FS Route and Transportation Surveys 1 — Questions and Answers
Question 1: Using the arc definition, what is the degree of curve for a simple circular curve with a radius of 573 feet?
- 5°
- 15°
- 10° (Correct answer)
- 20°
Correct answer: 10°
Using the arc definition, D = 5729.578 / R = 5729.578 / 573 ≈ 10°.
Question 2: The tangent length (T) of a simple horizontal curve with radius R and intersection angle Δ is calculated as:
- T = R × sin(Δ/2)
- T = R × tan(Δ/2) (Correct answer)
- T = R × cos(Δ/2)
- T = R × (sec(Δ/2) − 1)
Correct answer: T = R × tan(Δ/2)
The tangent length is T = R × tan(Δ/2), derived from the right triangle formed by the radius, tangent, and line to the PI.
Question 3: In route surveying, what does the abbreviation 'PI' stand for?
- Parabolic Inflection
- Primary Index
- Point of Intersection (Correct answer)
- Point of Inflection
Correct answer: Point of Intersection
PI stands for Point of Intersection, which is where the two tangents of a horizontal curve meet.
Question 4: A compound curve in route surveying consists of:
- Two circular arcs curving in opposite directions
- Two or more circular arcs with different radii curving in the same direction (Correct answer)
- A spiral followed by a straight tangent section
- A reverse curve followed by a circular arc
Correct answer: Two or more circular arcs with different radii curving in the same direction
A compound curve uses two or more circular arcs of different radii that both curve in the same direction, sharing a common tangent at the point of compound curvature (PCC).
Question 5: The external distance (E) of a simple horizontal curve is the distance from:
- The PC to the midpoint of the arc
- The PI to the PT along the back tangent
- The PI to the midpoint of the curve (Correct answer)
- The midpoint of the long chord to the PC
Correct answer: The PI to the midpoint of the curve
The external distance E is measured from the PI to the midpoint of the curve (the point on the arc closest to the PI), calculated as E = R(sec(Δ/2) − 1).
Question 6: The arc length (L) of a simple horizontal curve with radius R and central angle Δ expressed in radians is:
- L = R + Δ
- L = 2R sin(Δ/2)
- L = R × Δ (Correct answer)
- L = R / Δ
Correct answer: L = R × Δ
Arc length equals the radius multiplied by the central angle in radians: L = R × Δ.
Question 7: In the chord definition of degree of curve, D is the central angle subtended by a chord of what length?
- 50 feet
- 200 feet
- 100 feet (Correct answer)
- 500 feet
Correct answer: 100 feet
The chord definition defines D as the central angle subtended by a 100-foot chord, commonly used in railroad surveying in the US.
FS Route and Transportation Surveys 1
Using the arc definition, what is the degree of curve for a simple circular curve with a radius of 573 feet?