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Transportation Engineering for FE Civil
Transportation Engineering on the FE Civil exam is geometry plus a few well-defined models: lay out horizontal and vertical curves, check stopping sight distance, and use the basic relationships between traffic flow, speed and density. Most questions follow the handbook formulas directly once the given values are sorted out.
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Horizontal curves
A simple circular curve joins two straight tangents. The handbook geometry relates the radius, the central (intersection) angle, and the working lengths you are asked for most often — curve length, tangent length, chord and offsets:
\[L = R\Delta \qquad (\Delta \text{ in radians})\]
\[T = R \tan\left(\frac{\Delta}{2}\right)\]
| R | radius of the circular curve |
|---|---|
| Δ | central (intersection) angle of the curve |
| L | length of curve, measured along the arc |
| T | tangent length, from the point of curvature (or point of tangency) to the point of intersection |
Two related lengths appear as concept and calculation questions: the long chord joins the start and end of the curve in a straight line, while the external distance and the middle ordinate measure the offsets between the curve and its tangents/chord at mid-curve. The single commonest error in this section is using \(\Delta\) in degrees in \(L = R\Delta\) — that formula needs radians.
Vertical curves
Vertical curves, usually equal-tangent parabolas, join two grades smoothly. The key quantities are the algebraic grade difference, the location of the high or low point, and elevations along the curve measured from the PVC (point of vertical curvature):
\[A = |g_{2} - g_{1}|\]
\[x = \frac{g_{1}L}{A} \text{ (distance from the PVC to the high or low point)}\]
| g1, g2 | entering and exiting grades (signed; upgrade positive) |
|---|---|
| A | absolute algebraic difference in grades |
| L | length of the vertical curve |
| PVC | point of vertical curvature (start of the curve) |
Use signed grades consistently: in the high/low-point formula, \(g_{1}\) carries its sign, while \(A\) is always positive. Elevations along the curve follow the parabolic offset from the tangent — find the tangent elevation at the station first, then apply the curve correction.
Stopping sight distance
Stopping sight distance (SSD) is the distance a driver needs to perceive an obstruction, react, and brake to a stop. The handbook splits it into exactly those two parts:
\[\text{SSD} = d_{pr} + d_{b}\]
\[d_{pr} = v \, t_{pr}\]
\[d_{b} = \frac{v^{2}}{2a}\]
| dpr | perception–reaction distance |
|---|---|
| db | braking distance |
| v | design (initial) speed |
| tpr | perception–reaction time |
| a | deceleration rate |
Speed must be in distance per unit time consistent with \(t_{pr}\) and \(a\) — for example ft/s with seconds and ft/s2. Convert mph to ft/s (multiply by 1.47) before substituting; braking distance grows with the square of speed, so a speed error is amplified.
Traffic flow fundamentals
Traffic questions at FE level rest on one identity linking flow, density and speed, plus clear use of headway and spacing:
\[q = k \, v\]
| q | flow rate (vehicles per hour) |
|---|---|
| k | density (vehicles per unit length) |
| v | space-mean speed |
| Headway | time between successive vehicles passing a point; the inverse of flow |
| Spacing | distance between successive vehicles; the inverse of density |
Keep the pairs straight: headway goes with flow (time-based), spacing goes with density (distance-based). If a question gives an average headway, the flow is its reciprocal — with unit conversion from seconds to hours where needed.
Pavement and highway capacity concepts
Pavement and capacity appear mainly as concept questions at FE level: what the terms mean, what governs performance, and which factors increase or decrease capacity:
Flexible pavement: load spread through successive granular and asphalt layers to the subgrade
Rigid pavement: a concrete slab distributes load over a wide area by slab action
Capacity: the maximum hourly flow a facility can carry under stated conditions; level of service grades operating quality from free-flowing to forced flow
For concept questions, anchor on function: pavement structure exists to protect the subgrade from traffic stresses, and capacity falls as interruptions, narrow lanes, or adverse conditions increase. Detailed pavement design and capacity calculations belong to the PE level, not the FE.
Worked example Horizontal curve length and tangent
Given: A horizontal curve has radius \(R = 500\) ft and central angle \(\Delta = 40^{\circ}\). Find the curve length and the tangent length.
Solution:
- Convert the angle to radians: \(\Delta = 40^{\circ} \times \pi/180 = 0.6981\) rad.
- Curve length: \(L = R\Delta = (500)(0.6981) = 349.07\) ft.
- Tangent length: \(T = R \tan(\Delta/2) = 500 \tan(20^{\circ}) = 181.99\) ft.
Answer: \(L = 349.07\) ft; \(T = 181.99\) ft \(\approx 182.0\) ft.
Worked example High point of a vertical curve
Given: A vertical curve of length \(L = 400\) ft joins grades \(g_{1} = +2\%\) and \(g_{2} = -3\%\). The PVC elevation is 100.00 ft. Find the location and elevation of the high point.
Solution:
- Grade difference: \(A = |g_{2} - g_{1}| = |-3 - (+2)| = 5\%\).
- Distance from the PVC to the high point: \(x = g_{1}L/A = (2)(400)/5 = 160\) ft from the PVC.
- Elevation at the high point: the tangent rises at 2% for 160 ft (\(+3.20\) ft) and the parabolic curve correction at that point is \(-1.60\) ft, giving \(100.00 + 3.20 - 1.60 = 101.60\) ft.
Answer: High point 160 ft from the PVC, at elevation 101.60 ft.
Worked example Stopping sight distance
Given: A vehicle travels at 60 mph (\(= 88\) ft/s). The perception–reaction time is 2.5 s and the deceleration is 11.2 ft/s2. Find the stopping sight distance.
Solution:
- Perception–reaction distance: \(d_{pr} = 88 \times 2.5 = 220.5\) ft (equivalently \(1.47 \times 60 \times 2.5\)).
- Braking distance: \(d_{b} = 88^{2}/(2 \times 11.2) = 7{,}744/22.4 = 345.7\) ft.
- Add the two parts: \(\text{SSD} = 220.5 + 345.7 = 566.2\) ft.
Answer: SSD \(\approx 566\) ft.