What is the first step in determining the radius of a curve?

What is the first step in determining the radius of a curve?

• A. Measure the chord
• B. Find the midpoint and measure the middle ordinate
• C. Use the radius formula
• D. Determine the tangents

Answer: (A)

Measuring the chord length is the first essential step because it gives the straight-line span between the curve’s endpoints, establishing the basic distance you’ll relate to the radius. Without this span, you can’t determine the half-chord or apply the standard circle-segment relationships. Once you have the chord, you typically measure the middle ordinate (the sagitta) from the chord’s midpoint to the arc. With both measurements, L (the chord length) and s (the sagitta), you can find the radius using R = ((L/2)^2 + s^2) / (2s). If you know the subtended angle instead, you could use R = L / (2 sin(θ/2), but you still need a fundamental dimension from the chord. So starting with the chord length is the practical first move.

Measuring the chord length is the first essential step because it gives the straight-line span between the curve’s endpoints, establishing the basic distance you’ll relate to the radius. Without this span, you can’t determine the half-chord or apply the standard circle-segment relationships. Once you have the chord, you typically measure the middle ordinate (the sagitta) from the chord’s midpoint to the arc. With both measurements, L (the chord length) and s (the sagitta), you can find the radius using R = ((L/2)^2 + s^2) / (2s). If you know the subtended angle instead, you could use R = L / (2 sin(θ/2), but you still need a fundamental dimension from the chord. So starting with the chord length is the practical first move.