Tacheometer Distance Calculator
1. Staff Readings (Meters)
2. Vertical Angle & Constants
Horizontal Distance (D)
0.00 m
Vertical Difference (V)
0.00 m
Staff Intercept (S) = 0.00 m
What is Tacheometric Surveying?
Tacheometry is a branch of angular surveying in which horizontal and vertical distances are determined by optical means, rather than using a measuring tape or chain. It is extremely useful in rough terrain (hills, valleys) where chaining is difficult.
(Shows the view through the telescope with Top, Middle, and Bottom cross-hairs)
The Stadia Method
This method uses a Theodolite fitted with a stadia diaphragm (two horizontal hairs above and below the central cross-hair).
- Staff Intercept (S): The difference between the Top and Bottom hair readings. \(S = \text{Top} - \text{Bottom}\).
- Multiplying Constant (k): Usually 100 for modern instruments.
- Additive Constant (C): Usually 0 for telescopes with an Anallactic lens.
Formulas used in this Calculator
1. Horizontal Distance (D)
$$ D = k S \cos^2 \theta + C \cos \theta $$
If line of sight is horizontal ($\theta = 0$), then \(D = kS + C\).
2. Vertical Elevation (V)
$$ V = \frac{1}{2} k S \sin 2\theta + C \sin \theta $$
This is the height difference between the instrument axis and the middle hair reading.
3. Reduced Level (RL) of Object
$$ \text{RL of Object} = \text{RL of Inst} + \text{HI} \pm V - h $$
Where \(h\) is the middle hair reading.
Solved Example
Given:
Top Hair = 2.500, Bottom Hair = 1.500
Vertical Angle = \(+10^\circ\)
Constants: \(k=100, C=0\)
Step 1: Find S
\(S = 2.500 - 1.500 = 1.000 \text{ m}\)
Step 2: Calculate Horizontal Distance (D)
\(D = 100(1.0) \cos^2(10^\circ)\)
\(D = 100 \times (0.9848)^2 = 96.98 \text{ m}\)
Step 3: Calculate Vertical Comp (V)
\(V = 50(1.0) \sin(20^\circ)\)
\(V = 50 \times 0.342 = 17.10 \text{ m}\)
Top Hair = 2.500, Bottom Hair = 1.500
Vertical Angle = \(+10^\circ\)
Constants: \(k=100, C=0\)
Step 1: Find S
\(S = 2.500 - 1.500 = 1.000 \text{ m}\)
Step 2: Calculate Horizontal Distance (D)
\(D = 100(1.0) \cos^2(10^\circ)\)
\(D = 100 \times (0.9848)^2 = 96.98 \text{ m}\)
Step 3: Calculate Vertical Comp (V)
\(V = 50(1.0) \sin(20^\circ)\)
\(V = 50 \times 0.342 = 17.10 \text{ m}\)