7.2 Intersection Sight Distance and Sight Triangles

7.2 Intersection Sight Distance and Sight Triangles

Intersection Sight Distance (ISD) is the distance along a roadway that a driver should be able to see to safely perform maneuvers at an intersection. Inadequate ISD increases the risk of high-severity T-bone and sideswipe collisions. Designers evaluate ISD using sight triangles—clear, unobstructed areas along the intersection corners that allow drivers to see approaching vehicles.

Dimensional Standards of Sight Triangles

All ISD calculations utilize standardized values for driver eye height and object height:

• Height of Driver’s Eye: 3.50 ft for passenger cars; 4.25 ft for heavy trucks.
• Height of Object (Oncoming Vehicle): 3.50 ft above the pavement surface, representing the height of an oncoming passenger car's headlights or roofline.

Types of Sight Triangles

1. Approach Sight Triangles: Designed for intersections without control (uncontrolled) or yield-control. They allow approaching drivers on both roads to see each other in time to adjust speed or stop.
2. Departure Sight Triangles: Designed for stop-controlled or yield-controlled approaches. They assume a vehicle is stopped at the minor road decision point and needs to see far enough along the major road to safely depart and complete a turn or crossing.

The Decision Point ($D$)

For departure sight triangles, the stopped vehicle’s driver is assumed to be at a specific decision point.

• Position of Driver's Eye: Located a distance $D$ from the edge of the major-road travel way.
• Standard Value: AASHTO recommends a design value of 14.5 ft (representing a stop bar set 10 ft back from the edge of the travel lane plus 4.5 ft from the vehicle's front bumper to the driver's eye). A value of 18.0 ft may be used in some situations, but 14.5 ft is the standard minimum for PE exam problems.

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Stop-Controlled Intersections (Case B)

Case B governs intersections where the minor road is controlled by a stop sign. It is split into three sub-cases based on the maneuver:

Case B1: Left Turn from Minor Road

A stopped vehicle on the minor road must turn left and merge into the major-road traffic stream. The driver needs sufficient sight distance to clear the near lanes (traffic from the left) and accelerate into the far lane (traffic from the right) without forcing major-road vehicles to decelerate by more than 30%.

The required sight distance is calculated using: $ISD = 1.47 \times V_{major} \times t_g$

Where:

• $ISD$ = Intersection Sight Distance (ft)
• $V_{major}$ = Design speed of the major road (mph)
• $t_g$ = Design time gap (seconds)

Base Time Gaps ($t_g$) for Case B1:

• Passenger Car: 7.5 seconds
• Single-Unit (SU) Truck: 9.5 seconds
• Combination Semi-Trailer (WB-50/62): 11.5 seconds

Adjustments to $t_g$:

1. Multi-lane Highways: Add 0.5 seconds for passenger cars (or 0.7 seconds for trucks) for each additional lane of the major road crossed beyond the basic 2-lane case.
2. Approach Grade: If the minor-road approach grade is an upgrade exceeding 3%, add 0.2 seconds per percent of grade to $t_g$.

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Case B2: Right Turn from Minor Road

A stopped vehicle must turn right and accelerate to the design speed of the major road. The driver only needs to look to the left for oncoming traffic.

Base Time Gaps ($t_g$) for Case B2:

• Passenger Car: 6.5 seconds
• Single-Unit (SU) Truck: 8.5 seconds
• Combination Semi-Trailer (WB-50/62): 10.5 seconds

Adjustments to $t_g$:

1. Multi-lane Highways: No additional time is added for passenger cars because a right turn does not cross any lanes. (For trucks, add 0.1 seconds per lane if turning into a multi-lane road).
2. Approach Grade: If the minor-road approach grade is an upgrade exceeding 3%, add 0.1 seconds per percent of grade to $t_g$.

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Case B3: Crossing Maneuver from Minor Road

A stopped vehicle must cross the major road from a stopped position.

Base Time Gaps ($t_g$) for Case B3:

• Passenger Car: 6.5 seconds
• Single-Unit (SU) Truck: 8.5 seconds
• Combination Semi-Trailer (WB-50/62): 10.5 seconds

Adjustments to $t_g$:

1. Multi-lane Highways: Add 0.5 seconds (passenger cars) or 0.7 seconds (trucks) for each additional lane crossed.
2. Approach Grade: Add 0.1 seconds per percent of grade for upgrades exceeding 3%.

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Yield-Controlled Intersections (Case C)

At yield-controlled intersections, drivers on the minor road are not required to stop but must slow down to a design speed ($V_{minor}$, typically assumed to be 15 mph for design) and yield to major-road traffic.

• Case C1 (Crossing): $t_g = 8.0$ seconds for passenger cars.
• Case C2 (Left/Right Turns): $t_g = 8.0$ seconds for left turns; $t_g = 7.0$ seconds for right turns.
• Adjustments: Similar to Case B, adjustments apply for multi-lane configurations and grades.

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Left Turns from Major Road (Case F)

This case governs situations where a vehicle is traveling on the major road and is waiting in a left-turn lane (or shared lane) to turn left across oncoming traffic. The driver must have sufficient sight distance to see oncoming vehicles and clear their path.

• Base Time Gap ($t_g$): 5.5 seconds for passenger cars.
• Trucks: 6.5 seconds for SU trucks; 7.5 seconds for WB-50/62.
• Adjustments: Add 0.5 seconds for passenger cars (or 0.7 seconds for trucks) for each additional oncoming lane crossed.

Left-Turn Lane Offsets (Line of Sight Obstructions)

When opposing vehicles are waiting to turn left at an intersection, they can block each other’s view of oncoming through traffic. This is particularly problematic on multi-lane highways or intersections with wide medians.

• Negative Offset: The left-turn lane is aligned directly opposing the other left-turn lane, or is offset to the right. When two vehicles wait to turn left, the driver's line of sight to oncoming traffic is obstructed by the opposing left-turning vehicle.
• Positive Offset: The left-turn lanes are shifted laterally to the left (closer to the outer edge of the median). This alignment provides the driver with an unobstructed line of sight to oncoming through traffic, even when opposing left-turn vehicles are present. AASHTO recommends positive offsets for all median left-turn lanes where the major road design speed is 45 mph or higher.

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Step-by-Step Example Calculation

Problem Statement:

A minor road intersects a 4-lane undivided major road (two lanes in each direction) at a stop-controlled intersection. The design speed of the major road is 55 mph. The minor road has a 4.0% uphill grade at the approach. The design vehicle is a passenger car. Determine the required Intersection Sight Distance ($ISD$) to the left and to the right for a vehicle turning left from the minor road (Case B1).

Solution:

Step 1: Identify the Base Time Gap ($t_g$)

For a passenger car turning left from a stop (Case B1), the base time gap is: $t_{g,\text{base}} = 7.5\text{ seconds}$

Step 2: Apply the Multi-lane Adjustment

The major road has 4 lanes, undivided. A vehicle turning left must cross the two near-side lanes coming from the left to enter the far-side lane going right. The base time gap assumes a 2-lane major road. Since there are 4 lanes, the vehicle must cross 1 additional lane to reach the double-yellow center line. $\text{Lane adjustment} = 1 \times 0.5\text{ seconds} = 0.5\text{ seconds}$

Step 3: Apply the Grade Adjustment

The minor road approach has a 4.0% uphill grade. Since this grade is greater than 3%, the grade adjustment applies: $\text{Grade adjustment} = 4.0\% \times 0.2\text{ s/\%} = 0.8\text{ seconds}$

Step 4: Calculate the Total Adjusted Time Gap ($t_g$)

$t_g = t_{g,\text{base}} + \text{Lane adjustment} + \text{Grade adjustment}$ $t_g = 7.5 + 0.5 + 0.8 = 8.8\text{ seconds}$

Step 5: Compute the Intersection Sight Distance ($ISD$)

$ISD = 1.47 \times V_{major} \times t_g$ $ISD = 1.47 \times 55\text{ mph} \times 8.8\text{ seconds}$ $ISD = 711.48\text{ ft} \approx 715\text{ ft}$

Note: For the right turn (Case B2), the sight distance to the left would be calculated using a base $t_g = 6.5$ seconds, with an adjustment of $4.0 \times 0.1 = 0.4$ seconds for the grade. No lane adjustment is needed. Thus, $t_g = 6.9$ seconds and $ISD = 1.47 \times 55 \times 6.9 = 557.86$ ft.