Understanding Tacheometry

1. Stadia Method for Horizontal Sights

When the line of sight is horizontal, distance is determined by observing the length of a staff intercepted between two horizontal stadia hairs in the telescope.

Key Formulas:

D = Ks + C Horizontal Distance
Where:
K = Stadia Interval Factor (usually 100)
s = Stadia Intercept (Upper Hair reading - Lower Hair reading)
C = Stadia Constant (usually 0 for internal focusing telescopes)

2. Stadia Method for Inclined Sights

When surveying uneven terrain, the line of sight is often inclined. The staff is still held vertically. The formulas adjust for the angle of elevation or depression (θ).

Key Formulas:

H = Ks cos²θ + C cosθ
Horizontal Distance (often denoted as D)
V = ½ Ks sin(2θ) + C sinθ
Vertical Distance

Calculating Elevation

To find the elevation of the point where the staff is held (Point B) relative to the instrument station (Point A):

Elev B = Elev A + h ± V - RR

h: Height of instrument
V: Vertical distance (+ for elevation, - for depression)
RR: Rod reading (center hair)

3. Subtense Bar Method

This method provides a convenient and relatively accurate way to find the horizontal distance between two points. A bar of fixed length (usually 2 meters) is set up horizontally at one point, and the angle it subtends is measured by a theodolite at the other point.

A key advantage is that the horizontal distance is calculated directly, independent of the elevation angle of the line of sight.

Formula:

D = L / (2 * tan(θ/2))

D = Horizontal Distance
L = Length of the subtense bar (typically 2m)
θ = Subtended horizontal angle