Q3. Offsets from the tangents method of curve setting can be adopted if:
📚 Detailed Explanation: When Offsets from Tangents Is Suitable
Curve-setting methods divide broadly into linear methods (using only a chain/tape, no angular instruments) and instrumental methods (using a theodolite or total station). The offsets-from-tangents method is a purely linear technique, and its applicability is limited by the geometry of the curve itself.
The offsets-from-tangents method measures perpendicular (or radial) offsets directly from the tangent line to points on the curve, using a chain and tape only — no angle-reading instrument is needed. This works well only for sharp curves: a small radius keeps the curve compact so offsets remain short and easy to measure accurately with a tape, and a small deflection angle keeps the curve’s overall extent manageable for this simple linear approach. For long, gentle curves (large radius, potentially large deflection), the offsets would become impractically long and inaccurate to measure by tape alone.
Why the Other Options Are Wrong
A — Both large: A large deflection angle combined with a large radius would produce a very long, sweeping curve with correspondingly very long offsets — impractical to measure accurately by tape, and exactly the opposite condition this method suits.
B — Large deflection, small radius: While the small radius helps, a large deflection angle on a sharp curve creates a curve that sweeps through a wide arc, making the offset method increasingly impractical as the curve progresses away from the tangent point.
D — Small deflection, large radius: A large radius with even a small deflection angle can still produce a long curve length, and large-radius curves are typically set out with more efficient instrumental methods (like the theodolite-and-tape or two-theodolite method) rather than simple tangential offsets.
Key Concepts for Students
- Linear methods suit short, sharp curves; instrumental methods suit long, gentle curves: This is the general rule governing curve-setting method selection. Offsets from tangents (or from chords) belong to the linear-method, sharp-curve category alongside the method of ties (Q4) for general detail surveying.
- “Sharp curve” means small radius: In highway/railway terminology, a “sharp” curve has a small radius (and correspondingly large degree of curve, see Q11, Q15, Q18, Q26) — exactly the condition under which manual offset measurement remains practical.
- Practical accuracy consideration: Offsets measured by tape are subject to sag, alignment, and reading errors that accumulate with distance — keeping offsets short (via small radius and deflection) keeps these errors within acceptable engineering tolerance.