INTEROFFICE MEMORANDUM
TO:
Neil E. Boudreau, State Traffic Engineer
[signature on original]
THRU:
Charles Hale, Manager of Electrical Systems
[signature on original]
FROM:
Jim Danila, P.E., PTOE, Assistant State Traffic Engineer [signature on original]
DATE:
January 8, 2013
SUBJECT:
MassDOT Guidance on Calculating Clearance Intervals at Traffic Signals
Background
At present time MassDOT provides minimal guidance to Designers for the calculation of
yellow, all-red, and pedestrian clearance intervals. Since no national standard exists, there
are several different methodologies currently used by engineers for calculating yellow and
all-red clearances. In addition, the Manual on Uniform Traffic Control Devices (MUTCD)
provides standards for calculating pedestrian clearance times, but there are several options
for how it relates to both the pedestrian change interval and the buffer interval. The
intention of this memorandum is to provide both the Designer and MassDOT staff
guidance for calculating yellow, all-red, and pedestrian clearance times in order to reduce
crashes at signalized intersections across the Commonwealth. The Designer may still elect
to use a separate methodology for calculating these timings, but should only do so upon
using engineering judgment that justifies the alternate method.
Note: the National Cooperative Highway Research Program (NCHRP) released Report 731,
“Guidelines for Yellow and All-Red Intervals at Signalized Intersections” in November, 2012.
Much of the guidance contained within this memorandum is based upon the findings in
that report.
Calculating the Yellow Clearance Interval
Designers should use the following equation to calculate the yellow clearance interval:
𝐄𝐪𝐮𝐚𝐭𝐢𝐨𝐧 𝟏:
𝑌=𝑡+
1.47𝑉
2𝑎 + 64.4𝑔
Where:
Y = yellow interval (s). Y shall be a minimum of 3.0 s in all scenarios;
t = perception-reaction time (1 s);
V = 85th percentile approach speed (mph);
a = deceleration rate (10 ft/s2); and
g = grade of approach (percent / 100, downhill is negative grade).
MassDOT – Highway Division, Traffic Engineering Section
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The following considerations should be made when determining V:
 The 85th percentile approach speed for through traffic should be determined at a
point far enough away from the traffic signal that its operation does not affect freeflow operation.
 If the 85th percentile speed cannot be obtained, V may be estimated by using the
posted speed limit plus 7 mph.
 The 85th percentile speed may be approximated by subtracting 5 mph from the
posted speed limit for left-turns.
The grade measurement should be taken at a point approximately 5.0 seconds upstream
of the stop line, based upon V.
Calculating the All-Red Clearance Interval
Designers should use the following equation to calculate the all-red clearance interval:
𝐄𝐪𝐮𝐚𝐭𝐢𝐨𝐧 𝟐:
𝑅=
𝑊+𝐿
−1
1.47𝑉
Where:
R = red interval (s). R shall be a minimum of 1.0 s in all scenarios;
V = 85th percentile approach speed (mph). See previous section for methodologies for
estimating V, if not field measured;
W = intersection width measured from the back/upstream edge of the approaching
movement stop line to the far side of the intersection as defined by the extension of
the curb line or outside edge of the farthest travel lane (ft); and
L = length of vehicle, typically 20 ft.
The value of W should be modified for the following conditions:
 If crosswalk with pedestrian signals has its near-side crosswalk line 40 feet or more
from the extension of the farthest edge of the farthest conflicting travel lane, W
should be measured from the back edge of the approaching movement stop line to
the near-side crosswalk line.
 The value of W should be measured along the vehicle turn path from the stop line
to the no-conflict point for exclusive left-turn movements.
For calculating the red clearance interval for left-turns, the 85th percentile speed should be
20 mph, regardless of the posted speed limit.
Clearance Intervals for Left-Turn Phases
Calculations for yellow and all-red clearance Intervals for left-turning vehicles should
consider the following:
 For protected-only left-turn movements, the yellow and all-red intervals should be
calculated for each approach and implemented as calculated. The intervals do not
have to be the same duration for opposing approaches.
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 For permissive-only left-turn movements, the yellow and all-red intervals should be
calculated for opposing approaches, including the through movements. The
implemented intervals shall be the longest of the calculated values (left, through, or
combination). The intervals shall be the same duration for the left-turn and through
movements on opposing approaches to ensure that phase and interval termination
is concurrent.
 For protected/permissive left-turn movements, the yellow and all-red intervals
should be calculated and implemented as described above for the respective
protected and permissive portions of the phase.
Equations 1 and 2 may result in excessively long clearance intervals running permissiveonly or protected/permissive left-turn phases at intersections with wide cross-sections or
offset approaches. In these situations the Designer may increase V for left-turns using
engineering judgment, change the phasing scheme to protected-only left-turns, or
consider the following:
1. Calculate Y and R for both the left-turn (YLT, RLT) and through (YTh, RTh) movements
as shown in Equations 1 and 2, ignoring any minimum values at this time.
2. Sum Y and R for each respective movement. The lowest sum calculated for either
the left-turn or through movement represents the minimum total clearance time
(CTmin) required for the approach.
3. The design value of Y for the approach should be equal to the value required to
satisfy the through movement: Y = YTh. Y shall be a minimum of 3.0 seconds.
4. The design value of R for the approach should be the difference of CTmin and Y:
R = CTmin – Y. R shall be a minimum of 1.0 seconds.
Pedestrian Clearance Time
The pedestrian clearance time, which consists of the pedestrian change interval and the
buffer interval, shall be calculated to conform to Sections 4E.06 and 4E.07 of the MUTCD. A
portion of Figure 4E-2 from the MUTCD is shown below to better illustrate:
MassDOT – Highway Division, Traffic Engineering Section
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Calculated values for pedestrian clearance times should consider the following:
 The buffer interval should be at least 3 seconds and consist of all or part of the
yellow clearance interval for use with concurrent pedestrian phasing.
 Some traffic signal controllers may limit the ability to run the pedestrian change
interval concurrently with the vehicular yellow clearance interval. This shall not
justify a pedestrian clearance time that does not meet or exceed the calculated
minimum.
 There are additional options in Figure 4E-2 that have not been included in this
memorandum that may be considered to accommodate the buffer interval.
However, to keep from unnecessarily lengthening phases when not required
and/or to provide additional time for the walk interval, MassDOT recommends that
the buffer interval be accommodated at the start of the yellow clearance interval for
use with concurrent pedestrian phasing.
 The pedestrian change interval should be approximately 4 seconds less than the
calculated minimum pedestrian clearance time for exclusive pedestrian phasing.
This remaining 4 seconds should be applied to an all-red clearance interval during
which a steady, upraised hand indication should be displayed.
Rounding Calculated Values
Calculated values for yellow and all-red clearance Intervals should be rounded to the
nearest half-second (0.5 s), using the following methodology:
 Values ending in n.0 to n.1 should be rounded down to the nearest whole number;
 Values ending in n.2, n.3, and n.4 should be rounded up to the half-second;
 Values ending in n.6 should rounded down to the half second; and,
 Values ending in n.7, n.8, and n.9 should be rounded up to the next whole number.
The pedestrian change interval shall always be rounded up to the nearest whole number
or the buffer extended beyond 3 seconds to accommodate a minimum calculated
pedestrian clearance time that is not a whole number.