2.3 Control Surveys, Networks, Traverses, and Benchmarks
Key Takeaways
- Horizontal control is built with traverses (and GNSS networks); vertical control is built with differential leveling between benchmarks.
- A closed traverse provides a check: angular misclosure should be near n×(instrument rating), and linear misclosure is reported as a ratio of error to perimeter (e.g., 1:10,000).
- The compass (Bowditch) rule distributes linear closure in proportion to leg length; the transit rule favors angles; least squares is the rigorous, weighted method.
- Benchmarks and monuments are permanent vertical/horizontal references; differential leveling balances backsight and foresight distances to cancel collimation error.
What Control Is and Why It Comes First
Control surveys establish a framework of points with known, reliable coordinates and elevations that every later observation — topographic, construction, cadastral — references. Horizontal control fixes northing/easting (typically on a State Plane or NAD 83 system) and is built with traverses, triangulation, or GNSS networks. Vertical control fixes elevation on NAVD 88 and is built with differential leveling run between benchmarks.
Control is organized by order and class (precision tiers): primary control is observed to higher accuracy and then densified with lower-order points for production work. A core principle is working from the whole to the part — establish strong control first, then fill in detail, so errors do not accumulate uncontrolled. Mixing datums or orders without documentation is a classic blunder the exam probes.
Traverse Closure and Adjustment
A closed traverse returns to its start (loop) or ties between two known points (link), giving an independent check. Two misclosures are evaluated:
- Angular misclosure — the sum of interior angles should equal (n − 2) × 180°. The leftover is distributed (often equally) among angles; it should be on the order of the instrument rating times √n.
- Linear misclosure — after computing latitudes and departures, the closure in northing/easting gives a linear misclosure, reported as a relative precision ratio: error of closure divided by total perimeter, e.g., 1:10,000. Smaller closure over a longer perimeter means a better ratio.
Adjustment methods distribute the linear misclosure:
| Method | Distributes closure in proportion to | Note |
|---|---|---|
| Compass (Bowditch) rule | Leg length | Most common; assumes angles and distances of comparable quality |
| Transit rule | Latitude/departure magnitude | Favors angle observations |
| Crandall / least squares | Statistical weights | Least squares is the rigorous, redundancy-using standard |
The compass rule is the FS default for a simple traverse; least squares is the rigorous, weighted method preferred when observations have mixed quality or there is redundancy in a network.
Benchmarks and Differential Leveling
Benchmarks are permanent, stable monuments of known elevation; monuments more generally mark horizontal positions. Differential leveling transfers elevation by reading a graduated rod on a known point (backsight, BS) and on the unknown point (foresight, FS):
HI = elevation(known) + BS
elevation(new) = HI − FS
where HI is the height of instrument (line of sight). A key field procedure is balancing backsight and foresight distances: if BS and FS sight lengths are equal, residual collimation error (line of sight not truly horizontal) adds to one reading and subtracts from the other and cancels. A closed level loop returns to its starting benchmark; the misclosure is distributed (often proportional to distance leveled) and compared to a tolerance such as C√K mm, with K in kilometers. Turning points should be on firm, well-defined objects, and the rod kept vertical.
Recognizing an unbalanced setup or an unchecked loop as the error source is exactly what the FS exam rewards.
A closed-loop traverse has a total perimeter of 2,400 ft and a linear misclosure of 0.24 ft. What is the relative precision?
In differential leveling, why are backsight and foresight sight distances kept approximately equal?
Which traverse adjustment method distributes linear misclosure in proportion to the length of each leg?
For a five-sided closed traverse, the interior angles should sum to:
Orders of Accuracy and Densification
Control is not one tier but several. Order and class define the accuracy a network must meet, and a project ties new work to the highest reliable control available — often NGS-published marks or CORS — then densifies with lower-order points spaced for production. Working from high-order to low-order control prevents the propagation of error and keeps every later measurement on a single, documented datum.
| Control type | Built by | Datum example |
|---|---|---|
| Horizontal control | Traverse, triangulation, GNSS network | NAD 83 / State Plane |
| Vertical control | Differential leveling | NAVD 88 |
| Densification | Lower-order traverse / RTK from primary | Same as primary |
A network adjustment (typically least squares) is the rigorous way to combine redundant observations — traverse angles and distances, GNSS vectors, leveled differences — into one consistent set of coordinates while producing error ellipses and statistics that flag weak or blundered observations. This is why least squares is preferred over the compass or transit rule whenever the data has redundancy or mixed quality: it weights each observation by its precision instead of assuming all are equal.
The FS exam expects you to know that a closed figure provides the check, while the adjustment merely distributes the misclosure that the check revealed — a traverse that does not close on a known point or benchmark has no independent verification at all.
Level Loop Tolerances and Blunders
Vertical control accuracy is judged against a distance-based tolerance of the form C√K millimeters, where K is the one-way distance leveled in kilometers and C reflects the order of leveling (smaller C for higher-order work). A loop misclosure within tolerance is distributed and accepted; one outside tolerance signals a blunder — a misread rod, an unstable turning point, a sinking tripod, or a rod not held vertical — that must be found and reobserved, not simply adjusted away.
Distinguishing acceptable random misclosure from an unacceptable blunder is a recurring FS judgment, and it is why redundant, closed leveling runs are required for any control-grade elevation.