Intersection Geometry

10% of exam

Intersection sight distance and sight triangles, at-grade and roundabout layout geometry, and interchange/ramp design including acceleration and deceleration lane lengths and gap acceptance.

5 concepts

Exam areas

A. Intersection sight distance

Intersection Sight Distance

Build the departure and approach sight triangles, size intersection sight distance from the gap-acceptance time as ISD = 1.47·V·t_g, and keep the triangle clear of obstructions.

Intersection sight distance (ISD) is a different animal from stopping sight distance: it is not about a single driver stopping for a hazard, but about whether a driver waiting at — or approaching — an intersection can see far enough down the cross street to complete a maneuver before a conflicting vehicle arrives. Get it wrong and you design a corner where a stopped driver simply cannot see an oncoming car in time to pull out safely. This entire topic lives in the AASHTO Green Book (A Policy on Geometric Design of Highways and Streets, GDHS-7); the NCEES PE Civil Reference Handbook contains only generic horizontal-curve geometry in §5.2 and has no ISD method at all — so do not go looking for a handbook page here. The mechanics are simple, but the points are lost in choosing the right time gap and in mis-handling the

1.47

that converts miles per hour to feet per second.

The two sight triangles

AASHTO frames the problem with sight triangles — triangular areas at each quadrant that must be kept free of sight obstructions. The departure sight triangle applies to a stopped driver (Cases B and F) deciding when to depart from the minor road; its vertex is at the stopped vehicle's driver position, set back from the edge of the major road's traveled way. The approach sight triangle applies to vehicles approaching an uncontrolled or yield-controlled intersection (Cases A and C), where both drivers must see each other in time to adjust speed or stop. In both, one leg lies along each approach, and the hypotenuse is the line of sight; any obstruction inside the triangle — a building, a sign, a parked car, vegetation, or a crest — defeats it.

ISD from the gap-acceptance time

The governing idea is gap acceptance: the departing driver needs a gap in the major-road traffic long enough to complete the maneuver. AASHTO converts a chosen time gap

t_g

(seconds) into a length of major road that must be visible — the major-road leg of the triangle. With the major-road design speed

V

in mph and the

1.47

factor turning mph into ft/s, the required intersection sight distance is the distance a major-road vehicle travels during that gap. This single equation is the heart of every ISD problem on the exam.

\text{ISD} = 1.47\,V_{\text{major}}\,t_g

Choosing the time gap

The time gap is not free to invent — AASHTO tabulates base values by maneuver and design vehicle. For a stop-controlled minor road (Case B), a passenger car turning left onto a two-lane major road uses a base

t_g = 7.5\ \text{s}

; turning right or crossing uses

t_g = 6.5\ \text{s}

. Two adjustments matter. For multilane major roads, add

0.5\ \text{s}

for each additional lane the turning vehicle must cross beyond the first (passenger cars;

0.7\ \text{s}

for trucks). For a minor-road approach on an upgrade steeper than

3\%

, increase the time gap because the stopped vehicle accelerates more slowly. Trucks and combination vehicles carry substantially larger base gaps, which is why a design that works for cars can still strand a semi.

t_g = t_{g,\text{base}} + 0.5\,(n_L - 1)\quad(\text{passenger car, multilane crossing})

The minor-road leg and the decision point

The departure sight triangle has a second leg along the minor road: the distance back from the edge of the major-road traveled way to the stopped driver's eye. AASHTO places that decision point a nominal

14.5\ \text{ft}

back (roughly the distance from a passenger car's front bumper to the driver, plus the setback of the stop line from the through lane). The driver's eye height is taken as

3.5\ \text{ft}

and the height of the approaching object as

3.5\ \text{ft}

as well. Everything inside the triangle bounded by these two legs — the

14.5\ \text{ft}

minor-road leg and the ISD major-road leg — must be clear between those heights.

Approach triangles and the other cases

Where the intersection has no control (Case A) or yield control on the minor road (Case C), use the approach sight triangle instead: each leg is the distance a vehicle travels at its approach speed during the time needed to perceive, react, and adjust — AASHTO uses a base travel time of about

6.5\ \text{s}

for the major road, reduced for lower speeds. Yield-controlled approaches (Case C) split into crossing (C1) and turning (C2) sub-cases with their own gap times. The key exam distinction is simply this: a stopped vehicle uses a departure triangle keyed to a gap time; a moving vehicle uses an approach triangle keyed to a travel time. The arithmetic —

1.47 \times

speed

\times

time — is identical.

Clearing the triangle and comparing to SSD

Once ISD is computed, the design check is geometric: is the major-road leg actually visible? Set back obstructions, regrade a crest, or trim the sight triangle on the inside of a horizontal curve. AASHTO also requires that the available sight distance never drop below the stopping sight distance of the major road — a major-road driver must always be able to stop for a vehicle that has entered the intersection. So compute ISD, then sanity-check it against SSD for the major-road design speed; if a constrained site cannot provide ISD, providing at least SSD with additional control (multiway stop, signal) becomes the fallback.

Exam strategy

Read for three things: the controlling maneuver (which sets

t_g

), the major-road design speed (which carries the

1.47

), and the number of lanes crossed (the

+0.5\,(n_L-1)

adjustment). Write

\text{ISD} = 1.47\,V\,t_g

first, then build

t_g

from its base and adjustments before substituting. Keep speed in mph and remember the

1.47

is ft/s per mph — using

V

already in ft/s and multiplying by

1.47

again is the classic doubled-conversion error. Finally, never cite a handbook section for the ISD method; cite the AASHTO Green Book. If a problem hands you a sight-triangle clearance distance and asks for allowable speed, just invert the equation:

V = \text{ISD}/(1.47\,t_g)

Key equations

Intersection sight distance (departure)

\text{ISD} = 1.47\,V_{\text{major}}\,t_g

Major-road leg of the sight triangle, ft. $V_{\text{major}}$ = major-road design speed (mph), $t_g$ = time gap (s), $1.47$ = ft/s per mph. AASHTO Green Book Case B/F.

Time gap with multilane adjustment

t_g = t_{g,\text{base}} + 0.5\,(n_L - 1)

Passenger-car gap for crossing/left turns; $n_L$ = number of through lanes crossed. Base $7.5$ s (left turn) or $6.5$ s (right turn/cross) onto a two-lane road; $0.7$ s/lane for trucks.

Allowable speed from a fixed sight triangle

V_{\text{major}} = \dfrac{\text{ISD}_{\text{avail}}}{1.47\,t_g}

Inverts the ISD relation when the available major-road leg is fixed by the site, mph.

Approach-triangle leg

d = 1.47\,V\,t_a

Leg length for uncontrolled (Case A) / yield (Case C) approaches; $t_a$ = travel time (≈ 6.5 s base, reduced at low speed), ft.

Stopping sight distance (lower-bound check)

\text{SSD} = 1.47\,V\,t_r + \dfrac{V^2}{30\left(\tfrac{a}{32.2}\pm G\right)}

Major-road SSD that ISD must not fall below; $t_r=2.5$ s, $a=11.2$ ft/s², $G$ = grade (decimal). From AASHTO sight-distance criteria.

Sight-line eye and object heights

h_{\text{eye}} = 3.5\ \text{ft},\quad h_{\text{obj}} = 3.5\ \text{ft}

AASHTO design heights defining the clear plane within the sight triangle for intersection design.

Minor-road (decision-point) leg

a = 14.5\ \text{ft}

Nominal set-back of the stopped driver's eye from the edge of the major-road traveled way (passenger car, Case B departure triangle).

Worked examples

Left turn from a stop onto a two-lane highway

Problem. A minor street is stop-controlled at its intersection with a two-lane rural highway with a design speed of $45\ \text{mph}$ . For a passenger car turning left, find the intersection sight distance that must be cleared along the major road.

Solution. This is AASHTO Case B1 (left turn from stop). Base time gap for a passenger car turning left onto a two-lane road:

t_g = 7.5\ \text{s}

(no multilane or grade adjustment).

\text{ISD} = 1.47\,V\,t_g = 1.47 \times 45 \times 7.5 = 496\ \text{ft}

. Sanity check:

45\ \text{mph} = 66\ \text{ft/s}

; in

7.5\ \text{s}

a major-road car travels

66 \times 7.5 = 496\ \text{ft}

— consistent. The sight triangle's major-road leg of

\approx 496\ \text{ft}

, with its

14.5\ \text{ft}

minor-road leg, must be clear of obstructions between

3.5\ \text{ft}

heights. Answer:

\text{ISD} \approx 496\ \text{ft}

\text{ISD} = 1.47(45)(7.5) = 496\ \text{ft}

Crossing a multilane road

Problem. A stop-controlled minor road must allow a passenger car to turn left onto a major arterial whose design speed is $50\ \text{mph}$ . The turning vehicle crosses three lanes to reach its destination lane. Determine the required ISD.

Solution. Base left-turn gap

t_{g,\text{base}} = 7.5\ \text{s}

. Multilane adjustment: add

0.5\ \text{s}

for each lane crossed beyond the first. Crossing three lanes gives

n_L = 3

t_g = 7.5 + 0.5\,(3 - 1) = 7.5 + 1.0 = 8.5\ \text{s}

\text{ISD} = 1.47 \times 50 \times 8.5 = 625\ \text{ft}

. Sanity check: relative to the two-lane base of

1.47(50)(7.5) = 551\ \text{ft}

, the extra

1.0\ \text{s}

adds

1.47(50)(1.0) = 73.5\ \text{ft}

, giving

625\ \text{ft}

— consistent. Answer:

\text{ISD} \approx 625\ \text{ft}

\text{ISD} = 1.47(50)\big[7.5 + 0.5(2)\big] = 625\ \text{ft}

Back-calculating an allowable speed

Problem. A constrained corner can provide only $335\ \text{ft}$ of clear sight along the major road for a right-turning passenger car departing from a stop ( $t_g = 6.5\ \text{s}$ ). What major-road design speed does this sight triangle support?

Solution. Invert the ISD relation:

V = \dfrac{\text{ISD}}{1.47\,t_g} = \dfrac{335}{1.47 \times 6.5} = \dfrac{335}{9.555} = 35.1\ \text{mph}

. So the available triangle supports about

35\ \text{mph}

. If the posted/design speed exceeds this, the corner must be opened up (remove the obstruction, increase setback) or additional control provided. Sanity check: at

35\ \text{mph}

\text{ISD} = 1.47(35)(6.5) = 334\ \text{ft} \approx 335\ \text{ft}

— consistent. Answer:

V \approx 35.0\ \text{mph}

Common pitfalls

•Citing an NCEES handbook page for the ISD method — there is none. ISD, sight triangles, and time gaps come from the AASHTO Green Book; the handbook's §5.2 covers only generic curve geometry.
•Doubling the unit conversion: if you write the speed in ft/s and then multiply by $1.47$ , you convert twice. The $1.47$ goes with speed in mph only.
•Using the left-turn gap ( $7.5$ s) when the maneuver is a right turn or a crossing ( $6.5$ s), or vice versa — read the maneuver before picking $t_g$ .
•Forgetting the multilane adjustment $0.5\,(n_L-1)$ s, which can add hundreds of feet to ISD on a wide arterial.
•Confusing the approach triangle (moving vehicle, travel time) with the departure triangle (stopped vehicle, gap time) — different cases, same arithmetic but different time values.
•Sizing the triangle for a passenger car when the design vehicle is a truck; truck gaps are larger ( $0.7$ s/lane and bigger base values), so a car-based ISD can strand a combination vehicle.
•Reporting ISD without checking it against the major road's stopping sight distance — ISD must never be less than SSD for the major-road design speed.

References

AASHTO, A Policy on Geometric Design of Highways and Streets (Green Book, GDHS-7) — Intersection Sight Distance (Cases A–F)
NCEES PE Civil Reference Handbook — §5.2 Horizontal Design — Provides only generic curve geometry; contains no ISD or sight-triangle method.
AASHTO Green Book — Stopping Sight Distance criteria — Lower-bound check that available ISD must satisfy.

Gap Acceptance & Turn Lanes

Use critical gap and follow-up headway to compute the gap-acceptance capacity of a minor movement, and size left/right turn lanes from warrants, deceleration, and storage length.

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B. Interchanges

Interchange & Ramp Design

Distinguish diamond, cloverleaf, and directional interchanges; set ramp design speed from the mainline; and size acceleration/deceleration lanes and gore geometry from the AASHTO speed-change tables.

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C. At-grade layout incl. roundabouts

At-Grade & Roundabout Geometry

Lay out a modern roundabout — inscribed-circle diameter, entry/circulating/exit geometry, and the fast-path radius that sets speed and deflection — plus conventional at-grade turn-lane layout.

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At-Grade Intersection Layout & Channelization

Lay out an at-grade intersection — intersection angle and skew, corner radii for the design vehicle, channelizing islands, and turning-path templates — from the AASHTO Green Book.

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