collimation (line-of-sight not horizontal), since these errors are equal and opposite on the two sights of a setup.

Describe the two-peg test and what instrument error it detects/quantifies.

The two-peg test checks a level's collimation error: set up midway between two pegs A and B and read both rods (this difference is true because errors cancel), then set up near one peg and re-read both. Discrepancy between the two computed elevation differences reveals the collimation (line-of-sight tilt) error per unit distance for adjustment.

What is the difference between calibration and field standardization of survey equipment?

Calibration is the formal determination of instrument constants/errors against a known reference (e.g., a certified EDM baseline, leveling collimator), often by a lab or certified facility. Field standardization is the routine in-field checking and adjustment (e.g., two-peg test, tape comparison, prism constant check) to maintain instruments between calibrations.

For an interior-angle closed-polygon traverse with $n$ sides, what is the theoretical sum of interior angles, and how is angular misclosure distributed?

$$\sum \text{interior angles} = (n-2)\times 180^{\circ}$$ The angular misclosure (observed minus theoretical) is distributed, commonly equally, among the angles (or weighted by precision). Acceptable misclosure is often specified as $K\sqrt{n}$ where $K$ is the instrument's least count.

Define departure and latitude of a traverse course of length $L$ with azimuth $\alpha$.

Latitude (north-south component): $\text{Lat}=L\cos\alpha$. Departure (east-west component): $\text{Dep}=L\sin\alpha$. North latitude (+) / South (−); East departure (+) / West (−).

Write the expressions for the linear closure error and the relative precision (accuracy ratio) of a traverse.

Linear misclosure: $$E=\sqrt{(\sum \text{Dep})^2+(\sum \text{Lat})^2}$$ Relative precision: $$\frac{E}{\text{perimeter}}=\frac{1}{\,\text{perimeter}/E\,}$$ expressed as a ratio like $1{:}10000$.

State the Compass (Bowditch) Rule for traverse adjustment and the correction formulas.

The Compass Rule assumes angular and linear precision are equal and distributes closure proportional to course length: $$C_{\text{Lat},i}=-\,(\sum \text{Lat})\frac{L_i}{\sum L}\qquad C_{\text{Dep},i}=-\,(\sum \text{Dep})\frac{L_i}{\sum L}$$ Corrections are subtracted (opposite sign) from each course's latitude and departure.

State the Transit Rule for traverse adjustment and when it is preferred over the Compass Rule.

The Transit Rule distributes closure proportional to the latitude/departure magnitudes: $$C_{\text{Lat},i}=-(\sum \text{Lat})\frac{|\text{Lat}_i|}{\sum|\text{Lat}|},\quad C_{\text{Dep},i}=-(\sum \text{Dep})\frac{|\text{Dep}_i|}{\sum|\text{Dep}|}$$ It is preferred when angular measurements are more precise than linear (distance) measurements.

What is the principle of the Least Squares method for traverse/network adjustment, and what does it minimize?

Least squares is a rigorous, statistically optimal adjustment that minimizes the weighted sum of squares of the residuals: $$\min \sum w_i v_i^2$$ It simultaneously adjusts all observations, handles redundancy and weighting properly, yields a unique solution, and provides error estimates (covariances). It is the only adjustment giving statistically valid uncertainty.

How is the azimuth of the next course computed from the current azimuth and a measured interior/deflection angle?

Using deflection angles: $\text{Az}_{next}=\text{Az}_{prev}\pm \text{deflection}$ (right +, left −). Using interior angles traversing counterclockwise: $\text{Az}_{next}=\text{Az}_{prev}+\text{interior angle}\pm 180^{\circ}$. Always reduce results to the $0^{\circ}$–$360^{\circ}$ range.

Give the inverse coordinate geometry formulas for distance and azimuth between two points $(N_1,E_1)$ and $(N_2,E_2)$.

$$\text{Distance}=\sqrt{(N_2-N_1)^2+(E_2-E_1)^2}$$ $$\text{Azimuth}=\tan^{-1}\!\left(\frac{E_2-E_1}{N_2-N_1}\right)$$ The quadrant of the azimuth is determined by the signs of $\Delta E$ (departure) and $\Delta N$ (latitude).

Give the forward COGO formulas to compute coordinates of a new point from a known point, a distance $L$, and an azimuth $\alpha$.

$$N_2 = N_1 + L\cos\alpha$$ $$E_2 = E_1 + L\sin\alpha$$ This is the basic coordinate computation (forward computation) used to lay out traverse and stakeout points.

Write the coordinate (shoelace) formula for the area of a closed polygon with vertices $(E_i, N_i)$.

$$A=\frac{1}{2}\left|\sum_{i=1}^{n}\left(E_i N_{i+1}-E_{i+1}N_i\right)\right|$$ where vertex $n+1=1$. Equivalently using double meridian distances (DMD method): $A=\frac{1}{2}\sum (\text{DMD}\times \text{Lat})$.

Define redundancy (degrees of freedom) in a survey network and its formula.

Redundancy = number of redundant (extra) observations beyond the minimum needed to determine the unknowns: $$r = m - n$$ where $m$ is the number of observations and $n$ the number of unknowns (independent coordinates). Redundancy enables error detection, blunder isolation, and statistical quality assessment.

What is reliability in network design, and how do internal and external reliability differ?

Reliability is a network's ability to detect and resist undetected blunders. Internal reliability: the smallest blunder detectable in an observation by statistical testing (controlled by redundancy numbers). External reliability: the effect an undetectable blunder would have on the final coordinates. Good geometry and high redundancy improve both.

List key principles of good geodetic/control network design.

Provide adequate redundancy (multiple ties to control), strong geometry (avoid weak/sliver triangles, favor well-conditioned angles), distribute observations to minimize and balance error, connect to a sufficient number of higher-order control points, and ensure each station is over-determined so blunders are detectable. Pre-analysis (simulation) optimizes the design before fieldwork.

Distinguish horizontal control establishment by GNSS versus traverse, and the meaning of densification.

Control can be established by GNSS (static/RTK observations tied to CORS/NSRS) or by conventional traverse/triangulation from existing monuments. Densification is adding lower-order control points within an existing higher-order framework to increase point density for local work, always referenced to and consistent with the higher-order network.

What is the order/class hierarchy of geodetic control, and what does it convey?

Control is classified by orders (First, Second, Third) and classes denoting relative accuracy standards (e.g., FGCS standards), with first-order being the most accurate. Higher-order control governs (is held fixed for) the adjustment of lower-order densification, so accuracy degrades downward through the hierarchy.

What essential metadata and elements must appear in proper survey field notes?

Date, time, weather, crew names and roles, instrument make/serial number, project/station identification, sketch (with north arrow and scale), measured values with units, and remarks. Notes must record observations, sketches, computations/tabulations, and descriptions—kept in real time, in ink, never erased.

State the cardinal rules for keeping survey field notes (legal/archival standards).

Record directly in the field in permanent ink; never erase—draw a single line through errors and rewrite; keep notes legible and complete enough for another surveyor to reconstruct the work; do not copy/recopy notes; number pages; include who/what/where/when/how. Field notes are a legal record.

How are positional accuracy standards expressed under the FGDC/ASPRS framework, and what confidence level is used?

The FGDC National Standard for Spatial Data Accuracy (NSSDA) reports accuracy at the 95% confidence level as a radial (horizontal) or linear (vertical) value, e.g., 'tested X meters horizontal accuracy at 95% confidence.' Horizontal accuracy $\text{Acc}_r=2.4477\,\sigma$ (for circular) and vertical $\text{Acc}_z=1.9600\,\sigma$.

Compute the RMSE-based NSSDA horizontal accuracy from checkpoint errors.

$$RMSE_x=\sqrt{\frac{\sum (x_{data}-x_{check})^2}{n}}$$ similarly $RMSE_y$. Horizontal radial RMSE $RMSE_r=\sqrt{RMSE_x^2+RMSE_y^2}$. NSSDA horizontal accuracy at 95%: $\text{Accuracy}_r \approx 1.7308\times RMSE_r$ (when $RMSE_x\approx RMSE_y$).

Contrast a positional tolerance (relative accuracy) standard with a network (absolute) accuracy standard.

Network (absolute) accuracy is the uncertainty of a point's coordinates relative to the national datum/CORS at 95% confidence. Local (relative) accuracy is the uncertainty between two directly connected adjacent points. ALTA/NSPS surveys, for example, specify an allowable relative positional tolerance between corners.

What factors govern equipment selection (e.g., choosing GNSS RTK vs. total station) for a survey task?

Required accuracy/order, sky visibility and multipath (GNSS needs open sky; total station needs line of sight), distances/terrain, point density, proximity to control/CORS, project budget and schedule, and environment (canopy, urban canyon). RTK suits open areas and rapid topo; total stations suit obstructed sites and high-precision short ranges.

List the primary field safety considerations and PPE for survey crews.

High-visibility apparel and hard hats near traffic/construction, traffic control (cones, signs, flaggers) per MUTCD, awareness of utilities (call-before-you-dig/811), terrain/wildlife/weather hazards, proper lifting, eye protection from laser instruments, and hydration. A job hazard analysis and communication plan precede fieldwork.

Why must EDM and tape distances be reduced to grid (state plane) coordinates, and what two scale factors are involved?

Ground distances must be reduced to the mapping plane for coordinate computations: (1) the elevation (sea-level/ellipsoid) factor $\frac{R}{R+h}$ reduces ground length to the ellipsoid, and (2) the grid scale factor projects ellipsoid to grid. Their product is the combined factor: $$\text{Grid dist}=\text{Ground dist}\times (\text{elevation factor})\times(\text{grid scale factor})$$