Fundamentals of Surveying Exam (FS) Construction, Engineering, and Specialty Surveys Syllabus

In horizontal curve geometry, what do PC, PI, and PT stand for?

PC = Point of Curvature (beginning of curve, where tangent meets curve); PI = Point of Intersection (where the two tangents intersect); PT = Point of Tangency (end of curve, where curve meets the forward tangent).

How is the station of the PT computed from the station of the PC and the curve length?

$$\text{Sta}_{PT}=\text{Sta}_{PC}+L$$ The PT is found by adding the curve length $L$ along the curve to the PC station (NOT by adding $2T$ through the PI).

What is the deflection angle to any point on a horizontal curve from the PC, in terms of the arc length $\ell$ to that point?

$$\delta=\frac{\ell}{2R}\ \text{(radians)}=\frac{D\,\ell}{200}\ \text{(degrees)}$$ The deflection from the back tangent equals half the central angle subtended by the arc.

What is superelevation on a horizontal curve and what is its purpose?

The banking (cross-slope) of the roadway on a curve so the pavement is higher on the outside edge. It counteracts centrifugal force, allowing vehicles to negotiate the curve at design speed with reduced reliance on side friction.

Give the basic equation relating superelevation rate $e$, side friction $f$, design speed $V$, and curve radius $R$.

$$e+f=\frac{V^{2}}{gR}$$ In US customary form with $V$ in mph and $R$ in ft: $$e+f=\frac{V^{2}}{15R}$$

What defines an equal-tangent vertical (parabolic) curve, and why is a parabola used?

It has equal horizontal tangent lengths each side of the vertex (PVI), with the curve length $L$ split evenly. A parabola is used because it produces a constant rate of change of grade, giving a smooth, uniform vertical acceleration.

For an equal-tangent vertical curve, write the elevation equation along the curve.

$$y=y_{PVC}+g_{1}x+\frac{(g_{2}-g_{1})}{2L}x^{2}$$ where $x$ is horizontal distance from the PVC, $g_{1},g_{2}$ are entering/exiting grades, and $L$ is the curve length.

What is the rate of change of grade $r$ on a vertical curve, and how is it used?

$$r=\frac{g_{2}-g_{1}}{L}$$ (per station). It is constant along the parabola and is used in the elevation equation $y=y_{PVC}+g_{1}x+\frac{r}{2}x^{2}$ and to evaluate ride comfort/sight distance.

How do you locate the high or low point of a vertical curve (the turning point)?

Set the first derivative of the elevation equation to zero. The distance from the PVC is $$x_{t}=\frac{-g_{1}L}{g_{2}-g_{1}}=\frac{-g_{1}}{r}$$ valid when a true high/low point exists (grades of opposite sign).

Distinguish a crest vertical curve from a sag vertical curve by the sign of the grades.

A crest curve occurs when the algebraic difference $A=g_{2}-g_{1}$ is negative (e.g., +grade to -grade), forming a hill. A sag curve occurs when $A=g_{2}-g_{1}$ is positive (e.g., -grade to +grade), forming a valley.

What is the K-value of a vertical curve and how is it defined?

$$K=\frac{L}{A}$$ where $A=|g_{2}-g_{1}|$ in percent and $L$ is the curve length in feet. $K$ is the horizontal distance (ft) required to change grade by $1\%$; it is used to design curves for required sight distance.

What is the middle ordinate (mid-curve offset) of an equal-tangent vertical curve from the PVI?

$$m=\frac{A\,L}{8}$$ (with $A$ in decimal grade and $L$ in same units, or $\frac{AL}{800}$ with $A$ in percent and $L$ in ft) — the vertical offset from the PVI tangent intersection to the curve at its midpoint.

What is the primary controlling design criterion for crest vertical curves versus sag vertical curves?

Crest curves are controlled by stopping sight distance (line of sight over the crest). Sag curves are typically controlled by headlight sight distance at night (and also comfort, drainage, and overhead clearance).

What is a spiral (transition) curve and why is it inserted between a tangent and a circular curve?

A curve whose radius varies continuously from infinity (at the tangent) to the radius $R$ of the circular curve. It provides a gradual introduction of curvature and superelevation, eliminating the abrupt lateral acceleration of a tangent-to-circle transition.

What geometric property defines the clothoid (Euler spiral) used as a highway transition curve?

Its curvature increases linearly with arc length: the radius of curvature $\rho$ is inversely proportional to distance $\ell$ along the spiral, so $\rho\,\ell=R\,L_{s}=\text{constant}=A^{2}$.

What is the spiral angle (central angle of the spiral) $\theta_{s}$ in terms of spiral length $L_{s}$ and end radius $R$?

$$\theta_{s}=\frac{L_{s}}{2R}\ \text{(radians)}=\frac{L_{s}\,D}{200}\ \text{(degrees)}$$ where $D$ is the degree of the circular curve.

In a spiraled curve layout, what do the points TS, SC, CS, and ST denote?

TS = Tangent-to-Spiral (start of entry spiral); SC = Spiral-to-Curve (entry spiral meets circular arc); CS = Curve-to-Spiral (circular arc meets exit spiral); ST = Spiral-to-Tangent (end of exit spiral).

What is the shift (throw) $p$ of a spiral curve and what does it represent?

$$p\approx\frac{L_{s}^{2}}{24R}$$ It is the small inward offset of the circular curve from the tangent caused by inserting the spiral; the circular arc is shifted toward the center by $p$ to accommodate the transition.

What general accuracy standards classify geodetic control surveys in the US?

The FGCS/FGCC orders: First Order (highest accuracy, e.g. $1{:}100{,}000$), Second Order Class I ($1{:}50{,}000$) and Class II ($1{:}20{,}000$), and Third Order Class I ($1{:}10{,}000$) and Class II ($1{:}5{,}000$), defined by relative positional accuracy between control points.

How are modern GNSS/GPS relative accuracy standards (FGDC) expressed, and how do they differ from older closure-ratio standards?

They are expressed as local and network accuracy at the $95\%$ confidence level in absolute distance terms (e.g., $\pm 1$ cm local, network accuracy relative to the national datum), rather than as a proportional closure ratio like $1{:}100{,}000$ between two points.

What does a relative accuracy/closure standard of $1{:}50{,}000$ mean for a control survey?

That the misclosure (positional error) is no more than $1$ unit per $50{,}000$ units of distance surveyed — e.g., a maximum error of $1$ ft in $50{,}000$ ft of line, or equivalently $0.02$ ft per $1000$ ft.

What is the difference between a horizontal datum and a vertical datum in control surveying?

A horizontal datum (e.g., NAD83) defines latitude/longitude/Northing-Easting positions on a reference ellipsoid; a vertical datum (e.g., NAVD88) defines orthometric heights/elevations referenced to a geoid/equipotential surface.

What is a deformation (monitoring) survey?

A repeated survey of a structure or natural feature over time to detect and measure movement (settlement, displacement, tilt, or strain) by comparing positions of monitoring points between epochs against stable reference points.

In deformation monitoring, distinguish reference (datum) points from object (target) points.

Reference points are located on stable ground outside the zone of expected movement and assumed fixed; object points are placed on the monitored structure and their position changes relative to the reference network reveal deformation.

How is detected movement distinguished from measurement noise in a deformation survey?

By statistical testing: a displacement is considered significant only if it exceeds the survey's measurement uncertainty (e.g., exceeds $2\sigma$ or $3\sigma$ at a chosen confidence level). Movement within the error band is treated as noise, not real deformation.

Name three instruments/techniques commonly used for high-precision deformation monitoring.

Precise (geodetic) total stations with automatic target recognition, precise digital/geodetic leveling, GNSS arrays, and complementary geotechnical sensors such as tiltmeters, extensometers, and InSAR/laser scanning.

What is a hydrographic survey?

A survey to map and measure the physical features of bodies of water and their adjacent land — water depth, bottom configuration, shoreline, currents, and hazards — primarily to support navigation, dredging, and marine construction.

What is bathymetry and what is the primary instrument used to measure it?

Bathymetry is the measurement and mapping of underwater depth (the topography of the seabed/lakebed). It is primarily measured with an echo sounder (single-beam or multibeam sonar) that times acoustic pulses to the bottom.

How does a single-beam echo sounder compute water depth from a sound pulse?

$$d=\frac{c\,t}{2}$$ where $c$ is the speed of sound in water (about $1500$ m/s, varies with temperature, salinity, pressure) and $t$ is the two-way travel time; division by 2 accounts for the round trip.

Contrast single-beam and multibeam echo sounders for bathymetric surveying.

A single-beam sounder measures depth directly below the vessel along a single track, giving sparse line coverage. A multibeam system emits a fan of beams perpendicular to the track, giving a wide swath of full-bottom coverage in one pass, far higher resolution and efficiency.

In hydrographic surveying, why must measured depths (soundings) be corrected for tide/water-level, and to what are they reduced?

Because the water surface changes height with tides, the raw sounding from the transducer must be reduced by the instantaneous water level to a fixed reference datum — typically a chart datum such as Mean Lower Low Water (MLLW) — so charted depths are consistent and conservative for navigation.