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Difference between upper and lower stadia reading gives __________
A) stadia slope
B) stadia coordinate
C) stadia intercept
D) staff intercept
stadia intercept
In tacheometry, the difference between the upper stadia hair reading and the lower stadia hair reading observed on a vertical leveling staff is known as the stadia intercept (or staff intercept). It is denoted by the variable S, calculated as S=Upper Reading−Lower Reading. This value is directly proportional to the distance between the instrument station and the staff.
In tacheometry, the difference between the upper stadia hair reading and the lower stadia hair reading observed on a vertical leveling staff is known as the stadia intercept (or staff intercept). It is denoted by the variable S, calculated as S=Upper Reading−Lower Reading. This value is directly proportional to the distance between the instrument station and the staff.
S=Readingupper−Readinglower — Stadia Intercept equation
D=K⋅S+C — Tacheometric Distance formula for horizontal sight
Tacheometry relies on the principle of similar triangles. When sighting through a telescope equipped with a stadia diaphragm, the fixed vertical spacing between the outer horizontal hairs subtends a proportional height on a distant staff. As the staff is moved farther away, the intercepts observed between the upper and lower stadia lines increase linearly with horizontal distance.
The diaphragm of a tacheometer contains three horizontal cross-hairs: top, central (axial), and bottom.
Multiplying constant K=if is typically 100 for standard instruments.
Additive constant C=(f+c) is typically 0 for modern or anallatic lens systems.
Eliminates the need for physical chaining or taping over rough terrain.
Allows rapid determination of both horizontal distances and vertical elevations.
Sight distances are limited by staff visibility and optical magnification.
Reading errors on the staff scale directly impact calculated horizontal distances.
Topographical surveys in hilly, steep, or broken ground where chaining is difficult.
Contour mapping and location surveys for roads, railways, and reservoirs.
The central axial reading gives the height of the line of sight on the staff.
Option A (stadia slope) refers to the angle of inclination of the telescope line of sight.
Option B (stadia coordinate) is not a standard surveying parameter term.
Option D (staff intercept) is sometimes used synonymously, but 'stadia intercept' precisely describes the distance measured between stadia hair readings on the reticule.
C is correct — The difference between upper and lower stadia hair readings on a leveling staff defines the stadia intercept.
For horizontal line of sight, D=KS+C; if an anallatic lens is used, C=0, simplifying the relation to D=100S.