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Soak Length Activity Factors for Hot Soak Emissions
Report Number M6.FLT.004
Edward L. Glover
David J. Brzezinski
U.S.EPA Assessment and Modeling Division
1.0 INTRODUCTION
MOBILE6 will compute and report (as a user option) hourly emission factors for
start, running, and evaporative emissions. These outputs will be in addition to the standard
daily emission estimates which are currently calculated by MOBILE5. The hourly
emission factors will allow the MOBILE6 model to provide more precise output that
accounts for the time of day that vehicle emissions occur. The temporal distribution of
emissions is an important factor in the formation of diurnal evaporative and start emissions.
The hourly emission estimates require considerable vehicle activity information and
analysis. The term "activity" refers to the vehicle's operating mode, such as running,
idling, parked (soaking), etc. The specific activity information needed for emissions
estimates includes soak durations, time of soak, trip lengths, time of trip, and other
information. This document (M6.FLT.004) discusses the issue of vehicle soak time only
as it pertains to hot soak emissions. Other activity estimates needed to develop daily
emission factors for exhaust, diurnal, running loss or resting loss emissions will be
documented in other MOBILE6 documents listed with the report numbers "M6.FLT.XXX".
2.0 DATA SOURCES USED
The primary data source for this analysis is an EPA instrumented vehicle studies
conducted in Baltimore and Spokane. In this studies, instrumentation to monitor vehicle
usage was installed with the motorists' permission on 168 randomly selected vehicles while
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they were tested at an Inspection / Maintenance (I/M) station. The motorists returned one
or two weeks later to have the instrumentation removed. Information from more than
8,500 vehicle-trips was recorded. The raw data collected from the studies were processed
by the Radian Corporation under EPA contract to create a "trip characteristics" file. This
processed file was used to develop the hourly soak time distributions. For more details
regarding the instrumented vehicle study and the data processing, please refer to the
document "Travel Trip Characteristics Analysis" Final Report under EPA Contract 68-C1-
0079 WA 2-05 with Sierra Research.
3.0	METHODOLOGY
This section describes the basic methodology to develop the soak activity estimates
used to calculate hot soak emissions. The process consisted of several steps. These are
discussed below.
3.1	Definition of a Hot Soak
Hot Soak emissions are evaporative emissions which may be produced by a warm,
but no longer running vehicle. Operationally, hot soak emissions are defined as those
produced for a duration of time following a vehicle trip which lasted a minimum length of
time. This is a general definition. By convention (and assumption) a hot soak duration (the
length of time following the key off) is defined to range from a minimum of 1 second
(instantaneous) to a maximum of 1 hour. The one hour limit was chosen for consistency
with the Federal Test Procedure definition of a hot soak.
The length of time of the trip prior to the hot soak can vary considerably. However,
a minimum trip length of 4 minutes was chosen to qualify the subsequent soak as a valid
hot soak. The choice of 4 minutes was fairly arbitrary; however, it is believed that a trip
of less than 4 minutes will not sufficiently warm the engine or the fuel or over-saturate the
evaporative canister so as to produce sufficient hot soak emissions. Thus, trips less than
four minutes were assumed to produce no hot soaks and are not reflected in the hourly
activity factors for hotsoaks.
3.2	Hourly Intervals
The 24 hour day was divided into 14 different hourly groups. Thirteen of these
groups have a duration of one hour. These start at 6:00AM and run through 7:59:59PM.
The fourteenth hour contains the remaining nighttime hours as one interval. Collapsing
these hours into one group was done for three reasons: (1) the emissions contributed during
the night have a relatively smaller impact on daily ozone or CO formation than those
contributed during the morning or day, (2) there were relatively little data for these time
periods, and (3) what data were available produced results which showed very little hour
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to hour variance. The hourly intervals are shown in Table 1. In addition to hot soak
activity estimates, they are the same hourly groups used in the calculation of activity
estimates for start emissions, running emissions, running loss emissions, resting loss
emissions, and diurnal emissions.
3.3 Factors Affecting Hot Soak Activity Values
3.3.1 Weekdays Versus Weekends
For a number of the activity parameters a significant difference existed between the
value for the weekday and the value for the weekend. Conceptually this make sense since
most motorists have different usage patterns for their vehicles on weekdays than on
weekends. Differences may also exist for the various days of the week; however, the
database was too small to reliably discern these differences.
The MOBILE6 model will distinguish between weekend and weekday in terms of
activity and emissions, and a user input will be required to tell the model which one is to
be reported. The default will likely be the "weekday."
Table 1
Hourly Ranges
Nominal Name
Hourly Range
Time
6
6-7
6 am to 7 am
7
7-8
7 am to 8 am
8
8-9
8 am to 9 am
9
9 - 10
9 am to 10 am
10
10 - 11
10 am to 11 am
11
11 - 12
11 am to noon
12
12- 13
noon to 1 pm
13
13 - 14
1 pm to 2 pm
14
14- 15
2 pm to 3 pm
15
15 - 16
3 pm to 4 pm
16
16- 17
4 pm to 5 pm
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17
17- 18
5 pm to 6 pm
18
18 - 19
6 pm to 7 pm
24
19 - 24 and 24 - 5
7 pm to 6 am
3.3.2 Vehicle Type and Model Year
The hot soak activity parameters such as the number of trips per day, and the
distribution of soak time after the trip end were also investigated by vehicle type or vehicle
age. Slight differences were found between cars and trucks in terms of trips per day, with
trucks having slightly more trips per day (shown in Tables 2a and 2b). However, little
significant difference in the hourly distributions were found between cars and trucks or
even by vehicle model year. The lack of difference in the hourly distributions between cars
and trucks was not particularly surprising since the number of trips per day are fairly
similar, and most light trucks today play virtually the same role as cars. Exceptions might
be in rural areas or heavily industrial areas where trucks frequently are used to haul
equipment or products.
The lack of difference between model years is a little more surprising. One would
expect an older vehicle to have a higher percentage of longer soaks, and possibly shorter
trips (i.e., the vehicle sits more and goes on fewer long trips because it is a second vehicle).
However, a limited analysis of the data did not conclusively demonstrate these hypotheses.
One reason might be the relatively small sample of older vehicles. For example, less than
15 percent of the vehicle sample were more than 10 years old at the time of the testing.
This was also too small a sub-sample to further split into 28 hourly and weekday/weekend
groups, and still obtain reasonable results. The other reason might be recruitment process
which was biased to obtain vehicles which were primary vehicles rather than spare second
vehicles. As a result, the hourly distributions shown in Tables 3, 4a and 4b represent both
cars and trucks and all vehicle ages.
Since the default MOBILE6 hourly activity estimates are based exclusively on 168
vehicles, and cannot possibility reflect all geographical areas, times, or other variables, the
user will have the option of providing hot soak activity data into the MOBILE6 model from
an external file.
3.4 Hot Soaks per Car-Day
The first necessary parameters in the model are the estimates for Hot Soaks/car-day.
The starting point for this calculation are the trips/car-day values shown in Table 2a. This
is a convenient starting point because by definition each hot soak must have a
corresponding trip. Four different estimates were obtained from the instrumented vehicle
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database. There is one estimate for each combination of car versus truck and weekday
versus weekend.
To calculate the number of hot soaks per car per day, the values shown in Table 2a
were reduced to account for trips which were less than 4 minutes in length. The reduction
is a simple percentage of the total trips which were less than 4 minutes. For weekdays, the
reduction is 26.1 percent and for weekends it is 28.6 percent. For example, this reduces the
average number of weekday trips per day per car from 7.28 trips/car-day to 5.38 hs/car-day.
The average number of hot soaks/car-day are shown in Table 2b.
These estimates are subject to revision pending completion of a thorough analysis
of national trip data by an EPA contractor. The values could potentially vary considerably
from those shown here.
Table 2a
Trips per Car per Day
Cars
Trucks
Weekday
Weekend
Weekday
Weekend
7.28
5.41
8.06
5.68
Table 2b
Hot Soaks per Car per Day
Cars
Trucks
Weekday
Weekend
Weekday
Weekend
Reduction = 26.1%
Reduction = 28.6%
Reduction = 26.1%
Reduction = 28.6%
5.38
3.86
5.96
4.06
3.5 Daily Hot Soak Distribution by Time of Day Increment
Table 3 contains the distribution of the vehicle hot soaks by time of day. An
estimate is provided for each of the fourteen groups, and separate estimates are provided
for weekends and weekdays. All of the estimates were calculated after removing the hot
soaks which had preceding trip durations less than 4 minutes. For example, Table 3 shows
that approximately 2.33% percent of the weekday hot soaks occur during the period from
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6:00 AM to 6:59:59 AM. The data which underlies Table 3 were obtained from the
instrumented vehicle database. Each column sums to 100 percent.
Table 3
Daily Distribution of Hot Soaks (in
percent)
Hour
Weekday
Weekend
6
2.33
0.99
7
6.05
2.26
8
6.30
3.38
9
4.62
6.41
10
5.08
6.98
11
6.32
8.80
12
7.80
9.23
13
7.32
7.40
14
7.87
8.10
15
8.63
6.62
16
8.71
8.03
17
7.99
6.91
18
5.88
6.27
24
15.10
18.62
3.6 Hot Soak Length Distribution by Hourly Group
The MOBILE6 model will contain a cumulative soak length distribution for each
of the 14 hourly groups, and for both weekdays and weekends. As a result, there will be
28 cumulative soak length distributions. These 28 distributions are based on data from the
instrumented vehicle study. To make the distributions smoother for use in the MOBILE6
model, a Weibull function fit was generated for each of the 28 soak length distributions
using the non-linear fit algorithms in the statistical software package SPSS. Only the first
59 minutes of the cumulative distribution were fitted. Since the 60 minute (the last minute)
contained all of the soaks which were 60 minutes or greater in length it produced a
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discontinuous function which jumped up to 100 percent. The 60 minute point will be
accounted for separately in the MOBILE6 model by coding the value of 100 percent for the
60 minute point. Also, in a few cases negative values for the Weibull distribution function
were obtained for short duration soaks (1 or 2 minutes). In these cases, a value of zero will
be assumed. Overall, the Weibull function produced a fairly close fit for all of the 28
distributions. The typical r-squared value was 0.97 or better for weekdays, and 0.92 or
better for weekends. The better fit for the weekdays versus the weekends is the result of
a considerably larger weekday database.
The Weibull function fit is of the form:
where bl, b2, b3 and b4 are regression coefficients, and soaklength in minutes (0 to 59) is
the independent variable. The variable Y is the cumulative distribution in percent.
Tables 4a and 4b lists all of the regression coefficients (bl, b2, b3, and b4) and r-
squared values for each of the 28 hourly and weekday/weekend groups. Figure la shows
the raw data distribution and the corresponding Weibull fit for the 7 to 8 AM weekday
group. The heavier dots in the figure are the points fitted by the weibull function, the
lighter dots are the actual data points. The 7 to 8 AM function was plotted because it is
generally typical of the fit of the other 27 hourly/week groups.
Y
bl - b2 * exp( -b3 * Soaklengthb4)
Eqn 1
Fig 1a - Hot Soak Distribution
7AM to 8AM Weekdays
50
CO

O
CO 30
o
X
20
 Predicted Values
HOTSK MIN
o
c
0 10. 
0 
Q- o,_
o
HOUR7
HOTSK MIN
10
20
30
40
50
60
Hot Soak Length (0-59 Minutes) 60 has remainder
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Table 4a
Weekdays
Hot Soak Length Distribution Coefficients by Hourly Group
Hourly
Group
Coefficient
B1
Coefficient
B2
Coefficient
B3
Coefficient
B4
R-squared
Value
6
1143.5
20.261
-4.028
-0.001095
0.947
7
1749.6
24.655
-4.259
-0.001225
0.990
8
2483.7
29.051
-4.449
-0.000981
0.981
9
3212.9
32.712
-4.589
-0.001003
0.971
10
4010.7
36.230
-4.709
-0.000929
0.955
11
2985.7
31.546
-4.552
-0.001310
0.988
12
3208.4
32.605
-4.590
-0.001202
0.985
13
4042.0
36.357
-4.714
-0.009702
0.964
14
3066.0
31.957
-4.565
-0.001189
0.987
15
3207.6
32.627
-4.590
-0.001167
0.987
16
2957.4
31.546
-4.549
-0.001149
0.977
17
2435.8
28.726
-4.440
-0.001239
0.995
18
2096.7
26.827
-4.361
-0.001445
0.969
24
1906.5
25.712
-4.306
-0.000900
0.977
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Table 4b
Weekends
Hot Soak Length Distribution Coefficients by Hourly Group
Hourly
Group
Coefficient
B1
Coefficient
B2
Coefficient
B3
Coefficient
B4
R-squared
Value
6
51.25
5.911
-18.036
-0.0359
0.935
7
55.31
0.0000633
-13.695
-0.0325
0.924
8
2732.31
0.1819
-9.620
-0.000651
0.943
9
2208.97
0.1645
-9.507
-0.000750
0.978
10
2706.57
0.1784
-9.631
-0.000628
0.951
11
2432.70
0.1674
-9.591
-0.000862
0.945
12
1824.07
0.1564
-9.364
-0.000857
0.972
13
1930.61
0.1506
-9.464
-0.000904
0.950
14
2424.95
0.1761
-9.531
-0.000692
0.980
15
1921.98
0.1496
-9.464
-0.000861
0.922
16
2129.29
0.1602
-9.498
-0.000819
0.978
17
1292.06
0.1333
-9.183
-0.001161
0.969
18
178.02
0.0327
-8.586
-0.007661
0.957
24
520.28
0.0902
-8.653
-0.001729
0.991
3.7 Using the Hourly Hot Soak Activities in MOBILE6
3.7.1 Average Hourly Hot Soak Emissions
The average hourly hot soak emissions will be calculated by multiplying the hot
soak emissions function (discussed in document M6.EVP.003) with the corresponding hot
soak activity function (calculated from the coefficients in Tables 4a and 4b and Eqn. 1), and
summing the products to produce an overall hourly average. This average is then
multiplied by the number of hot soaks per day per vehicle which occur in the given hourly
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group to produce the average hot soak emission emission level for the given hourly group.
In the MOBILE6 model this is done by multiplying the 60 (one for each minute of the hot
soak) hot soak emission estimates with the 60 activity values (activity distribution at each
one minute point), and summing the result. This calculation will be done separately for
each of the 28 hourly and weekday/weekend groups to produce hourly hot soak emission
estimates. The number of hot soaks per day per vehicle is obtained in Table 2b, and the
factors which determine how many hot soaks to allocate to a particular hourly group is
shown in Table 3. For example, the 10 to 11 AM weekday hourly group for cars would be
allocated 5.38 hot soaks/day-car x 5.08 percent (Table 3) = 0.273 hot soaks/car.
Calculation of the average hourly hot soak is shown mathematically as:
given:	HS emissions[soak length]
HS activity[soak length]
Soak length: i = 1, 59 minutes
Hourly group: j = 1, 28 hourly/weekday-weekend groups
Wt HS emissions(i) = HS emissions(i) * [HS activity(i+l) - HS activity(i)]	Eqn. 2
Average HS emissions(j) = SUM(WtHS emissions(i))
where the range of the SUM(Wt HS emissions(i)) is: i = 1, 59 minutes
Both the activity function (Weibull fit) and the hot soak emissions function are
continuous functions. However, both were turned into discrete functions with 60 intervals
in the MOBILE6 model. This was done for computation purposes, and to allow the
MOBILE6 user to input a set of alternative hot soak activity values in an attached file rather
than a set of different Weibull function parameters.
3.7.2 Average Daily Hot Soak Emissions
An average daily hot soak value will also be calculated in the MOBILE6 model.
This hot soak emission value is analogous to the hot soak emission values reported by
MOBILE4 and MOBILE5. It will be the product of the number of hot soaks per day, and
a weighted average of the individual hourly average hot soaks. The average number of hot
soaks per day are shown in Table 2a. The weighting factors used to weight the hourly
groups together are the values shown in Table 3.
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COMMENTS
Comments on this report and its proposed use in MOBILE6 should be sent to the attention
of the author, and submitted electronically to mobile@epamail.epa.gov, or by fax to
(313)741-7939, or by mail to M0BILE6 Review Comments, US EPA Assessment and
Modeling Division, 2565 Plymouth Road, Ann Arbor MI 48105. Electronic submission
of comments is preferred, since we will make any comments available on our web site. In
your comments, please note clearly the document that you are commenting on including the
report title and the code number listed. Please be sure to include your name, address,
affiliation, and any other pertinent information.
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