Practice Problems: Highway Design
Question 1
A highway design engineer is tasked with designing a horizontal curve for a rural two-lane highway. Given the following information:
- Design speed: 60 mph
- Degree of curve: 6°
- Superelevation rate: 0.06 ft/ft
- Side friction factor: 0.12
What is the radius of the curve (in feet)?
(a) 850 ft
(b) 955 ft
(c) 1,020 ft
(d) 1,146 ft
Question 2
A traffic engineer is evaluating sight distance on a crest vertical curve. The curve connects a +3% grade to a -2% grade. Given the following:
- Design speed: 55 mph
- Required stopping sight distance: 495 ft
- Height of driver's eye: 3.5 ft
- Height of object: 2.0 ft
What is the minimum length of the vertical curve (in feet)?
(a) 580 ft
(b) 612 ft
(c) 695 ft
(d) 750 ft
Question 3
A civil engineer is designing a sag vertical curve for a highway. The curve connects a -4% grade to a +2% grade. Given the following:
- Design speed: 50 mph
- Stopping sight distance: 425 ft
- Headlight beam height: 2.0 ft
- Upward divergence angle: 1°
What is the minimum length of the vertical curve using the headlight criterion (in feet)?
(a) 520 ft
(b) 565 ft
(c) 618 ft
(d) 670 ft
Question 4
A highway designer is determining the stopping sight distance for a roadway section. Given the following information:
- Design speed: 65 mph
- Perception-reaction time: 2.5 seconds
- Deceleration rate: 11.2 ft/s²
- Grade: -3%
What is the required stopping sight distance (in feet)?
(a) 545 ft
(b) 598 ft
(c) 625 ft
(d) 670 ft
Question 5
A transportation engineer is designing a superelevation transition for a horizontal curve. Given the following data:
- Design speed: 55 mph
- Radius of curve: 1,200 ft
- Normal crown slope: 2%
- Superelevation rate: 0.08 ft/ft
- Number of lanes rotated: 2 (both lanes in one direction)
- Lane width: 12 ft
What is the minimum length of superelevation runoff (in feet)?
(a) 180 ft
(b) 210 ft
(c) 245 ft
(d) 280 ft
Question 6
A highway engineer is evaluating the adequacy of a horizontal curve. Given the following information:
- Design speed: 70 mph
- Radius: 1,500 ft
- Coefficient of side friction: 0.10
What is the required superelevation rate (ft/ft)?
(a) 0.058
(b) 0.072
(c) 0.085
(d) 0.098
Question 7
A design engineer is calculating the middle ordinate for a horizontal curve survey layout. Given the following:
- Radius of curve: 800 ft
- Central angle: 45°
- Point of intersection (PI) is accessible
What is the middle ordinate distance (in feet)?
(a) 58.6 ft
(b) 68.3 ft
(c) 72.4 ft
(d) 85.2 ft
Question 8
A roadway designer is determining the passing sight distance for a two-lane highway. Given the following:
- Design speed: 60 mph
- Average passing vehicle speed: 66 mph
- Speed of passed vehicle: 55 mph
What is the minimum passing sight distance per AASHTO guidelines (in feet)?
(a) 1,800 ft
(b) 2,000 ft
(c) 2,100 ft
(d) 2,250 ft
Question 9
A civil engineer is analyzing the external distance of a horizontal curve for right-of-way requirements. Given the following:
- Radius: 1,000 ft
- Central angle: 60°
- Tangent distance calculated: 577.35 ft
What is the external distance (in feet)?
(a) 134.0 ft
(b) 154.7 ft
(c) 176.3 ft
(d) 192.5 ft
Question 10
A highway engineer is designing a vertical curve at an underpass. Given the following information:
- Back tangent grade: -2.5%
- Forward tangent grade: +1.5%
- Design speed: 45 mph
- Required clearance: 16.5 ft
- Station of PVI: 125+50
- Elevation of PVI: 845.00 ft
What is the minimum length of vertical curve to provide adequate clearance using \( L = 2S \) criterion (in feet)?
(a) 320 ft
(b) 400 ft
(c) 480 ft
(d) 560 ft
Question 11
A transportation engineer is determining the degree of curve needed for a horizontal alignment. Given the following:
- Design speed: 50 mph
- Maximum superelevation: 0.08 ft/ft
- Maximum side friction factor: 0.14
What is the minimum radius required (in feet)?
(a) 568 ft
(b) 625 ft
(c) 758 ft
(d) 850 ft
Question 12
A highway designer is calculating the length of a vertical curve. The curve connects a +2.8% grade to a -1.6% grade. Given the following:
- Design speed: 60 mph
- K-value for crest curves: 151
- Station of PVI: 85+25
What is the length of the vertical curve (in feet)?
(a) 554 ft
(b) 664 ft
(c) 745 ft
(d) 825 ft
Question 13
A civil engineer is designing a horizontal curve with a compound configuration. The first curve has a radius of 1,200 ft and central angle of 25°. The second curve has a central angle of 35°. Given the following:
- Design speed: 55 mph (both curves)
- Common tangent point must be smooth transition
- First curve radius: 1,200 ft
What should be the radius of the second curve for balanced design (in feet)?
(a) 800 ft
(b) 1,000 ft
(c) 1,200 ft
(d) 1,400 ft
Question 14
A highway engineer is evaluating the spiral transition length for a horizontal curve. Given the following:
- Design speed: 65 mph
- Radius of circular curve: 1,400 ft
- Superelevation rate: 0.06 ft/ft
- Rate of change of lateral acceleration: 3 ft/s³
What is the minimum spiral length (in feet)?
(a) 215 ft
(b) 245 ft
(c) 280 ft
(d) 320 ft
Question 15
A roadway designer is determining the station of the low point on a sag vertical curve. Given the following:
- PVC station: 52+00
- PVC elevation: 756.00 ft
- Initial grade: -3.5%
- Final grade: +2.0%
- Curve length: 400 ft
What is the station of the low point?
(a) 52+85
(b) 53+25
(c) 53+55
(d) 54+00
Question 16
A civil engineer is designing a reverse curve for a frontage road. Given the following information:
- First curve radius: 600 ft
- Second curve radius: 800 ft
- First curve central angle: 40°
- Second curve central angle: 35°
What is the total length of the reverse curve (in feet)?
(a) 785 ft
(b) 837 ft
(c) 906 ft
(d) 975 ft
Question 17
A highway engineer is calculating sight distance on a horizontal curve with an obstruction. Given the following:
- Radius to centerline of inside lane: 950 ft
- Sight distance required: 550 ft
- Middle ordinate to line of sight: needs to be calculated
What is the minimum clearance (middle ordinate) required from the centerline of the inside lane to provide adequate sight distance (in feet)?
(a) 18.5 ft
(b) 20.3 ft
(c) 22.8 ft
(d) 25.6 ft
Question 18
A transportation engineer is evaluating a crest vertical curve for decision sight distance. Given the following:
- Design speed: 55 mph
- Required decision sight distance: 1,030 ft (avoidance maneuver)
- Grade change: +3.2% to -2.8%
- Height of eye: 3.5 ft
- Height of object: 2.0 ft
What is the minimum curve length required (in feet)?
(a) 1,450 ft
(b) 1,685 ft
(c) 1,920 ft
(d) 2,145 ft
Question 19
A roadway designer is calculating the widening required for a horizontal curve on a two-lane highway. Given the following:
- Radius of curve: 500 ft
- Design speed: 40 mph
- Design vehicle: WB-67 (wheelbase 50 ft)
- Number of lanes: 2 (each 12 ft wide)
What is the total required curve widening (in feet)?
(a) 3.2 ft
(b) 4.5 ft
(c) 5.8 ft
(d) 7.1 ft
Question 20
A civil engineer is designing the grade and station for a vertical curve. Given the following information:
- PVI station: 110+75
- PVI elevation: 1,245.50 ft
- Initial grade: +2.4%
- Final grade: -1.8%
- Curve length: 600 ft
What is the elevation at station 111+25 (in feet)?
(a) 1,246.35 ft
(b) 1,246.73 ft
(c) 1,247.08 ft
(d) 1,247.52 ft
