Bonde 1
Richard Bonde
PHYS/MATH 714
Problem: Traffic Circle
Traffic circles have a number of criteria in determining design. According to the Center for
Advanced Transportation Systems Simulation (CATSS) [1], traffic circle requests must meet a series of
minimum points in order to qualify. There are 3 different areas that assign points:
1. Accidents at the intersection in the area
2. Traffic speeds
3. Traffic volume
The more cases in each are rewarded more points to building a traffic circle. CATSS also takes the traffic
volume data and puts it into certain equations to determine the number of entry lanes and inner circle
lanes. These equations are as follows:
𝑞𝑐 = 1218 − 0.74𝑞𝑒
𝑞𝑐 = 1250 − 0.532𝑞𝑒
𝑞𝑐 = 1380 − 0.50𝑞𝑒
𝑞𝑐 = 1409 − 0.42𝑞𝑒
The first equation corresponds to one entry lane, 1 inner circle; the second equation corresponds to one
entry lane and two to three inner circles; the third equation corresponds to 2 entry lanes and 2 inner
circles; and the final equation corresponds to 2 entry lanes and 3 inner circles. qc is the traffic capacity
while qe represents the traffic flow upstream (right after entry). The type of vehicle is given a a
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passenger car equivalent (pce): Bus/Truck=1.5pce, Truck with trailer=2pce, Standard car=1pce,
Motorcycle=0.5pce. The amount of traffic flow will then determine the number of lanes and a range of
given diameters. According to the Transportation Research Board, the following represents the types of
traffic circles in the U.S. [2]:
Percentage of Traffic Circles in the
U.S. With Given Diameter
(Inscribed Circle)
<98 (ft)
98-108 (ft)
109-121 (ft)
148-200 (ft)
410-476 (ft)
Figure 1
As seen in figure 1, most traffic circles in the U.S. occur as a one lane circle (not including a by-pass lane).
One lane traffic circles: The Federal Highway Administration requires that one lane traffic circles have
less than 1800 vehicles per hour traffic flow, while a one lane exit must be less than 1200 vehicles per
hour [3]. Anything more than that, and a two lane exit must be looked at. Design speeds for the circle
can be calculated as a function of the radius, super elevation and friction. The equation is given by:
𝑉 = √15𝑅(𝑒 + 𝑓) [3]
Where f is the coefficient of friction and e represents the super elevation which is normally 2% (never to
be exceeded) [3]. 1.5% may be used when considering traffic where trucks or other vehicles with high
centers of gravity may be a problem. The super elevation is used for drainage and can be either graded
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away from the inner circle or towards. Figure 2 gives a graph of speed limits in the circle versus the
inscribed radius, with both possible super elevations normally used.
Figure 2
Figure 3
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Figure 3 shows the side force of friction as a function of speed [3]. These values were no doubt found by
applying Newton's second law, which could have been possibly modified.
𝑓=
𝑚𝑉 2
𝑅
This equation shows that in our case of the car, the force of friction, f, is the centripetal force needed
to keep the car continuing on a circle, from Newton's first law. The mass of the vehicle is given by m,
and the velocities and radii were determined from the previous equations and traffic volume criteria.
The stopping distance must also be taken into account when determining the speeds and radius
of the traffic circle. The equation is given by:
𝑑 = 1.468𝑡𝑉 + 1.087
𝑉2
𝑎
[3]
Where t is the perception-brake reaction time (assumed 2.5s), a is the acceleration (assumed 11.2 ft/s2)
and V is the initial speed.
Modeling traffic: A simple approach to modeling traffic flow might be to consider the traffic as a "fluid."
Then starting with a simple law, conservation of mass, which can be written as:
𝑚𝑖 − 𝑚𝑒 −
𝑑𝑚𝑐
=0
𝑑𝑡
Which says that the mass of the cars into the circle must equal the mass of the cars out of the circle plus
the rate of change of the mass of the cars in the circle, which should be very close to zero otherwise
severe backup in the circle will happen. This is of course just a basic model and assuming steady flow of
the cars in and out of the circle. With yield signs there a delay into the circle. That delay can be found
by:
Bonde 5
𝑑=
3600
+
𝑐𝑚,𝑥
900𝑇 +
𝑉𝑥
𝑐𝑚,𝑥
𝑉𝑥
𝑐𝑚,𝑥
− 1 + √(
2
− 1) +
3600
𝑉
)( 𝑥 )
𝑐𝑚,𝑥 𝑐𝑚,𝑥
(
450𝑇
[3]
Where Vx is the flow movement (veh/h), cm,x is the capacity of movement (veh/h) and T is the analysis
time period (fraction of an hour). This of course does not take into account other considerations and
"human factors" like stopping when there is no car to yield to, not yielding, pedestrian and bicycle
crossing, etc...
Traffic Circle Design: One thing to consider is the percentage of people making just a right turn onto a
busy street. If this number is elevated, you can input a by-pass lane as shown here:
Figure 4 [3]
This allows the car to make a right turn without the need for entering the circle and would force anyone
not making a right turn to take the left side of the island. One could consider also a 2 lane circle that
really as 4 by-pass lanes, which acts like a one lane circle. Here is an example of that [2]:
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Figure 5
In this case the exit traffic would have to be greater than 1200 vehicles per hour as it utilizes a two lane
exit.
Another consideration be that the circle itself lies along a major street. In this case, a lot of
traffic would be "passing through" the circle. You might consider putting a one or two lane bridge
(depending on traffic flow) to go over the circle. Cars going straight would take this bridge while cars
turning right, left or making a u-turn would take the circle. The entry point would need to be expanded
accordingly.
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References
[1] Center for Advanced Transportation Systems Simulation,
http://www.catss.ucf.edu/projects/documents/reports/htm/roundabouts_aty_project_7.htm, June 12,
2009
[2] "Modern Roundabout Practice in the United States: A Synthesis of Highway Practice",
Transportation Research Board, National Research Council
[3] "Roundabouts: An Information Guide", FHWA-RD-00-67, U.S. Department of Transportation, Federal
Highway Administration