Tacheometry and Curves

Tacheometry measures horizontal and vertical distances rapidly using a theodolite and a graduated staff, without chaining, by reading the staff intercept between stadia hairs. It is valuable in rough terrain where taping is difficult.

The stadia formula D = ks + c relates the horizontal distance to the staff intercept through the multiplying constant k (usually 100) and the additive constant c; for inclined sights the reading is corrected by the vertical angle.

Curve setting-out applies to roads and railways, where a horizontal curve joins two straights. The simple circular curve’s elements — tangent length, curve length, apex distance, mid-ordinate and long chord — follow from the radius and deflection angle, and the curve is pegged out by deflection angles or offsets.

(multiplying constants)

(Δ in degrees)

(approximate for highway)

Relation 1 —

(multiplying constants)

Write this relation with symbols exactly as in Surveying — BC Punmia before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 2 —

(Δ in degrees)

Write this relation with symbols exactly as in Surveying — BC Punmia before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 3 —

(approximate for highway)

Write this relation with symbols exactly as in Surveying — BC Punmia before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

In stadia tacheometry the staff intercept s (difference between top and bottom stadia readings) is proportional to distance; with the anallactic lens the additive constant c is effectively zero and D = ks, so a 1 m intercept at k = 100 means 100 m. For inclined sights, the cos²θ term reduces the reading to horizontal distance.

The multiplying and additive constants are instrument properties determined by calibration; knowing them lets any staff intercept be converted directly to distance, and the vertical angle simultaneously gives the difference in elevation.

A simple curve is defined by its radius R and the deflection angle Δ between the tangents; the tangent length T = R tan(Δ/2) locates the tangent points, the curve length L = πRΔ/180 gives the arc, and the mid-ordinate and apex distance describe the curve’s offset from the chord and intersection point.

Setting out is commonly by Rankine’s deflection-angle method, where each chord subtends a deflection angle from the tangent that the theodolite turns off; on transition curves an additional spiral is introduced so curvature builds up gradually, its length set by the speed and comfort criterion.

State assumptions explicitly before using any relation for tacheometry and curves — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.

Wrong assumptions invalidate the entire solution even when the formula is correct. In Surveying viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

1. Read the question and list given data with SI units (common in Surveying papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to tacheometry and curves.
4. Use equation 1: .
5. Use equation 2: .
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Tacheometry and Curves appears in layout, mapping, and alignment. In Indian civil curricula this topic is tested because it connects theory to measurement of land and levels.

GATE and semester exams often combine tacheometry and curves with earlier units — revise prerequisites before attempting mixed problems.

Industry interview panels sometimes ask: "Where did you use tacheometry and curves?" — answer with a lab, mini-project, or plant visit example if possible.

• Forgetting the cos²θ correction for inclined tacheometric sights.
• Using the wrong multiplying/additive constants for the instrument.
• Confusing tangent length with curve (arc) length.
• Omitting the transition curve where high-speed comfort requires it.

Before attempting tacheometry and curves problems, confirm you can:

1. Stadia tacheometry for quick horizontal and vertical distance
2. Curve elements: tangent, apex, long chord, middle ordinate
3. Setting out by deflection angle or chord offset method

Revise the solved examples in Surveying — BC Punmia and one previous-year GATE or university paper for this unit.