Setting out a simple circular curve: For a curve of radius R = 600 m, what is the maximum practical chord length commonly adopted for calculating offsets (to control accuracy and field convenience)?

Introduction / Context:Offsets from chords or from the long chord are used extensively to set out simple circular curves. The choice of peg interval (chord length) influences both accuracy (through small-angle approximations) and site productivity. For moderate to large radii, standard practice fixes an upper bound on the chord length for reliable offset computations.

Given Data / Assumptions:

• Simple circular curve with R = 600 m.
• Offsets computed by common field formulas such as mid-ordinate y ≈ c^2 / (8R) and ordinates to chord.
• Need a practical maximum chord length used in routine highway/rail setting out.

Concept / Approach:

For typical highway curves with R in hundreds of meters, peg intervals of 20–30 m are standard. The small-angle approximations used in offset formulae remain sufficiently accurate at c ≤ 30 m for R around 600 m, while longer chords would reduce point density and may degrade fit at transitions or in rugged terrain. Hence many manuals specify 30 m as the maximum peg interval for offsets on such curves, with 10–20 m used where finer control is desired.

Step-by-Step Solution:

Verification / Alternative check:

Using y = c^2/(8R): with c = 30 m, y ≈ 900/(4800) ≈ 0.1875 m, an easily measurable offset; errors from chord-arc substitution are negligible at this scale.

Why Other Options Are Wrong:

Shorter lengths (10–25 m) are acceptable but not the requested maximum commonly adopted; choosing them increases point density without necessity for R = 600 m.

Common Pitfalls:

Using excessive peg spacing on sharp curves; forgetting that terrain or accuracy needs may still warrant shorter chords.

Final Answer:

30 m