Route surveying and higher surveying form the critical foundation for planning, designing, and constructing linear infrastructure such as highways, railways, pipelines, canals, and transmission lines. While basic surveying (plane surveying) treats the earth as a flat plane for small-scale projects, higher surveying (geodetic surveying) accounts for the true shape of the earth, allowing for precise measurements over vast distances. A fundamental element of route design is the simple horizontal curve, which smoothly connects straight path segments.

Route surveys differ slightly depending on the specific type of linear infrastructure:

In route surveying, a continuous referencing system called "stationing" (or chainage) is used to pinpoint locations along the centerline of the proposed facility.

A "full station" typically represents a horizontal distance of 100 meters (or 100 feet in the US system) or sometimes 20 meters in certain metric conventions. A point located 1,234.56 meters from the starting point ($0+000$) is designated as Station $1+234.56$ (if using 1000m km stations) or $12+34.56$ (if using 100m stations). This means it is 12 full stations (1,200 meters) plus a "plus station" of 34.56 meters.

The reconnaissance survey is an extensive preliminary study of the entire area that might be used for the route. Its primary objective is to identify one or more feasible routes between the starting and ending points.

During this phase, surveyors rely heavily on existing maps, aerial photographs, satellite imagery, and geographic information systems (GIS). Modern methods frequently use Unmanned Aerial Vehicles (UAVs) or drones to rapidly capture high-resolution imagery and preliminary topography. Field visits may be conducted to verify map data, identify critical control points (like mountain passes or river crossings), and assess major obstacles. The output is a selection of the most promising alternatives for further detailed study.

The preliminary survey is a highly detailed instrumental survey of the alternative routes selected during reconnaissance. The goal is to collect precise topographic data to prepare accurate maps and profiles.

This phase involves establishing a primary traverse, running levels to determine elevations, and capturing cross-sectional data. The resulting topographic map (often called a strip map) is used by engineers to design the paper location of the facility, compare the alternatives, and select the final, single optimal route.

Once the final route is designed on paper, the location survey is conducted to transfer this design from the plans to the actual terrain.

This involves staking out the centerline of the facility, including all tangents, horizontal curves, and points of intersection. Precise leveling is performed along the staked centerline to establish the profile, and cross-sections are taken to determine earthwork quantities. The established stakes serve as a guide for the subsequent construction phase.

The construction survey provides the critical control for the actual building of the facility. Surveyors replace stakes that are destroyed during earthmoving operations and set detailed stakes for various structures.

Tasks include setting slope stakes to mark the limits of cut and fill, establishing grade stakes for the finished roadbed, and providing precise layout for bridges, culverts, and retaining walls. As-built surveys are also conducted upon completion to verify that the project was constructed according to the design plans.

Before exploring complex curves, it is essential to master the simple horizontal curve. A simple curve is a circular arc of constant radius connecting two intersecting straight road segments (tangents).

To accurately survey the earth, two primary models are used:

The difference in elevation between the Geoid and the Ellipsoid at any given point is known as the Geoid Undulation.

When sight lines extend over long distances, the earth's curvature causes a level line (which is a curved line parallel to the earth's surface) to diverge from a horizontal line of sight. Furthermore, the varying density of the atmosphere bends the line of sight downward, a phenomenon known as atmospheric refraction.

Geodetic surveying principles are crucial when the extent of the survey covers large areas, typically greater than $250 \text{ km}^2$. At this scale, treating the Earth as a flat surface introduces unacceptable errors.

Key differences from plane surveying include:

Higher surveying is primarily concerned with establishing geodetic control networks. These networks consist of a series of highly precise, monumented points whose horizontal and vertical positions are known with extraordinary accuracy.

These points serve as a unified reference framework for all other subordinate surveys (including plane and route surveys) within a region or country, ensuring consistency and preventing the accumulation of errors over large projects.

Triangulation is a classic geodetic method based on the trigonometric principles of triangles. A baseline is measured with extreme precision, and then a network of interconnected triangles is established by measuring all the angles using high-precision theodolites. Since the length of one side (the baseline) and all angles are known, the lengths of all other sides can be computed using the Law of Sines.

Trilateration is similar to triangulation but relies on the measurement of distances rather than angles. With the advent of Electronic Distance Measurement (EDM) devices and satellite positioning, trilateration became highly efficient. By measuring the lengths of all sides in a network of triangles, the geometry of the network is fully determined.

When surveying over very large areas, triangles cannot be assumed to be planar. Instead, they are spherical triangles on the surface of the ellipsoid.

A fundamental property of a spherical triangle is that the sum of its internal angles is always greater than $180^\circ$. This difference is called Spherical Excess ($E$). The amount of spherical excess depends on the area of the triangle and the radius of the earth, and it must be subtracted from the measured angles to correctly adjust the survey network.