Vertical Design

The road in profile: parabolic vertical curves, grades and their limits, clearance under structures, and the stopping sight distance crest and sag curves must provide, and the passing sight distance over crests. It carries 8–12 of the 80 questions on the Transportation exam.

What the problems look like

Calculation from a profile figure, plus a few Green Book judgment items. Recurring shapes — curve elevations and the high or low point; clearance under an overpass; a length set so the high point lands on a cross street; minimum length for a crest, an unlit or lit sag, or an undercrossing; the design speed an existing curve supports; maximum grades; and critical length of grade and where a climbing lane starts.

By exam day you should be able to —

• compute curve elevations, the grade at any station, and the turning point;
• check vertical clearance across the full width of a structure;
• pick the governing criterion — crest, unlit sag, lit sag, curbed sag, undercrossing — and solve it for L or S;
• use K = L/A both ways: length from a design speed, design speed from a length;
• read stopping sight distance on grades and critical length of grade, including a two-grade climb.

Where people lose points

• The parabola: measure x from the PVC. The offset constant is (g2 − g1)/(2L); the rate of change of grade is twice that. The turning point sits at the PVI station only when the grades are equal and opposite.
• Clearance: check under the whole deck. Under level girders the minimum is where the road is highest — the sag's low point gives the most room, not the least.
• Crest vs sag: a crest is governed by the driver's sight line over the hump, an unlit sag by the headlight beam, a sag checked for ride by the comfort criterion, an undercrossing by a truck driver's view. Swapped relations still give plausible numbers.
• S < L or S > L: solve with one form, then check the answer against its assumption.
• K tables: stopping, passing and sag controls are separate. The supported speed is the highest one whose K the curve provides, not the nearest row. Passing uses a taller object than stopping.
• Drainage on a curbed sag caps the length — it is a maximum, not a minimum.
• Two successive grades: carry the speed already lost into the second grade instead of restarting.

Have these at your fingertips

Vertical-curve relations (offsets, turning point, E = AL/800 with A in percent, or AL/8 with grades as decimals, K = L/A), and where they live in the Handbook. The crest, sag and undercrossing length relations come from the Green Book (7th ed., 2018) Chapter 3, supplied for both the current and the April 2027 exam windows. The functional-class chapters give maximum grades and clearances.

Going deeper

• Horizontal Design — the alignment this profile is coordinated with

Part of the Transportation exam. Practice this area with exam-real problems — the tutor walks any one you miss. → Start practicing free — free with an account.