Which of the following distance between intersection point to apex point of curve?

Question

Examoogle · Accepted Answer

Option D: External distance

Explanation & Concepts:
The external distance (also called apex distance) is the distance between the point of intersection (PI) and the apex point (highest point or midpoint) of a simple circular curve. It represents the clear distance between the intersection of two tangents and the curve's centerline vertex.

Working Principle: In circular curve geometry, the secant line from the intersection point to the center of the curve passes through the apex point on the curve. By trigonometry on the right triangle formed by the radius, tangent, and secant, the distance from the intersection point to the curve apex is derived as $E = R (\sec(\Delta/2) - 1)$.

Key Formulas: $E = R \left(\sec\frac{\Delta}{2} - 1ight)$ — External distance ($E$) in terms of Radius ($R$) and Deflection angle ($\Delta$); $E = R \cdot 	an\frac{\Delta}{2} \cdot 	an\frac{\Delta}{4}$ — Alternative form for external distance; $T = R 	an\frac{\Delta}{2}$ — Tangent distance ($T$); $M = R \left(1 - \cos\frac{\Delta}{2}ight)$ — Mid-ordinate distance ($M$)

Key Points: External distance ($E$) is measured along the bisector of the deflection angle $\Delta$ from PI to the apex point.; Apex point is the highest point of a summit curve or the midpoint of a simple circular arc.; External distance is crucial in road design to determine mountain/hill cutting or embankment limits.

Applications: Determining property line clearances during highway alignment design.; Calculating excavation depths or clearance demands at curve summits and valley centers.

Additional Info: Option A is incorrect: Tangent distance is the distance from the Point of Commencment (T1) or Tangency (T2) to the Point of Intersection (PI).. Option B is incorrect: Length of long chord is the straight distance between tangent points T1 and T2.. Option C is incorrect: Mid ordinate distance is the distance between the midpoint of the long chord and the apex point of the curve.

Answer: D is correct — The distance measured from the point of intersection (PI) to the apex point of a curve along the angle bisector is defined as the external distance.

Exam Tip: Remember that $E = R(\sec(\Delta/2) - 1)$ while $M = R(1 - \cos(\Delta/2))$; their relation is also expressed as $M = R - \sqrt{R^2 - (L/2)^2}$ where $L$ is the length of the long chord.

Examoogle · Answer

Option A: Tangent distance

Examoogle · Answer

Option B: Length of long chord

Examoogle · Answer

Option C: Mid ordinate distance

Correct Answer

Discussion (0)

Correct Answer

Related Questions

Discussion (0)