Roundabout Geometric Design

A modern roundabout is an at-grade intersection where traffic circulates counterclockwise (in the United States) around a central island. Unlike older traffic circles or rotaries, modern roundabouts operate under yield control on entry, require deflection to slow entering vehicles, and utilize a compact design to limit speeds and improve safety.

Key Geometric Features

A modern roundabout contains several distinct geometric elements:

  • Inscribed Circle Diameter (ICD): The overall outer diameter of the roundabout, measuring from the outer edge of the circulatory roadway.
    • Single-Lane Roundabouts: Typically $90$ to $150\text{ ft}$ ($27$ to $45\text{ m}$).
    • Multi-Lane Roundabouts: Typically $150$ to $220\text{ ft}$ ($45$ to $67\text{ m}$).
  • Central Island: The non-traversable circular area in the center of the roundabout.
  • Truck Apron: A mountable, low-profile concrete ring surrounding the central island. It is designed to accommodate the rear wheel tracking of large trucks (e.g., WB-67) while keeping the entry and circulatory lanes narrow to restrict the speeds of passenger cars.
  • Splitter Island: A raised or painted triangular island on each approach. It serves three purposes: deflecting and slowing entering traffic, preventing wrong-way movements, and providing a mid-crossing refuge for pedestrians.
  • Circulatory Roadway: The active travel lanes around the central island.
Truck ApronIsland

Design Principles and Speed Control

The most critical principle of roundabout design is speed control, achieved through physical geometry rather than speed limit signs.

  • Deflection: The entry alignment must be deflected (bent to the right) by the splitter island and central island. The entering path must never be a straight line through the intersection.
  • Target Speeds:
    • Single-Lane Roundabouts: $15$ to $20\text{ mph}$ ($24$ to $32\text{ km/h}$).
    • Multi-Lane Roundabouts: $20$ to $25\text{ mph}$ ($32$ to $40\text{ km/h}$).

Fastest Path Analysis

The fastest path is the smoothest, flattest vehicle path through the roundabout, assuming a driver ignores lane markings (when no other traffic is present). Designers analyze five critical radii along this path:

  1. $R_1$ (Entry Path Radius): The minimum radius on the entry path, located near the yield line. Controls the entry speed (most critical safety check).
  2. $R_2$ (Circulatory Path Radius): The minimum radius around the central island.
  3. $R_3$ (Exit Path Radius): The minimum radius on the exit path.
  4. $R_4$ (Left-Turn Path Radius): The radius of the path for a left-turning vehicle.
  5. $R_5$ (Right-Turn Path Radius): The radius of the path for a right-turning vehicle.
R1 (Entry)R2 (Circulating)R3 (Exit)

Speed-Radius Relationship

The speed along any curve of the fastest path is governed by:

$$V = 3.86 \sqrt{R (f \pm e)}$$

Where:

  • $V$ = vehicle speed (mph)
  • $R$ = radius of the curve (ft)
  • $f$ = side friction factor (varies with speed; typically ranges from $0.20$ to $0.30$)
  • $e$ = super-elevation or cross slope (decimal). In roundabouts, the circulatory roadway usually slopes outward at $-2.0\%$ (or $-0.02$) for drainage, representing adverse super-elevation for turning vehicles.

Safety Criteria: To prevent high-speed collisions, the entry speed ($V_1$) should be the lowest speed in the sequence, and the speed differential between consecutive movements should not exceed $10\text{ mph}$ (e.g., $|V_1 - V_2| \le 10\text{ mph}$).

Sight Distance Requirements

Two types of sight distance must be checked:

  1. Stopping Sight Distance (SSD): Must be provided at the entry, on the circulatory roadway, and at the pedestrian crosswalks.
  2. Intersection Sight Distance (ISD): The entering driver must have a clear line of sight to conflicting vehicles approaching from the left (on the circulatory roadway and the adjacent entry). The time gap ($t_g$) for roundabout entry is typically $5.0\text{ s}$ for passenger cars.

Worked Example

A designer is verifying the entry geometry of a single-lane roundabout.

  • The entry path radius ($R_1$) is determined to be $90\text{ ft}$.
  • The circulatory roadway has an outward cross slope of $-2.0\%$ ($e = -0.02$).
  • The side friction factor ($f$) for this speed range is $0.26$.
  1. Calculate the fastest entry path speed ($V_1$).
  2. Determine if this speed complies with AASHTO speed recommendations for a single-lane roundabout.
  3. Calculate the required Intersection Sight Distance ($ISD$) along the circulatory roadway, assuming a design speed of $20\text{ mph}$ on the circulatory roadway.

Solution

1. Calculate Fastest Entry Path Speed ($V_1$): Using the speed-radius equation with adverse super-elevation ($e = -0.02$):

$$V_1 = 3.86 \sqrt{R_1 (f - e)}$$

$$V_1 = 3.86 \sqrt{90 \times (0.26 - 0.02)}$$

$$V_1 = 3.86 \sqrt{90 \times 0.24} = 3.86 \sqrt{21.6}$$

$$V_1 = 3.86 \times 4.648 = 17.94\text{ mph} \approx 18\text{ mph}$$

2. Check Compliance: The calculated entry speed is $18\text{ mph}$. This falls within the recommended single-lane roundabout entry speed range of $15$ to $20\text{ mph}$, indicating that the entry deflection is geometrically sufficient.

3. Calculate Intersection Sight Distance ($ISD$):

  • Major road speed ($V_{\text{circ}}$) = $20\text{ mph}$ (circulating speed).
  • Time gap ($t_g$) = $5.0\text{ s}$.
$$ISD = 1.47 V_{\text{circ}} t_g$$

$$ISD = 1.47 \times 20 \times 5.0 = 147\text{ ft} \approx 150\text{ ft}$$

The entering driver must have an unobstructed line of sight to vehicles circulating on the roadway for a distance of at least $147\text{ ft}$ to the left.

References

  • A Policy on Geometric Design of Highways and Streets (AASHTO Green Book), 7th Edition, 2018, Section 9.8.
  • NCHRP Report 672: Roundabouts: An Informational Guide, 2nd Edition, 2010.
  • NCEES PE Civil Reference Handbook, Section 4.3.2.