EPA-460/3-74-005
JANUARY 1974
AUTOMOBILE EXHAUST
EMISSION MODAL
ANALYSIS MODEL
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Water Programs
Office of Mobile Source Air Pollution Control
Certification and Surveillance Division
Ann Arbor, Michigan 48105
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EPA-460/3-74-005
AUTOMOBILE EXHAUST EMISSION
MODAL ANALYSIS MODEL
Prepared by
Paul Kunselman, H. T. McAdams,
Charles J. Domke, and Marcia Williams
Calspan Corporation
Buffalo, New York 14221
Contract No. 68-01-0435
EPA Project Officer: Charles J. Domke
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Water Programs
Office of Mobile Source Air Pollution Control
Certification and Surveillance Division
Ann Arbor, Michigan 48105
January 1974
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This report is issued by the Office of Mobile Source Air Pollution Control,
Office of Air and Water Programs, Environmental Protection Agency, to
report techp'ical data of interest'to a limd-tfed number of readers'. 'Copies
of this report are"available free of charge to Federal employees, current
contractors and grantees, and nonprpf^organizations - as supplies L.
permit - from therAir Pollution Technical .Information Center', Erivirpn-
mental Protection Agency, Research Triangle Park, North Carolina 27711,
or may be obtained, for a nominal cost, from the National Technical
Information Service, 5285 Port Royal Road, Springfield, Virginia 22151.
This report was furnished to the Environmental Protection Agency
by Calspan Corporation, Buffalo, New York, in fulfillment of Contract
Number 68-01-0435. The opinions, findings, and conclusions expressed
are those of the author and not necessarily those of the Environmental
Protection Agency. Mention of company or product names is not to be
considered as an endorsement by the Environmental Protection Agency.
Publication Number EPA-460/3-74-005
11
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ABSTRACT
Sections 1 through k of this report on modal analysis of automobile
emissions were prepared by Calspan Corporation for the United States
Environmental Protection Agency's Division of Certification and Surveillance,
Ann Arbor, Michigan, under EPA Contract No. 68-01-0^35- These sections and
the appendices, tables, and figures which accompany them are directly
incorporated into this report.
The mathematical model and allied computer programs described in
Section 3 and Appendix U of the report enable an analyst to calculate the amounts
of hydrocarbons, carbon monoxide and oxides of nitrogen emitted by individual
vehicles or vehicle groups over any specified driving sequence. The model
requires as input, the amounts of the three pollutants emitted by individual
vehicles over short duration driving sequences (modes) in which speed is a
monotonic function of time. Therefore, it is understood that the mathematical
model should be used only within the region of speed and acceleration space
which is spanned by the input modal data.
In Section k, the validity of the model is investigated by using it
to predict emissions for individual vehicles over the Surveillance Driving
Sequence (SDS) and the first 505 seconds of the hot Federal Test Procedure
(FTP) driving sequence. The ability of the model to predict actual vehicle
emissions is compared with the reproducibility of the actual vehicle emissions
measured in replicated tests. When results are averaged over all available
data, the model is able to predict emissions as well as an original test
can predict a replicated test. Because of the specifics of the study design
111
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and the data collection process, the input data vehicles (from the FY71 EPA
Emission Factor Program) were tested over the SDS and FTP. Therefore,
the test of model performance may have "been more favorable than would have
been the case if the data had been obtained from two different vehicle fleets.
The general user should find that the model is most useful as a
predictor of group emissions of warmed-up vehicles. Therefore, in Section 5»
the input data collected from individual vehicles during the FY71 EPA Emission
Factor Program have been synthesized into model-year/city groups. The
predictive ability of the model is then, investigated by using it to predict
vehicle group emissions from independent data samples which are representative
of the national population of in-use vehicles.
IV
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TABLE OF CONTENTS
Page No.
1. INTRODUCTION 1
1.1 Modal Analysis of Vehicle Emissions 3
1.2 Composite Analysis of Vehicle Emissions 6
1.3 Report Scope and Preview 9
2. PROBLEM DEFINITION 10
2.1 Input Data 10
2.2 Output Data 12
3. OVERVIEW OF THE MATHEMATICAL MODEL I1*
3.1 The Emission Rate Function 1^
3-2 Steady-State and Accel/Decel Emission Rate Functions 16
3.3 Determination of the Coefficients (K, S. ) 18
3-U The Composite Emission Rate Function 21
3-5 Vehicle and Vehicle Group Characterization 21
It. MODEL PERFORMANCE 23
U.I Statistical Indicators of Performance 23
k.2 Performance Results 25
U.3 Discussion and Evaluation 25
5. APPLICATIONS OF THE MATHEMATICAL MODEL FOR THE GENERAL USER 3^
5-1 Determination of Group Structure 3^
5.2 Computer Implementation 37
5.3 Model Performance on Group Predictions ^0
6. SUMMARY AND CONCLUSIONS ^7
TABLES ^9
FIGURES 75
APPENDIX I - Specification of the 37 Modes and Evaluation of the 1-1
Average Values of the Basis Functions
APPENDIX II - Speed vs. Time Curves for the Surveillance Driving II-l
Sequence and First 505 Seconds of the Federal Test
Procedure
APPENDIX III - The Mathematical Model III-l
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TABLE OF CONTENTS (cont'd)
Page No.
APPENDIX IV - Computer Implementation of the Generalized IV-1
Mathematical Model
APPENDIX V - Vehicle Classification by Discriminant Function V-l
Analysis
APPENDIX VI - Computer Applications for the General User VI-1
VI
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LIST OF TABLES
gable No. Table Page No.
1 Bag Value Statistics for the Surveillance 51
Driving Sequence
2 Bag Value Statistics for the First 505 Seconds 52
of the Federal Test Procedure Driving Sequence
3 Distribution of HC Bag Value Error from the 53
Surveillance Driving Sequence
U Distribution of CO Bag Value Error from the 51*
Surveillance Driving Sequence
5 Distribution of NOX Bag Value Error from the 55
Surveillance Driving Sequence
6 Distribution of HC Bag Value Error from the First 56
505 Seconds of the Federal Test Procedure Driving
Sequence
7 Distribution of CO Bag Value Error from the First 57
505 Seconds of the Federal Test Procedure Driving
Sequence
8 Distribution of NOX Bag Value Error from the First 58
505 Seconds of the' Federal Test Procedure Driving
Sequence
9 Replicate Modal Analyses of HC for 6l Vehicles 59
10 Replicate Modal Analyses of CO for 6l Vehicles 60
11 Replicate Modal Analyses of NO for 6l Vehicles 6l
X
12 Variance Component Analyses for 6l Replicate Tests 62
13 Federal Short Cycle - Group Prediction of Six-City 63
Data
lU Cold Stabilized Portion of the Federal Test Procedure - 65
Group Prediction of Six-City Data
15 Hot Transient Portion of the Federal Test Procedure - 67
Group Prediction of Six-City Data
16 Federal Short Cycle --Group Prediction of Short 69
Cycle Project
vii
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LIST OF TABLES
(cont'd)
Table No. Table Page No.
17 Hot Transient Portion of the Federal Test Procedure - 70
Group Prediction of Short Cycle Project
18 Cold Stabilized Portion of the Federal Test Procedure - 71
Group Prediction of Short Cycle Project *
19 Cold Stabilized Portion of the Federal Test Procedure - 72
Group Prediction of ATL Study
20 Hot Transient Portion of the Federal Test Procedure - 73
Group Prediction of ATL Study
1-1 Modal Specifications 1-5
1-2 Values of the Averages of the Basis Functions Over ..!-$
Each Mode
II-l Surveillance Acceleration-Deceleration Driving Sequence 11-3
II-2 First 505 Seconds of Federal Test Procedure Driving 11-7
Sequence
IV-1 Listing, Main Program I IV-7
IV-2 Listing, Main Program II IV-9
IV-3 Listing, Subroutine SETUP IV-12
IV-U Listing, Subroutine EDOT IV-15
IV-5 Listing, Subroutine PAD IV-17
IV-6 Listing, Subroutine ESUM IV-18
IV-7 Listing, Subroutine EDGRP IV-20
IV-8 Listing, Subroutine INVERS IV-21
V-1 Two Group Classification Matrices V-10
V-2 Four Group Classification Matrices V-ll
VI-1 Group Prediction Model - Computer Programs and VI-3
Sample Input
viii
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LIST OF FIGURES
Figure No. Figure Page No.
1 Mean Steady-State HC Emission Rate Values 77
vs. Speed
2 Mean Steady-State CO Emission Rate Values 78
vs. Speed
3 Mean Steady-State NO Emission Rate Values 79
vs. Speed x
h Distribution of HC Bag Error from Surveillance 80
Driving Sequence
5 Distribution of CO Bag Error from Surveillance 8l
Driving Sequence
6 Distribution of NO Bag Error from Surveillance 82
x
Driving Sequence
7 Distribution of HC Bag Error from First 505 83
Seconds Federal Test Procedure Driving Sequence
8 Distribution of CO Bag Error from First 505 81+
Seconds Federal Test Procedure Driving Sequence
9 Distribution of NO Bag Error from First 505 85
Seconds Federal Test Procedure Driving Sequence
IV-1 Flow Chart, Main Program I IV-23
IV-2 Flow Chart, Main Program II IV-2U
V-l Discriminant Analysis, Hydrocarbons V-12
V-2 Discriminant Analysis, Carbon Monoxide V-13
V-3 Discriminant Analysis, Oxides of Nitrogen V-lk
VI-1 Flow Chart, Main Program for the General User VI-10
VI -2 Group Prediction Model - Sample Output VI-11
IX
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1. INTRODUCTION
In many geographic regions, the major portion of hydrocarbons (HC),
carbon monoxide (CO), and nitrogen oxides (NO ) present in the environment is
due to motor vehicle emissions. The impact of motor vehicles on the environment
in a given location is a function of many factors. Among these factors
are the emission characteristics of individual vehicles, the mix of vehicles
in a particular traffic way, the numerical concentration of vehicles per mile
or per unit of area, and the driving pattern in which the vehicles are employed.
This driving pattern is influenced by the functional use of the traffic artery
(i.e., whether inter or intra city, whether it serves industrial or recreational
purposes, etc.) as well as a number of other items. Other items include the
design of the highway (e.g., whether it is designed for high or low speed) and
the extent to which it passes through and is limited by population density.
It has been well established that emission rates for a particular
automobile depend upon the manner in which the vehicle is operated — that is,
emission rates are different for different accelerations or decelerations. In
a particular trip taken by an automobile in traveling from Point A to Point B,
that automobile will exhibit a particular time profile of acceleration and
velocity. The trip may entail a number of starts and stops, as well as a range
of speeds determined by traffic conditions, local speed controls, and other
factors. As the vehicle travels from A to B, this time profile or "driving
sequence", together with the emission characteristics of the vehicle, determines
the pollution contribution to the atmosphere. Due to the fact that emissions,
expressed in grams per mile, vary along the route, the distribution of the
vehicle emissions, as well as the total contribution of pollutants to the
atmosphere, can be determined. Indeed, the traffic way can be considered as
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a line source of pollution, the strength of which depends on vehicle density,
vehicle mix, driving sequence, and the emission characteristics of individual
automobiles. Finally, the local concentration of pollution along this route
is determined by this line source distribution mechanism acting in concert
vith meteorological transport processes such as wind and diffusion.
To assess the impact of vehicular emissions on a particular section
of highway requires, therefore, a number of data inputs. These include
characterization of both traffic and emission parameters. Traffic parameters
include numerical traffic density, traffic composition (makes and models of
vehicles), and traffic flow characteristics (speed, starts and stops, rates
of acceleration and deceleration). Emission parameters include emission rates
for various categories of vehicles where these rates are expressed as functions
of driving variables such as speed and acceleration.
The required traffic parameters can be readily obtained by
monitoring traffic along the route in question. The number of vehicles passing
various points along the way per unit of time can be counted, and the total
number of vehicles can be broken down into homogeneous groups according to make,
model, age or other factors influencing emissions. Moreover, speeds and
accelerations prevailing along the route can be measured by observing a "tagged"
automobile or by instrumenting a vehicle and injecting this vehicle as a "probe"
into the traffic stream.
In contrast to the relatively straightforward approach to traffic
parameter assessment, the evaluation of applicable vehicle emission functions
proves to be quite difficult unless a means can be found for modeling the
infinite multiplicity of driving sequences which can arise. It is to be noted,
for example, that the EPA Surveillance Driving Sequence is only one of the
infinitude of possible sequences. Standard emission tests based on a prescribed
driving sequence serve the purpose of comparing vehicles according to a
standard set of operating conditions and make it possible to implement emission
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control standards and to check complicance with these standards. Hovever,
they are not structured in such a vay as to readily provide the ability
to predict vehicle emissions over an arbitrary driving sequence. A generalized
prediction capability can be accomplished by breaking the standard sequence,
or any other available sequence, into segments having specified speeds and
accelerations. Then, these segments can be appropriately recombined to form
other driving sequences. In this way, one hopes to be able to approximate
any desired driving sequence by appropriately weighting the various segments
according to their time duration in the sequence to be modeled. The segments
are referred to as operating "modes" and any analysis based on the use of these
modes as a "modal analysis".
1.1 MODAL ANALYSIS OF VEHICLE EMISSIONS
In 1971, the Surveillance Driving Sequence (SDS) was developed by EPA
to measure vehicle emissions over a variety of steady state and transient
driving conditions. The acceleration and deceleration modes represented in
the SDS consist of all possible combinations of the following five speeds:
0 mph, 15 mph, 30 mph, U5 mph, 60 mph. The average acceleration or deceleration
rate observed for each mode in the Los Angeles basin is used during operation of
20 of the transient modes. In addition, six of the transient modes are
repeated using accel/decel rates higher or lower than the average rate in
order to determine the effect of accel/decel rate on emissions. These
accelerations and decelerations were chosen to represent the full range of
*
accelerations and decelerations observed in the CAPE-10 project.
"Construction of Chassis Dynamometer Test Cycles", Scott Research Laboratories,
Inc., November 18, 19T1-
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The concept of modal analysis examined in this report employs as input
data the emissions measured for the 37 distinct modes of the SDS. These modes
can be characterized by an average speed and an average acceleration. Of the
37 modes, five are regarded as "steady state" — that is, the acceleration
is zero. The five modes represent average speeds of 0, 15» 30, 1+5 and 60 miles
per hour. The other 32 modes represent either periods of acceleration or
deceleration and are characterized by an average acceleration, which is constant,
and an average speed. The importance of the speed constraint can be appreciated by
noting that if a vehicle accelerates from 0 to 15 miles per hour in t seconds,
its emissions response is not the same as when it accelerates from 15 to 30
miles per hour or 1*5 to 60 miles per hour in the same time of t seconds.
The mathematical model which has been developed to predict vehicle
emissions over any specified driving sequence is derived from vehicle data on
emissions from the 37 modes of the SDS. One difficulty presented by the use
of these discrete modes as inputs to a continuous driving sequence model is
that during much of the sequence, the vehicle may be operating at speeds
and accelerations not included in the set of five steady state and 32 accel/decel
modes. For example, a vehicle traveling at 23 mph is neither in the 15 mph or
30 mph steady state mode. To arrive at a continuous predictive model, one must
be able to interpolate or otherwise estimate the appropriate emission rates for
all combinations of speed and acceleration encountered in the driving sequence.
The primary contribution of this report is the development of a scheme
whereby emissions from the 37 discrete modes can be expanded into a continuous
function of time. Any driving sequence can be reduced to a speed time profile.
Since acceleration is a function of speed change and time, both speed and
acceleration can be expressed as continuous functions of time. The emission
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rate of a vehicle at a given point in time is dependent upon its speed and
acceleration. Using these functional relationships, it is possible to integrate
the emission rate function according to the time history of speed and acceleration
associated vith the driving sequence in question.
An essential feature of the model presented in this report is a regression
function which can, for purposes of visualization, be presented as a "surface"
in speed-acceleration space as shown below.
Emission Response Surface
For any point (v, a) in the speed-acceleration plane there corresponds an
instantaneous emission rate e (v,a). The surface can be represented by a
mathematical equation of the form: e = f(v,a) in which the function f contains
a number of adjustable constants. These constants can be selected to represent
the emission characteristics of a particular automobile or can be selected to
represent the mean emission characteristics of a collection of automobiles.
This collection need not be homogeneous with regard to make, model, age or
other identifying characteristics of automobiles. However, if a comparison
of homogeneous sets of vehicles is desired, a characteristic emission function
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for each set can be derived. In short, the model presented in this report
can be applied to individual vehicles or to composite groups of vehicles
selected in whatever way is meaningful to pollution assessment. The flexibility
of the model in this connection rests on the fact that the emission rate
function is developed as a linear function of adjustable constants which can
be particularized to an individual vehicle. Since the pooling of emissions
for a composite group of vehicles is itself a linear summing operation, the
composite emission function can be derived in a straightforward manner as a
weighted linear sum of the emission functions for individual vehicles.
Determination of the best process for pooling emissions from a collection of
vehicles is beyond the scope of this report, but, to provide perspective for
the use of the modal analysis, it is essential that certain aspects of composite
emissions modeling be considered since they affect the modal analysis model.
These aspects are treated in Section 5 and in Appendix V.
1.2 COMPOSITE ANALYSIS OF VEHICLE EMISSIONS
Computation of the emissions emanating from a particular traffic way in
a given period of time is a composite of the emissions produced by all the
vehicles which traversed that traffic way during that time. Quite clearly, it
is not possible to assess the instantaneous emission rate functions for each
automobile. However, if the composition of the vehicle mix is known or can be
determined or postulated, one can define what might be called a "pilot mix" or
analog of the actual traffic composition. For example, suppose that a fraction
p.. of the vehicles belong to Category 1, a fraction p of the vehicles belong to
Category 2, and so on, and that the number of vehicles traversing the traffic way
per unit of time is N. An analog of this mix is n vehicles, where n «N, in
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which there are p n vehicles of Category 1, p?n vehicles of Category 2, etc. in
the sample. If the constants for the emission-rate function are determined for
each of the n vehicles in the sample, these constants can be averaged over
all vehicles comprising the sample to produce an emission rate function which
is "typical" for the mix. This composite emission rate function can then be
used to compute a typical or average emission for the specified driving sequence,
where by "typical" is meant "representative of the vehicle mix in question."
By multiplying this average emission by N, the total number of .vehicles
traversing the traffic way per unit of time, an estimate of the total emission
contribution in the time can be obtained. Note that, by virtue of the additive
nature of the model, the result-will be the same, as if separate contributions
to the composite were computed for each vehicle in the sample by means of its own
specific emission-rate function, and then these individual emission outputs
were added and scaled up by multiplying by the factor N/n.
The approach taken above can be referred to as the method of proportional
sampling — that is, the number of vehicles in each category in the sample
is proportional to the corresponding number of vehicles of each type in the
population. An alternative approach is one in which no attempt is made to
produce an analog of the mix in the population but rather an emission-rate
function for each category is established independently of all other categories.
For example, n vehicles of Category 1 would be subjected to modal analysis .
and an average emission rate function determined for Category 1 vehicles.
Similarly, n vehicles of Category 2 would be analyzed to determine an average
emission rate function for Category 2 vehicles, and so on. It is presumed
that the number of vehicles tested in each category (that is, n.., n,, )
would be such that the desired precision is realized; among other things, these
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numbers would depend on the intra-class variability. Then, given that
• »
each category of vehicle has been characterized by an emission-rate function,
a composite emission-rate function for any mix of vehicles could be
computed as a weighted average of the emission-rate functions for the several
categories.
In view of the flexibility of the modal-analysis model, the definition
of homogeneous categories of vehicles is not necessary. Indeed, categories
of vehicles can be constructed arbitrarily, so long as these arbitrary
categories are useful in the particular problem under study and can be weighted
appropriately in the composite result. Nevertheless, it was considered of
interest to examine available modal data to determine if any significant
groupings were evident and whether these groupings might influence the
application of the emission model. In this connection it was found, by
discriminant-function analysis, that vehicles in Denver exhibit somewhat
different emission-rate functions from comparable vehicles in other cities
»
(see Appendix V). The only way in which this observation affects the
use of the model, however, is in the choice of input data. In short, to model
traffic ways or to compare alternatives in Denver or in high-altitude locations
one must use input modal data appropriate to these locations. In all other
respects, the application of the emission model would be unaffected.
Due to the presence of the city effects described above as well as
model year effects, the general user will find that when the EPA modal data
are used as input to the model, the model is most effective when it is used
to predict the overall emissions of vehicle groups. This group structure
is discussed further in Section 5.
The model is particularly valuable if the analyst wishes to examine
alternatives, such as alternative routes or highway designs, before an actual
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highway is built. By postulating the anticipated mix of vehicles and the
anticipated driving sequences, the relative desirability of alternatives
can be ranked according to their pollution impact.
1.3 REPORT SCOPE AND PREVIEW
In the ensuing sections of this report, a methodology will be presented
that will enable an analyst to predict the amount of hydrocarbons (HC),
carbon monoxide (CO) and oxides of nitrogen (NO ) given off by individual or
specified distributions of light duty vehicles as these vehicles move from
point A to point B by some defined speed-time profile.
The methodology will be presented in a somewhat classical modeling
approach. First, a description of the problem and the proposed model
objectives will be given in terms of the data that are available (the
iconic model). Secondly, a mathematical model will be developed that parallels
the iconic model in its objectives. This model will be amenable to computer
implementation. The model's.performance will then be analyzed to see if it
is able to meet the objectives set for it.
The proposed methodology is intended to be flexible enough to
accomodate changes in emission parameters which are expected to result from
improvements in emission control systems. This flexibility will also allow
modification or extensions of the model's objectives as the need for such
modifications arise.
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2. PROBLEM DEFINITION
Problem definition can best be understood in terms of the inputs and
outputs of the model. Input data consist of vehicle modal emission
measurements and speed versus time profiles for specified driving sequences.
Output data consist of estimates of emissions for any given driving sequence.
2.1 INPUT DATA
Vehicle emission data are given for 1020 individual light duty vehicles
that represent variations in model year, manufacturer, engine and drive train
equipment, accumulated mileage, state of maintenance, attached pollution
abatement devices and geographic location The individual vehicle characteristics
and emission data were obtained by Automotive Environmental Systems, Inc.
it
under EPA Contract No. 68-OU-OOU2. The principal function of this surveillance
program, "A Study of Emissions from Light Duty Vehicles in Six Cities", (1971),
vas the collection of data from which average emission factors could be formulated,
These factors are necessary so that the contribution of the automobile popu-
lation to the nation's air pollution burden can be defined. They also provide
the information necessary to estimate vehicle emission levels in metropolitan
areas and to evaluate various pollution control strategies such as transportation
controls. To achieve this objective, the best available methodology and
technology were employed to accurately determine mass emissions under vehicle
operating conditions representative of road use. Because 1957-1971, model year
vehicles comprised more than 95% of the vehicle population as of 1971, a
statistically representative sample of this population was tested in each of
six cities. The cities chosen were representative of variations in climate,
terrain, and urban development.
*
APTD-1U97, "A Study of Emissions from Light Duty Vehicles in Six Cities",
March, 1973-
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For each of the 1020 vehicles in the data base, the following emission
data are given for the three pollutants (HC, CO and NO ) under consideration:
X.
[A] Modal Emission Data
The amount of each pollutant emitted in each of 37 defined speed-time
profiles. There are three cases: speed is monotonically increasing and
acceleration is constant and positive over time (accel); speed is monotonically
decreasing and acceleration is constant and negative over time (decel); speed is
constant over time and acceleration is zero (steady-state), as shown below.
Accel Speed
Time
Decel Speed
Time
Speed
Steady State
Time
The 37 speed-time curves are referred to as modes. There are 32 accel/decel
modes and five steady state modes. (See Appendix I for modal specifications.)
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[B] Driving Sequence Emission Data
[l] The total amount of each pollutant emitted during the Surveillance
Driving Sequence: The Surveillance Driving Sequence represents a speed-time
curve of duration 105^ seconds; it is made up of the 32 accel/decel speed-time
curves Joined together by the five steady state modes. The Surveillance
Driving Sequence was performed after the vehicle had performed the Federal
Test Procedure Driving Sequence. Therefore, emissions measured over the
Surveillance Driving Sequence represent emissions from a warmed-up vehicle.
(See Appendix II for the speed-time values in the Surveillance Driving
Sequence.)
[2] Emissions measured for each vehicle twice using the FTP, once
from a cold start and once from a hot start: Emissions were collected from
the "transient" and "stabilized" portions of these tests and the data are
reported as "cold transient", "cold stabilized", "hot transient" and "hot
stabilized" values. Emissions from the Federal Short Cycle were also
measured. In the study of model effectiveness, the values used were the
amount of each pollutant given off during the Federal Short Cycle and all
segments of the FTP except the "cold transient" part of the driving sequence
(see Appendix II for the first 505 seconds of the Federal Test Procedure
Driving Sequence). Cold transient data were not used since the model has
maximum effectiveness as a predictor of emissions for warmed-up vehicles.
NOTE: The total amount of a pollutant emitted by a vehicle as it executes
a driving sequence is often referred to as the "bag value".
2.2 OUTPUT DATA
Given the modal emission data on an individual vehicle, the basic objective
of the model is to develop a method which can predict the emission response
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13
of this vehicle over any specified driving sequence. The predictive ability
of the model is restricted to accelerations and speeds in the sequence which
do not exceed the range of accelerations and speeds spanned by the input modal
data. In addition, it is desired to extend these individual vehicle responses
so that the emission responses of specified homogeneous groups of vehicles
can be predicted.
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lU
3. OVERVIEW OF THE MATHEMATICAL MODEL
In this section a general description of the mathematical model
development is given. A more detailed version of the model appears in
Appendix III.
3.1 THE EMISSION RATE FUNCTION
The mathematical model used to describe the emission response of a
vehicle or group of vehicles is "built around the concept of an instantaneous
emission rate. (The instantaneous emission rate is defined as the rate at
which a pollutant is given off at a specific point in time.)
If the amount of a pollutant emitted by a vehicle from time = 0 to any
time = t is denoted by e(t), then the instantaneous emission rate function
e(t) is defined as the time rate of change of e(t)
(1)
The instantaneous emission rate at a specified time T is the value of the
emission rate function evaluated at this time
(2) e(T) =
de(t)
dt
t = T
In the development of this model, it has been assumed that the instantaneous
emission rate of a vehicle is a function of its speed, v, and acceleration, a.
Since speed and acceleration are considered to be time dependent, the emission
rate function can be expressed as
(3) e(t) = e(v(t), a(t)) = e (v,a) .
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15
Inherent in the definition of a driving sequence is a speed-time
(and therefore acceleration-time) profile. The amount of a pollutant given off
by the vehicle over a driving sequence lasting T seconds is then given by
integrating the emission rate function over the speed-time curve for the
driving sequence of interest
(U)
e(T) = J e(v(t), a(t))dt
0
where v(t) and a(t) are the values of speed and acceleration at time = t
specified by the driving sequence.
In practice the driving sequences are specified by a series of speed-
time points along the speed-time curve that are equidistant in time, as shown
below
SPEED
TIME
where
= t - t .. = At .
n n-1
The integration in equation (U) is then approximated by the following summation
N-1
(5)
e(T) =
e(v ,a ) At
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where
*. V — V
« - i+1 1
ai ~ At
NAt = T .
At this point, it is necessary to determine a suitable functional form
of the instanteous emission rate function in terms of speed and acceleration.
3.2 STEADY STATE AND ACCEL/DECEL EMISSION RATE FUNCTIONS
It is necessary to determine a functional form for the emission rate
function for the steady state case and the case of accel/decel. In the steady
state case (acceleration equals zero, constant speed) the emission rate
function is a function of speed only. This case is presented first.
For each of three pollutants, steady state emission rates averaged over
the 1020 vehicles in the data base were plotted against speed. Inspection
o
of these plots (Figures 1, 2 and 3) suggested that the steady state emission
rate function e could be expressed as a quadratic function of speed
s
(6) es(v) = Sx + S2 v + S3v2 ,
where S , S and S are constants.
In the case of non-zero acceleration (accel/decel), the assumption is
made that the acceleration occurring at a given speed is a perturbation to
the steady state emission rate at this speed. This perturbation can be
accounted for by letting the coefficients S , S and S_ become functions of
If a(t) = acceleration at time t, then a(t)<0* decel., a(t)>0**> accel.
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17
acceleration. If it is assumed that quadratic functions of acceleration repre-
sent good approximations to these coefficients, the coefficients can be expressed
as follows
C ~ Q / \ A . (—
11 k ; " qil q!2a q!3
(7) S2 = S2 (a) = q21 H
S^ = S (a) = q + ^-a2a * ^??a '
where the q's are constants. The emission rate function used during times of
non-zero acceleration e. can then be written in the form
Fit
(8) e.(v,a) = b + b0v + b_a + b, av + brv2 + b/-a + b_v a + bQa v + bna v ,
A I*i34 5 o TO 9
where the b's are constants and can be expressed in terms of the q's. It is
noted that if a = 0 equation (8) reduces to
(9) Vv'a = 0) = bi+ V + V2 '
which has the identical form as the equation for e . Thus, e. could be used
S A
to determine emissions for both steady state and non-zero acceleration periods.
At this point in the discussion, however, separate functions for steady state
and accel/decel emission rates will be retained; the reason for doing so will
be given later in this report.
The instantaneous emission rate function e for a given vehicle and
pollutant is a composite function given by
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18
(10) e(v,a) = h(a)e (v) + (I - h(a)) e (v,a) ,
S •**
where h(a) is a weighting function which is bounded, by the values 0 and 1
and which is dependent on acceleration. Note that h(a) allows for a smooth,
continuous transition from steady state to accel/decel emission rate functions
or vice versa.
The next step is to evaluate the twelve coefficients (b.,i = 1,9;
S. ,i = 1,3) for each vehicle and pollutant. These coefficients will completely
specify the instantaneous emission rate function describing this vehicle's
response with respect to the given pollutant.
3.3 DETERMINATION OF THE COEFFICIENTS (b^ S±)
The coefficients that specify the instantaneous emission rate function
could be determined by a straightforward application of the least squares
regression method if values of the instantaneous emission rates were available.
However, the data base on vehicle emissions does not contain any instantaneous
emission rate observations for accel/decel modes; instead, the observations
reported are the total amounts of the pollutants collected over each mode or
the average emission rate for the mode (which covers many speeds). In this
light, the.following method allows the determination of the coefficients that
specify the accel/decel instantaneous emission rate function.
[A] Specification of the Accel/Decel Emission Rate Function
It can be shown that if the proposed form of the instantaneous
accel/decel emission rate function is used to evaluate the functional form of
the average emission rate function, the same coefficients that specify the
emission rate function also appear in the average emission rate function in a
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19
linear fashion (see Appendix III). Now, the values for the average emission
rate can "be determined for each mode "by dividing the amount of pollutant
given off in the mode by the time in mode. A standard least squares regression
analysis can then be performed on the average emission rate function which will
determine the values of the coefficients that specify the instantaneous emission
rate function. For example, suppose the instantaneous emission rate function
is given as
»
e(v,a) = b + b v + b ya .
Then the average emission rate function over T seconds is defined
as T
T = | j e(v,a) dt = | e(T) .
0
Substituting the functional form of the instantaneous emission rate function
into the integral gives
T = ^ (b + b2v + b va) dt = e(T)/T .
oJ
T
\ dt + i
0
T
V dt + i
0 J
T
b va dt.
0
Let v = — v dt, av = — av dt, and since — dt = 1, have
e(T)/T
This expression is only an example, deliberately simplified for illustrative
purposes.
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20
The total emission e(T) given off in each mode and the time in each mode T are
known, v, and av can be determined for each mode. The coefficients (b.) can
therefore be obtained through least squares regression analysis applied to
the average emission rate function.
For the general model, there are nine coefficients to determine and 32
accel/decel modes. A least squares regression analysis can be performed on
an individual vehicle or on the mean of a group of vehicles. This approach
forms a logical bridge from the experimental observations to the specification
of the accel/decel emission rate function.
[B] Specification of the Steady State Emission Rate Function
In the case of steady state conditions, the speed does not change
with time. Thus, the average emission rate is equal to the instantaneous
emission rate. Values of the steady state emission rate function are then
available from the experimental observations, and the coefficients are evaluated
directly using least squares regression techniques.
There is, however, one problem that crops up with the above straight-
forward least squares approach. The values of the emission rate vary greatly
between speed zero (idle) and a speed of 60 mph. As a result, the least
squares approach sometimes produces a steady state emission rate function which
predicts negative emission rates for certain speeds. In this event, the function
is adjusted by means of a constraint on its minimum value. The two lowest
emission rates measured experimentally are determined and averaged. Similarly,
the speeds corresponding to these two rates are also averaged. The average rate
and average speed determined in this way are then taken as the coordinates of the
minimum point of the emission rate function. Two of the three coefficients that
specify the steady-state emission rate function are thus determined; the third
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21
is computed "by the least squares method subject to this constraint (see
Appendix III for details).
3.k THE COMPOSITE EMISSION RATE FUNCTION
As stated earlier, two separate emission rate functions were desired
in order to describe accel/decel and steady state conditions. The two functions
are then Joined by means of the weighting function as defined by equation (10).
The reason for retaining a separate function for steady state conditions when
the accel/decel function appears flexible enough to handle the steady state case
is that the accel/decel rate function also produces negative emission rates in
some cases for steady state speeds; any efforts to modify the coefficients to
constrain the function to yield only positive steady state emission rates would
produce serious errors when the function is used to evaluate accel/decel
emission rates. The composite emission rate function allows the freedom to
adjus.t the coefficients of the steady state emission rate function without
disturbing the accuracy of the accel/decel emission rate function.
3.5 VEHICLE AND VEHICLE GROUP CHARACTERIZATION
Once the emission rate function for a vehicle and pollutant is specified,
it can be used to obtain this vehicle's response, over any given driving
sequence, by integrating the rate function over the speed-time curve defined
by the driving sequence. Each vehicle is characterized by 36 parameters
or coefficients; 12 parameters for the specification of each emission
rate function describing the HC, CO and NO response.
The characterization of a group of vehicles can be achieved by defining
the emission rate function for the average vehicle within the group.
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22
Let b.,, = k'th coefficient in the emission rate function for the j'th
ijk
vehicle within the group and i'th kind of pollutant,
N = number of vehicles in the group ,
O
b., = k'th coefficient in the emission rate function describing the
IK
average^vehicle's i'th kind of pollutant response.
Then,
N
- _ 1 Tg
(11) bik - N~ ^ bijk
g j=l
Thus, the group emission rate functions are determined by averaging the
coefficients which make up the emission rate functions of each vehicle
in the group. The emission response of the group over any driving sequence
is then determined by multiplying the average vehicle's response by the number
of vehicles in the group. The average vehicle's response is obtained by
integrating its rate function over the speed-time curve specified by the
driving sequence.
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23
U. MODEL PERFORMANCE
Evaluation of the performance of the model can be approached only by
comparing computed and measured quantities. This section evaluates the
model performance by examining the effect of applying the model to each of
the 1020 vehicles in the input data set. For this purpose, it was found
convenient to use the Surveillance Driving Sequence and the first 505 seconds
of the Hot Federal Test Procedure driving cycles as measurable quantities and
to compare these quantities with the corresponding outputs predicted by the
model. Also, it must be appreciated that the degree of agreement between
computed and observed results will vary from vehicle-to-vehicle and that
ultimate evaluation of the validity of the model must take into account this
statistical variability. Toward this end, several statistical quantities
were employed, as discussed below.
U.I STATISTICAL INDICATORS OF PERFORMANCE
Notation
0 = observed amount of i kind of pollutant given off by j
vehicle over a specified driving sequence (observed bag value)
C. , = calculated amount of i kind of pollutant given off by j ••'
i J
vehicle over a specified driving sequence (calculated bag value)
N = number of vehicles in sample (1020)
R. . = bag value error = 0 - C
IJ IJ IJ
To analyze the performance of the emission rate model in predicting bag
values, the following statistics are evaluated:
[A] The Mean Bag Error or Bias (R^) for Each Type of Pollutant
Nc
JT J "^ J
-1
-------
or
[B] The Standard Deviation of the Bag Error (aR.) for Each Pollutant
R. N - 1
i c
N
J=l
, R \2
'. . ~ n. j
ij i
[C] Root Mean Square Deviation of the Bag Error (RMSj) for Each Pollutant
/^ 2 2
RMS. = / R. + a_
1 1 n.
1
[D], [E], [F] The Mean. Standard Deviation and Root Mean Square
Deviation of the Bag Error Expressed in Terms of Percent
of the Observed Mean Bag Value for Each Pollutant (6.)
N
w
0. = I 0.
i , , i
J7 c
_
t\.
oi) . 100%
/o,) •
I A.2 + a^ /Oi j •
1005S
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25
The mean, standard deviation, and root mean square deviation of the
bag error together provide insight into how the bag errors are distributed.
Expressing these statistics in terms of percent of the observed mean gives an
indication of how serious the bag error distribution is.
U.2 PERFORMANCE RESULTS
The values of the statistics for bag values obtained in the Surveillance
Driving Sequence and first 505 seconds of the Hot Federal Test Procedure
driving sequence (hot transient) are given in Tables 1 and 2.
A visual inspection of the distribution of bag value errors is offered
by Tables 3 through 8 and corresponding histograms on Figures k through 9.
U.3 DISCUSSION AND EVALUATION
To focus attention on the adequacy of the model, it is helpful to
condense Table 1 and Table 2 to a somewhat more concise form, as shown below.
PERCENT RMS ERROR
BETWEEN CALCULATED AND OBSERVED BAG VALUES
FOR 1020 VEHICLES
Surveillance
Driving Sequence
HC . 26.1
CO 23.9
NO 27.1
First 505 Seconds Federal
Test Procedure
32.0
29.1
28.0
The percent RMS error is defined as
K
+ R 2/0> . 100$
and represents the combined systematic and random errors. It is a particularly
meaningful quantity if one assumes that the mean or expected difference between
the calculated and observed values should be zero. As will be noted in Tables
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26
1 and 2, the RMS values are largely dominated by the random error component,
2
as represented by 0 . Moreover, these tables, together with the histograms
K
showing the error distributions, suggest that the difference between computed
and observed results cluster rather closely around the average error R and
that this average value deviates from zero by only a few percent of the
average measured bag values.
A logical question arises, however, as to the interpretation which
should be put on such terms as "cluster rather closely around the average" or
on such quantitative measures of performance as "25$ RMS error". Against what
criterion are these measures of performance to be judged and is the model to
be judged satisfactory or unsatisfactory?
To answer this question, the quality of the input data and the manner
in which errors in the input propagate into errors in the output must be
considered. In particular, the repeatability of emission measurements
performed on the same vehicle and ostensibly under identical test conditions
must be investigated. If the results of the Surveillance Driving Sequence
or any other specified driving sequence fail to repeat on replicate tests,
this failure can not be traced to the inadequacy of a computational model,
because no such model is involved. The accruement of instantaneous emissions
over the driving sequence is a physical, not a mathematical, process of
integration, and the vehicle and the measuring instrumentation constitute
the only "computer" in the system.
Of the 1020 vehicles in the input data set, 6l had been tested twice
each. Thus, there were available 6l "replicate" measurements from which
a measure of repeatability of measurements can be obtained.
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27
This measure of repeatability can be easily obtained as follows.
For a particular vehicle, the mean X, of the two replicate measurements
can be computed. Then the quantity
/ Y Y ^ j. / v
^ ? I IV ~ \' ^*Plc
^ *I*JV A. r ft-
k N - 1
can be computed where X.., and X^, are the two replicate measurements for the k
* 2
vehicle. Since N = 2 in this case, the formula for 0. reduces to the simple
form
"* 2
Now it can be assumed that the quantity CJ is one estimate of the variance of
1C
replicate determinations and that each of the other 60 pairs of values provide
an additional estimate. These 6l estimates can be pooled or averaged to obtain
"* 2 n1 " 2
o 2 = 1/61 I ok2
k=l
as a best estimate of the variance of replicate values. Similarly, the
quantities X, (k = 1, 2 ...... , 6l) can be pooled to obtain an estimate of the
mean X for the total collection of vehicles, and the quantity $ /X, can be
taken as a relative or percent standard deviation characterizing the
repeatability of measurements.
The values $k/X, are shown below for the Surveillance Driving
Sequence and for the first 505 seconds of the Federal Test Procedure.
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28
HC
CO
HO
PERCENT STANDARD DEVIATION BETWEEN
REPLICATE BAG VALUES FOR 6l VEHICLES
Surveillance
Driving Sequence
68.6
15-5
First 505 Seconds Federal
Test Procedure
70.6
26.9
15-8
Comparision of these values with those obtained by comparing calculated and
measured results suggests that the errors are comparable in the two cases.
Consequently, it is concluded that the model is performing quite acceptably
and that, indeed, its performance is substantially limited by the variability
inherent in the test measurements themselves.
Further support for this point of view is found in Tables 9, 10 and 11.
^ ^
Based on the 6l replicates, the quantities X, a and (a/X)-100/& are presented
for each of the 37 modes as well as the Surveillance Driving Sequence and
the FTP. The percent standard deviations for individual modes range from
30? to nearly 100% for HC, from about 20% to 85^ for CO, and from about 20$
to nearly 138/» for NO . These errors are reflected as errors in the
determination of the regression coefficients, and these errors in. turn
determine the error of estimating the instantaneous emission rate at any
point in the (a,v) - space. Procedures are available to trace the error
propagation through this rather involved process and to produce "variance
«
maps" in (a,v) - space, but this type of analysis is beyond the scope of
E. T. McAdams, "A Computer Method for Hypsometric Analysis of Abrasive
Surfaces," Advances in Machine Tool Design and Research, 1968, Pergamon Press,
Oxford, 1969, pp. 11U9-1171.
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29
this report. Moreover, even if such a variance surface were available, one
must further translate this surface into its effect on the integrated emissions
for a particular driving cycle. In view of the relatively large errors in
modal input data, however, the 25$ to 35$ RMS errors obtained for model
performance do not appear unreasonable.
Further insight into this matter can be had by an elementary and
straightforward application of analysis of variance as follows. Denote by
X (i = 1, 2; J =1, 2; k = 1, 2, ...... 6l) the Jtn replicate of the kth
1 J J£
vehicle, where i = 1 denotes measured values and i = 2 denotes values computed
from the model . For each vehicle , therefore , there are four values of total
emission for each of the pollutants HC, CO and NO . These are
X , = Bag value measured for first replicate 9
X = Bag value measured for second replicate,
-L^lC
X = Bag value computed for first replicate ,
= -Bag value computed for second replicate.
These four values can each be decomposed into components representing the
effects of the model, the effects of replication, and the interaction
between replications and models.
The effect of the model can be visualized in the following sketch.
INPUT »- MT ^ OUTPUT "Identity" model
INPUT »- M_ *- OUTPUT "Computational" model
In the "identity model", the measured emissions are subjected to no computation,
the bag values being those obtained directly from the measurement process itself.
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30
In the "computational model", the modal measurements are used as the "basis
for generation of an emission-rate Surface, and bag values are computed "by
integration over the appropriate driving sequence. Thus if the data from
replicate tests are fed to these two "models" as inputs, the outputs will
differ "because of the difference in the "transfer functions", M_ and M , of
i. L-
the two models. The difference between the outputs of the models can be
called the "model effect" and is a measure of the extent to which the
computationally integrated results fail to agree with the physically
integrated results. In previous discussion, this difference has been referred to
as a measure of the "validity" of the computational model. In the present
analysis, however, this difference is examined in relation to the
repeatability of the input measurements.
An appropriate statistical model for the analysis is
Xijk = \ + "ik + 3Jk + (tt3)ijk • i = 1, 2; J = 1, 2; k = 1, 2 6l
•f~Vi 4*Vi ~f~Vt
X is the output of the i model for the j replicate on the k vehicle.
i JK
The convention, of course, is that i = 1 denotes the identify or physical
model and i = 2 denotes the computational model. The quantity u is the
K
mean of the four output values for each vehicle and can be thought of as
the common or reference value against which model and replication effects
\
can be compared. The quantity a is a departure from this mean occasioned
IK
by the effect of the particular model; since ot + a = 0, one of the models
Ik C.K.
will be represented as a negative departure, the other as a positive departure
from the mean. The quantity B.v is a departure from the mean occasioned by
JK
replication. As far as 3. is concerned, it is assumed that the difference
Jk
between replicates, in the statistical sense, is the same for the identity
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31
model and. for the computational model; hence, 8,, represents a pooled
Jk
estimate incorporating both expressions of the replication effect. Since
6.,, - B0, = 0, one of the replicates will be represented as a negative
.Lit ^&
departure from the mean, the other as a positive departure from the mean.
In reality, there is a distinct possibility that replication will be
influenced by the model—that is, it might be anticipated that replicate results
emerging from the computational model might be different from replicate
results emerging from the identity model. If such is the case, then there is
interaction between replication and models. This interaction is measured
by the term (a0) , which represents a "correction", in a sense, to the
1J K.
assumption that repeatability of the output does not depend on whether one
is considering the identity or the computational model.
Decomposition of X. ., into compo'nents is easily accomplished by the
1JK
matrix transformation
-1 -1
-1
1 -1
1 -1 -1
llk
21k
22k
"
ik
22 2
Moreover, a , 6 and (aB) ... represent, respectively, the mean squares
ik JK ijk
for models, replication and interaction in a two-way analysis of variance. Each
of these mean squares has one degree of freedom.
The analysis is completed by computing these mean squares for each of
the 6l vehicles and averaging these values. These results are presented in
Table 12 under the heading "Mean Squares". Viewed directly, however, these mean
squares are somewhat misleading, because the statistical expectation of the mean
2
squares for—say, the models effect—is not the variance 0 associated with
a
models but rather
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32
2 2
2V * V
2
where o is the interaction variance. Similarly, the expected mean squares
ctp
2
for replications is not the variance Q0 associated with replications but rather
P
2
The expected value of the mean squares for interaction is O Q , however. By
dp
solving the system of equations
J + ^ a
a a$
2 2
2O + a „ = models mean squares
2 2
2o~0 + a 0 = replicates mean squares
P cxp
2
0 o = interaction mean squares
22 2
the variance components o" , (7,, and o~ 0 can "be extracted. These are displayed
ex p otp
in Table 12 under the heading "Variance Components".
Though the analysis for HC, CO and NO as well as the analysis for the
two driving sequences give different results, the general impression is that
the models and replications effects are of comparable magnitude (note, in
particular, the results for CO and NO for the Surveillance Driving Sequence).
X.
In the case of HC, it appears that the replications effect is much larger than
the models effect for both the first 505 seconds of the Federal Test Procedure
and for the Surveillance Driving Sequence. However, examination of the data
for individual vehicles revealed that there was one vehicle for which the bag
values replicated so poorly that the case might be considered an outlier. This
single vehicle is largely responsible for the large replications mean square
for HC.
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33
Special attention must be given to the interaction components. Although
there are several examples in which this component is of appreciable magnitude,
it can not be concluded that the computational model has poorer repeatability
than the identity model, because all of the variance components denote magnitude
only, not direction. Indeed, examination of the data for individual vehicles
reveals that the interaction effect is about as likely to be negative as positive.
Often the interaction is occasioned by the fact that the ranking of the
two replicates is reversed when one goes from the identity model to the
computational model. For example, in the identity model, the first replication
might yield a higher bag value than the second, but in the computational model
the reverse might be true, yet the magnitude of the difference between the two
replicates might be the same in both cases.
In conclusion, the computational model performs remarkably well in view
of the relatively large errors in the modal emission rates which serve as
inputs. Since the model reproduces the measured bag values about as well as a
replicate does, it is postulated that the model can predict emissions from a
non-standard driving sequence about as well as might be expected from an
actual test performed on that driving sequence. This aspect of model performance
is treated further in Section 5. However, the model has maximum effectiveness
as a predictor of vehicle group emission characteristics, since the input
variability of a homogeneous group of vehicles is in general less than the
input variability of any individual vehicle.
-------
5. APPLICATIONS OF THE MATHEMATICAL MODEL FOR THE GENERAL USER
The modal emissions data used to generate the coefficients for this
mathematical model were collected as part of a major EPA surveillance
program as described in Section 2.1. As was stated, the individual vehicles
represent a wide variation in model year, manufacturer, engine and drive train
equipment, accumulated mileage, state of maintenance, attached pollution
abatement devices and geographic location. Therefore, the modal prediction
model is most useful as a predictor of emissions for vehicle groups. It is
necessary to determine the most useful group structure by considering the
mix of vehicles tested in the EPA surveillance program.
5.1 DETERMINATION OF GROUP STRUCTURE
Fifteen makes and/or manufacturers were identified in the set of input
modal data. Since fifteen model years were also involved and a fleet of only
170 vehicles was tested in each city, the situation which occurred most
frequently was that the sample of any one make/model year was very small or
nonexistent. In addition, this study was performed on vehicles in an
as-received condition. Thus, although the overall sample is very repre-
sentative of the overall vehicle population on the road, the ability to
stratify the sample is severely limited. That is, the sample of vehicles
from a given make/model year/city stratum is not sufficiently large to
accurately represent the emissions from the corresponding vehicle population.
However, the study was designed to estimate the overall impact of emissions
on air quality and therefore sufficient sample sizes existed to stratify the
data in order to test the presence of city effects and model year effects.
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35
Enissions data from the FTP were analyzed in EPA report no. APTD-15^.
This analysis shoved that emissions data collected in Denver vere clearly
*
different from those in the other five cities. Consistent with previous
findings, high levels of HC and CO emissions were measured with correspondingly
low levels of NO in Denver. These differences are believed to be attributable
x
to the effect of altitude on air-fuel ratios. Consequently, Denver data
should be considered separately from the other cities reported, Los Angeles,
Chicago, Houston, St. Louis and Washington, D. C.
Due to engineering considerations, emission characteristics of vehicles
should vary over years. Vehicles produced prior to 1966 for sale in California
and prior to 1968 for sale in the other ^9 states were not subject to any
emission standards. The first nationwide standards were promulgated for 1968
model year vehicles and they applied to HC and CO emissions. In 1970,
the standards for HC and CO were reduced to lower levels. Examination of
the data shows that the imposition of stricter standards tends to cause a
step-function improvement in vehicle exhaust emissions. HC and CO emissions
steadily decrease from pre-controlled vehicles to 1971 model year vehicles while
NO emissions increase over this same time period. Although influenced by
X
changes in the standards, the differences detected in the study are also due
to several additional factors. Gradual reduction in pollutant levels can be
the result of engineering refinements to the exhaust emission control systems.
In addition, all emissions measurements were made in 1971. Therefore, the
data reflect mileage effects, age effects, and state-of-maintenance effects.
Due to the presence of city and year effects, as well as vehicle-to-vehicle
variability, the model is most effective when it is used to predict the overall
*
This conclusion is also discussed in Appendix V as it relates specifically
to modal emissions.
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36
emissions of a population (for a given driving sequence) by estimating the
percentage of vehicles in each of the following 11 groups:
Group 1
Group 2
Group 3
Group U
Group 5
Group 6
Group 7
Group 8
Group 9
Group 10
Group 11
GROUP STRUCTURE
Percentage of
Group in
Input Data
.09
.1*5
.03
.08
.09
.08
.10
.02
.02
.02
.02
Group Definition
Denver pre-controlled
All low altitude cities
pre-controlled
1966-196T California
1968 low altitude cities
1969 low altitude cities
1970 low altitude cities
1971 low altitude cities
1968 Denver
1969 Denver
1970 Denver
1971 Denver
Using the model in this way, the model estimates one set of emission
values for each group for any one driving seqeunce. For example, for the first
505 seconds of the hot FTP, the model predicts that all group 11, 1971
Denver, vehicles will have the following emissions:
HC = 1^.6 grams ,
CO = 3^3.0 grams ,
N0x = 13-5 grams .
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37
If 100 caxs were run over this sequence, a distribution of emissions
would result. If these 100 vehicles were randomly selected and represented
the overall population of 1971 Denver vehicles in Denver, then the model
should predict the average emissions of these 100 vehicles.
Groups more detailed than the eleven groups specified are not composed
of sufficiently large enough samples to be considered representative and
therefore, the value predicted by the model would in many cases not estimate
the actual emissions of a random sample of vehicles from this more restricted
population. Thus, the model is most useful as a predictor of group emissions
for the eleven model year/city breakdowns given above. In addition, it
assumes that within each of these group breakdowns, the vehicles on which
predictions are desired are distributed in such a way as to represent the
overall population of such vehicles. Further work is planned in order to
study the sensitivity of the model to the size and composition of the input
groups.
5.2 COMPUTER IMPLEMENTATION
The two main computer programs given in Appendix IV of the report
require the recomputation of model coefficients with each computer run. They
were used to develop and test the model. They are completely general and can
use any set of input modal data to generate model coefficients, not necessarily
the SDS collected for use in this study. For the case of the SDS inputs,
these programs require as input, data on three pollutants for 1020 cars in
each of 37 modes as well as a second-by-second speed time matrix of the SDS.
At the present time, it is anticipated that the greatest use of the model will
be to predict group emission rates based on the SDS input modal data base and
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38
11 groups previously defined. Thus, the necessity to recompute the group
coefficients with each computer run is eliminated. The computer program
M
listed in Table VI-1 includes the data set of 11 group coefficients as input.
A flow chart for this program is shown in Figure VI-1.
A single run of the present computer program will evaluate emissions
over one driving sequence for many different vehicle mixes. There are many
ways to modify the program to run several driving sequences on one run if
that should be necessary. The inputs needed to run the computer program are
described below:
[A] Computer Program Inputs
Card Type 1 - NSEC, NUMB, INC - 3110 format - 1 card
[a] NSEC is the number of seconds + 1 in the input driving
sequence
[b] NUMB is the total number of vehicles in the group for which
predicted emissions are desired
[c] INC controls a printer plot of the driving sequence. If a
plot is not desired, set INC = 0. If a plot is desired, INC
equals the increment in seconds of the time axis.
Card Type 2 - WT - 16F5.0 format - (NSEC/16. + l) cards
WT(I) is speed vs. time (in one second intervals) of any
driving sequence over which emissions are to be calculated.
WT(l) = speed at time (l-l) seconds. Use as many cards as
needed.
*
This version of the program is recommended for the general user. Those
persons who wish to use the programs in Appendix IV will need to access
the entire set of SDS data. A listing of these data is available at EPA,
Ann Arbor, Michigan.
-------
39
Card Type 3 - COEF - 4E15.8 format - 99 cards
COEF (l,J,K) contains 12 coefficients for each pollutant
and reference group of vehicles. There are 99 cards
numbered from 1 to 99 in columns 79-80. These coefficients
were computed from the input modal data.
Card Type U - DEC - 11F5.2 format - k cards
For predictive purposes, this program allows input vehicles
to come from any of 11 groups of vehicles. The breakdown
of vehicles is:
Group 1 - 1957-1967 Denver
Group 2 - 1957-1967 low altitude cities (non-California
1966, 1967)
Group 3 - 1966, 1967 California
Group 1* - 1968 low altitude cities
Group 5 - 1969 low altitude cities
Group 6 - 1970 low altitude cities
Group 7 - 1971 low altitude cities
Group 8 - 1968 Denver
Group 9 - 1969 Denver
Group 10 - 1970 Denver
Group 11 - 1971 Denver
For each mix of vehicles desired, one of these cards
must be supplied. The fraction of cars in each of the 11
groups is specified. (0.0 implies no cars are from a given
group, 1.0 implies 100 percent of the cars are from a given
group.) The sum of the fractions over the 11 groups should
add up to 1.0
-------
[B] Computer Program Output
The output from the computer program prints displays, for each mix of
vehicles selected, the total emissions in grams for NUMB vehicles over the
specified driving sequence. In addition, a speed vs. time plot of the driving
sequence is an optional output. A sample output is given in Figure VI-2.
5-3 MODEL PERFORMANCE ON GROUP PREDICTIONS
The coefficients used in this computer program are based on the input
modal data collected in 1971 on 1957-1971 model year vehicles. Therefore,
the predictive ability of the model is restricted to predicting how a vehicle
or group of vehicles would have performed in 1971- At this time, any
deterioration factors to be considered must be built in by the user. Accurate
evaluation of deterioration factors for in-use vehicles would imply retesting
the same set of vehicles at specified age/mileage intervals. A less informative
estimate of group deterioration can be obtained by testing two different
groups of vehicles from the same overall population at different points in
their mileage/age history. Limited data on group deterioration factors over
the SDS will be obtained in future programs.
The fact that deterioration factors are not presently in the model
does not affect the ability of the model to compare the vehicle emissions of
one mix of vehicles over two different driving sequences or to compare two
different mixes of vehicles over the same driving sequence. That is, as a
first approximation, it is reasonable to assume the same deterioration factor
would be applied to all vehicles of a given model year and that vehicle emissions
are monotonically increasing with increasing vehicle age. Although the specific
emission values predicted by the model would change if the exact deterioration
factors were incorporated, the relative magnitude of emissions from two
strategies should remain comparable.
-------
In Section U of this report the performance of the mathematical model
was investigated by using it to predict emissions for individual vehicles
over the SDS and the first 505 seconds of the hot FTP driving sequence. The
input modal data used to determine model coefficients vere collected after
the vehicle performed the FTP. A minimum amount of soak time separates the
collection of the two data sets. Therefore, the modal data collection method
implies that the coefficients based on this data should be used to predict
emissions from warmed-up vehicles and not vehicles in a cold transient mode
of operation. In Tables 13, 1^ and 15> the analysis of Section k is presented
in a different way and it is extended by using the model to predict emissions
over the stabilized portion of the FTP and the Federal Short Cycle driving
sequences. These tables evaluate the ability of the model to predict
P—S
group emissions. The table column labelled —r— gives an absolute estimate
b
of the percent error between the value predicted by the model and the observed
sample mean. This quantity is, however, a conservative estimate of how well
the model performs. Neither the predicted value nor the sample mean value
are constants. They are the best available estimates of the population mean
obtained by two different procedures. Presumably, there is less error in the
sample mean estimate than the predicted value. At the present time, procedures
to determine confidence intervals around the predicted value have not been
developed. The table column labelled "95% Confidence Interval Around the
Sample Mean" indicates the variability associated with the sample data. If
the predicted value lies within the confidence interval around the sample mean,
there is no statistical difference between the two estimates. If the predicted
value lies outside the confidence interval, an accurate determination of
statistically significant differences in emission estimates would depend upon
-------
an estimate of model variability. The ability to estimate model variability
is planned as future work.
NO emissions deserve special comment. A humidity correction factor
is normally applied to the NO data collected during the FTP. The application
X
of this factor reduces the variability in the NO measurement since it corrects
all data to a common humidity point. However, this correction factor is only
valid for the FTP. Therefore, the predicted NO values given in Tables 13 and
X
lU are uncorrected while the sample mean NO values are corrected.
Ji
Up until this point, the model has been evaluated by using it to
predict the emissions for the same vehicles which were run over the SDS
and which were used to compute the model coefficients. Therefore, the test
P—S
of model performance as shown by may have been more favorable than
D
would have been the case if the data were obtained from two different
vehicle fleets. If the vehicle fleet used as input to the model was randomly
selected and representative of the overall vehicle population in question,
the sample mean with a confidence interval around it should overlap the mean
and corresponding confidence interval of any other sample which is tested to
represent the same population. Therefore, applying the model to independent
data samples from the same population quantifies to some extent, the
representiveness of the input data sample.
The model is based on a sample of vehicles which represented the total
population of in-use 1957-1971 model year vehicles in early 1972. Therefore,
to evaluate the ability of the model to predict emissions from independent
samples of the population, and also, to evaluate how well the input data
represent the overall population, other samples of data which represent the
-------
same total population were examined. Tables 16 to 20 apply the model to
two studies which meet these criteria.
The Short Cycle Project was a two-phase study performed for the EPA
under Contract No. 68-01-0^10 by Olson Laboratories, Inc. It was designed to
study the effectiveness of short emission inspection tests in reducing
emissions through maintenance. The program testing was performed in early
1972 and data were collected on 600 Michigan and California vehicles
representative of the respective vehicle populations in vehicle age and make.
(The study tested 1957-1971 model-year vehicles.) The study was performed
in two phases and the results of the two phases are presented in Tables 16
to 18 for the following cycles: hot transient part of FTP, cold stabilized
part of FTP, and Federal Short Cycle.
Values computed from the model for hydrocarbons and carbon monoxide
predict the sample values extremely well. The absolute error is less than
33% in all cases and in most cases, the predicted value lies within the 95$
confidence interval around the sample mean. The prediction of oxides of
nitrogen is not as good. This is to be expected since the modal input data
on NO are not corrected for humidity. The error resulting from lack of
humidity correction can be expected to be around 5%- However, this error would
be increased if the temperature and humidity of an independent sample test
site varied from that observed at the input data test sites.
In early 1972 a laboratory study was conducted for the EPA by
Automotive Testing Laboratories under Contract 68-01-01+39. This study tested
in-use 1968-1972 model year vehicles in Denver in order to evaluate the
"Vehicle Testing to Determine Feasibility of Emission Inspection at Altitude",
ATL for EPA, September 1972.
-------
effectiveness of vehicle emission reduction concepts investigated and applied
at lower elevations. The model was used to predict the sample mean of HC,
CO and NO emissions for the cold stabilized and hot transient portions of
x
the FTP. These data are shown in Tables 19 and 20. The HC and NO predictions
are extremely accurate. The predicted CO emissions, especially for the hot
transient portion of the FTP, are not as accurate. This lack of accuracy is
more than likely a direct result of the small sample size of vehicles used
as input by the prediction model to determine the emission surfaces by model
year for the Denver vehicles. Due to the large variability inherent in
vehicle emission testing, the small sample sizes result in an inability to
correctly represent the true population in question. As stated earlier, the
ability to predict the variability in the model by fitting a confidence surface
around the model prediction mean value has not yet been developed.
In conclusion, the presence of city and model-year effects as well
as the large car-to-car variability indicate that the most effective use
of this model is as a predictor of group emissions. Based on engineering
considerations and sample size, the maximum number of groups which can be
separated from the total population is eleven. Based on Tables 13-15> these
eleven groups can predict the overall mean emissions of the input data set
with a maximum overall error of 13$ for HC and CO over three driving sequences.
For most pollutants and driving sequences, the predicted mean lies within the
confidence interval around the sample mean indicating that the absolute error
is within the inherent variability in the data. By examining the group-by-group
performance of the model, it can be seen that the model performs best for
those groups where the input sample size was at least 5% of the total vehicle
sample. Thus, when predicting individual group means, the model performs
-------
significantly better for groups 1, 2, k, 5> 6 and 7 than for groups 3, 8, 9,
10 and 11. However, the performance of the model is improved for those
cases in which the national population is simulated and the user has greater
flexibility when group 3 (1966-1967 California cars) and groups 8, 9, 10
and 11 (Denver 1968, 1969, 1970 and 1971) are treated as individual groups
rather than combined groups; that is, group 3 could be combined with group k
(1968 low altitude cities) and groups 8-11 could be combined into one group.
Tables 16-20 illustrate the ability of the model, when eleven input
vehicle groups are used, to predict vehicle emissions which were measured
in independent vehicle testing programs. The model was able to predict HC
and CO emissions within 28$ for each of groups 1, 2, 3, *+, 5> 6 and 7 and
within lB% for overall combinations of these groups. The ability to predict
HO emissions was not nearly as good and in certain cases, the model could
X
only predict within QQ%. This is to be partially expected, however, since
the predictive model is based on uncorrected oxides of nitrogen and the input
modal data were collected in different locations with different environmental
conditions from the independent study data. Thus, a large error could be
introduced when the input uncorrected NO values are used to predict corrected
NO values. The model was able to predict overall HC and NO emissions within
x x
11% for groups 8, 9» 10 and 11. The predictions for individual group HC and
NO emissions as well as the overall CO emissions were not as accurate. The
x
model was able to predict these groups within 55$. This is largely due to
the small sample sizes of input data from groups 8, 9» 10 and 11.
Future work incudes the fitting of confidence surfaces around the
prediction surface. This will enable the user to have a predicted value for
the emissions over a given driving sequence as well as a confidence interval
-------
around the prediction. Such a confidence interval vill reflect the sample
size and variability of the input modal data for the group of interest. In
addition, future work is being planned to deal with the question of modal
deterioration.
-------
1*7
6. SUMMARY AND CONCLUSIONS
In the preceeding discussion, a method was presented to calculate
the amounts of HC, CO and NO emitted by individual vehicles and vehicle
ji.
groups over any specified driving sequence. The method uses, as inputs,
the modal emission data on individual warmed-up vehicles. It is to be
understood, of course, that the mathematical model should be used only within
the region of the speed and acceleration space which is spanned by the input
modal data. The model has maximum effectiveness as a predictor of group emissions
for warmed-up vehicles.
The method, given in terms of a vehicle emissions model, is characterized
by the concept of an instantaneous emission rate. From this concept, the
emissions response of individual vehicles and vehicle groups are given in terms
of instantaneous emission rate functions. The development of the instantaneous
emission rate functions for a vehicle contains two important computational
features: the assessment of the coefficients that specify the instantaneous
emission rate function and a method to bound the steady state emission rate
function so that the function is non-negative (does not produce negative
emission rates) on the speed interval (0, 60) mph.
In a least squares fitting procedure, it is possible to obtain negative
predicted values for some points on the speed and acceleration/deceleration
surface. Such a possibility is most likely in extrapolated areas of the surface
or areas with very few actual data points. Due to the complexity of the
prediction procedure over the range of accel/decel space, the current model
does not check for negative emissions for each possible point on the prediction
surface of each vehicle. This type of problem did not occur for the set of
vehicles considered when appropriate weighting functions were used. However,
a test for negative emissions over accel/decel space and an appropriate
mathematical correction is planned as a future refinement to the model.
-------
U8
The instantaneous emission rate function can be used to characterize
an individual vehicle's emission response over any driving sequence as well
as to describe a vehicle group's emission response. The latter is accomplished
by the determination of the group's average vehicle emission rate function.
Further, a means of investigating the homogeneity of hypothesized vehicle
groups using linear discriminant function analysis is presented. (Appendix V)
The content of the discussion and structure of the model allows for
the immediate use of the emissions model by an analyst to predict vehicle
emissions and serves as a base for further research in predicting vehicle
emissions and their effect on the environment.
-------
TABLES
-------
50
-------
TABLE i
BAG VALUE STAT I.LJT1CS KOK THE SURVEILLANCE DRIVING CEQULflCE
POLLUTANT
HC
CO
NO
X
0
53.5
625.0
1+8.2
R
7-2
U3.1
-2.7
^
J.U3.3
201+20.8
163.0
°R
12.0
11+3.0
12.8
/* * % 2
1U.O
11+9.3
13.0
— .100$
0
13.5
6.9
-5.6
uu
— .100JB
0
P2.1+
22.9
26.5
' ^ + °R THH^
0
26.1
23.9
27.1
\n
I-1
-------
TABLE 2
BAG VALUE STATISTICS FOR THE FIRST 505 SECONDS OF THE
FEDERAL TEST PROCEDURE DRIVING SEQUENCE
POLLUTANT
HC
CO
NO
X
0
21.0
223.7
17-2
R
2.8
9.2
0.5
-------
53
TABLE 3
DISTRIBUTION OF HC BAG VALUE ERROR (OBSERVED - CALCULATED)
ERROR (CMS)
-70 to -6S
-65 to -60
-60 to -55
-55 to -50
-50 to -45
-45 to -40
-40 to -35
-35 to -30
-30 to -25
-25 to -20
-20 to -15
-15 to -10
-10 to - 5
- 5 to - 0
0 to 5
5 to 10
10 to 15
15 to 20
20 to 25
25 to 30
30 to 35
35 to 40
40 to 45
45 to 50
50 to 55
55 to 60
60 to 65
65 to 70
70 to 75
75 to 80
80 to 85
85 to 90
90 to 95
95 to 100
100 to 105
105 to 110
110 to 115
115 to 120
FROM THE SURVEILLANCE DRIVING SEQUENCE
NUMBER OF VEHICLES
1
1
0
0
0
0
1
0
2
4
5
9
24
149
309
246
97
' . . 80
37
16
18
3
4
5
1
0
2
2
0
2
1
.... o
0
0
0
0
0
1
TOTAL 1020
-------
TABLE U
DISTRIBUTION OF CO BAG VALUE ERROR (OBSERVED - CALCULATED)
FROM THE SURVEILLANCE DRIVING SEQUENCE
' ERROR (CMS) NUMBER OF VEHICLES
-750 to 700 1
-750 to -650 0
-650 to -600 0
-600 to 550 0
-550 to -500 1
-500 to -450 1
-450 to -400 0
-400 to -350 1
-350 to -300 4
-300 to -250 3
-250 to -200 10
-200 to -150 22
-150 to -100 57
-100 to - 50 . 94
- 50 to 0 170
0 to 50 272
50 to 100 143
100 to 150 92
150 to 200 53
200 to 250 32
250 to 300 27
300 to 350 6
350 to 400 7
400 to 450 . 7
450 to 500 . 2
500 to 550 5
550 to 600 2
600 to 650 1
650 to 700 2
700 to 750 1
750 to 800 0
800 to 850 0
850 to 900 0
900 to 950 4
TOTAL 1020
-------
55
TABLE 5
DISTRIBUTION OF NOX BAG VALUE ERROR (OBSERVED - CALCULATED)
FROM THE SURVEILLANCE DRIVING SEQUENCE
ERROR (CMS) NUMBER OF VEHICLES
-65 to -60 1
-60 to -55 0
-55 to -50 0
-50 to -45 . 2
-45 to -40 1
-40 to -35 3
-35 to -30 8
-30 to -25 13
-25 to -20 26
-20 to -15 81
-15 to -10 98
-10 to -5 203
-5 to 0 . 298
0 to 5 145
5 to 10 60
10 to 15 44
15 to 20 22
20 to 25 17
25 to 30 14
30 to 35 5
35 to 40 6
40 to 45 1
45 to 50 0
50 to 55 1
55 to 170 1
TOTAL 1020
-------
56
TABLE 6
DISTRIBUTION OF HC BAG VALUE ERROR (OBSERVED - CALCULATED)
FROM FIRST 505 SECONDS OF THE FEDERAL TEST PROCEDURE
DRIVING SEQUENCE (HOT TRANSIENT PORTION)
ERROR (CMS) NUMBER OF VEHICLES
45 to -40 ..................... 1
-40 to -35 ..................... 0
-35 to -30 .......... . ........... 1
-30 to -25 ... .................. 2
-25 to -20 ..................... 3
-20 to -15 .......... ... ........ 5
-15 to -10 ..................... 3
-10 to -5 ..................... 21
-5 to 0 ..................... 158
0 to 5 ..................... 592
5 to 10 ..................... 172
10 to 15 ..................... 35
15 to 20 ..................... 11
20 to 25 . . ................... 9
25 to 30 ..................... 1
30 to 35 ............... ...... 3
35 to 40 ..................... 1
40 to 45 ..................... 1
45 to 50 ..................... 0
50 to 55 .................. ... 0
55 to 60 ..................... 0
60 to 65 ..................... 1
TOTAL 1020
-------
57
TABLE 7
DISTRIBUTION OF CO BAG VALUE ERROR (OBSERVED - CALCULATED)
FROM FIRST 505 SECONDS OF FEDERAL TEST PROCEDURE -
DRIVING SEQUENCE (HOT TRANSIENT PORTION^
ERROR (CMS) NUMBER OF VEHICLES
350
300
250
200
150
100
50
0
50
100
150
200
250
300
350
400
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
-300
-250
-200
-150
-100
- 50
0
50
100
150
200
250
300
350
400
1000
2
1
1
8
24
72
279
483
103
30
3
5
0
1
1
1
TOTAL 1020
-------
58
TABLE 8
DISTRIBUTION OF NOX BAG VALUE ERROR (OBSERVED - CALCULATED)
FROM FIRST 505 SECONDS OF FEDERAL TEST PROCEDURE"
DRIVING SEQUENCE (HOT TRANSIENT PORTION)
ERROR (CMS) NUMBER OF .VEHICLES
-25 to -20
-20 to -15
-15 to -10
-10 to - 5
- 5 to 0
0 to 5
5 to 10
10 to 15
15 to 20
20 to 25
TOTAL 1020
-------
59
TABLE 9
REPLICATE MODAL ANALYSES OF HC FOR 6l VEHICLES
NTJDF
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
FTP (gins.)
SDS (gins.)
X (gms/min.)
3.8570
1.6284
2.4522
2.8327
3.5073
1.9178
5.2240
2.7310
4.4227
2.9622
4.9806
3.0453
4.9745
3.2702
1.8480
1.4517
4.2265
2.2881
3.7102
2.3403
5.7121
3.1666
3.5338
4.2144
2.9225
1.8284
4.2448
3.0080
3.1500
4.5983
2.6819
1.9091
1.2829
1.2182
1.6903
2.5522
3.2911
21.3255
54.4599
d (gm/min)
2.2342
1.1856
1.2589
2.7032
3.2759
1.0114
3.2673
2.1971
3.7429
1.3290
3.6829
1 . 3054
4.1268
1.8522
0.8133
0.5117
3.4144
1.5467
3.0242
1 . 3852
4.1975
1.2412
2.8711
3.7651
1.6542
1.0534
3.3618
1 0.9896
2.6789
3.8230
1.4452
1.1396
0 . 3898
0.9104
1.0114
2.3242
2.6043
15.0555
37.3647
a/x . 100$
57.93
72.81
51.34
95.43
93.40
52.74
62.54
80.45
84.63
44.86
73.95
42.87
82.96
56.64
44.01
35.25
80.79
67.60
81.51
59.19
73.48
39.20
81.25
89.34
56.60
57.61
79.20
32.90
85.04
83.14
53.89
59.69
30.39
74.73
59.84
91.06
79.13
70.60
68.61
-------
6o
TABLE 10
RF.PI.TfATR MODAL ANALYSES OF CO FOR 61 VEHICLES
MODE
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
FTP (gms)
SDS (gms)
X (gms/min)
49.4840
15.3812
32.4560
36.1708
40.5807
17.4203
96.5027
24.6048
65.0038
22.3535
90.2337
21.4964
80.1931
25.9958
16.1499
19.9149
63.0919
20.5962
59.6194
21.1044
106.7290
24.1967
50.1886
71.2064
25.8109
17.0626
65.9579
25.9421
44.9232
85.6044
26.3899
18.1339
16.9898
17.3020
16.7257
28.9744
45.2389
239.8225
677.9143
a ( gm/min )
14.9649
13.0886
9 . 8602
11.1998 .
11.3075
8.4930
23.5758
10.4125
31 .8901
9.3043
50.5725
9.9618
50.5111
5.0928
5.1828
5.4151
16.0394
7.7882
25.6127
8.6146
51.5901
9.0618
11.6789
50.5271
10.7750
9.7663
17.3853
12.5521
13.5433
49.4810
10.8379
8 . 8996
4.7618
5.1765
4.7752
7.7927
8.8608
64.6112
97.8159,,
a/X .1005?
30.24
85.09
30.38
30.96
27.86
48.75
24.43
42.32
49.06
41.62
56.05
46.34
62.99
19.59
32.09
27.19
25.42
37.81
42.96
40.82
48.34
37.45
23.27
70.96
41.75
57.24
26.36
48.38
30.15
57.80
41.07
49.09
28.03
29.92
28.55
26.90
19.59
26.94
14.43
-------
61
TABLE 11
REPLICATE.MODAL ANALYSES OF NO FOR 6l VEHICLES
Mode
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
FTP (gin)
SDS (gm)
X (em/min)
3.5689
0.6435
0.9107
2.8518
5.2695
1.5707
6.9947
2.9842
7.9071
1 . 8646
7.2462
1.7380
7.0501
1.9580
0.6813
0.3179
4.9960
1.1132
4.8965
0.9471
6.6968
1.3989
2.9016
6.9010
2.0334
0.6391
6.5950
1 . 3037
2.5598
6.6468
2.1487
0.6203
0.1174
0.1826
1.0192
3.1829
6.3341
18.2670
50.8930
0 (gm/min)
1.0305
0.2893
0.4624
0.9324
1.1874
0.6046
2.2683
1.2236
2.5482
0.8339
1.6195
0.7112
1.4354
0.8544
0.3585
0.3019
1.1497
0.6661
1.3169
0.3277
1.6761
0.5392
0.9026
1 . 3887
0.7985
0.2832
1.2575
0.4668
0.6831
1.7541
0.8939
0.2489
0.1618
0.2170
0.2395
0.6877
1.2201
2.8891
7.8712
a/x .100$
028.87
044.96
050.77
032 . 70
022.53
038.50
032.43
041.00
032.23
044.72
022.35
040.92
020.36
043.64
052.62
094.94
023.01
059.83
026.89
034 . 59
025.03
038.54
031.11
020.12
039.27
044.31
019.07
035.80
026.69
026.39
041.60
040.12
137.83
118.81
023.50
021.61
019.26
15.82
15.47
-------
62
TABLE 12
VARIANCE COMPONENT ANALYSES FOR 6l REPLICATE TESTS
First 505 Seconds - Federal Test Procedure
Source
Models
Replications
Interaction
Mean Squares
HC CO N0x
5.74 832.57 3.39
94.00 784.67 2.64
2.65 673.39 2.37
Variance Component
HC CO NO
1.54 79.59
45.67 55.64
2.65 673.39
x
1.01
0.63
1.37
Surveillance Driving Sequence
Source
Kb dels
Replications
Interaction
Mean Squares
HC CO N0x
24.95 5560.34 29.76
600.84 4759.36 26.37
9.54 2770.54 5.13
Variance Conponent
HC
7.75
295.65
9.54
CO
1394.90
994.41
2770.54
NO
X
12.31
10.61
• 5.13
-------
TABLE 13
FEDERAL SHORT CYCLE
GROUP PREDICTION OF SIX CITY DATA (Emissions in Grams)
HC
CO
NO
Group
1
2
3
4
5
6
7
% Of
Total
Vehicles
0.09
0.45
0.03
0.08
0.09
0.08
0.10
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
5.67
4.85 6.43 -0.25
7.19
4.56
4.60 4.97 -0.07
5.38
3.96
3.52 5.00 -0.30
6.04
2.56
3.02 3.52 -0.14
4.48
2.42
2.74 3.04 -0.10
3.66
2.12
2.17 2.46 -0.12
2.80
1.81
1.81 2.03 -0.11
2.25
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
71.28
76.29 80.18 -0.05
89.08
44.64
44.59 47.40 -0.06
50.16
47 . 31
30.88 58.69 -0.47
70.07
31.98
37.30 41.33 -0.10
50.68
29.43
30.32 34.21 -0.11
38.99
23.74
24.89 27.46 -0.09
31.18
23.48
22.28 28.34 -0.21
33.20
95% Conf.
Interval
Around
Pre- . Sample P-S Sample
dieted Mean S Mean
1.10
1.67 1.30 0.28
1.50
2.00
2.77 2.12 0.31
2.24
1.49
2.23 2.06 0.08
2.63
2.31
3.31 2.63 0.26
2.95
2.99
4.51 3.43 0.31
3.87
3.00
3.91 3.32 0.18
3.64
2.53
3.50 2.81 0.25
3.09
cr\
U)
-------
TABLE 13 (cont'd)
FEDERAL SHORT CYCLE
GROUP PREDICTION OF SIX CITY DATA (Emissions in Grams)
HC
CO
NO
Group
8
9
10
11
% of
Total
Vehicles
0.02
0.02
0.02
0.02
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
3.55
3.04 4.56 -0.33
5.57
2.52
2.25 3.60 -0.37
4.68
3.00
2.93 4.14 -0.29
5.28
2.60
2.51 3.16 -0.21
3.72
Group 4.00
Totals 1.00 3.67 4.24 -0.13
4.48
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
50.24
52.50 72.48 -0.28
94.72
31.13
28.98 48.16 -0.40
65.19
43.27
45.41 54.45 -0.17
65.63
47.72
41.01 61.56 -0.33
75.40
44.37
41.15 46.49 -0.11
48.61
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
1.12
2.26 1.44 0.57
1.76
1.33
2.36 1.79 0.32
2.25
1.17
2.45 2.44 0.00
3.71
1.14
2.42 2.33 0.04
3.52
2.26
2.99 2.36 0.27
2.46
-------
/
-- i,
9^,^ .
-------
TABLE 14
COLD STABILIZED PORTION OF FTP
GROUP PREDICTION OF SIX CITY DATA (.^missions D*ta in Grams)
HC
CO
NO
Group
!f
i J
<*'
2/
'^V
3
4 ^
5 ^
6 -?
SI*
% of
Total
Vehicles
0.09
0.45
0.03
0.08
0.09
0.08
0.10
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
34.16
36.08 38.84 -0.07
43.52
31.47
33.64 34.70 -0.03
37.93
26.25
23.51 32.00 -0.27
37.75
13.87
22.32 21.63 0.03
29.39
15 ".54
20.38 19.50 0.05
23.46
12.39
15.20 14.48 0.05
16.57
10.08
12.79 11.25 0.14
12.42
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
444.62
526.27 486.71 0.08
528.80
328.80
331.23 346.42 -0.04
364.04
302.12
219.13 363.32 -0.40
424.52
211.26
281.69 268.89 0.05
326.52
215.27
242.17 245.36 -0.01
275.45
164.64
196.77 189.40 0.04
214.16
134.87
181.69 158.05 0.15
181.23
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
5 .48
8.12 6.40 0.27
7.32
11.16
14.12 11.81 0.20
12.46
7 .43
11.61 10.20 0.14
12.97
12.54
16.89 14.07 0.20
15.60
16.36
23.21 17.89 0.30
19.42
14.80
19.71 16.03 0.23
17.26
13.68
17.59 14.87 0.18
16.06
-------
TABLE 14 (cont'd)
COLD STABILIZED PORTION OF FTP
GROUP PREDICTION OF SIX CITY uATA (^missions uata in Grams)
HC
CO
NO
Group
8
9
10
11
Group
Total
% of
Total
Vehicles
0.02
0.02
0.02
0.02
s 1.00
95% Conf.
Interval
Around
Pre- Sample P-S Sample
0 dieted Mean "S> Mean
20.48
21.42 25.40 -0.16
30.32
14.20
16.29 20.32 -0.20
26.44
15.94
21.53 23.05 -0.07
30.16
16.25
17.95 19.01 -0.06
21.77
25.87
26.68 27,67 -0.04
29.47
951 Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
293.05
395.03 405.13 -0.02
517.21
157.18
240.42 240.10 0.00
323.02
265.58
353.17 323.71 0.09
381.84
234.13
335.98 300.63 0.12
367.13
298.68
306.17 311.17 -0.02
323.66
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
6.26
10.40 7.65 0.36
9.04
7.11
11.60 9.11 0.27
11.11
7.73
11.87 9.65 0.23
11.57
7.04
11.88 11.28 0.05
15.52
12.01
15.03 12.46 0.21
12.91
-------
TABLE 15
HOT TRANSIENT PORTION OF FTP
GROUP PREDICTION OF SIX CITY DATA (Emissions in Grams)
HC
CO
NO
Group
1
2
3
4
5
6
7
% of
Total
Vehicles
0.09
0.45
0.03
0.08
0.09
0.08
0.10
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
27.34
26.71 30.80 -0.13
34.26
23.28
23.49 25.48 -0.08
27.68
19.77
16.67 22.77 -0.27
25.77
12.00
15.29 15.94 -0.04
19.88
12.58
14.00 15.01 -0.07
17.44
10.61
10.94 11.88 -0.08
13.15
8.81
9.18 9.49 -0.03
10.17
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
375.29
437.84 408.40 0.07
441.51
228.01
228.53 239.99 -0.05
251.97
204.97
143.25 248.12 -0.42
291.27
144.33
176.32 181.56 -0.03
218.79
130.59
136.62 148.08 -0.08
165.57
106.81
112.85 124.34 -0.09
141.87
88.61
110.08 101.17 0.09
113.73
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
6.63
9.17 7.55 0.21
8.47
14.43
16.13 15.17 0.06
15.91
11.18
14.99 13.44 0.12
15.70
17.36
19.79 19.17 0.03
20.98
21.87
26.17 23.76 0.10
25.65
20.87
24.31 22.54 0.08
24.21
19.85
22.40 21.54 0.04
23.23
-------
TABLE 15 (cont'd)
HOT TRANSIENT PROTION OF FTP
GROUP PREDICTION OF SIX- CITY DATA (Emissions in Grams)
HC
CO
NO
Group
8
9
10
11
\ of
Total
Vehicles
0.02
0.02
0.02
0.02
i*
951 Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
18.52
17.46 21.75 -0.20
24.98
14.53
12.47 18.96 -0.34
23.39
13.62
16.33 20.86 -0.22
28.10
14.49
14.59 16.45 -0.11
18.41
Group 19.85
Totals 1.00 18.97 21.05 -0.10
22.25
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
277.10
369.68 336.29 0.10
395.48
162.40
243.70 241.38 0.01
320.36
216.42
332.61 299.98 0.11
383.54
230.09
342.85 293.02 0.17
355.95
214.44
218.75 223.69 -O.(02
232.94
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
5.84
10.81 7.87 0.37
9.90
7.66
13.33 10.64 0.25
13.62
8.89
13.40 11.51 0.16
14.13
9.43
13.51 11.71 0.15
13.99
15.84
17.68 16.39 0.08
16.94
ON
Oo
-------
TABLE 16
FEDERAL SHORT CYCLE
GROUP PREDICTION OF SHORT CYCLE PROJECT (Emissions in grams/miles)
NO
HC
CO
Group
2
3
4
5
6
7
Group
Total.
\ of
Total
Vehicles
0.48
0.09
0.11
0.14
0.12
0.06
; 1.00
951 Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
6.19
6.13 7.13 -0.14
8.07
3.21
4.69 4.93 -0.05
6.65
3.04
4.03 3.86 0.04
4.68
3.68
3.65 4.56 -0.20
5.44
2.91
2.89 3.29 -0.12
3.67
2.52
2.41 3.03 -0.20
3.54
4.99
4.81 5.50 -0.12
6.01
951 Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
58.35
59.45 64.13 -0.07
69.91
40.75
41.17 51.39 -0.20
62.03
35.21
49.73 44.47 0.12
53.73
40.31
40.43 47.59 -0.15
54.87
31.58
33.19 37.71 -0.12
43.84
26.03
29.71 34.60 -0.14
43.17
50.05
49.13 53.52 -0.08 °
56.99
x 951 Conf.
Interval
Aro-und
Pre- Sample P-S Sample
dieted Mean S Mean
2.37
3.69 2.55 0.45
2.73
2.12
2.97 2.60 0.14
3.08
2.60
4.41 3,04 0.45
3.48
2.98
6.01 3.40 0.77
3.82
2.91
5.21 3.33 0.57
3.75
2.64
4.67 3.13 0.49
3.62
2.72
4.27 2.86 0.49
3.00
ON
-------
TABLE 17
HOT TRANSIENT PORTION OF FTP
GROUP PREDICTION OF SHORT CYCLE PROJECT (Emissions in Grams)
HC
CO
NO
Group
2
3
4
5
6
7
Group
Totals
% of
Total
Vehicles
0.48
0.09
0.11
0.14
0.12
0.06
1.00
951 Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
22.53
23.49 25.78 -0.09
29.03
14.23
16.67 19.25 -0.13
24.27
12.86
15.29 15.90 -0.04
18.94
14.73
14.00 18.37 -0.24
22.01
12.42
10.94 13.85 -0.21
15.28
11.15
9.18 12.67 -0.28
14.19
19.05
18.28 20.83 -0.12
22.61
951 Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
238.62
228.53 258.77 -0.12
278.92
172.64
143.25 214.34 -0.33
256.04
137.70
176.32 168.74 0.04
199.78
153.36
136.62 175.35 -0.22
197.34
131.13
112.85 150.79 -0.25
170.45
113.95
110.08 150.25 -0.27
186.55
201.33
181.25 213.56 -0.15
225.79
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
12.85
16.13 13.67 0.18
14.49
11.48
14.99 13.36 0.12
15.24
13.83
19.79 15.85 0.25
17.87
16.25
26.17 18.14 0.44
20.03
15.64
24.31 17.57 0.38
19.50
14.77
22.40 17.15 0.31
19.53
14.55
19.19 15.18 0.26
15.81
-------
TABLE 18
COLD STABILIZED PORTION OF FTP
GROUP PREDICTION OF SHORT CYCLE PROGRAM (Emissions Data in Grams)
HC
CO
NO.
Group
2
3
4
5
6
7
1 of
Total
Vehicles
0.48
0.09
0.11
0.14
0.12
0.06
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean 13 Mean
31.88
33.51 36.74 -0.09
41.60
16.49
23.68 26.19 -0.10
35.89
15.07
22.36 19.99 0.12
24.91
14.65
20.33 16.68 0.22
18.71
15.10
15.14 17.49 -0.13
19.88
12.46
12.81 15.16 -0.16
17.86
Group 25.84
Totals 1.00 26.11 28.58 -0.09
31.32
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean "~S~" Mean
374.32
329.29 403.86 -0.18
433.40
268.38
217.67 325.20 -0.33
382.02
217.61
282.30 270.59 0.04
323.57
249.04
242.21 282.57 -0.14
316.10
218.64
198.01 255.26 -0.22
291.88
190.30
185.23 251.95 -0.26
313.60
319.56
277.49 337.91 -0.18
356.26
951 Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
9.51
14.06 10.20 0.38
10.89
7.93
11.59 9.21 0.26
10.49
9.92
16.80 11.44 0.47
12.96
12.25
23.12 13.88 0.67
15.51
11.63
19.48 13.28 0.47
14.93
11.41
17.55 13.40 0.31
15.39
10.81
16.27 11.32 0.44
11.83
-------
TABLE 19
COLD STABILIZED PORTION OF FTP
GROUP PREDICTION OF ATL STUDY (Emissions Data in Grams)
HC
CO
NO
Group
8
9
10
11
Group
Total
1 of
Total
Vehicles
0.23
0.26
0.28
0.23
s 1.00
951 Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
17.70
21.29 28.02 -0.24
38.34
12.92
16.28 24.61 -0.34
36.30
12.62
21.25 17.67 0.20
22.72
12.17
17.81 16.23 0.10
20.29
17.50
19.18 21.54 -0.11
25.58
951 Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
217.79
383.09 320.63 0.19
423.47
246.72
237.36 308.19 -0.23
369.66
166.46
349.68 233.43 0.50
300.40
121.46
331.26 201.75 0.64
282.04
228.39
323.92 265.79 0.22
303.19
* 95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
7.88
10.30 10.21 0.01
12.54
9.94
11.20 11.98 -0.07
14.02
8.61
11.74 9.90 0.19
11.19
7.73
11.67 10.56 0.11
13,39
'3 . 69
11.25 10.67 0.05
11.65
ro
-------
TABLE 20
HOT TRANSIENT PORTION OF FTP
GROUP PREDICTION OF ATI STUDY (Emissions Data in Grams)
HC
CO
NO
Group
8
9
10
11
% of
Total
Vehicles
0.23
0.26
0.28
0.23
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
15.40
17.46 ,20.11 -0.13
24.82
10.41
12.47 19.87 -0.37
29.33
11.08
16.33 14.30 0.14
17.52
10.75
14.59 13.90 0.05
17.05
Group 14.23
Totals 1.00 15.18 17.01 -0.11
19.79
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
184.14
369.68 246.87 0.50
309.60
204.38
243.70 237.35 0.03
270.32
149.11
332.61 189.64 0.75
230.17
100.59
342.85 153.96 1.23
207.33
183.69
320.37 207.09 0.55
230.49
95% Conf.
Interval
Around
Pre- Sample P-S Sample
dieted Mean S Mean
10.32
10.81 12.52 -0.14
14.72
12.21
13.33 14.66 -0.09
17.11
10.94
13.40 12.72 0.05
14.50
9.54
13.51 13.23 0.02
16.92
12.12
12.81 13.30 -0.04
14.48
-J
U)
-------
-------
75
FIGURES
-------
76
-------
TT
3.0
2.8
2.6
2.4
2.2
2.0
1.8
1.6
z 1.4
o
S 1.2
1.0
.8
.6
.4
L °~'
FIGURE 1
WEAN STEADY STATE HC
EMISSION RATE VALUES
VS. SPEED.
.2
15
30 45
SPEED (MPH)
60
-------
78
34
33
32
31
30
29
28
27
CO
S 25
LU
" 24
z
o
CO
2 23
21
20
19
18
17
16
o
X
FIGURE 2
MEAN STEADY STATE CO
EMISSION RATE VALUES
VS. SPEED.
15
30 45
SPEED (MPH)
60
-------
79
(/>
s
C3
/
41 J
/
FIGURE 3
/ MEAN STEADY STATE NOx
, O EMISSION RATE VALUES
w I /VS. SPEED.
0 *•>*•»«•• ^ i i i i
0 15 30 45 60
SPEED (MPH)
-------
500
FIGURE 4
DISTRIBUTION OF HC BAG ERROR
FROM THE SURVEILLANCE DRIVING
SEQUENCE.
MEAN = 7.2 GMS
STD. DEVIATION = 12.0 GMS
400
V)
la
u.
o
UJ
00
300
200
100
CD
o
-30 -25 -20 -15 -10
-5
5 10 15
BAG ERROR (GMS)
20
25
30
35
40
45
50
55
-------
500
FIGURE 5
400
CA
UJ
DISTRIBUTION OF CO BAG ERROR
FROM THE SURVEILLANCE DRIVING
SEQUENCE.
MEAN =43.1 GMS
STD. DEVIATION = 143.0 GMS
ui
u.
Q
K
til
m
S
3
300
200
100
-300 -250 -200 -15|0 -100 -50 0 50 100 150 200 250 300 350 400 450 500
BAG ERROR (GMS)
-------
500
FIGURE 6
400
V)
LU
o
o
Of
LU
m
300
200
100
DISTRIBUTION OF NO; BAG ERROR
FROM THE SURVEILLANCE DRIVING
SEQUENCE.
MEAN = -2.7 QMS
STD. DEVIATION = 12.8 GMS
O>
ro
-40
-35 -30 -25 -20 -15 -10
-505
BAG ERROR (GMS)
10
15
20
25
30
35
40
45
-------
500
400
X
UJ
>
u.
o
cc
UJ
CD
300
200
100
FIGURE 7
DISTRIBUTION OF HC BAG ERROR
FROM THE FIRST 505 SEC OF THE
FEDERAL TEST PROCEDURE
DRIVING SEQUENCE.
MEAN = 2.8 GMS
STD. DEVIATION = 6.1 GMS
O3
U)
-30 -2? -20 -15
-10 -5 0 5 10
BAG ERROR (QMS)
15
20
25
30
-------
500
400
UI
u
X
ui
u.
o
oe
ui
00
300
200
100
FIGURE 8
DISTRIBUTION OF CO BAG ERROR
FROM THE FIRST 505 SEC. OF THE
FEDERAL TEST PROCEDURE
DRIVING SEQUENCE.
MEAN = 9.2 GMS
STD. DEVIATION = 64.5 GMS
00
tr
O
-300 -250 -200 -150 -100 -50 0 50 100 150
BAG ERROR (GMS)
200
250 300
-------
FIGURE 9
500
400
V)
Ul
X
UJ
oc.
Ul
00
300
200
100
DISTRIBUTION OF NOx BAG ERROR
FROM THE FIRST 505 SEC OF THE
FEDERAL TEST PROCEDURE
DRIVING SEQUENCE.
MEAN = 0.5 GMS
STD. DEVIATION = 4.8 GMS
oo
VI
-30 -25 -20 -15 -10
-505
BAG ERROR (GMS)
10
15
20
25
30
-------
86
-------
1-1
APPENDIX I
SPECIFICATION OF THE 37 MODES AND EVALUATION
OF THE AVERAGE VALUES OF THE BASIS FUNCTIONS
-------
1-2
-------
1-3
APPENDIX I
SPECIFICATION OF THE 37 MODES AND EVALUATION OF THE
AVERAGE VALUES OF THE BASIS FUNCTIONS
The nine functions of speed (v) and acceleration (a) which form the
basis functions of the instantaneous emission rate function must be averaged
over each mode in order to determine the coefficients which specify the
emission rate functions (See Appendix III).
To demonstrate how these average values are evaluated for the basis
22 22 22
functions: 1.0, v, a, va, v,a,va,av, va, the case of determining
the average value of the third basis function, va, over the i'th mode is
considered.
Let T. = duration of i'th mode,
v.(t) = speed at time = t in the i'th mode, t< T. ,
dv.(t)
and a.(t) = —— = acceleration at time = t in the i'th mode,
•*- Ctv
t < T .
By definition
T
T
va 1
i T.
T
0
Ti
i = T~ f Vi(t) ai(t) dt '
i i
This integration is evaluated by the following approximation
-------
1-4
, 1 V1 (V1.1 * Vl, .1+1) (vi. .1 *l-Yi, .1) At ,
it - T- r
where v^ = initial speed of model,
ij Vi, J+l = average speed over the J'th time interval
2
of mode i,
v — v
i? 3+i i-t_J- = average acceleration over the J 'th time interval
of mode i,
and, N. At = T.
The averages of the other eight basis functions are similarily determined.
The modal specifications for the 37 modes are given in Table 1-1. Values
for the averages of the basis functions over each mode are given in Table 1-2.
-------
1-5-
TABLE 1-1
MODAL SPECIFICATIONS
•'ODE
1
u
13
Ib
17
ia
19
2J
22
23
24
26
27
28
30
31
3i'
36
.17
I'JUh , »< if C) ill STANCE !."• I I
Ic.J 0.06020
SPEED (Kprtl AT LNL SEC.
lo.O
a.O
11.0
13.0
12.u
17.u
12.0
14.J
30.0
26.C
21.0
32.0
23.0
9.0
8.0
22.0
16.0
18.0
19.0
25.0
15.0
25. 0
18.0
10.0
38.0
15.0
18.(j
21 . _.
14..,
13.0
t u. 0
ou. 0
•>0.u
3u • J
oO.O
0.07410
J. 02010
0.07050
O.UciOO
0. 126RO
0.21630
0.17160
J. 20430
0.33670
0.31360
0.19730
0.33130
0.29940
0.05790
0.01730
0.17590
0.13920
3.15280
0.13040
0.26540
0.26340
0.07370
U. 31340
0.23620
0.04440
0.40090
0.32930
J. 08860
0.2599J
0. 181 iO
0.05920
0.0
0.25000
0.5C )CO
J. 750JJ
UC.OGQO
c.o
30.0
3u.O
6.4
0.0
15.0
30.0
44.4
43.0
30.0
3C.O
51.6
60.0
45.1
45.0
58.5
60.0
49.2
22.1
15.0
45.0
58.9
60.0
31.2
0.0
34.5
54.5
60.0
47.8
30.0
15.0
0.0
34.4
45.0
20.7
15.0
36.9
45.0
17.8
0.0
41.8
59.3
60.0
43.6
5.2
0.0
27.8
30.0
44.6
59.3
60.0
41.6
30.0
0.0
29.6
49.6
53.9
60.0
49.3
20.1
C.O
25.2
30.0
48. I
10.0
32.1
30.0
J.3
SPEED
SPEED
SPEED
SPEED
SPEED
1.0
29.6
3.7
1.7
15.9
30.7
45.0
44.7
30.0
53.6
60.0
45.6
59.3
59.7
47. <,
20.2
16.7
46.3
59.3
59.4
26.6
1.5
36.8
55.5
59.7
45. d
29.5
14.4
2.4
36.2
44.5
18.1
15.9
3d. 8
44.5
13.8
2.6
44.2
60.0
59.6
40.6
3.0
1.2
28.7
30.5
46.0
6C.O
5S.6
28.9
29.1
0.9
31.7
50.8
59.3
59.7
47.6
17. 1
0.3
26.5
30. 7
49.8
59. 5
30. 4
29.4
0.0
= J.
= 15.
= 30.
= -.5.
= bO.
5.1
28.9
1.0
4.6
17.3
31. 7
44.1
31.0
55.5
59.7
46.5
60.0
59.3
45.5
18.4
20.0
46.5
60.0
58.5
21.9
5.2
39.0
56.4
59.3
43. 7
28.7
13.3
6.3
37.8
43.9
16. 1
17.3
40.5
43.7
9.9
7.1
46.4
59.0
37.8
1.3
3.5
29.6
31.4
47.5
59.1
36.3
27.7
4.0
33.7
51.9
60.0
59.2
45.7
14.6
2. 1
27.4
31.8
51.5
5rt.7
30.0
26.5
OFUR 60
OFOR 60
OFOR 60
OFOP 60
OFOh 60
9. t
26.1
0.3
7.6
18.9
32. 't
43.4
32.5
57.2
59.1
47.6
5b.t
43.4
17.0
. 23.1
50.1
57.4
17.3
8.6
41.0
57.2
58.9
41.6
27.3
11.3
10.0
39.2
43.0
15.1
18.9
42.0
42.7
6.4
11.5
48.5
58.3
34.6
0.3
6.4
30.0
32.4
48.9
58.4
34.0
25.4
6.9
35. 7
52.9
58.7
43.6
12. C
4.9
28.3
33.1
53.0
57.6
27.2
SEC
SEC
SEC
SEC
SEC
13.2
2fc.S
0.0
10.3
20.6
34,2
42.2
34.3
58.6
58.5
48.7
58.3
41.1
15.9
26. 1
51.5
56. 1
12.6
12.0
43.0
57.9
58.3
39.4
25.3
8.5
13.5
40.5
41.3
15.0
20.7
43.4
41.4
3. 5
15.7
50.3
57.4
11.3
o.o
9.6
33.0
50.4
57.6
32.1
22.0
9.8
37.5
53.8
58.1
41.4
9.5
7.5
29.0
34. 5
5*. 0
56.1
25.4
17.1
25.4
12.3
22.4
35.6
40.7
36.2
59.3
57.2
50.0
57.6
38.3
15.2
28.9
52.8
54.4
ft. 7
15.3
44.3
56.5
57.. '>
37.3
22.7
5.2
16. a
41.6
40.2
22.4
44.5
39. 3
1.)
19.6
52.0
56.5
27.9
12.8
34.8
51.7
56.5
30.7
17. 6
12.4
39. 3
54.7
57. 't
3^.0
7.2
10. 1
29.3
36. J
56.0
54.3
22. )
20.6
23.5
13.7
24.2
37.0
38.9
38.3
55.7
51.3
56.9
36.4
15.0
31.6
54.0
5?. 4
5.1
18.4
46.5
58.9
56.7
35.4
19.9
2.1
19.9
42.6
38.2
24.5
45.0
37.8
0.1
23.4
53.5
55.3
24.3
15.9
36.0
53.0
55.1
30.0
12.5
15.3
41. G
55.5
56.7
36.6
5.2
12.8
30.0
37.6
57.2
51.5
19.0
23. ',
21.2
14, S
25.9
38.5
36.8
40.5
53.8
52.6
56.3
34.0
34.2
55.1
49.9
2.3
21.4
48.1
59. 3
55.7
33.6
17.3
0.2
22.8
43.4
35.8
26.4
35.3
0.3
26.9
54.9
54.0
20.3
18.8
37.4
54.3
53.4
7.4
17. J
42.'.
56.3
55. J
34.0
3.'«
15.4
39.3
58.4
4S.5
16.4
25.7
If. 5
15.0
27.5
39.9
34.6
42.7
51.7
53.9
54.9
31.5
36.6
56.1
46. 9
0.5
24.2
49.6
63. 0
54.5
32.1
1?.4
0.0
25.5
44.0
33. 1
38. 7
32.5
33.3
56.1
52.4
IT. 3
21.3
38.7
55.5
51.5
2.9
?0.4
'.*.?
56.9
54.8
»!.-»
1.9
17.8
'i 1.0
59.3
V5.1
12.5
27. !
15. S
29. S
41.2
3?. 6
45.3
49.5
55.2
53.8
29.0
38.9
5S.9
43.6
0.0
27.0
51.3
53.1
30.9
15.3
28.0
44.5
30. I
3J.d
29.2
33.4
57.1
50.5
14.3
23.5
40.2
56.6
49.3
a. :<
27.1
45. 'j
57.5
53.7
28.6
0.9
20.1
i'.e
oO.O
41. b
J.^
?8. •-
12.5
?9.P.
42.4
31.0
47.3
47.5
56.4
52.4
26.6
41.1
57.7
39. a
29.6
52.3
51.5
30.2
30.3
45.0
26,9
32.9
25.6
36.4
53.0
48. 5
10. T
25.2
41.6
57. h
46.8
0.3
25.2
47.0
58.1
52.4
?5.H
0.2
22.1
44.4
13.3
5.0
2°. 1
9.<.
30.0
43.5
30.1
49.5
45.9
57.5
50.9
24.3
43.1
58.3
35.7
32.1
53.5
49.7
30.0
3?. 4
^^.^
34.9
21.8
39.2
5B.7
46.2
7.8
26.7
43.1
59.5
44.3
27.4
48.4
51.5
50.9
22.9
0.0
?•).«
4A.?
34. 7
2. '.
-------
TABLE 1-2
VALUES OF THE AVERAGES OF THE BASIS FUNCTIONS OVER EACH MODE
MODE
1
3
4
5
6
7
8
9
' io
11
12
13
14
15
It
17
16
19
<£0
21
22"
23
24
25
26
27
26
29
30
31
3^
33
34
35
36
37
1
l.'JCOG
1.0000
l.COn.
1..0"66o
1.0000
1.0000
l.OOCO
1.0000
1.0000
1.0000
1.0000
1.0000
l.OOCO
I. 0000
i.cooo
1.0000
l.OOCO
l.OOCO
1.0000
i.uGU"
1.0000
I.COOO"
I.COOO
l.OCCO
1.0000
I.COLO
1.0000
l.OOOTJ "
l.COl'C
I.COOO
I.COOO
1.0000"
1.0000
"i.croco
1.00(0
l.OOCO
l.OOOC
V
IS. 0500
16.6625
23.C727
37.6536
38.tf.CO
45.fiOuO
53.0083
52.5428
4 C. "4 033
43.4154
33.8333
36.2375
46.6609
23.1775
7.8U'5
28.8454
31.325!.
30.550C
24.7158
38.276C
33.87^0
17.7333
45. 144(.
47.2333
lt>.9VwC
36.0053
33.fl"6"ii6
17.7333
45.26o7
46.o2tlo
16.4COC
0.0
' 15.~OGOC
30.000C
45.0CUC
60.000C
a
-1.6750
1.8750
1 . 3o3e>
1.1538
-1.^5)00
1.7647
-I. t50C
1. j?14
-i.so'oo
1.7308
-2.8571
i.8750
-1.3"u43
-1.6067
-K6750
...0455
-1.6750
1 .6667
-t.3684
2.4000
-£.1429
c.OOOO
1.200C
-1 .6667
-3.0000
1.5789
-1.7143
1.6667
l.4286~
-2.1429
-2.3077
0.0
"0.0
0.0
» .'-
0.0
va
30.68 18
43.2692
-46.875'.
79.4118
-65.6250
56.25CC
-56.2500 ""
64.9038
-85.7143
56.25CO
-58.6956
-37.5CCO
-14.0620
46.0277
-5 6.25 "0
50.0000
-53.2895
72. CO 00
-64.2857"
30.0000
54.0000
-75.0000
-45. COCO
47.3684
-SY.T2~86"
25.0000
64.2857
-96.4286
~~-34.6l54
0.0
~0".TT
c.o
c . ?
0.0
v2
556.5l>oi.
144C.5222
l'.7t>.^113
2192.9562
2836. 4iaO
2783.14^1
1873.3556"
2067.4376
157<..5bC4
1789.5073
2303.4566
564.019C
89 ."a 48 7
lOlc.1611
1093.6(45
1026.4346
861.2722
1791.6623
1575.964V
411 ,6b27
2128.2651
2334. 08V5
36V.3C02
177C.0486
1 575.8225
412.2U(j»
2140.4352
2283. t472
"379. tfb&C
L . ^
"225.00CC
900.000C
2C2i.<"<< t'(
3600.00C<)
^5*
V.7567
4. 3HC
2.0600
1.4046
2.3417
3.4C94
2.0500
1.2; 14
2.8120
3.7085
1C.2C76
4.4462
L.1313
3.553?
4.6950 ""
5.2827
4.^450
2.9778
7.1937
7.2248
5.7421
4.8573
1.5128
3.4C22
11.8100
3.1421
3.6766
3.3911
2.1562
5.8200
6.8246
o.C
" ' 0.0"
C.O
C..'.:
o.c
747.7 bob
139.7132
715.6334
1644.0825
-17bO.V4t3
3705.3125
-3468.4369
2973.0977
-2362.0152
2725.21C6
-3425.2217
2248.9990
-2736. 8 1C!
-«74.3C14
"-139.5406
137l;.3948
-1827.1115
1024.5391
-1596.6755
2877. 94Y5
-2570.0153
59fc.9142
2519.8353
-3499. 3ol3
-895.7151
1394. 14i7
-2056.41«1
499.3674
2999. 718C
-4498.5436
-690.4485
O.t
;j.c~
o.c
o.c
c.c
va
61 .991.0
29.2C04
46.5847
52. 537C
75.486b
152.6414
1C6.50KI
62.9974
100.7445
122.4465
<;82.9l09
10 7. 7 '"'.. 7
9 3 . 5 s ', 7
7B.0627
32.836"
V6.7243
131.236C
88.682 1
14V.697C
176.^425
159.2388
6^.4714
67.7954
149.23C4
164.2715
75.7415
101.8697
45.6602
96.6297
255.5805
94.9561
I .•?
0.0
C.C
I .'"
c . •'.
16 v. . i;^
It 75.^oVo
19t.6.c)04b
281b.37:;t
7Co4. 65^-6
•JE61.0C5L-
3322.111V
3951. 2C9^
46C6. J66 j
10063. 61. "76
367C.17ol
4210. 4S1:.-
1761 .S/9HV
29C .9^;j5
2467.4704
4035.1918
2826. io61.
399^.4460
6001.10615
566H.654V
1140. 746L
3133.727 /
673l..cM82
2912.CI-.C V
2585.3045
3624.6628
80i.V473
4465.1001
11536.7246
1686.8623
(.• .L-
0.0
t -u
c.c
C •".
-------
II-l
APPENDIX II
SPEED vs. TIME CURVES FOR THE SURVEILLANCE
DRIVING SEQUENCE AND FIRST
505 SECONDS OF THE FEDERAL TEST
PROCEDURE DRIVING SEQUENCE
-------
II-2
-------
II-3
TABLE II-l
SURVEILLANCE ACCELERATION-DECELERATION DRIVING SEQUENCE
Time Speed
Csec) (mph)
1.
2.
3.
1*.
5.
6.
7.
8.
9.
10.
11.
12.
13.
11*.
15'.
16.
IT.
18.
19.
20.
21.
22.
23.
21*.
25.
26.
27.
28.
29-
30.
31.
32.
33.
3U.
35-
36.
37.
38.
39-
1*0.
1*1.
1*2.
1*3-
1*1*.
1*5.
1*6.
1*7.
0.0
0.0
0.0
• o.o
0.0
0.0
0.0
o.o
' 0.0
0.0
1.8
5.1
9-1
.13.2
17.1
V20.6
23.U
25.7
27.3
28.6
29.6
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
29-6
28.9
28.1
26.9
25.it
23.5
21.2
18.5
0.5.6
12.5
Time
(sec)
1*8.
1*9.
50.
51.
52.
53-
51*.
55.
56.
57.
58.
59-
60.
61
\J± •
62.
63.
61*.
65.
66.
67.
68.
69-
70.
71-
72.
73.
7U.
75.
76.
77-
78.
79-
80.
81.
82.
83.
81*.
85.
86.
87-
88.
89.
*"/ S •
90.
x v m
91.
.x-*- •
92.
S *~ "
93.
S —f *
91*.
Speed
(mph)
9-U
6.1*
3.7
1.6
0.3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1.7
i*.6
7.6
10.3
12.3
13.7
1U.6
15.0
15-0
15.0
15-0
15.0
15.0
15-0
15-0
15.0
15.0
15-0
15.0
15.0
15.0
15.0
15.0
15-9
17.3
18.9
20.6
22.1*
2l*.2
25-9
27.5
Time
(sec)
95-
96.
97.
98.
99.
100.
101.
102.
103.
101*.
105-
106.
107.
108.
109-
110.
111.
112.
113.
111*.
115.
116.
117-
118.
119.
120.
121.
122.
123.
121*.
125.
126.
127-
128.
129-
130.
131.
123.
133.
13U.
135-
136.
137.
138.
139-
ll*0.
lUl.
Speed
(mph)
28.8
29.8
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30*7
31.7
32.9
3l*. 2
35.6
37.0
38.5
39-9
1*1.2
1*2.1*
1*3.5
1*1*. 1+
1*5.0
1*5.0
1*5.0
1*5.0
1*5.0
1*5.0
1*5-0
1*5.0
1*5.0
1*5.0
1*5.0
1*5.0
1*5.0
1*5-0
1*5.0
1*5.0
1*1*. 7
Time
(sec )
ll*2.
ll*3.
ll*l*.
11*5.
ll*6.
ll*7.
ll*8.
ll*9.
150.
151.
152.
153.
151*.
155.
156.
157.
158.
159.
160.
l6l.
162.
163.
161*.
165.
166.
167.
168.
169.
170.
171.
172.
173.
171*.
175.
176.
177-
178.
179-
180.
181.
182.
183.
181*.
185.
186.
187.
188.
Speed
(mph)
1*1*. 1
1*3.1*
1*2.2
1*0.7
38.9
36.8
31*. 6
32.6
31.0
30.1
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
31.0
32.5
31*. 3
36.2
38.3
1*0.5
1*2.7
1*5.0
1*7.3
1*9.5
51.6
53.6
55-5
57.2
58.6
59.8
60.0
60.0
60.0
60.0
60.0
Time
(sec)
189.
190.
191-
192.
193.
191*.
195.
196.
197.
198.
199.
200.
201.
202.
203.
201*.
205-
206.
207-
208.
208.
210.
211.
212.
213.
2ll*.
215-
216.
217.
218.
219-
220.
221.
222.
223.
221*.
225-
226.
227.
228.
229.
230.
231.
232.
233.
231*.
235-
Speed
(mph)
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
59-7
59.1
58.3
57.2
55-7
53.8
51.7
1*9.6
U7.5
1*5.9
1*5.1
1*5.0
1*5.0
1*5.0
1*5.0
1*5.0
1*5.0
1*5.0
1*5.0
1*5-0
1*5-0
1*5.0
1*5.0
1*5.0
1*5.0
1*5.0
1*5.0
1*5.6
1*6.5
1*7.6
1*8.7
50.0
51-3
52.6
53.9
55.2
Time
(sec)
236.
237.
238.
239.
2l*0.
2l*l.
21*2.
2l*3.
21*1*.
2l*5.
21*6.
2l*7.
2U8.
2l*9.
250.
251-
252.
253.
25l*.
255.
256.
257,
258.
259.
260.
261.
262.
263.
_. /*\
26U.
265.
266.
267.
268.
269.
260.
271.
272.
273.
27!*.
275,
276.
277-
278.
279-
280.
281.
282.
Speed
(mph)
56.1+
57.5
58.5
59-3
60.0
60.0
60.0
60-0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
59.7
59.3
58.8
58.3
57.6
56.9
56.0
5!+. 9
53.8
52.1*
50.9
1*9.2
1*7.1*
1*5.5
1*3.1*
1*1.1
38.8
36.1*
31*. o
31.5
29.0
26.6
2l*,3
22.1
20.2
18.1*
-------
II-4
TABLE II-l (cont'd)
SURVEILLANCE ACCELERATION-DECELERATION DRIVING SEQUENCE
Time
(sec)
283.
281*.
285.
286.
287.
288.
289-
290.
291.
292. .
293,
29!*..
295-
296.
297.
298. •:.
299,
300.
301.
302. •
303.
301*.
305.
306."
307.-
308.
309.
310.
311.
312.
313.
311*.
315.
316.
317.
318.
319.
320.
321.
322.
323.
32U.
325-
326.
327.
328.
329.
330.
Speed
(mph)
17-0
15.9
15.2
15-0
15-0
15-0
15-0
15-0
15-0
15.0
..1-5.0
15.0
15.0
. 15.0
'15.0
15.0
15.0
15.0
15.0
16.7
20.0
.1
.1
.9
23
26
28,
31.6
3U.2
36.6
38.9
1*1.1
1*3.1
"1*5.0
1*6.8
1*8.5
50.1
51.5
52.8
5l+. 0
55.1
56
56.9
57
58
58
59
60.0
60.0
60.0
60.0
Time
(sec )
331.
332.
333.
33l*.
335-
336.
337.
338.
339-
3l*0.
31*1.
3l*2.
31*3.
31*1*.
31*5.
31*6.
3l*7.
31*8.
31*9.
350.
351.
352.
353.
351+.
355-
356.
357.
358.
359.
360.
36l.
362.
363.
361*.
365.
366.
367.
368.
369.
370.
371.
372.
373.
371+.
375.
376.
377.
378.
Speed
(mph)
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
59.1+
58.5
57.1+
56.1
51+.1+
52.1*
1+9.9
1*6.9
1*3.6
39.8
35-7
31.2
26.6
21.9
17.3
12.8
8.7
5-1
2.3
0.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1-5
5.2
8.6
12.0
15.3
Time
(sec)
379.
380.
381.
382.
383.
381*.
385.
386.
387.
388.
389.
390.
391.
392.
393.
39!+.
395-
396.
397.
398.
399.
1*00.
1*01.
1*02.
1*03.
1*01*.
1*05.
1*06.
1*07-
1*08.
1*09.
1*10.
1*11.
1*12.
1+13.
Ull*.
1+15.
1*16.
1*17.
1*18.
1*19.
1*20.
1*21.
1*22.
1*23.
1*21*.
1*25.
1*26.
Speed
(mph)
18.1*
21.1*
2l*.2
27.0
29.6
32.1
31*. 5
36.8
39-0
1*1.0
1*3.0
1*1*. 8
1*6.5
1*8.1
1*9.6
51.0
52.3
53.5
5l+. 5
55.5
56.1+
57.2
57-9
58.5
58.9
59-3
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
59-7
59.3
58.9
58.3
57-6
56.7
Time
(sec )
1*27.
1*28.
1*29.
1*30.
1*31.
1*32.
1*33.
l*3l*.
1+35-
1*36.
1*37.
1*38.
1+39-
1*1*0.
1*1*1.
1*1*2.
1*1*3.
1*1*1*.
1*1*5.
1*1*6.
1*1*7.
1*1*8.
1*1*9.
1*50.
1*51.
1*52.
1+53.
l*5l+.
1+55.
1*56.
1+57.
1*58.
1*59.
1*60.
1*61.
1*62.
1*63.
1*61*.
1*65.
1*66.
1*67.
1*68.
1*69.
1*70.
1*71.
1*72.
1*73.
1*7U.
Speed
(mph)
55-7
5l+. 5
53.1
51-5
1*9.6
1*7.8
1*5-8
1*3.7
1*1.6
39.^
37.3
35.1+
33.6
32.1
30.9
30.2
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
29.5
28.7
27.3
25-3
22.7
19-9
17.3
15.1+
15.0
15.0
15.0
15.0
15.0
15.0
15-0
15.0
Time
,(sec)
1+75-
1*76.
1*77.
1*78.
1+79.
1*80.
1*81.
1*82.
1*83.
1*81*.
1*85.
1*86.
1*87.
1*88.
1*89-
1*90.
1*91.
1*92.
1*93.
l*9l+.
1+95.
1*96.
1+97-
1*98.
1*90.
500.
501.
502.
503.
501*.
505.
506.
507.
508.
509-
510.
511.
512.
513.
511+ .
515.
516.
517.
518.
519.
520.
521.
522.
Speed
(mph)
15.0
15-0
15.0
15.0
15.0
15.0
15-0
15-0
ll*.l*
13.3
11.3
8.5
5-2
2.1
0.2
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
2.1*
6.3
10.0
13.5
16.8
19-9
22.8
25-5
28.0
30.3
32.1*
31*. 1*
36.2
37.8
39.2
1*0.5
1*1.6
1*2.6
1*3.1*
1*1*. 0
1*1*. 5
1*5.0
Time
(sec)
523.
52l*.
525.
526.
527-
528.
529.
530.
531.
532.
533.
531*.
535.
536.
537.
i— **. f\
538.
539.
5l+0.
51+1.
_ \ _
5l*2.
_ \ _
5U3.
_ \ \
51+1*.
_ \
51+5.
t- \ X"
51+6.
_ \ __
5i+7.
r- \ O
51+8.
_ i _
51+9.
550.
551.
552.
553.
i- r-l
554.
555.
_. __ x*
556.
•557.
r- 1- Q
558.
559.
r- X" .".
560,
56l.
562.
563.
561*.
565.
566.
567.
568.
569.
570.
Speed
(mph)
1*5.0
1*5.0
1*5-0
1*5.0
1*5.0
1*5.0
1*5.0
1*5.0
1*5.0
1*5.0
1*5.0
1*5.0
1*5.0
1*5-0
1*5-0
11 __
1*1*. 5
1+3.9
1*3.0
1*1.8
i _ ._
1*0.2
n f\ x«i
38.2
_ _ o
35.8
33,1
30.1
_ /* -.
26.9
23.7
20.7
_ rt -i
18.1
j»
16.1
15-1
15.0
15-0
15.0
15-0
15-0
15-0
15.0
15-0
15-0
15.0
15-0
15.0
15-0
15.0
15.0
15.0
15-9
17.3
-------
II-5
TABLE II-l (cont'd)
SURVEILLANCE ACCELERATION-DECELERATION DRIVING SEQUENCE
Time
(sec)
571-
572.
573.
S7l+
>M ^ •
575.
576.
577-
578.
579.
580.
581.
582.
583.
581+ .
585.
586.
587.
588.
589.
590.
591.
592.
593.
591*.
595-
596.
597.
598.
599-
600.
601.
602.
603.
601+.
605.
606.
607.
608.
609-
.610.
611.
612.
.613.
6lU.
615.
616.
617.
6l8.
6l
26.6
28.7
30.8
32.9
31*. 9
36.9
38.8
1+0.5
1+2.0
1+3.1*
1+1+.5
1+5.0
1+5.0
1+5.0
1+5.0
1+5.0
1+5.0
1+5.0
1+5.0
1+5.0
1+5.0
1+5.0
1+5.0
1+5.0
1+5.0
1+5.0
1+5.0
1+1+.5
1+3.7
1+2.7
1+1.1+
39.8
37.8
35.3
32.5
29-2
25.6
21.8
17.8
13.8
9.9
6.1+
3-5
1.3
0.1
0.0
Time
(sec)
621.
622.
623.
gpl+
W^" •
625.
626.
627.
628.
629.
630.
631.
632.
633.
631*.
635.
636.
637-
638.
639.
6i+o.
61+1.
61+2.
61+3.
61+1*.
61+5.
61+6.
61+7.
61+8.
61+9.
650.
651.
652.
653.
65!*.
655.
656.
657.
658.
659.
660.
661.
662.
663.
661*.
665.
666.
667.
668.
669.
670.
Speed
(mph)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
2.6
7-1
11.5
15.7
19-6
23.1+
26.9
30.3
33A
36.1+
39.2
1+1.8
1+1+.2
1+6.1+
1+8.5
50.3
52.0
53.5
51*. 9
56.1
57.1
58.0
58.7
59-3
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
Time
(sec )
671.
672.
673.
671*.
675.
676.
677.
678.
679-
680.
681.
682.
683.
681+ .
685.
686.
687.
688.
689.
690.
691.
692.
693.
69^..
695.
696.
697.
698.
699-
700.
701.
702.
703.
701*.
705.
706.
707.
708.
709-
710.
711.
712.
713.
711*.
715.
716.
717-
718.
719-
720.
Speed
(mph)
59-6
59.0
58.3
57.H
56.5
55.3
5U.O
52.1+
50.6
1+8.5
1+6.2
1+3.6
1+0.8
37.8
3l+. 6
31.3
27-9
21+.3
20.8
17-3
ll+.O
10.7
7-8
5.2
3.0
1.3
0.3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1.2
3.5
6.1+
9.6
12.8
15.9
18.8
21.3
23.5
25.2
26.7
27.8
Time
(sec )
721.
722.
723-
72l+.
725-
726.
727.
728.
729-
730.
731.
732.
733.
731*.
735.
736.
737.
738.
739.
71*0.
7l+l.
7U2.
71*3.
7l*l*.
71*5.
71*6.
7**7.
7U8.
1^9*
750.
751.
752.
753.
751*.
755-
756.
757-
758.
759.
760.
76l.
762.
763.
76U.
765.
766.
767.
768.
769.
770.
Speed
(mph)
28.7
29.6
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.5
31.1*
32.1*
33.6
31*. 8
36.0
37. **
38.7
1*0.2
1+1.6
1*3.1
1+1+.6
1+6.0
1*7-5
1+8.9
50.1+
51.7
53.0
51*. 3
55.5
56.6
57.6
58.5
59-3
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
Time
(sec)
771.
772.
773.
771*.
775.
776.
777.
778.
779.
780.
781.
782.
783.
781*.
785.
786.
787.
788.
789-
790.
791-
792.
793-
791*.
795.
796.
797-
798.
799.
800.
801.
802.
803.
801*.
805.
806.
807.
808.
809.
810.
811.
812.
813.
8ll+.
815.
816.
817.
818.
819.
820.
Speed
(mph)
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
59-6
59-1
58.1+
57.6
56.5
55-1
53.1*
51-5
1+9.3
1+6.8
1+1+.3
1+1.6
38.9
36.3
31*. o
32.1
30.7
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
29-1
27.7
25-1*
22.0
17-6
12.5
7.1*
Time
(sec)
821.
822.
823-
821*.
825-
826.
827.
828.
829.
830.
831.
832.
833.
831*.
835.
836.
837.
838.
839-
8UO.
81*1.
81+2.
81+3.
81+1+ .
81+5.
8U6.
81+7-
81+8.
8U9.
850.
851.
852.
853.
85H.
855.
856.
857.
858.
859.
860.
861.
862.
863.
86U,
865-
866.
867.
868.
869.
870.
Speed
(mph)
2.9
0.3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.9
i*.o
6.9
9.8
12.6
15.3
17.9
20.U
22.8
25.2
27- **
29-6
31.7
33.7
35.7
37.5
39-3
1*1.0
1+2.6
1+1+.2
1*5.6
1+7.0
1+8.1+
1+9.6
50.8
51-9
52.9
53.8
5^.7
55-5
56.3
56.9
57.5
58.1
58.5
58.9
59.3
-------
II-6
TABLE II-l (cont'd)
SURVEILLANCE ACCELERATION-DECELERATION DRIVING SEQUENCE
Time
(sec)
871.
872.
873.
87U.
875-
876.
877.
878.
879.
880.
881.
882.
883.
88U. '
885.
886.
887.
888.
889.
890.
891.
892.
893.
89U.
895.
896.
897.
898.
899-
900.
901.
902.
903.
901*.
905.
906.
907-
908.
909.
910.
911-
912.
913.
9lU.
915-
916.
Speed
(mph)
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
.60.0
60.0
: 60.0
60.0
.. 60.0
- 60.0
60.0
.. 60.0
59.
59.
58,
. 58.
57.
56.
- 55.8
5U.8
53.7
50.9
U9.3
U7.6
U5.7
U3.6
Ul.U
39-0
36.6
3U.O
31.3
28.6
25.8
22.9
20.1
17-3
1U.6
12.0
9-5
7-2
5-2
.7
.2
.7
.1
.U
.7
Time
(sec)
917-
918.
919-
920.
921.
922.
923.
92U.
925-
926.
927.
928.
929-
930.
931.
932.
933.
93U.
935.
936.
937.
938.
939-
9UO.
9Ul.
9U2.
9U3.
9UU.
9U5.
9U6.
9Vf.
9U8.
9^9.
950.
951.
952.
953.
951*.
955.
956.
957.
958.
959.
960.
96l.
962.
Speed
(mph)
3.U
1.9
0.8
0.2
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.8
2.7
U.9
7-5
10.1
12.8
15. U
17-8
20.1
22.1
23.8
25.2
26.5
27. u
28.3
29.0
29.8
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
Time
(sec)
963.
96U.
965.
966.
967.
968.
969.
970.
971.
972.
973.
97U.
975.
976 .
977-
978.
979-
980.
98l.
982.
983.
98U.
985-
986.
987.
988.
989.
990.
991.
992.
993.
99U.
995-
996.
997.
998.
999.
1000.
1001.
1002.
1003-
100U.
1005-
1006.
1007.
1008.
Speed
(mph)
30.0
30.0
30.7
31.8
33.1
3^.5
36.0
37.6
39-3
Ul.O
U2.8
UU.6
U6.3
U8.1
U9.8
51.5
53.0
5U.6
56.0
57.2
58. U
59.3
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
59.5
58.7
57-6
56.1
5U.O
51.5
U8.5
U5.1
Time
(sec)
1009.
1010.
1011.
1012.
1013.
101U.
1015.
1016.
1017.
1018.
1019-
1020.
1021
1022.
1023.
102U.
1025-
1026.
1027.
1028.
1029.
1030.
1031.
1032.
1033.
103U.
1035-
1036.
1037-
1038.
1039.
10UO.
lOUl.
10U2.
10U3.
10UU.
10U5.
10U6.
10U?.
10U8.
10U9.
1050.
1051.
1052.
1053.
105U.
Speed
(mph)
Ul.6
38.0
3U.7
32.1
30. U
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
29. u
28.5
27.2
25. u
22.9
19-9
16. U
12.5
. 8.6
5-0
2.1
0.3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-------
II-7
TABLE II-2
FIRST 535 SECONDS OF FEDERAL TEST PROCEDURE DRIVING SEQUENCE
Time
(sec)
0
1
2
3
i+ •
5
6
7
8
9
10
11
12
13
Ik
15
16
IT
18
19
20
21
22
23.
21+
25
26
27
28 •
29
30 .
31
32
33
31+
35
36
3T
38
39
1+0
1+1
1+2
1+3
Speed
(mph)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3.0
5.9
8.6
11.5
1U.3
16.9
17-3
18.1
20.7
21.7
22. 1+
22.5
22.1
21.5
20.9
20.1+
19.8
17-0
1U.9
11+.9
15-2
15.5
16.0
Time
(sec)
1+1+
U5
1+6
^7
1+8
1*9
50
51
52
53
51*
55
56
57
58
59
60
6l
62
63
61+
65
66
67
68
69
70
71
72
73
71+
75
76
77
78
79
80
8l
82
83
81*
85
86
87
Speed
(mph)
17.1
19.1
21.1
22.7
22.9
22.7
22.6
21.3
19.0
17-1
15.8
15.8
17-7
19.8
21.6
23.2
21+.2
21+.6
2U.9
25.0
2U.6
21+.5
2U.7
21+.8
2U.7
21*. 6
2U.6
25.1
25.6
25.7
25.1*
2U.9
25.0
25. U
26.0
26.0
25.7
26.1
26.7
27.5
28.6
29.3
29.8
30.1
Time
(sec)
88
89
90
91
92
93
9U
95
96
97
98
99
100
101
102
103
101*
105
106
107
108
109
110
111
112
113
111*
115
116
117
118
119
120
121
122
123
121*
125
126
127
128
129
130
131
Speed
(mph)
30.1*
30.7
30.7
30.5
30.1*
30.3
30.1*
30.8
30.1*
29.9
29-5
29.8
30.3
30.7
30.9
31.0
30.9
30.1+
29.8
29.9
30.2
30.7
31.2
31.8
32.2
32.1*
32.2
31.7
28.6
25.3
22.0
18.7
15.U
12.1
8.8
5.5
2.2
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Time
(sec)
132
133
131*
135
136
137
138
139
lUo
11*1
ll*2
ll*3
ll*l*
11*5
ll*6
ll+J
1U8
ll*9
150
151
152
153
151*
155
156
157
158
159
160
161
162
163
161*
165
166
167
168
169
170
171
172
173
171*
175
Speed
(mph)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3.3
6.6
9.9
13.2
16.5
19.8
22.2
21+.3
25-8
26.1*
25.7
25-1
Time
(sec)
176
177
178
179
180
181
182
183
181*
185
186
187
188
189
190
191
192
193
19k
195
196
197
198
199
200
201
202
203
201*
205
206
207
208
209
210
211
212
213
2ll*
215
216
217
218
219
Speed
(mph)
2U.7
25.0
25.2
25.1*
25.8
27.2
26.5
21+.0
22.7
19.1+
17.7
17.2
18.1
18.6
20.0
22.2
2U.5
27.3
30.5
33.5
36.2
37.3
39-3
1*0.5
1*2.1
1*3.5
1*5.1
1*6.0
1*6.8
1*7.5
1*7-5
1+7.3
1*7.2
1*7.0
1*7.0
1*7-0
1*7.0
1*7.0
1+7.2
1*7.1+
1+7.9
1+8.5
1+9.1
1*9.5
-------
II-8
TABLE II-2 (cont'd)
FIRST 505 SECONDS OF FEDERAL TEST PROCEDURE DRIVING SEQUENCE
Time
(sec)
220
221
222
223
22U
225
226
227
228
229
230
231
232
233
23*4
235
236
237
238
239
2l+0
2Ul
2U2
2U3
2UU
2*45
2h6
21*7
21*8
2h9
250
251
252
253
25!*
255
256
257
258
259
260
261
262
263
26k
265
266
Speed
(mph)
50.0
50.6
51.0
51-5
52.2
53.2
5U.1
5^.6
5U.9
55-0
5*4.9
51*. 6
5U.6
5U.8
55-1
55.5
55-7
56.1
56.3
56.6
56.7
56.7
56.5
56.5
56.5
56.5
56.5
56.5
56. U
56.1
55.8
55.1
51*. 6
5U.2
51*. o
53.7
53.6
53-9
5U.O
5)4.1
5H.1
53.8
53. 1*
53.0
52.6
52.1
52. U
Time
(sec)
267
268
269
270
271
272
273
2714
275
276
277
278
279
280
281
282
283
28U
285
286
287
288
289
290
291
292
293
29U
295
296
297
298
299
300
301
302
303
30k
305
306
307
308
309
310
311
312
313
Speed
(mph)
52.0
51.9
51.7
51.5
51.6
51.8
52.1
52.5
53.0
53.5
5U. 0
5*4.9
55A
55-6
56.0
56.0
55.8
55-2
5*4.5
53.6
52.5
51-5
51-5
51.5
51.1
50.1
50.0
50.1
50.0
1*9.6
U9-5
U9.5
149.5
U9.1
1*8.6
1*8.1
U7.2
146.1
1*5.0
U3.8
U2.6
141.5
140.3
38.5
37-0
35.2
33.8
Time
(sec)
3114
315
316
317
318
319
320
321
322
323
32U
325
326
327
328
329
330
331
332
333
33U
335
336
337
338
339
SUO
3Ul
3U2
3l43
3l4U
3U5
3146
3*47
3U8
3l49
350
351
352
353
35U
355
356
357
358
359
360
Speed
(mph)
32.5
31.5
30.6
30.5
30.0
29.0
27-5
2U.8
21.5
20.1
19-1
18.5
17.0
15.5
12.5
10.8
8.0
14.7
1.1*
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
l.o
U.3
7.6
10.9
lU.2
17-3
20.0
22.5
23.7
25.2
26.6
28.1
30.0
30.8
Time
(sec )
361
362
363
36U
365
366
367
368
369
370
371
372
373
37*4
375
376
377
378
379
380
381
382
383
38U
385
386
387
388
389
390
391
392
393
39U
395
396
397
398
399
1400
1401
U02
U03
14014
1405
1*06
1407
Speed
(mph)
31.6
32.1
32.8
33.6
3U.5
314.6
3l4.9
314.8
3U.5
314.7
35.5
36.0
36.0
36.0
36.0
36.0
36.0
36.1
36.14
36.5
36.U
36.0
35.1
SU.l
33.5
31.14
29.0
25.7
23.0
20.3
17.5
1U.5
12.0
8.7
5.H
2.1
0.0
0.0
0.0
0.0
0.0
0.0
2.6
5-9
9-2
12.5
15-8
Time
(sec)
1*08
14C9
UlO
1411
1*12
U13
l*ll*
U15
Ul6
Ul7
1*18
Ul9
1420
1421
U22
1423
U2U
1425
1*26
1*27
1*28
U29
U30
1431
U32
U33
U3U
U35
U36
1437
1*38
1439
UUO
UUl
UU2
UU3
UUU
14145
kh6
UU7
14W
U149
1*50
U5l
1*52
1453
1*514
Speed
(mph)
19-1
22. U
25.0
25.6
27-5
29-0
30.0
30.1
30.0
29.7
29-3
28.8
28.0
25.0
21.7
18. U
15.1
11.8
8.5
5.2
1.9
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
3.3
6.6
9-9
13.2
16.5
19-8
23.1
-------
Time
(sec)
U55
1*56
1*57
1*58
1*59
1*60
l*6l
1*62
1*63
1*61*
1*65
1*66
1*67
1*68
U69
UTO
1*71
1*72
1*73
1*71*
U75
1*76
1*77
1*78
1*79
1*80
U8l
1*82
1*83
1*8U
1*85
1*86
1*87
1*88
1*89
1*90
1*91
1*92
1*93
1*9U
1*95
1*96
1*97
Speed
(mph)
26.1*
27.8
29-1
31.5
33.0
33.6
3l*. 8
35.1
35.6
36.1
36.6
36.1
36.2
36.0
35.7
36.6
36.0
35.0
35.5
35-1*
35.2
35.2
35.2
35.2
35-2
35.2
35-0
35-1
35.2
35.5
35.2
35-0
35-0
35-0
31*. 8
3U. 6
3U.5
33.5
32.0
30.1
28.0
25.5
22.5
II-9
TABLE II-2 (cont'd)
FIRST 505 SECONDS OF FEDERAL TEST PROCEDURE DRIVING SEQUENCE
Time Speed
(sec) (mph)
1*98 19.8
1*99 16.5
500 13.2
501 10.3
502 7.2
503 U.O
501* 1.0
-------
11-10
-------
III-l
APPENDIX III
THE MATHEMATICAL MODEL
-------
III-2
-------
III-3
APPENDIX III
THE MATHEMATICAL MODEL
The mathematical model presents a method to calculate the amount of
a particular pollutant given off by a vehicle or vehicle group over any specified
driving sequence given the modal emissions data on the individual vehicles.
Notation
e(t) = amount of a pollutant given off "by a vehicle from time = 0
to time = t.
e(t) = —77—^— = instantaneous emission rate function.
dt
e.(t) = accel/decel instantaneous emission rate function.
e (t) = steady state instantaneous emission rate function.
s
E. = amount of a pollutant given off by a vehicle in the J'th mode.
J
T. = duration of jth mode, (in seconds)
J
v.(t) = speed at time = t in the j'th mode.
J
v(t) = speed at time = t for any driving sequence.
dv (t)
a.(t) = —~r— = acceleration at time = t in the j'th mode.
J dt
a(t) = —~~~ = acceleration at time = t in any driving sequence.
T1
1 f J
Ce(via)>T = ^ J e (t)dt =
J On
average value of the emission rate function for the
J'th mode.
-------
III-4
[A] Functional Form of the Steady State and Accel/Decel Emission Rate Functions
Based on Figures 1, 2, and 3 where average steady state
emission rates over the 1020 vehicles in the data base are plotted versus
speed, the asumption is made that the steady state emission rate function
e can be represented as a quadratic function of speed
S
(III-1) e (v) = S + S v + S v2
S J_ ^ .3
where S , S , and S are constants.
The functional form of an emission rate function that will be applicable
during periods of acceleration/deceleration is obtained by assuming the
constant coefficients (S. ) become functions of the acceleration and that
this functional dependence can be sufficiently represented by quadratic
functions of acceleration. Therefore
Sl = Si^a^ = qii + 412 a + q!3 a '
(III-2) S2 = S2^ = ^21 + ^22 a + 423 ^ »
p
S = S (a) = q + q a + q a ,
where the q's are constants
and
(III-3) e (v,a) = S (a) + S_(a) v + S_(a) v2 ,
** JL f- .3
(III-U) eA (v,a) = (qu + q12 a + ^ a2) + (q^ + q^ a + ^ a2) ' v
+ (q31 + q32 a + q^ a2) ' v2 .
Upon multiplying and redefining the constant coefficients the expression for
the accel/decel emission rate function
(III-5) eA (v,a) = b.,^ + b2 v + b3 a + b^ va = b5 v2 + bg a2
+ * v2 a + b a2v + ^
-------
III-5
[B] The Instantaneous Emission Rate Function
Although the accel/decel emission rate function is functionally
identical to the steady-state rate function when the acceleration is zero,
both functions will be retained to allow independent adjustment of the
coefficients (b. and S.) specifying the accel/decel and steady state emission
rate functions.
The two functions can be joined by an acceleration dependent
weighting function h(a) to form the instantaneous emission rate function
e(v a) = h(a) es(v) + (l - h(a)) eA(v a) ,
where h(a) = - —
a
a >a> 0
- 7T a + 1,
a a.
a < a,.
-------
III-6
By specifying the constants a and a the weightings of the two rate
functions will vary between 0 and 1 in a continuous manner when the transition
is made between accel/decel and steady state periods of driving. If the
accel/decel and steady state emission rate functions are thought of as a response
surface S in (v,a)-space then h(a)e + (l - h(a))efl: h(a) £ 0 can "be visualized
S A
as a ramp function that joins the two responses e , efl.
S *i
Ex:
h(a)e + (l-h(a))e
In practice a and a^ have been arbitrarily set to -1.2 mph/sec and 1.0 mph/sec
respectively.
[C] Specification of The Ifrnission Rate Function
Given the functional form of the emission rate function, the coefficients
(b., S.) must be determined in order to specify the emission rate function which
characterizes a vehicle's emission response.
-------
III-7
Determination of the Accel/Decel Emission Rate Function
Coefficients (To±)
The only modal emission observations available are the total amount
of each pollutant given off in each mode of the SDS; there are no measures
of the instantaneous emission rate given for accel/decel modes. Therefore,
the following procedure is used to determine the coefficients (b. ) that
specify the instantaneous emission rate function for a given vehicle
pollutant
Let: ' ^ = 1.0, fg = v, f = a
fu = av, f5 = v2, f6 = a2
2 2 22
f = v a, fg = a v, f g = v a
where the f . , i =1, 9 => basis functions of the accel/decel emission
rate function.
Then equation (III-5) gives
9
(III-6) eA (v,a) =
For an accel/decel mode the weighting function h(a) — 0, then
* (v»a) = e (v»a) •
Now consider the average emission rate over the k'th mode,
r"
- i- 4 (v,
v J
,a) dt .
k
0
-------
III-8
By equation (III-T)
i
= = £~ [ ^ (v,a) dt
lr lr V J
However, the average emission rate over the k'th mode is also equal to the
total emission amount (EL.) divided by the time in mode T, both observable
quantities. Therefore
(111-10) T
and
T. T.
E. k k
(111-11) T* = i- | e (v,a) dt = f- MI b..f,. | dt
k 0
Since the b. are constants
(111-12) l^/Tk = I b. ( i- j f. dt]
1 K -
K
J'i
Now, 1/TV I f.. dt is Just the average value of the i'th basis function
0
over the k'th mode, which can be easily evaluated knowing the speed as
function of time for the k'th mode* v (t), and acceleration as a function
k
of time, a (t).
Tk
Let' fik = fr fidt
-------
III-9
(see Appendix I for values of f., )
Thus,
(111-13) \ __ ^ _
Tk i=l 1 lk
and since E, /T is known for all modes and the f., can be evaluated then
k k ik
the b. can be determined using standard least squares regression techniques,
The result of the least squares regression method can best be given
by defining the following matrices and elements
K
Y, Y(k) = -f- (where) k = 1, 32;
k
(32 accel/decel modes)
X, X(i,k) = ? where i = 1,9 and k = 1, 32;
1J£
B, B(i) = b. where i = 1, 9-
Using the convention
Y1 = Transpose of Y
Y"1 = Inverse of Y
equation (111-13) gives
(111-lU) Y = BX .
The method of least squares then gives
(III -15) B = (X' X)"1 X' Y .
Let A = (X1 X)~ X' . (AA basis function factor array)
-------
111-10
Then, B = AAY
and the i'th coefficient is given by (b. )
32
(111-16) b. = I A (i,k) Y(k) , i = 1, 9
In summary, the average emission rate, which can be evaluated by using
experimental observables, is used to determine the coefficients that
specify the instantaneous accel/decel emission rate function.
[2] Determination of the Steady State Emission Rate Function Coefficients (S.)
In the case of steady state emissions the average emission rate is equal
to the instantaneous emission rate because the speed is constant in time.
Let: flk=1'°> f2k=V f3k=Vk2
Then, by equation (III-l),
3
(III-1T) es (vk) = l^ S. f.k .
Consider the k'th steady state mode, h(a) —1.0.
T,
(111-18)
f
= - ^ - i- Js f
V V V Ir • V
•vl dt
., j i A, IK]
o
Since both S. and f., are now constants»
(111-19) „,
\ f
^- I SifikJ
dt/Tk= Sifik
-------
III-ll
The coefficients can now be determined using standard least squares regression
techniques.
Consider the situation in which the S. have been determined by the
above procedure and the specified emission rate function produces negative
emission rates as shown below.
Steady state
Emission rate
\
\
Negative Emission
Rates
=>observed pts
Speed (v)
Regression Curve
When this happens (each steady state emission rate function is tested for
this possibility) a new set of coefficients (S.) is calculated in a manner
that will guarantee the steady state emission rate function will be positive
for all values of speed between 0 and 60 mph. The procedure to determine
the new set of coefficients is described below.
-------
111-12
The minimum of the regression curve representing the steady state
emission rate function is forced through the point given by the average of
the two lowest emission rates and the average of their speeds. In the
example above,this point (e, v) is given by
e =(e2 + e3)/2 , v =
Requiring the minimum of the regression curve (steady state emission rate
function) to go through (e, v) specifies two of the three coefficients. Since
e is a quadratic function of speed, the coordinates of the minimum are given by
s
S1S3-
Therefore
v = -S2/2S3 ,
e =
Solving for S and S in terms of S , v and .e gives
=;+v2 .
Substituting these values into equation (Hl-i) gives
(111-20)
eg (v) = ? + v S3 + (-2vS3)v + S3 v
-------
111-13
Regrouping,
(111-21) eo (v) = e + S, (v 2 - 2vv + v2) . '
s j
The only coefficient left to determine is now S_ vhich is obtained "by
the standard least squares method.
This method will remove any negative emission rates over the 0 to 60 mph
speed interval and still retain the general trend of the observed data.
[D] Characterization of Individual Vehicle and Vehicle Group Emission Responses
Assuming input modal data are available, each vehicle's emission response
can be characterized by the 36 coefficients that specify the three emission
rate functions for HC, CO and WO (12 coefficients per function).
A vehicle group can be similarly characterized by determining the
y
coefficients for the average vehicle in the group.
Let b. , = k'th coefficient of the emission rate function for the j'th
1JK
vehicle in group sample and i'th kind of pollution,
N = number of vehicles in sample representing group,
O
b.. = k'th coefficient of the emission rate function for the
average vehicle for i'th kind of pollutant.
The coefficients describing the average vehicle's emission rate function are thus
given by
N
g
(111-22) b = -i I b
g J=l J '
[E] Determination of Individual Vehicle and Vehicle Group Emissions Over a
Specified Driving Sequence
The amount of a pollutant e(T) given off by a vehicle in undergoing a
driving sequence from time = 0 to time = T is obtained by integrating the
-------
111-14
instantaneous emission rate function describing this vehicle's response with
respect to the pollutant under consideration over the sequence
(111-23)
T T
e(T) = | e (v,a) dt = f (h(a) es (v) + (l - h(a)) eA (v^a)) dt
• ' fT 2
= I {h(a) (S± + S2v + S3v ) + (1 - h(a))
0
b2v
+ b^av + b v2 + bga + b_v2a + bga2v + b a v )} dt .
The integral is then approximated by the following summation
(III-2U)
N
e(T) = I
bUaivi + b5 Vi + b6 ai + b7 Vi ai + b8 ai vi + b9
where
NAt = T
(111-25) v± =[v^
and a, =[v(t
The total amount of a pollutant given off by a vehicle group is
obtained by integrating the average vehicle's emission rate function over
the sequence and then multiplying the average vehicle's emission response
by the number of vehicles in the group.
-------
IV-1
APPENDIX IV
COMPUTER IMPLEMENTATION OF THE GENERALIZED
MATHEMATICAL MODEL
-------
IV-2
-------
IV-3
APPENDIX IV
COMPUTER IMPLEMENTATION OF THE GENERALIZED
MATHEMATICAL MODEL
The computer version of the generalized mathematical model to calculate
emissions given off from individual vehicles and vehicle groups over any
specified driving sequence is made up of two main programs. These programs
require modal data as input.
Main Program I
A main program to compute emissions from individual vehicles over
any specified driving sequence. The modal emissions for each individual
vehicle are required as input.
Main Program II
A main program to compute emissions from a specified group of vehicles
over any specified driving sequence. The modal emissions for each vehicle
in the group are required as input.
The main programs are used to read in the speed-time values of the
driving sequences, to perform any filtering operations needed to define vehicle
groups, to write out calculated emission values, and to call in proper sequence
the following set of routines which perform the majority of calculations
Subroutine SETUP
Output: Subroutine SETUP determines the basis function factor arrays
for the accel/decel and steady state emission rate functions. These arrays
are labeled AA and AS, respectively.
Input: Speed-time values for the Surveillance Driving Sequence.
-------
IV-4 Appendix IV
Utilization: Called once in each main program.
Other Subroutines Used: Subroutine INVERS (to calculate the inverse
of a matrix).
Subroutine EDOT
Output: Subroutine EDOT calculates the 36 coefficients specifying the
three emission rate functions for an individual vehicle.
Input: [i] The amount of each pollutant given off "by an individual
vehicle in each of 37 modes.
[ii] The basis function factor arrays AA and AS determined
by subroutine SETUP.
Utilization: EDOT is called once for each individual vehicle considered
in main programs I and II.
Other Subroutines Used: Subroutine PAD.
Subroutine PAD
Output: Subroutine PAD calculates a set of three coefficients that
specify the steady state emission rate function for an individual vehicle such
that the emission rate function does not produce any negative emission rates.
Input: The amount of pollutant given off by an individual vehicle in
the five steady state modes.
Utilization: Called once from subroutine EDOT for each individual
vehicle that originally had a steady state emission rate function that produced
negative emission rates.
Other Subroutines Used: None.
Subroutine EDGRP
Output: A set of 36 coefficients that specify the emission rate functions
for the average vehicle within a group of vehicles.
-------
IV-5
Input; [i] The 36 coefficients specifying the emission rate functions
of individual vehicles determined by subroutine EDOT.
[ii] Sequence indicator INT.
Utilization: Called by Main Program II only; once for each vehicle
in tae group (INT = 1 for first vehicle in the group, INT = 2 for all the
following vehicles in the group), and once after all vehicles in the group
have been considered (INT =3).
Other Subroutines Used: None.
Subroutine ESUM
Output: The amounts of the three pollutants (HC, CO, NO ) given off
A.
by an individual vehicle or a group average vehicle over any specified driving
sequence.
Input: [i] The 36 coefficients that specify the emission rate functions
determined by subroutine EDOT (Program I) or subroutine EDGRP (Program II).
[ii] The velocity-time values for the driving sequence under
consideration.
Utilization: Called once for each vehicle in Main Program I, called
once for the group under consideration in Main Program II.
Other Subroutines Used: None.
Subroutine INTERS
Output: The inverse of any two-dimensional square matrix of dimension
less than 20.
Input: [i] The matrix whose inverse is desired.
[ii] Dimension of the matrix.
Utilization: Called once by subroutine SETUP.
Other Subroutines Used: None.
-------
IV-6
Flow charts for the main programs (see Figures IV-1 and IV-2) show
the calling order for the four main subroutines: SETUP, EDOT, EDGRP and
ESUM. In any main program the following calling sequence of the main
subroutines must be strictly observed:
SETUP
I
EDOT-
EDGRP
ESUM-
Listings of the main programs and subroutines are given in Tables IV-1
through IV-8.
-------
IV-7
TABLE IV-1
LISTING, MAIN PROGRAM I
LEVEL 21.6 { MAY 72 )
OS/360 FORTRAN H
COMPILER OPTIONS - NAME = MAIN,OPT=02 ,LINtCNT=60 ,SI ZE=OOOOK ,
SOURCE. EBCDIC. NOLI ST. NODFCK. LOAD. MAP.NOEDIT. I D.XRFF
C
C
C
C
C
r.
C
r.
c
c
c
c
c
c
c
c
******************* MAIN PROGRAM I ****************************
MAIN PROGRAM I DFTFRM1NES THF AMOUNT DF EMISSIONS GIVFN OFF BY
INDIVIDUAL VEHICLES OVER A DRIVING SEQUENCE SPECIFIED BY ARR'VVT1.
VTM(I)=>VELOCITY VS. TIMEilN ONE SECOND INTERVALS) OF THE SURVEIL-
-LANCE DRIVING SEQUENCE .VTM 1 1 ) =VE LOCI TY C MPH J AT TIME II-llSEC
(REAL*4)
WT(I)=>VELOCITY VS. TIMEIIN ONE SECOND INTERVALS) OF ANY DRIVING
SEQUENCE OVER WHICH EMISSIONS ARE TO BE CALCUL ATED.VVTi II sVELOC-
-ITY AT TIME (1-1) SEC. (REAL*4)
AMTC(I,J)=> AMOUNT OF I «TH EMMITTANT GIVEN OFF IN J»TH MODE.
DS(I)=DISTANCEIMILES)TRAVELED IN I «TH MODE .NOTE* STEADY STATE MODES
ARE 60 SEC IN DURATION.
C
ISN OO03
ISN 0004
ISN OOO5
ISN 0006
DIMENSION ITAB(20.2I.IDATi4.26) .RDATI 12 1 .26 J .OS ( 37 1
DIMENSION VTMtl055),VVT(2000l,AMTC(3t37),C(3)
RFAL*8 AAI9.^2I. AS(3.5) .BADI3.12)
DATA DS /. 0602, .0741, .0201, .0705, .1360, .1268, .2163, .1716
C.. 2043.. 3367.. 3136.. 1973.. 3313.. 2994. .0579.. 0173.. 1759.. 1392.. 1528
C..1304,. 2654,. 2634,. 0737,. 3134, .2362,. 0444,. 4009 ,.3293,. 0886,. 2599
C..1813. .O592..0OO0..2500..5O00..75OO.1.OOO/
ISN 0007
ISN 0008
ISN 0009
ISN 0010
ISN 0011
ISN 0012
ISN 0013
ISN 0015
ISN OO16
ISN OO17
ISN 0018
ISN 0019
ISN 0020
ISN O021
ISN 0023
ISN O024
ISN 0025
ISN 0026
c
c
c
c
c
c
r,
. c
c
r,
c
c
DEFINE FILE 99( 75,3256,U,N1 I
READ IN SURVEILLANCE DRIVING SEQUENCE
DO 3000 1=1,100
NX1={ (1-11*161+1
NX2=NX1+15
RFAD(5.100) (VTM(K).K=NX1.NX2)
100 FORMAT(16F5.0)
IF( VTM(NXl) .GT.99.0)GOT03111
3000 CONTINUE
3111 CONTINUE
READ IN DRIVING SEQUENCE OVER WHICH EMM I SS IONS ARE TO BE CALCULATED
IN THIS EXAMPLE VVT=> FIRST 505 SEC. OF FTP
DO 1500 1=1.100
NX1 = «I-1)*16) + 1
NX2=NX1+15
READ15,100)(VVT(K),K=NX1,NX2)
IFIVVT(NX1).GT.99.0)GOT01555
1500 CONTINUE
1555 CONTINUE
SET UP BASIS FUNCTION FACTOR ARRAYS AA.AS.
CALL SETUPfVTM.AA, AS)
WRITE(6.500)
-------
IV-8
TABLE IV-1 (cont'd)
LISTING. MAIN PROGRAM I
ISN 0027 500 FORMAT(lHl)
C READ IN INDIVIDUAL VEHICLE MODAL EMISSIONS DATA.
C PUT MODAL EMISSIONS DATA INTO ARRAY AMTC
C
C IN THIS EXAMPLE THE MODAL EMSSIONS DATA IS READ OFF A DISK FILE
C
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0023
0029
0030
0031
0032
0033
003*
0035
0036
O037
0039
004O
0041
00*2
0044
0045
0046
0047
0048
NCART=0
READ(°9«75) ITAB
00 2000 IY=57,71
IREC=IY-56
JSTART=ITAB( IRECtl)
JEND=ITAB(IREC.2)
DO 2001 J=JSTART,JEND
READ! 99' J) ( (IDAT(L.K) .L = 1.4I. IROAT(L.K) .L=l. 121 > .K=l . 261
DO 2002 K=l,26
IF( TDAT(l.K) .EO.-91GOTO2001
NCART=NCART*1
DO 1000 IR=1.37
00=1.0
IF( IR.LE.321DD=DS(IR)
DO 1001 IC=1,3
IW=I (IR-1)*3»»10+IC
AMTC( IC,IR)=RDAT( IW,K)*DD
1001 CONTINUE
1000 CONTINUE
C
C DETERMINE INDIVIDUAL VEHICLE EMISSION RATE FUNCTION COEFFICIENTS
C
ISN
0049
CALL EDOT(AMTCtAA.AStBAD)
C
C
C TNTFGRATE THIS VEHICLES EMISSION RATE FUNCTION OVER THE
C DRIVING SEQUENCE.
C
ISN
0050
C
CALL ESUM(VVT.506.BAD.Cm.C(2).C(3).DIST)
C
C
C WRITE OUT EMISSION RESULTS....
C
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0051
0052
0053
0054
0055
0056
0057
WRITE<6,501)NCART,(CVfcLOCITY VS. TIMtdN ONE SECOND INTERVALS) OF THE SURVEIL-
LANCE DRIVING SEQUENCE .VTM( 1 ) =VFLPCI TY (MPH) AT TIME II-1ISFC
(REAL*4)
WT(I)=>VFLOCTTY VS. TIME! IN ONE SECOND INTERVALS) OF ANY DRIVING
SEQUENCE OVER WHICH EMMISSIONS ARE TO BE C ALCUL ATED. VVTC I) =VELQC-
-ITY AT TIMt (1-1) SEC. (REAL*4)
AMTC(I,J)=> AMOUNT OF I »TH EMM1TTANT GIVEN OFF IN J'TH MODE.
DS( I)=DISTANCE(MILES)T<*AVELED IN I »TH MODE .NOTE , STEADY STATE MODES
ARE 60 SEC IN DURATION.
r
ISN 0002
ISN 0003
ISN 0004
ISN 0005
DIMENSION I TAB (20, 2), ID AT (4, 26) ,RDAT( 1? 1 ,26 ) ,DS ( 37 )
DIMENSION VTMU055) ,VVT(2000) , AMTC ( 3 . 37 ) .C ( 3)
REAL*8 AA( 9, 32), AS (3, 5), BAD (3, 12)
DATA DS /.06O2.. 0741. .0201. .0705. .1360. .1268. .2163. .1716
C..2043, .3367,. 3136 , . 1973 , . 3313 i .2994, .0579, .0173 ,. 1759, .1392 , . 1528
C..1304. .2654. .2634.. 0737.. 3134. .2362 . U> 444. .4009. . 3293 . .0886. .2599
ISN 0006
ISN 0007
ISN 0008
ISN 0009
ISN 0310
ISN 0011
ISN 0012
ISN 0014
ISN 0015
ISN 0016
ISN 0017
ISN 0018
ISN 0019
ISN 0020
ISN 0022
ISN 0023
c
c
c
c
c
c
c
c
c
c
c
Ct. 1813,. 0592,. 0000,. 2 500,. 5000,. 7500,1. OOO/
DEFINE FILE 99 (75 .3256. U. Nil
READ IN SURVEILLANCE DRIVING SEQUENCE
DO 3000 1=1.100
NX1=((I-1)*16)+1
NX2=NX1*15
RE A 0(5 ,100) (VTM(K),K=NX1,NX2)
100 FORMATC 16F5.0)
IF(VTM FIRST 505 SEC. OF FTP
DO 1500 1=1,100
NX1=( ( I-l)*16)+l
NX2=NX1+15
READ(5.100HVVT
-------
IV-10
TABLE IV-2 (cont'd)
LISTING, MAIN PROGRAM II
ISN
TSN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
' ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0:^4
0025
0026
0027
0028
0029
0030
0031
0032
0033
0034
0036
0037
0038
0040
0041
0042
0043
0044
0046
0047
OJ48
0049
0050
0051
0052
0054 ,
J)056
~
C
L
C
C
C
C
C
C
C
1313
1001
1000
C
C
C
C
C
C
CALL SFTUP(VTM,AA,AS)
READ IN INDIVIDUAL VEHICLE MODAL EMISSION DATA
FILTER VEHICILES FOR GROUP REPRESENTATIVES
IN THIS EXAMPLE THE DATA IS BEING READ OFF A DISC FILF AND THF
1NIVIDUAL VEHICLE MODAL EMISSION DATA IS PUT INTO ARRAY AMTC
IN THIS EXAMPLE THE GROUP IS= DENVER. PR E 'MISSION CONTROL.
NVIG=0
DO 2000 IY=57,71
JSTART=ITAB( IREC. 11
JEND=ITAB(IREC,2 )
DO 2001 J=JSTART. JFND
READ(99«J) ( ( IDAT(L,K),L=1,4), PASS ONLY DENVER, PRE EMISSION CONTROL=>PRE67
NYR=IDAT< 1,K)/1000000
NLOC=IDAT(3.K1/1OOOOO
IF(NYR.LE.67.AND.NLOC.EQ.5)&OT01313
GOT02002
NVIG=NVIG*1
DO 1000 IR=1,37
DD=1.0
IF(IR.L£.32)DD=DS(IR)
00 1001 IC=1,3
AMTC(IC,IR)=RDAT( IH,K)*DD
CONTINUE
CONTINUE
DETERMINE INDIVIDUAL VEHICLE EMISSION RATE FUNCTION COEFFICIENTS
CALL EDOT(AMTC,AA,AS,BAD)
ENTER THIS VEHICLES'S COEFFICIENTS INTO THF GROUP'S EMISSION RATE
FUNCTION
IF(NVIG.E0.1)INT=1
IF(NVIG.GT.1)INT=2
CALL EDGRP(BAD.INT)
C
C
ISN
ISN
ISN
ISN
0057
0053
0059
0060
2002
2001
200C
C
C
C
C
CONTINUE
CONTINUE
CONTINUE
NOW THAT ALL VEHICLES IN GROUP HAVE BEEN CONSIDERED, INT=S
CETERMINE THIS GROUP'S EMISSION RATF FUNCTION COEFFICIENTS.
CALL EDGRPISAD.3)
-------
IV-11
TABLE IV-2 (cont'd)
LISTING. MAIN PROGRAM II
INTEGRATE THIS GROUP'S EMISSION PATE FUNCTION OVER THE DRIVING
SECiUENCL.
ISN 0061
CULL ESUH(VVT.5Q6.BftDfC(ll,C(2>.C(31.DISTI
DETERMINE TOATAL FMISSIQN=>MULTIPLY EACH EMISSION AMOUNT bY NO.
VEHICLES IN GROUP
ISN 0062
ISN 0063
VN=NVIG
DO 5030 1=1,3
ISN
50?'J C(I)=C(I)*VN
_C WRTTE OUT EMISSION RESULTS....
ISN OJ65
ISN 0066
WRITE(6,500)(C(L),L=1,3)
500 FORHATdH . «HC= ' . F1C.2 .2X . ' CQ= ' .F 10.2 .2X. »NQX= ' . P10.2 >
ISN OJ67
ISN oo&a
STOP
END
-------
IV-12
TABLE IV-3
LISTING, SUBROUTINE SETUP
LEVEL 21.6 ( MAY 72 (
Oi/360 FORTRAN H
COMPILcR OPTIONS - NA«1£= MAIN,OPT=02 ,LIN£CNT=60 ,S IZE=OOOOK t
SOURCF.EBCD1C.NQL1ST.NODECK.LUAD.MAP.NOEDIT.ID.XREF
ISN 0002
ISN 0003
ISN 0004
ISN 0005
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
SUBROUTINE SbTUPI VTM.AA.AS)
******************************************************************
SUBROUTINE SETUP COMPUTES THE BASIS FUNCTION FACTOR ARRAYS FOR
ACCEL/DECEL AND STEADY STATE EMISSION RATE FUNCTION DETERMINATIONS
.ARRAYS -AA« AND «AS« RESPECTIVELY. GIVEN THE VELOCITY VS. TIME
HISTORY OF THE SURVEILLANCE DRIVING SEQUENCE! ARRAY VTM).
VTMm=>VELOCITY VS. TIMEdN ONE SEC. INTERVALS) OF THE SURVEILL-
ANCE DRIVING SEQUENCE. VTM ( I )=VELOCITY AT TIME I.(REAL*4)
MVT(I)=TIME I»TH ACCEL/DECEL MODE STARTS IN THE SURVEILLANCE
DRIVING SEQUENCE. (REAL*4)
TM BASIS FUNCTION FACTOR ARRAY FOR ACCEL/DECEL. ( REAL*8 )
AS=>BASIS FUNCTION FACTOR ARRAY FOR STEADY STATE ,(REAL*8 )
DIMENSION VTM«1055).MVTI321.TM(321
REAL*8 X(32,9),SV,SA,TMD,C(9,9»,AA<9,32I,SUM,AS<3,5)
DATA MVT/ 11.. 38.. 64.. 87.. 113.. 141.. 167.. 199.. 227.. 257. .302.. 343..
ISN 0010
C374.,421.,459.,483.,501.,538.,569.,602.,631.,671.,709.,739.,780.,
C814..834..887..932..965..1001..1030./
ISN
ISN
ISN
ISN
0006
0007
0008
0009
DATA TM/12.
C8..22..16..
C/
NOBSA=32
NOBSS=5
NBFA=9
,16.
18. t
,8. ,11
19. .25
.,13.
..28.
,12. ,17.
.15. .25.
,12. ,14.
.18. .10.
,30.
.38.
,26. ,21
.35. .18
.,32. ,23.
..21. .14.
,9.,
.13.
NBFS=3
****** CALCULATE AA *************
CALCULATE BASIS FUNCTION ARRAY X
ISN 0011
ISN 0012
DO 1000 IM=1,NOBSA
NTS=MVTtIH)
ISN 0013
ISN 0014
NTM=TM(IM)
NTF=NTS*NTM-1
ISN 0015
ISN 0016
DO 999 IK=2,NBFA
999 X(IM.IK>=O.ODO
ISN 0017
ISN 0018
X(IM,1)=1.0DO
DO 1001 IT=NTS.NTF
ISN 0019
ISN 0020
KT=IT*1
SV=(VTH(IT>+VTM(K.T))/2.0
ISN 0021
ISN 0022
ISN 0023
ISN OJ24
ISN 0025
ISN QQ2A
SA=VTM(KT)-VTM(IT»
X(IM.2»=XUM.21*SV
X(IM,3)=X(IM,3)+SA
X1IM.4)=X(IM.4)*(SV*SA)
X(IM,5)=X(IM,5)*(SV**2)
X(IM.6)=X(IM.fe)*(SA**21
ISN 0027
ISN 0028
X(IM,7)=X(IM,7)»<(SV**2)*SA)
X(IM.8)=X(IM.6»*((SA**2)*SV)
-------
IV-13
TABLE IV-3 (cont'd)
LISTING, SUBROUTINE SETUP
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0029
0030
0031
003?
0033
O034
0035
0036
0037
0038
0039
0040
0041
0042
0043
0044
0045
C
C
C
c
C
1001
lQfl2_
1000
10O5
10O4
1003
X(IM,9)=X(IM,9) + ( (SV**2)*(SA**2H
CONTINUE
DO 1002 lK=2tNBFA
TMD=TMI IM»
X< IM,IKJ=X( IM,IK)/TMD
CONTINUE
CONTINUE
SET UP C ARRAY, C=(X1X)-»
00 1003 I=1,NBFA
DO 1004 J=lfNBFA
SUM=O.ODO
DO 10O5 K=1.NOBSA
SUM=SUM+(X(K, I)*X(K,J) )
CONTINUE
C(ItJ)=SUM
CONTINUE
CONTINUE
CALL INVERSIC.NBFA.NBFA )
C
c
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0046
0047
0043
0049
0050
0051
0052
0053
0054
0055
0056
0057
0058
0059
0060
0061
0062
0063
0064
0065
006o
0067
0068
OOt>9
C
c
c
c
c
c
c
c
r
c
100R
1007
1006
2000
20_Q_3_
2&Q2_
SET UP AA AKRAY
*s
DO 1006 1=1,NBFA
DO 1007 J=1.NOBSA I
SUM =0.000
DO 1O08 K=1.NBFA
SUM=SUM+(C(I,K)*X(J,K) )
CONTINUE
AA( I,J)=SUH
CONTINUE
CONTINUE
****** CALCULATE AS ARRAY *********
CALCULATE BASIS FUNCTIONS
00 2000 1=1, NOBS S
XI=I-1
V=XI*15.0
X(I.1)=1.0DO
X(I,2)=V
X(I.31=V**2
CONTINUE
SET UP C ARRAY, C=(X«X)-»
DO 2001 I=1,N8FS
DO 2002 J=1.NBFS
SUM=O.ODO
DO 2003 K=1,NOBSS
SUM=SUM+(X(K,I)*X(K,J))
CONTINUE
C«I,J»=SUM
CONTINUE
-------
IV-14
TABLE IV-3 (cont'd)
LISTING. SUBROUTINE SETUP
ISN
1SN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0070
OJ71
0072
0073
0074
0075
0076
OD77
0078
0079
0080
0081
0082
2001 CONTINUE
C
C
CALL INVERSf C.3.9)
C
C
00 2004 I=1,NBFS
DO 2005 J=1.NOBSS
SUM sO. 000
DO 2006 K=1,NBFS
SUM = SUM+(CII tK)*X(J*K))
2006 CONTINUE
AStItJ)=SUM
2005 CONTINUfc
2004 CONTINUE
RETURN
END
-------
IV-15
TABLE IV-U
LISTING, SUBROUTINE EDOT
LEVEL 21.6 ( MAY 72 )
OS/360 FORTRAN H
COMPILER OPTIONS - NAMt = MAIN,OPT=02,LINECNT=60,SIZE=OOOOK,
SOURCE. EBCDIC.NOLI ST.NUDECK.LOAD.MAP.NQEDIT.ID.XREf
ISN 0002
ISN 0003
ISN 0004
ISN 0005
ISN 0006
ISN 0007
ISN 0008
ISN 0009
ISN 001O
ISN 0011
ISN 0012
ISN 0013
ISN 0014
ISN 0015
ISN 0016
ISN 0017
ISN 0018
ISN 0019
ISN 0020
C
c
c
c
r.
c
r.
c
r.
c
f,
c
r.
c
r,
c
c
c
r.
c
r,
c
r,
c
r.
c
c
c
c
r,
c
c
r
c
SUbROUTINE EDOT( AMTC, AA ,AS , BAD)
SUBROUTINE EDOT COMPUTES THE COEFFICIENTS THAT SPECIFY AN AUTO'S
INSTANTANEOUS EMISSION RATE FUNCTIONS FOR HC. CD .NOX( ARRAY 'BAD').
GIVEN THE AMOUNT OF EACH EMITTANT GIVEN OFF BY THE AUTO IN 32 A/D
MODES AND 5 STEADY STATE MODESC ARRAY • AMTC'). AND THE BASI5
FUNCTION FACTOR ARRAYS! AA , AS ).
AMTCtl ,J)=AMOUNT(GMS) OF THE I «TH EMITTANT GIVEN OFF BY THIS AUTO
IN THE J'TH MODE. I=1=>HC. I=2=>CO. I =3=>NOX. J=l. 37(32 A/D MODES
5 STEADY STATE MODES) .( REAL*4)
BAD(IfJ)=J'TH COEFFICIENT OF THIS AUTO'S INSTANTANEOUS EMISSION
RATE FUNCTION FOR THE I|TH KIND OF EMITTANT. I=1=>HC, I =2=>CO,
I=3=>NOX.(REAL*8)
AA=>BASIS FI
AA=BASIS FUNCTION FACTOR ARRAY FOR AC EL/DECEL (CALCULATED BY SUBROU
-TINE SETUP).
AS=BASIS FUNCTION FACTOR ARRAY FOR STEADY STATE (CALCULATED BY
SUBROUTINE SETUP 1.
TM( I)=TIME(SEC) IN I'TH MODE. (REAL*4)
******************************************************************
DIMENSION TM(37),AMTC(3t37>
REAL*8 AA(9.32).AS(3.5).BAD(3.12).SUM.YA(32).YS(5) ,B( 3 ) . XO.X1.X2
C,A1,A2
DATA TM/ 12.. 16.. 8.. 11.. 13.. 12.. 17. .12 .. 14. .30. .26. .21 . .32. .23.. 9..
C8.»22.t 16., 18., 19., 25., 28., 15., 25., 18., 10. , 38. ,35. , 18 . ,21. , 14. , 13.
C.60 . • 60. .60. .60. . 60./
NOBSA=32
NOBSS=5
NBFA=9
NBFS=3
DO 1000 IC=1.3
IC=1=>HC.IC=2=>CO.I=3=>NOX
CALCULATE OBSERVED AVERAGE EMISSION RATES OVER 32 A/D MODES
DO 1100 1=1.32
A1=AMTC(IC,I)
A2=TM(I)
YA(I)=A1/A2
1100 CONTINUE
CALCULATE COEFFICIENTS THAT SPECIFY A/D EMISSION RATE FUNCTIONS
DO 1200 I=1.NBFA
SUM=O.ODO
DO 1250 J=1.NOBSA
SUM=SUM*(AA(I,J)*YA(J))
1250 CONTINUE
-------
IV-16
TABLE IV-U (cont'd)
LISTING, SUBROUTINE EDOT
1SN
ISN
ISM
ISN
ISN
ISN
TSN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0021
0022
0323
0024
0025
0026
0027
0028
0029
O030
0031
0052
0033
0034
0035
0036
0037
0039
004O
0042
0043
0044
OO45
0047
0048
0049
0051
0053
0054
0055
0056
0057
OO5fl
0059
C
r.
C
c
C
c
r,
c
r.
c
c
c
c
r.
c
c
c
• c
BAD(ICtU = SUM
1200 CONTINUE
CALCULATE DBSFRVFn AVFRAGF EMISSION RATES DVFR ^ S£ MODES
DO 2OOO 1=33.37
IP=I-32
A1=AMTCIIC.I)
A2=TM(I)
YSt IPI=A1/A2
2000 CONTINUE
CALCULATE COEFFICIENTS THAT SPECIFY SS EMISSION RATE FUNCTIONS
DO 2001 I=1,NBFS
SUM =O. ODD
DO 2100 J=1,NOBSS
SUMsSUM+(AS( I.JJ*YSJ JM
2100 CONTINUE
B( I)=SUM
2001 CONTINUE
CHECK ON EXISTANCE OF NEGATIVE EMISSION RATES
LOOP=0
IF(B(31 .EO.O.ODOIGOTO2151
X0= ( B ( 2 )**2 ) - ( 4. ODO*B ( 3 }*B { 1 1 )
IF1XO.LT.O.ODOIGOTO2153
XO=DSQRTNO NEGATIVE EMISSIONS FOR VELOCITYS BETWEEN 0,60
IF LOOP=1 OR 2=> NEGATIVE EMISSION RATES BETWEEN 0.60MPH.
CALL SUBROUTINE PAD TO FIND COEFFICIENTS WHICH DO NOT PRODUCE
NEGATIVE EMISSION RATES.
CALL PAD(YS.B)
2154 BAD! IC.10I=B(1)
BAO(IC,11)=B(2I
BAD( IC.12)=B(3)
1000 CONTINUE
RETURN
END
-------
IV-17
TABLE IV-5
LISTING, SUBROUTINE PAD
LEVEL 21.6 ( MAY 72 )
OS/360 FORTRAN H
COMPILER OPTIONS - NAME= MAINiOPT=02,LINECNT=60,SIZE=OOOOK,
S OURCE.EBCDIC.NQLI ST.NODECK.LOAD.MAP.NDEDIT.ID.XRFF
ISN 0002
SUBROUTINE PAD(ZiBT)
******************************************************************
SUBROUTINE PAD COMPUTES A SET Of COEFFICIENTS THAT SPFCIFYS AN
EMISSION RATE FUNCTION FOR STEADY STATE CONDITIONS THAT IS
NQN NEGATIVE BETWfcEN VFLDf-TY 0 AND 60 MPH.
**»*»***»*»*»»*»»***»»»»»***»«*******»*»*»»*»*»*»*****»»»»»»***»*»
ISN QQQ3
REAL*8 Z<5) .ZP<5 > .BT<3t .Zl .Z2.A.B.SUM1 .SUH2.V.C1
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0004
0005
0006
0007
0008
O010
0011
0012
0013
0014
0015
OO17
0018
O019
0021
O022
0023
0024
0025
O026
0027
0028
0029
0030
0031
0032
0033
O034
0035
0036
0037
0038
0039
0040
0041
0042
0043
0044
0045
0046
0047
0048
004<»
0050
Z1=Z(1)
Z2=Z(2)
11 = 1
12=2
IF(Z1.LT.Z2)GOT01
Z1=Z(2J
Z2 = ZU)
11 = 2
12=1
1 DO 2 1=3.5
IF(Z(I).GT.Z2)GOT02
Z2=Z(I»
I2 = t
IFIZ1.LT.Z2IGOT02
C1 = Z1
Z1 = Z2
Z2=C1
IX=I1
11 = 12
I2 = IX
2 CONTINUE
B=(Z1*Z2I/2.0DO
V1 = I1
V2=I2
V1=*(A**2) )
BT(2»=-2.0DO*BT(3)*A
RETURN
END
-------
IV-18
TABLE IV-6
LISTING. SUBROUTINE ESUM
LEVEL
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
21.6
0002
.onoa
0004
0005
0006
0007
0008
0009
0010
0011
0012
001,3
001-V
0015
0016
0017
0018
0019
0020
0021
0022
0023
( MAY 72
COMPILER
r
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
) OS/360 FORTRAN H
OPTIONS - NAME= MAINf OPT=02 ,LINECNT=60 .S IZE=OOOOK .
SOURC E, EBCDIC, NOLI ST. NOD ECK. LOAD. M AP.NOEDI T. ID.XRFF
SUBROUTINE ESUM( VVTfNT.BAD, AHC , ACO,ANOX,DIST)
SUBROUTINE ESUM CALCULATES THE AMOUNT OF HC, CO. NOX EMITTED
AND THE DISTANCE TRAVELED BY THE AUTO THAT HAS THE INSTANTANEOUS
fcMISSION RATE FUNCTION SPECIFIED BY THE ARRAY 'BAD'. AND A DRIVING
CYCLE SPECIFIED BY THE ARRAY «VVT».
WT(I)=>VELOCITY VS. TIME HISTORY< DRIVING CYCLE) IN ONE SECOND
INTERVALS. WT 1 I )=VELOCI TY 1 MPH ) AT THE I 'TH SECOND. REAL**
NT=>MAXIMUM NUMBER SECONDS IN DRIVING CYCLE+1 SECOND
BADI If J»=>J'TH COEFFICIENT OF THIS AUTO'S INSTANTANEOUS EMMISSION
RATE FUNCTION FOR THE I'TH KIND OF EMITTANT, l=l=>HCi
I=2=>COf I=3=>NOX- (RPAL*fi)
AHC=AMT(GMS) HC GIVEN OFF BY THIS AUTO IN GOING THRU DRIVING CYCLE
REAL**
ACO=AMT(GMS) CO GIVEN OFF BY THIS AUTO IN GOING THRU DRIVING CYCLE
REAL**.
ANOX=AMT(GMS) NOX GIVEN OFF BY THIS AUTO IN GOING THRU DRIVE CYCLE
REAL**
DIST=DISTANCE(MILES)IN SPECIFIED DRIVING CYCLE, REAL*4
***********************************************************************
DIMENSION VVTINT)
REAL*8 BAD(3,12),AMT(3),X< 12),DIS,AMIN,AMAX,A1,A2,HOA,SOA
AMAX=1.0DO
AMIN=-1.20DO
A1=-1.0DO/AMIN
A2=-1.0DO/AMAX
CLEAR AMT ARRAY
DO 1000 1=1.3
1000 AMI (1 1=0.000
c
c
c
INTEGRATE AUTO'S EMISSION RATE FUNCTION OVER DRIVING CYCLE
DIS=O.ODO
NTT=NT-1
DO 3000 IT=1.NTT
KT = IT«-1
X(U=1.0DO
X<2)=DBLE«VVT(IT)+VVT(KT) J/2.0)
X(3)=DBLEJVVT(KT)-VVT(IT))
X(*)=X(2J*X(3)
X(5)=X(2)**2
X(6)=X«3)**2
X(7)=(X(2)**2)*X(3)
X(8)=(X(3)**2)*X(2)
X(9)=(X(2)**2)*(X(3)**2)
-------
IV-19
TABLE IV-6 (cont'd)
LISTING, SUBROUTINE ESUM
ISN 002%
ISN 0025
TSN 0026
ISN 0027
T.SN 0020
ISN 0031
7.S\' 0033
ISN 0035
ISN 0036
ISN 00.-.7
TSN 0038
»SV 0040
*SV 004'.
rSM 0042
:.SN eo43
Tsv no44
*.r.-v 0045
"'",v GO'^6
r.SM 00^*7
ISM 0048
".SS! 0049
'.SM 0050
«3K' 0051
*SN OOS'H
ISN1 0054
^SM 0055
ISV 0056
TSV 0057
X(10)=X(1)
X(11)=X(2I
X(12)=X(5)
IF IX (31 -GF.AM4X1 HnA=O.OnO
IF(X(3) .LE.AMIN)HOA=O.ODO
1FI X(3) .GF.O.ODO.ANn.XI^I .LT.&MAX IHHA = ( A2*X(1I ) 4-1.000
IF(X(3).LE.O.ODO.AND.X(3).GT.AMIN)HOA=(A1*X(3))+1.0DO
DO 2999IC=1.3
DO 2998 IE=1,12
SOA=1.0DO-HOA
IF(IE.GT.9)SOA=HOA
AMTI If. 1=AMT( If. » + (X( IE )*SOA*BAD( 1C. IE) 1
2998 CONTINUE
2999 CONTINUE
DIS=DIS+X<2)
300O CONTINUE
AHC=AMTU)
ACO=AMTI2»
ANOX=AMT(3)
OIS=DIS/3600.000
DISTsDIS
DO 4OOO ICK=1.3
4000 IF(AMT(ICK).LT.O.ODO)GOT04001
W1TO4444
4001 WRITE(6,4002)
4002 FORMAT (1H .'MODEL IS UNABLE TO PREDICT THIS VEHICLES EMISSIONS1)
4444 RETURN
FNQ
-------
IV-20
TABLE IV-T
LISTING, SUBROUTINE EDGRP
LFVEL 21.6 ( MAY 72 )
OS/360 FORTRAN H
COMPILLR OPTIONS - NAME = MAINrOPT=02,L1NECNT=60,SIZE=OOOOK,
SQURCF.FBCDIC.NDLIST.NODFCK.LnAD.MAP.NnFDTT.in.XRFF
ISN
ISN
0002
0003
C
C
C
c
c
c
c
c
c
c
c
c
u
c
c
\*
c
c
c
c
SUBROUTINE EDGRP ( BAD, INT )
SUBROUTINE EDGRP COMPUTES THE COEFFICIENTS THAT SPFCTFY THF
INSTANTANEOUS EMISSION RATE FUNCTIONS OF THE 'AVERAGE* AUTO OF
SOMF GROUP OF AUTOS- FDGRP IS CALLED ONCE FOR EACH AUTO IN THE
GROUP, SPECIFYING EACH TIME THE INSTANTANEOUS EMISSION RATE
FUNCTIONS COEFFICIENT ARRAY 'BAD' FOR THE INDIVIDUAt AUTO. AFTER
EOGRP HAS BEEN CALLED FOR ALL AUTOS WITHIN THE GROUP, THE 'AVERAGE
AUTO'S INSTANTANFQUS EMISSION RATF FUNCTIONS ARRAY TS GTVFN BY
ARRAY 'BAD'.
BAD=>INSTANTANEOUS EMISSION RATE FUNCTIONS ARRAY. (REAL*8 J
SET INT=1 FOR THE FIRST AUTO IN THE GROUP
SET INT=2 FOR THE REST OF THE AUTOS IN THE GROUP
SET INT=3 AFTER ALL THE AUTOS IN THE GROUP HAVE BEEN CONSIDERED
REAL*8 BADf3.12J.B13.12J.CTN
c
c
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0004
0006
0007
0008
0009
OO1O
0011
0012
0014
0015
0016
OO17
0013
OO19
0020
0022
0023
OO24
0025
OO26
0027
0328
1001
1000
2OOO
2002
2001
4133
3001
3000
4000
IF(INT.GT.1)GOT02000
DO 1000 1=1.3
DO 1001 J=1,12
B(I.J)=O.ODO
CONTINUE
CONTINUE
CTN=O.ODO
IF( INT.E0.3IGOT04133
CTN=CTN+1.0DO
DO 2001 1=1.3
DO 2002 J=1.12
B(I . JI=B( I . Jl+BADI I .Jl
CONTINUE
CONTINUE
IF( INT.NE.3)GOT04000
DO 3OOO 1=1.3
DO 3001 J=l,12
BADd. J)=B( I f Jl/CTN ;
CONTINUE
CONTINUE
RETURN
END
-------
IV-21
TABLE IV-8
LISTING. SUBROUTINE IHVERS
LEVEL 21.6
ISN 0002
ISN 0003
ISN 0004
ISN 0005
ISN OOO&
ISN 0007
ISN 0008
ISN 0009
ISN 0010
ISN 0011
ISN 0012
ISN 0013
ISN 0014
ISN 0015
ISN 0016
ISN 0017
ISN 0018
ISN 0019
ISN 0320
ISN 0021
ISN 0022
ISN 0024
ISN 0025
ISN 0027
ISN 0028
ISN 0029
ISN 0030
ISN 0031
ISN 0032
ISN 0033
ISN 0034
ISN 0035
ISN 0036
ISN 0037
ISS 0038
ISN 0039
( MAY 72 ) OS/360 FORT°.4N H
COMPILER OPTIONS - NAME = MAIN,OPT=02 ,LINECNT=AO , S1ZE=OOOOK,
SOURCE.EBCDIC.NOLIST,N3DECK.LOAD.MAP.NOEDIT.ID.XREF
SUBROUTINE INVERSU.NfNl)
C*
C ******************************** INVERSE *****************************
C*
C*
C* REMARKS : THE ROUTINE COMPUTES THE INVERSE DF MATRIXA: DIMENSION <2O,
C* WHERE N IS THE DIMENSION OF A.
C*
C* THE INVERSE IS RETURNED IN MATRIX A.
C*
C* N IS RETURNED AS -1 WHEN A IS SINGULAR
C*
C ************************************************************************
C
DIMENSION A IFCSUEt IJ.NE.O.DOIGOT0800
27 LE = LE * 1
28 IF (LE-N) 26,261900
800 DO 35 J=1.K
BUFF = S(I,J)
S(I .J) = S(LE.J)
S(LE.J) = BUFF
35 CONTINUE
41 GO T(j 20
45 DVH = SI 1. 11
DO 46 J=1,K
46 Sd.Jl = SJI.J1/DVH
S(I,I) = 1.000
48 1F(I .GE. N ) GO TO 149
*
*******
*
*******
(A ,1)
OF S
-------
IV-22
TABLE IV-6 (cont'd)
LISTING, SUBROUTINE INVERS
ISN Ou41
ISN 004?
ISN 0044
ISN OO45
ISN 0046
ISN OO47
ISN 0048
ISN OO49
ISN 0051
ISN OO5?
ISN 0053
ISN 0054
ISN OO55
ISN 0056
ISN 0057
ISN 0058
ISN 0059
ISN 0061
ISN 0062
ISN 0063
ISN 0064
ISN 0065
ISN 0067
ISN 0068
ISN 0069
ISN 0070
ISN 0071
ISN 0072
ISN 0073
ISN OO74
ISN 0075
ISN OO76
ISN 0077
ISN 0078
ISN 0079
ISN 0080
ISN ooai
ISN 0082
ISN 0083
49
50
7O
75
100
120
140
150
C
350
351
370
375
380
384
385
C
390
395
396
400
402
C
900
7000
FPY = S(M,L)
IF < FPY . FQ. O.DO 1 Gfl Tfl 75
DO 70 J=1,K
BUFF = FPY * SITtJl
S(M,J) = S(MtJ) - BUFF
CONTINUE
JIN = M+l
IF 1 JIN - GT.N 1 GO ID 149
M = M + l
GO TO 49
CONTINUE
CONTINUE
DIAGONAL1ZA1ION OF S
DO 385 1=2. N
L = I
M = 1-1
FPY = S(M,L)
IF ( FPY . EO. O.DO 1 GO TO 375
DO 370 J=1,K
BUFF a FPY * SII.J1
S(M,J) = S(M,J) - BUFF
CONTINUE
IF ( M .LE. 1 ) GO TO 384
M = M-l
GO TO 350
CONTINUE
CONTINUE
STORE INVERSE IN A
DO 402 I1=1,N
LL=I1
DO 400 Jl=ltN
KK s N 4- Jl
AIIUJU = S(LLfKK)
CONTINUE
CONTINUE
RETURN
NO INVERSE
MRlTEf 6.7000)
FORMAT! 1HO« 'NO INVERSE1)
N=-l
RETURN
END
-------
IV-23
FIGURE IV-1
i
FLOW CHART, MAIN PROGRAM I
READ SPEED VS. TIME ARRAY
FOR THE SURVEILLANCE
DRIVING SEQUENCE.
READ SPEED VS. TIME ARRAY
FOR DRIVING SEQUENCE
OVER WHICH EMISSIONS
ARE TO BE CALCULATED.
1
DETERMINE BASIS FUNCTION
FACTOR ARRAYS.
I
READ IN VEHICLE
MODAL EMISSION DATA
SUBROUTINE SETUP
I
DETERMINE EMISSION RATE
FUNCTION COEFFICIENTS.
\
r
INTEGRATE EMISSION RATE FUNCTION
OVER SPECIFIED DRIVING SEQUENCE.
i
f
WRITE OUT AMOUNTS OF HC, CO, NOX GIVEN
OFF BY VEHICLE OVER SPECIFIED
DRIVING SEQUENCE.
\
SUBROUTINE EDOT
SUBROUTINE ESUM
-------
IV-24
READ SPEED VS. TIME ARRAY FOR THE
SURVEILLANCE DRIVING SEQUENCE.
READ SPEED VS. TIME ARRAY FOR THE
DRIVING SEQUENCE OVER WHICH EMISSIONS
ARE TO BE CALCULATED.
IS THIS VEHICLE
IN GROUP UNDER
CONSIDERATION?
DETERMINE BASIS FUNCTION FACTOR ARRAYS
READ IN VEHICLE SPECIFICATIONS.
FIGURE |V-2
FLOW CHART,
MAIN PROGRAM II
SPECIFIED GROUP FILTER
READ IN VEHICLE'S MODAL EMISSION'S DATA.
DETERMINE EMISSION RATE FUNCTION
FOR VEHICLE
ADD VEHICLE'S EMISSION RATE FUNCTION
COEFFICIENTS TO GROUP'S FUNCTION.
LAST
VEHICLE IN
GROUP?
DETERMINE EMISSION RATE FUNCTION FOR
"AVERAGE" VEHICLE REPRESENTING GROUP.
JL
INTEGRATE AVERAGE VEHICLES
EMISSION RATE FUNCTION OVER
SPECIFIED DRIVING SEQUENCE.
DETERMINE TOTAL EMISSIONS
GIVEN OFF BY GROUP.
4-
SUBROUTINE EDOT
SUBROUTINE EDGRP,
INT = 1,2.
SUBROUTINE EDGRP,
INT = 3.
SUBROUTINE ESUM
WRITE OUT AMOUNT HC, CO, NOX GIVEN OFF.
-------
IV-25
-------
V-l
APPENDIX V
VEHICLE CLASSIFICATION BY DISCRIMINANT FUNCTION ANALYSIS
-------
V-2
-------
V-3
APPENDIX V
VEHICLE CLASSIFICATION BY DISCRIMINANT FUNCTION ANALYSIS
The implementation of the emission-rate function model in assessing
the impact of a collection of vehicles on the environment requires that
the input data be appropriately chosen according to the problem under
consideration. A matter of central concern in this regard is whether
available data can be employed in a setting different from that in which it
originated. In particular, such questions as geographic location and time
frame are of interest. For example, can surveillance data obtained in one
location be employed as a basis for modeling emissions in a different
location, and can data collected in the past be used as a basis for modeling
present or future problems?
*
In a previous report, it was noted that a distinction exists between
the emissions of vehicles in Denver as compared with five other cities of
lower altitudes. Also, as would be expected, the implementation of emission
controls clearly affected the emissions of vehicles in both geographic
categories. The concept of discriminant function analysis was employed to
crystallize and quantify these differences.
The distinctions alluded to above were based on an analysis of total
emissions of HC, CO and NO Over the surveillance driving sequence. Though
X
it is presumed that these differences among categories of vehicles would
persist in other driving sequences, it was considered of interest to investigate
this assumption in a systematic way. Toward this end a discriminant function
approach was undertaken.
APTD-15UU, "Automobile Exhaust Emission Surveillance - A Summary", May, 1973.
-------
V-4
The logic of this approach is as follows. Each driving cycle consists
of a series of accel/decel and steady-state modes. Conceivably some of these
modes might be more sensitive to geographic or time differences than others.
This would result in a situation where driving sequences consisting of combinations
of these modes could themselves differ in this regard. A linear discriminant
function is a weighted combination of the modes constructed in such a way
that differences between vehicle categories, if they exist at all, will
be most clearly delineated.
Suppose that only Denver versus non-Denver vehicles are considered and
the emissions for a particular pollutant for the various modes are denoted
X , X_,....,X „. Then the linear discriminant function is defined as
F-
where a , a , ..., a are coefficients selected according to an optimization
logic. For each vehicle, a value of F can be computed. If all F values
for Denver vehicles and all F values for non-Denver vehicles are grouped
together, a mean value of F for each group and a variance or standard
deviation for each group can be computed. The two groups will separate
clearly, with minimal overlap of the two distributions of F values, if the
difference between the mean values for the groups is large and the dispersion
or scatter of F values within each group is small. The coefficients a. , a ,....,
a _ are chosen so as to make as large as possible the ratio of the dispersion
of the group means to the pooled dispersion of the individual vehicles within
groups .
-------
V-5
If only two groups are involved, it is possible to compute only one
i
discriminant function for each vehicle. However, if there are G groups,
G-l such functions can be computed, provided G-l does not exceed the number
of modes.
For example, consider the following groups of vehicles
GROUP 1 - Non-Denver, pre-emission control,
GROUP 2 - Denver, pre-emission control,
GROUP 3 - Non-Denver, emission control,
GROUP h - Denver, emission control.
In this case, three discriminant functions can be computed as follows
Fl=aixl+ a2X2+ ..... a37X37 '
F3 = C1X1 + C2X2 + ..... C37X3T '
These functions employ three distinct sets of weighting coefficients {a.},
{b.}, (c.) the efficacy of which can be appreciated best by a geometric
argument .
For each vehicle, F.., F , and F can be computed. These three values
can be considered as the coordinates of a point in three-dimensional space.
If each vehicle is plotted as such a point in 3-space, then there will result
a collection of points which, hopefully, will tend to cluster into four distinct
"clouds", these clouds being associated with the four groups of vehicles
under study. If the separation of these groups is complete, the space can
be partitioned into disjoint compartments and there will be no overlap or
spillover from one compartment to the other. In reality, this will not be
-------
V-6
the case, and there will be a certain amount of "mixing" or 'confusion" if
attempts are made to assign a particular vehicle to its correct group merely
by looking at the F-value coordinates of that vehicle. Quantification of
the degree of correct and incorrect classification is therefore required
in order to assess how "good" such a classification matrix is.
To appreciate the nature of this quantification, the case in which
there are only two categories—say, Denver and non-Denver—and only a single
discriminant function F is considered first. All vehicles are divided
into two sets on the basis of their known membership—that is, all Denver
vehicles are considered as a group and all non-Denver vehicles as a group.
There are 169 vehicles in the Denver group, 851 in the non-Denver group. For
the Denver group, F can be computed for each of the 169 vehicles and the
results displayed as a histogram. Similarly, F can be computed for each of
the 851 vehicles in the non-Denver group and the results displayed as a
histogram. The results are shown in Figures V-l, V-2, and V-3 for HC, CO
and NO respectively. Quite clearly, a certain amount of overlap is evident,
•A.
so that attempts to assign class membership on the basis of the F value only
would result in a certain number of both the Denver and non-Denver vehicles
being misclassified.
A technique which can be used to determine the quantitative separation
of groups is the construction of a "classification matrix" for the groups. The
concept, as illustrated below, classifies automobiles as coming
from City A or City B on the basis of a particular test value.
CITY A CITY B
CITY A
CITY B
83
U2
IT
58
CLASSIFICATION MATRIX FOR TWO CITIES
-------
V-7
The classification matrix should be interpreted in the following way.
1
A technique can be found which takes a test value for an automobile from City A
and, on the basis of probabilities for this test value, classifies this
automobile as coming from either City A or City B, whichever has the highest
probability for the given test value. If all the automobiles from City A
are subjected to this probability test, some are correctly classified as coming
from City A while others are incorrectly classified as coming from City B. The
same test can be performed on the automobiles from City B. Since the number
of automobiles from each city is known, the number of automobiles correctly
or incorrectly classified can be converted into percent of automobiles from
each city. The diagonal elements of the matrix represent the percent of
automobiles coming from City A and City B which .were correctly classified as
coming from City A and City B. The off-diagonal elements give the percent
of automobiles incorrectly classified. Therefore, 83 percent of the automobiles.
from City A were correctly classified as coming from City A, while 17 percent
were incorrectly classified as coming from City B. Likewise, 58 percent of
the automobiles from City B were classified as coming from City B while h2
percent were classified as coming from City A. In this case, the probability
for classifying automobiles was more heavily weighted in favor of City A.
Classification matrices for Denver versus non-Denver vehicles are
shown in Table V-l, and the corresponding histograms on which they are based
are shown in Figures V-l, V-2 and V-3. It can be seen that the separation
of the two groups is somewhat better for CO and NO than for HC. Also, in the
X,
case of HC, it is more likely that Denver vehicles will be misclassified as
non-Denver vehicles than that non-Denver vehicles will be classified as Denver
vehicles. Thus, once the probabilities for a set of groups have been
-------
V-8
determined for values of a given test, the classification matrix technique
t
can be used to give an easy-to-interpret quantitative measure of the separation
between groups.
If the number of groups used in the classification is increased, the
size of the classification matrix increases accordingly, with the diagonal
elements indicating the percent correct classification. In this more elaborate
situation, a vehicle can be misclassified in more than one way, and the nature
of the misclassification can provide insight into which categories of vehicles
are most "alike".
Just as the number of groups (cities) in the classification matrix can
be increased, the number of discriminant functions to be used as the basis of
classification can also be increased. In this case, the probability of
occurrence of each of the discriminant-function values associated with the
vehicle can be calculated for a given automobile. For reasons discussed
later, it can be assumed that the several discriminant functions are statistically
independent. Therefore, these probabilities can be multiplied together and it
can be assumed that the product is the probability of the joint occurrence
of the particular discriminant function values encountered for the vehicle in
question. Then the probability products calculated for all the groups can be
compared and the automobile is assigned to the group with the highest
probability product.
In the case of Denver and non-Denver vehicles before and after the
advent of emission controls, there are four categories and three F values.
By virtue of the theory on which discriminant functipn analysis rests, the
three F values are statistically uncorrelated. Also, by virtue of the fact
that each of the F values is a linear combination of the outcomes of 37 random
-------
V-9
variables, it can be presumed that the Central Limit Theorem of statistics
i
will cause the distribution of the F values to tend toward a Gaussian dis-
tribution. Under these conditions, the assumption of independence is believed
justified.
The classification matrices for HC, CO and NO according to Denver and
X.
non-Denver, pre-control and control eras are presented in Table V-2. The
type of inferences which can be drawn from these tables is exemplified by noting
the classification matrix for NO . For example, note that non-Denver, pre-emission
Jt
controls (category l) is misclassified more frequently as non-Denver emission
controls (category 3) than as either of the Denver categories (categories
2 and U). Similarly, the Denver pre-emission control is confused more with
Denver emission controls than with the other two categories, and the Denver
emission control category is more "like" the Denver pre-emission category
than any of the other categories. In short, it can be concluded that a more
definitive difference exists between the Denver and non-Denver categories
than exists between the pre-control and emission control periods.
To summarize, linear discriminant function analysis, coupled with the
principle of maximum likelihood, provides a means for assessing homogeneity
of subsets of vehicles and the degree to which one subset resembles another.
-------
V-10
TABLE, V-l
TWO GROUP
CLASSIFICATION MATRICES
GROUP 1 = NON-DENVER
GROUP 2 = DENVER
HC
_1 _2
1) 82 17
2) U2 57
CO
1) 8U 15
2) . 11 88
NO
X
1) 88 11
2) 11 88
-------
V-ll
TABLE V-2
1
FOUR GROUP
CLASSIFICATION MATRICES
GROUP 1 = NON-DENVER PRE-EMISSIQN CONTROL
GROUP 2 = DENVER PRE-EMISSION CONTROL
GROUP 3 = NON-DENVER EMISSION CONTROL
GROUP U = DENVER EMISSION CONTROL
HC
1)
2)
3)
U)
1
U7
19
16
5
_2
13
U8
3
15
3
23
3
58
11
u
lU
28
21
68
CO
1)
2)
3)
H)
1
56
12
15
12
_2
8
72
1
11
_3
25
0
79
U
_i
9
15
3
72
1)
2)
3)
U)
_1
58
7
27
5
_2
10
73
2
23
NO
X
_3.
20
2
66
2
Jj.
9
17
3
68
-------
UJ
o
35
30
25
20
15
10
5
40
35
30
25
20
15
10
5
'•'
—
—
—
—
I I I I . . 1
—
—
—
—
—
—
—
—
i i i r~
•MM
cz
••••1
FIGURE V-1
DISCRIMINANT ANALYSIS, HYDROCARBONS
••Ml
DENVER
1 1— • 1 I— I 1 '1 1 1 1
IM^HHtt
••••
NON-DENVER
_.
1 1 1 l 1 1 1 1 1
10 11 12 13 14 15 16 17 18 19 20 21
F —INTERVAL
-------
PERCENT
35
30
25
20
15
10
5
40
35
30
25
20
15
10
5
0
•w*
—
—
—
—
._
^^M
1
1
1
DENVER
I i r— FT
-
NON-DENVER
III!
FIGURE V-2
DISCRIMINANT ANALYSIS, CARBON MONOXIDE
j-f
1 1
I
^H
1
23456789 10 11
mm^m
I i
12
— |
13
I
r-|
14
•••m
m^mm
I— • i i- S
§••••
M^M
•^^
§••••
—1 1
15 16 17 18 19 20 21
F— INTERVAL
-------
35
30
25
20
15
10
5
l- 0
LU
o
g 40
Q.
35
30
25
20
15
10
5
0
_ FIGURE V-3
DISCRIMINANT ANALYSIS, OXIDES OF
^™~
~~ DENVER
—
—
••^
I I I I I I I I
—
~~~ NON-DENVER
—
—
—
—
—
_ , 1
I I i • — •— Ti I
I
!••••
| |
mm^
NITROGEN
^^••i
JI
_|
~h
•n^
^^mm
^._
1
1 .111111
8 9 10 11 12 13 14 15 16 17 18 19 20 21
F —INTERVAL
-------
VI-1
APPENDIX VI
COMPUTER APPLICATIONS FOR THE GENERAL USER
-------
VI-2
-------
VI-3
TABLE VI-1
1
GROUP PREDICTION MODEL - COMPUTER
PROGRAMS AND SAMPLE INPUT
PEAL*8 CCJEF( 1 1, 3, 12)
KEAL*8 C2(3,12)
OIYIEN.S1UN I T( 2000) , I UNO ( 121) , ILF TR ( 50) , I AST ( 121)
DIMENSION TUT (3),C(3),DEC(11),VVTI 2000)
DATA IBLNK/1 '/
DAI A I'JlSir)/' + ',9*'_' , ' + 't9*'_' , '+*»9*'_ *.'•••• »9**_* ,' + * ,9** _*
i • t-' ,9*'_« ,' + • ,9** _' ,' + '
2«+* , 9 *•_',' + '» y *'_«,'+•/
DATA I AST/121*' '/
JATA IS TAR/1*'/
OAT A ILET/« I V
DATA ILETR/20*' • ,'T' , • I' ,'M• ,'E'
120*' '/
OAT A TGT/3*0./
READ(5,100)NSEC,NUMB,INC
100 I UKMAT13I 10) ........
C NSEC IS THE NJMRER Of- SECONDS IN THE DESIRED DRIVING SEQUENCE + 1
Z StCCND
DO 1500 1=1,100
NX1 = I (1-1)*lo)+l
NX2=NX1+15
RFAD(5, 101) (VVT (K ),K=NX1,NX2)
IF tNX2.GE.NSEC) GO TO 1555
101 FORMAT ( 16F5.0)
1500 CONTINUE
1555 CONTINUE
: VVT(I) IS THE VELOCITY OF THE DRIVING SEQUENCE AT TIME (1-1).
C THE ARRAY VVT IS INPUT 16 ITEMS ON EACH CARD.
C READ IN THE TOTAL NUMBER OF VEHICLES IN SAMPLE POPULTAION.
C READ IN THE DECIMAL FRACTION OF DRIVING DONE BY CARS IN EACH OF THE
C 11 GROUPS
: GROUP i=1157-l<)67 DENVER, GROUP 2 = 1957-1967 LOW ALTITUDE CITIES
C EXCEPT
C 19t6,1967 CALIFORNIA, GROUP 3=1966,1967 CALIFORNIA, GROUP 4=1968
C LOW
: ALTITUDE CITIES, GROUP 5=1969 LOW ALTITUDE CITIES, GROUP 6=1970
C LOW
L ALTITUDE CITIES, GROUP 7=1971 LOW ALTITUDE CITIES GROUP8=1968
C DENVER,
C GROUP 9 = 1969 DENVER, GROUP 10=1970 DENVER, GROUP 11= 1971 DENVER
Ih(INC.EO.OJGO TO 2000
LL,OH= 1
ITtST=INC+l
310 irjRI TE( 6,301 )
301 FORMAT 11 HI, 50X, ' V ELOC IT Y (MP H) • )
WR1 TE(6,302)
302 FORMAniOXtlOX^SSyx^lO'fSXf1 15'tSXt^O1,8X1*25*,SXt'SO^SX,
1* 3;j' ,8X , *40* ,8X,'45« ,8X,« 50' ,8X,' 55
WK I T L(&,5 5 5 ) ( I UNO(L) ,L=1,121)
FORMAT(9X.121A1 )
-------
VI-U
TABLE VI-l,(cont'd)
UL 305 J=l ,N50
IR J.C J.l.AND.LOuP.EQ.DGO TO 305
If U.EO.l. AND.LOOP.NE .1 )WRlTE(6t 316H IAST(KI tK= It 121)
If < J.CQ.l .ANO.LHUP.NE .1 ) I AST ( IVEL)=IBLNK
FORMAT ( I H + , bX,121Al)
JKEY=(LOOP-1 )*N5G+J
I VLL=IFIX( VVT( JKEY)*2. + 1.5)
IF I IVtL .GT.121) IVEL = Ul
1AST{ IVEL)=1STAR
JVAL=JKEY- 1
IFtJKtY.bO.ITEST )Jl=Jl+l
IH JKEY.t U.I TEST) WRI Th (6,306) IL ETR ( Jl ) , JVAI. , ILET
FURMAT12X.A1.2X, 13. IX, Al, 120A1)
IR JKFY.FQ. ITESnvgRITE (6,355) (I AST (K)VK= 1.121)
3'35 HDRMATt lH+f8X,121Al)
lf-( JKEY.hQ. I TEST ) IT bST= IT EST -HMC
I F( J.NE? .N5011 AST( IVfcL)=IBLNK
IT(JKEY.GF. IMS FOGG TO 2000
30b CONTINUE
LrJUP=LOUP-f 1
GO TC 310
LI ST SPfcEi) VS TIME
2000 irjRITElot ^01 )
^01 FORMAT (1H1 ,20X, 'SPEED-TIME DRIVING SEQUENCE1,/
11X, ' TIMfct SfcC) « »2X,*SPEED(FIPH)1 , <* X, • TI ME ( SEC) ' ,2X , ' S PEfcD ( MPH ) « ,
2'*Xf ' T IMEl SEC) ', 2X, • SPEED IMP H) •, AX, • TIME ( SEC) ',2X, • SPOED(MPH) •)
HO >C5 KK = 1 ,NSEC
^05 IT(KK)=KK-1
WRITF (6,^02) ( IT(KK), VVTtKK ) ,KK=1,NSEC)
40^' FU'.MAT(M I6,5X,F6.2 ,BX) )
VI K IT F.{0,209 )
20'i f-liRP AT (1H1, 'BREAKDOWN OF VEH ICL ES ' t / 15X, ' GROUP 1=1957-1967 DENVcR'
l,',GRUUP 2=19137-1967 LOU ALTITUDECNON CALIF 1^66,1967), GROUP 3«,
2'= 196o,1967 CALIHS/ 15X. 'GROUP 4=1968 LOW ALTITUDE, GROUP 5 = ',
3' 19oy LOW ALTITUDE, GROUP 5 = 1973 LOW ALT IT J DE ',/ 15X, 'GROUP 7=',
^'IS/7L LOW ALTITUDE, GROUP 8 = 1968 DENVER, GROUP 9 = 1969 DENVER'
5,/i5X,f GROUP 10=1970 DENVER, GROUP 11=1971 DENVER')
!NlDEX=0
P.I 3«5 H3 = l ,11
Of jc-'j M2 = l ,3
i'"J 33L> Ml = lf3
IiOil X=INDEX-»-l
ML = ( M-l )* CuN flNUE
•>9 RFAU(5t103tbNU=UllMDEC{K|.K=l.lll
103 HHRMATl 11F5.0)
DD 200 1=1,11
DO 573 K£=l,3
DO 573 KT = 1 ,12
-------
VI-5
TABLE VI-1 (cont'd)
!>73 C2(KZ,ra )=COEh( I ,KZ,KT)
WP.t Tt(6 ,210) I ,DEC( I)
21J FDIMATl /20X, •GROUP=I , I 5 , 5X, ' FRA CT ION=» ,F5 .2 )
IMl'HCt I) .LT. .0001 )GO TO 200
CALL fcSUM{VVT,NSEC,C2 ,C(i),C{2),C<3),DIST)
L)(J 201 J = l,'3
20i TUT( J ) = TGT( J)+C( J)*l»ECl l)*NUMB
200 CONTINUE
W KIT E(6,109 )NUMB
DQ 505 KM=1 ,3
IFITOT (KM) .bE.O.lGO TO 240
505 CONTINUE;
WK I TO (6, 111) (TUT(K) ,K=1,3),OI ST
ill FORMAT (10X,«HC=',F10.2,2X, «CO=' ,F 10 .2 , 2X, 'NOX=« ,F 10. 2, 2X ,
I'OISTANCE IN MILES=» tF10.2 )
109 FORMAT ( lOXt 'EMISSIONS IN GRAMS FOR1, I 10, 5X, ' VEH I CL ES1 )
GO TO 245
240 WKI TE(6,241)
^tl FORMAT (10X , 'THE MODEL CANNOT PREDICT THE EMISSIONS FOR THIS VEHCI'
1,'CLIr. MIX. TRY INCREASING AMAX AND DECREASING AMIiM IN SUB. hSUM'J
245 COVJT INJE
TOT( 1)-0.
TDT( 2)=0.
TOT (3) =0.
GO TG S9
1111 ST3!J
ENO
SUBROUTINE ESUM( VVT ,NT ,BAU , AHC t ACOf ANQX , DIST )
= ****** «*^**<: ^c*********** ****** *******^** *************************
: SUBROUTINE ESUM CALCULATES THE AMOUNT OF HC, CO, NOX EMITTED
I AND THb DISTANCE TRAVELED BY THE AUTO THAT HAS THE INSTANTANEOUS
C EMISSION RATE FUNCTION SPECIFIED BY THE ARRAY 'BAD1, AND A DRIVING
CYCLE SPECIFIED BY THE ARRAY 'VVT1.
C
C VVT ( I)=>VELOC ITY VS. TIME HI STD RY ( DR I V ING CYCLE) IN ONE SECOND
: INI ERVALS.VVT (I ) = VELOCITY (MPH) AT THE I'TH SECOND. REAL*4
C
C NT=> MAXIMUM NUMBER SECONDS IN DRIVING CYCLE*! SECOND
C
C BAL)( I, J) = >J«TH COEFFICIENT OF THIS AUTO'S INSTANTANEOUS EMMISSION
C RATE FUNCTION FOR THE I'TH KIND OF EM I TTANT , 1 = 1 =>HC,
C I=2=>CO, 1 = 3=>NOX.(REAL*8)
C
kx
C AhC=AMT(GMS) HC GIVEN OFF BY THIS AUTO IN GOING THRU DRIVING CYCLE
C »EAL*4
C ACO=AMT(GMS) CO GIVEN OFF 3Y THIS AUTO IN GOING THRU DRIVING CYCLE
C REAL*4
-------
vi-6
TABLE VI-;! (cont'd)
C AXj.;jX = AMT ( CMS ) NOX GIVEN OFF BY THIS AUTO IN GOING THRU DRIVE CYCLE
I REAL*^
C
: DI ST=UISTANCE(MILES)IISi SPECIFIED DRIVING CYCLEtREAL*4
C
L
IEYU331 LCMMENTS DELETED ****************#****************************#=
DIMENSION VVT(NT)
RLAL*8 BADO ,12),AMT(3),X(12),DIS,AM IN,AMAX,A 1,A2,HOA,SOA
AMAX=1.ODO
AM IN = -1 .200
A1=-1.0DO/AMIN
A2 = - l.OQO/AMAX
C
C CLEAR AMT ARRAY
C
Of! 1000 1=1,3
100U AMT( I ) = O.ODO
C
: INTEGRATE AUTO'S EMISSION RATE FUNCTION OVER DRIVING CYCLE
C
L)I S'=0.000
NTT = NT- 1
DO 3000 IT=l,NTT
KT=IT+1
X( 1J=1.0DO
X(2)='JBLE((VVT( ITi*VVT(KTI)/2.0>
X(3)=OdLE(VVT(KT)-VVT(IT))
X(4)=X(2)*X(3)
X{5)=X(2)**2
X(6)=X(3)**2
X(7 ) = (Xl2)**2)*X( 3)
X(B) = IX (3)**2)*X (2)
X(9)=(X( 2)**2)*IX(3)**2)
X(10 ) = X (1)
X ( i 1 ) =X ( 2 )
XI 12
IMX
IF (X
IF(X
IK X
= X(5)
3) ,GE.AMAX)HOA=O.OCO
3) .LE.AMIN)HOA=O.ODO
31 .GE.O. CDO.AND.X(3).LT.AMAX)HOA = tA2*X(3) J+i.OUO
3).LE.G.ODO.AND.X(3).GT.AMIN)HOA={A1*X{3))+1.000
D'J 2l^99 1C = 1,3
DO 2998 IE=1,12
S3A= 1.000-HOA
IF (I t.GT.9)SOA=HOA
AMT(IC)=AMT(IC)+(X(IE)*SOA*BAD{1C,IE))
2998 CUMT INUE
2999 CONTINUE
D IS=DIS+X(2 )
300C CUNT INUE
AHC=AMT(1)
ACU=AMT12)
ANOX = AMT (3)
DIS=DIS/3600.0DO
UIST=DIS
-------
VI-7
TABLE VI-1 (cont'd)
Sample Input - Card Type 1
506
Sample Input - Card Type 2
0.0
0.0
22.5
22.9
24.6
25.7
30.4
32.2
0.0
0.0
0.0
0.0
0.0
22.1
22.7
24.5
26.1
29.9
32.4
0.0
0.0
0.0
0.0
0.0
2i.5
22.6
24.7
26.7
29.5
32.2
0.0
0.0
0.0
0.0
0.0
20.9
21.3
24.8
27.5
29.8
31.7
0.0
0.0
0.0
0.0
0.0
20.4
19.0
24.7-
28.6
30.3
28.6
0.0
0.0
3.3
0.0
3.0
19.8
17.1
24.6
29.3
30.7
25.3
0.0
0.0
6.6
0.0
S.9
17.0
15.8
24.6
29.8
30.9
22.0
0.0
0.0
9.9
0.0
8.6
14.9
15.8
25.1
30.1
31.0
18.7
0.0
0.0
13.2
0.0
11.5
14.9
17.7
25.6
30.4
30.9
15.4
0.0
0.0
16.5
0.0
14.3
15.2
19.8
25.7
30.7
30.4
12.1
0.0
0.0
19.8
0.0
16.9
15.5
21.6
25.4
30.7
29.8
8.8
0.0
0.0
22.2
0.0
17.3
16.0
23.2
24.9
30.5
29.9
5.5
0.0
0.0
24.3
0.0
18.1
17.1
24.2
25.0
30.4
30.2
2.2
0.0
0.0
25.8
0.0
20.7
19.1
24.6
25.4
30.3
30.7
0.0
0.0
0.0
26.4
0.0
21.7
21.1
24.9
26.0
30.4
31.2
0.0
0.0
0.0
25.7
0.0
22.4
22.7
25.0
26.0
30.8
31.8
0.0
0.0
0.0
25.1
24.7 25.0 25.2 25.4 25.8 27.2 26.5 24.0 22.7 19.4 17.7 17.2 18.1 18.6 20.0 22.2
24.5 27.3 30.5 33.5 36.2 37.3 39.3 40.5 42.1 43.5 45.1 46.0 46.8 47.5 47.5 47.3
47.2 47.0 47.0 47.0 47.0 47.0 *f7.2 47.4 47.9 48.5 49.1 49.5 50.0 50.6 51.0 51.5
52.2 53.2 54.1 54.6 54.9 55.0 54.9 54.6 54.6 54.8 55.1 55.5 55.7 56.1 56.3 56.6
56.7 56.7 56.5 56.5 56.5 56.5 56.5 56.5 56,4 56.1 55.8 55.1 54.6 54.2 54.0 53.7
53.6 53.9 54.0 54.1 54.1 53.8 53.4 53.0 52.6 52.1 52.4 52.0 51.9 51.7 51.5 b,.6
51.8 52.1 52.5 53.0 53.5 54.0 54.9 55.4 55.6 56.0 56.0 55.8 55.2 54.5 53.6 52.5
51o5 51.5 51.5 51.1 50.1 50.0 50.1 50.0 49.6 49.5 49.5 49.5 49.1 48.6 48.1 47.2
46.1 45.0 43.8 42.6 41.5 40.3 38.5 37.0 35.2 33.8 32.5 31.5 30.6 30.5 30.0 29.0
27.5 24.8 21.5 20.1 19.1 18.5 17.0 15.5 12.5 10.8 8.0 4.7 1.4 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 4.3 7.6 10.9 14.2
17.3 20.0 22.5 23.7 25.2 26.6 28.1 30.0 30.8 31.6 32.1 32.8 33.6 34.5 34.6 34.9
34.8 34.5 34.7 35.5 36.0 36.0 36.0 36.0 36.0 36.0 36.1 36.4 36.5 36.4 36.0 35.1
34.1 33.5 31.4 29.0 25.7 23.0 20c3 17.5 14.5 12.0 8.7 5.4 2.1 0.0 0.0 0.0
0.0 0.0 0.0 2.6 5.9 9.2 12.5 15.8 19.1 ,22.4 25.0 25.6 27.5 29.0 30.0 30.1
30.0 29.7 29.3 28.8 28.0 25.0 21.7 18.4 15.1 11.8 8.5 5.2 1.9 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
3.3 6.6 9.9 13.2 16.5 19.8 23.1 26.4 27.8 29.1 31.5 33.0 33.6 34.8 35.1 35.6
36.1 36.6 36.1 36.2 36.0 35.7 36.6 36.0 35.0 35.5 35.4 35.2 35.2 35.2 35.2 35.2
35.2 35.0 35.1 35.2 35.5 35.2 35.0 35.0 35.0 34.8 34.6 34.5 33.5 32.0 30.1 28.0
25.5 22.5 19.8 16.5 13.2 10.3 7.2 4.0 1.0 0.0999.9
-------
Vl-8
TABLE VI-1 (cont'd)
Sample Input - Card Type 3
Oo90376674D=01=0
Oo82078507D=04=0
•Oo?2l98465D-04 0
Ool0208333D 01=0
Ool0485761D=02-0
>00272590450°03 0
=Oo35662605D~02 0
Oo46978058D=05 0
0034267888D=05 0
Oo74028528D=01=0
Oo57614160D-=-04=0
•Ool4491088D=04 0
Oo63558776D 00=0
0044947727D=03=0
•Oo67487073D=04 0
Oo50538071D=02 0
Oo20754213D~04-0
•Oo2398477lD=05 0
00272705530=01=0
Oo15032265U-04-0
= Oo34198U9D=05 0
Oo27933853D 00=0
Ool0696717D°03°0
043741313D=
o113899570=
o30577981D=
046084279D=
o!51704l30
o330713710
o58291855D=
o21313669D=
0297318770=
o306945350=
o73364414D=
o275512!40-=
024497029D=
047927091U=
o303423870
o168980550=
o32971637D=
o351626460=
o386486180-
077718214D=
o!87404010=
o46856115D=
o20270756D=
02 Oo467223910=
0 1 = 0 o 363453850=
01-=0o 224554280=
01 Ool2751923D=
00=Oo79925233D=
00=Oo2<*132161D=
03 Ool0214629D=
02 Oo31456202D=
02=00302068000=
02 Oo608728510=
02=0oll7030310=
01°Oo28560269D
01 Oo43832351D
01 Ool0912263D
00=0o273502530
03 Oo52965897D
03 Oo30740881D
02=Oo46493002D
03 Oo23088464D
•03=0o505432970
•01 Oo22501665D
•02 Oo43558462D
02 Ooll312567D
•02 0046404256D=03
-05 Oo134635760=02
>03 Ool6942791D°04
=01 Ool98069820=01
-04 Oo193953030=01
-02 Oo32059l27D°03
>02=Oo44023648D=04
>05°00189348860-03
=03 Oo22822312D=04
•02 Oo2H56588D=03
-05 Oo88867888D-03
=03 Ool4511582D=04
-01 Oo4964?502D=02
>04 Oo61504929D=02
•02 Ool34722900=03
•03 Oo37709623D°03
=05 Ool6569890D=03
=03 Oo324046330-04
=02 Oo44807488D°03
-05 Oo21336161D°03
=03 Oo27272747D=05
=01 Oo137243140=02
=04 Oo924999280°03
•Oo200947530=05
Oo96319220D=02=
Oo333501620=04=
•Oo81182460D=05
Oo47477793D=01=
Oo35848978D=04=
•0092615464D=05
Oo49624196D 00-
Oo21283906D=-03=
Oo37327878D=>04
Oo575173210=02
Oc276265250=-04-=
•Oo796249100°05
Oo48405216D=01-=
Oo36660281D=04-
-0093295635D=05
00499437080 00«
Oo22779095D=03=
Ool45l9295D=04
Oo600l8524D-=02
>Ool0257356D=04
Oo26l75337D~01<
Ool8898926D-=04-
•Oo32225540D°05
Oo39728843D 00=
Ool6235607D~03<
Oo22926725D
•Oo60640878D=
Oo280405270=
Oo322353480=
Oo195322050=
•Oo488744760=
Oo21555307D«
Oo146369290=
Oo683486840=
Oo262952HD
Oo 126139940=
Oo23853314D=
Oo4Q789420D=
Oo20866795D=
Oo58492631D=
Oo196845580=
•Ool74836120=
Ool2119517D=
Oo305303240
Oo52816454D=
0032004988D=
Oo49877ll6D=
•Oo882785280=
Oo192328360=
Ool2147180D=
Ool32658110=
•Oo450926230=
00=0o401949900=
03°0o 143642670-
02°0o236256240=
02°Oo445184l4D=
02 Oo40485512D<
02=Oo62457662D=
01 Oo615195060=
02 Ool05183480=
00=0o 181853340-
03=0o205743400=
02°Oo31980446D=
02=Oo51323107D=
02 Oo25244748D-
02°Oo39201595D«
01 O
01 0
00=O
03=O
02°O
02°O
03 O
02 O
01°O
01 O
02 O
o59544028D<
o 7447 13860-
o70231556D=
o49339078D<
ol0437640D-
o69092869D=
o29690382D<
ol6390772D<
oll020436D-
o58606945D-
o86448633D<
•02 Oo122425860=03
•03 Oo'622334530=03
•06 Oo48523421D~03
•03 Oo29931305D=04
>02 Oo439846980=04
•07 Oo592920140=03
=03 0072275960D=05
•01=Ool0722144D=02
•03 00979474030=03
•02 Oo83989837D=04
•02 Oo91007585D=03
•05 Oo46789764D=03
•03 Oo35522030D=04
•02 Oo130098630=03
=07 Oo633079l6D=03
-03 Oo80081449D=05
=01=0018335917D°02
•04 Ooll2413530=02
•02 Oo107839230=03
•02 Ool5512079D=02
•04 Oo62374660D°03
•03 Oo46568896D°04
•02 Oo62H6197D~05
•05 Oo26020350D=03
=03 Oo68630176D=05
•01=Ool9761118D=02
=04 Oo2314l751D°03
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
-------
Oo396888420<
Oo72752018D-=
Oo396040300-
•Ooll8777440*
Oo22623507D-
Oo163890040-
•Oo240623660-
Oo366755830
Oo182623980-
Oo54634248D-
Ool2421584D-
Oo45782098D<
>Ool3l08168D<
Oo43851l600-
00460755660-
>0013768204l>
Ool0577947D
Ool4051852D-
>Oo29l06335D-
>Ool3820912D-
•Ool07684210-
Oo55937995D<
Oo32588060D-
Oo29903562D-
•0070337689D-
Oo680528950
Oo97171775D<
•Oo 129584550=
Oo345391670-
Ool8377601D*
•0043006645D*
Oo51083437D=
Oo49148890D*
04 Qo2461678oO
02~0o883743660
04-0o395171470-02-0
04 Oo590685320=02-0
01~0079b79974L)~03 0
04-0o154239190-02 0
OS Ool04369380=01~0
00-0ol41066320=01 0
03 0°226749900=02 0
04 Oo225164220 00-0
01=00605391480=03=0
•04=0 0483711280-02-0
04 Oo577802040=02=0
01-0o210758810-02 0
04-00661746450-02=0
04 Ool80083280-01=0
01=0o675011040-01 0
02-0ol73423260 00 0
•03 00305203770 00 = 0
•01 Ool66833210=02-0
•04 Oo37110778D°02-0
05 Oo31480841D-02-0
01=0014703154D°02 0
04-00367510830°02 0
05 00145484560=01 0
00~Oo48927113D=01 0
03=0092381655D=01 0
03 Ool9974254D 00=0
02 Oo20004429D=03=0
04=0o120719800=02=0
05 Oo372785820=02-0
01=Oo2505l793D=02 0
04=00686123670=02=0
VI-9
TABLE VI-1 (cont'd)
00~Oo68528929D=02
•=04=0 o 29 1565590=02
o77227877D-=03
o206343800=02
o530629820=06
o83005685D-04
o68330423D~01<
o 136326840=03
o460958850°02
o30203352D°02
o 283046690=05
o707629630=-03
o 177454460=02
o 144274, 060-05
ol6620380D=03
o61774511D-01
ol2182580D°03
065813141D-02
o98179189D=03
ol90609010=05-
o30420262D-03
ol65149500-02
o99984040D=07
o40289463D=05
o90821840D~01
ol9081262D°03
o77636132D°02
o3l092781D-02
o7lll3076D°05
o 469963980-03
o72480284D=03
o32229688D=05
Ool0947186D=02
Oo68558261D°03
Oo477l63510°04
00712251500°04
Oo2154737lD-03
Oo51550624D-05
•Oo32935018D=02
Oo20214767D-04
Oo6978517lD=04
Oo74576435D=03
Oo43297542D-04
00346469460°03
0083700976D°03
Oo 143724290-04
Ooll206638D°01
Oo218095040°01
Oo36293649D-03
Oo214806090-03
•Oo348l48810°03
Oo245235590-04
Ool7853849D=03
Oo461699440=03
Oo93821962D-05
Oo41546847D-=02
Ool3352240D=01
Oo33750885D-03
Oo61662616D-03
Ool9937451D=03
Oo27883061D-04
Oo44586908D°03
Oo80598715D-03
>Ool3019530D-04
Ool08669030 01
Ool414930lD°02
=0030297070D-03
-Oo49950156D-03
Ool05773460=04
Ool0563998D=Q5
Oo393118470=01
Oo4l608873D=04
-Oo44909092D-05
Ool2208099D 01
Oo177533390=02
-Oo31137548D=03
=Oo5660590lO=02
Oo7586178lD=05
-Oo 107899730=06
Ool9020864D~01-
=0o7l4819980-0i
=Ool8237987D 00
Oo31745487D 00-
0059741257D=03
Ooll7093040=02
Oo36l931920-02=
=Ool9820680D=02
=Oo33728560D=02
Ool26595190=01=
=Oo89559456D=01
=Ool9418552D 00
Oo30541507D 00=
Oo84466415D=03=
Ool6886114D-02=
Oo34688833D-02<
Oo169416620-03 0
Oo55710509D=01 0
Oo 113444760=03 0
Oo97099418D°02 0
Oo787496000-03 0
Oo20614930D=05°0
Oo40599224D=03 0
Oo39116639D=02 0
Oo57404777D<=05 0
Ool5603205D°04 0
Oo95948922D=01 0
Oo30674629D°03 0
•Oo67971266D-=02 0
•Oo848994240=03 0
•Oo73452762D°05-0
•Oo37849597D=03 0
01H53131D~04
o!2137503D=01
o22737992D=01
o31332326D=03
0295577870=04
o83364700D-04
o31964374D=04
092958384D=04
0441164070=03
o84285708D=05
061589361D=02
o24519085D=01
o22582800D-03
o46072383D=03
o51523041D=04
o30487559D-04
51
52
53
54
55
b6
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
76
79
80
81
82
63
84
85
86
87
88
89
90
9i
92
93
96
97
98
99
Sample Input - Card Type
,48
,09
11
14
07
-------
VI-10
FIGURE VI-1
FLOW CHART, MAIN PROGRAM FOR THE GENERAL USER
READ
NSEC, NUMB, INC.
READ
DRIVING
SEQUENCE
YES
i
READ FRACTION
OF VEHICLES
IN EACH GROUP
CALCULATE EMISSIONS
IN GRAMS FOR
DESIRED VEHICLE MIX
NO
PRINTER PLOT
OF VELOCITY
VS. TIME
+
PRINTOUT OF
SPEED VS.
TIME SEQUENCE
READ
GROUP COEFFICIENTS
WRITE
RESULTS
-------
I )
VFLDCITY(HPH)
20 25
30
35
T
I
M
E
-
S
£
C
S
4
3 '
li: :
16 '
20
24 I
28 I
32 I
36 I
40 I
44 I
43 I
52 I
56 I
60 I
64 I
68 1
72 I
76 I
80 I
84 I
88 I
92 I
96 I
100 I
104 I
108 T
112 I
116 I
120 I
124 I
128 :
132 '
13b
140 '
144 :
8
Q
•n
H
O
d-
H
ro
I
H
-------
VI-12
FIGURE VI-2 (cont'd)
SPEED-TIME DRIVING SEQUENCE
(Partial Listing)
Tl "fc
0
4
8
12
16
20
24
28
32
36
40
'+'»
40
b
-------
IV-13
FIGURE VI-2 (cont'd)
BREAKDOWN OF VEHlCLcS
i,U.HJP 1=1^57-1907 DENVF-R.
GPiJUP 2 = 1957-1967 LOfc AL TI TUDE ( NON CAL I F 1966 ,_1967 ) ,
GROJP 3= 1966t 1967 CALIF
G^CUP 4_fl968 L9_w ALTITUDE, GROUP 5 = 1969 LOW ALTITUDE,
GROUP 6= 1970 LOW ALTI T"
GROUP 7=1971 LOW ALTITUDL, GROUP b=1968 DENVER, GROUP 9^1969 DtNVfcR
GRQ'JP i 0=1970 DENVER, GROUP 11=1S71 DENVER
GROUPs 1
GRGUP= 2
GROUP= 3
GROUP= 4
GROUPs 5
GRUUP= 6
GROUP= 7
GROUP= 3
GRUUP= 9
GROUP= 10
GRUUPs 11
EMISSIONS IN GRAMS FOR
HC=
17.
C0=
FRACTtOK= 0.0
FRACTIONS 0.43
FRACTION^ 0.09
FRACTION= 0.11
FRACTIONS 0.14
FRACTIONS 0.11
FRACTIGN= 0.07
FRACTIONS 0.0
FRACTION= 0.0
FRACTIONS 0.0
FRACTION'S 0.0
1
180.49 NOX=
VEHICLES
18.01 DISTANCE IN MILES= 3.59
-------
BIBLIOGRAPHIC DATA
SHEET
1. Report No.
3. Recipient's Accession No.
4. Title and Subtitle
Automobile Exhaust Emission Modal Analysis
5. Report Date
January, 197 ^
6.
7. Author(s)
P. Kunselman. H. T. Mr*Adams. C. J. Domke. M. E. Williams
8. Performing Organization Kept.
No.
9. Peiforming Organization Name and Address
CALSPAN Corporation
Buffalo, New York 1U221
10. Project/Task/Work Unit No.
11. Contract/Grant No.
EPA No. 68-01-OU35
12. Sponsoring Organization Name and Address
Environmental Protection Agency
Office of Air and Water Programs
Office of Mobile Source Air Pollution Control
(Vrtifi ration and Surveillance Division. Ann Arbor. Michigan
13. Type of Report & Period
Coveted
14.
15. Supplementary Notes sections 1-U of the report were prepared by CALSPAN Corporation under
Contract. Section 5 was prepared, by EPA personnel.
16. Abstracts
A mathematical model of an automobile's emission rate is described. This
model can be used to calculate the amounts of hydrocarbons, carbon monoxide,
and oxides of nitrogen emitted by individual vehicles or groups of vehicles which
are driven over arbitrary driving sequences. The model requires as input the amounts
of the three pollutants emitted by individual automobiles over short duration
driving sequences (modes) and therefore, the model is intended to be used to predict
emissions from vehicles being operated within the ranges of speed and acceleration
covered in the input emission data. The validity of the model has been investigated .
by predicting sections of the Federal Test Procedure and comparing predicted and
actual values.
17. Key Words and Document Analysis. 17o. descriptors
air pollution
motor vehicles
mathematical model
17b. identifiers/Open-Ended Terms
17e. COSATI Field/Group 13B
18. Availability Statement
Unlimited
19.. Security Class (This
Report)
UNCLASSIFIED
20. Security Class (This
Page
UNCLASSIFIED
21- No. of Pages
179
22. Price
FORM NTIS-39 (REV. 3-72)
USCOMM-OC I4*S2-P72
-------
INSTRUCTIONS FOR COMPLETING FORM NTIS-35 (10-70) (Bibliographic Data Sheet based on COSATI
Guidelines to Format Standards for Scientific and Technical Reports Prepared by or for ihe Federal Government,
PB-180 600).
1. Report Number. Each individually bound report shall carry b unique alphanumeric designation selected by the performing
organization or provided by the sponsoring organization. Use uppercase letters and Arabic numerals only. Examples
FASEB-NS-87 and FAA-RD-68-09. ,
2. Leave blank.
3. Recipient's Accession Number. . Reserved for use by each report recipient.
4. Title and Subtitle. Title should indicate clearly and briefly the subject coverage of the report, and be displayed promi-
nently. Set subtitle, if used, in smaller type or otherwise subordinate it to main title. When a report is prepared in more
than one volume, repeat the primary title, .'dd volume number and include subtitle for the specific volume.
5- Report Date, l-'ach report shall carry a date- indicating ai least month and year. Indicate the basis on which it was selected
(e.g., date of issue, date of approval, date of preparation.
6. Performing Organization Code. Leave blank.
7. Authors). Give name(s) in conventional order (e.g., John R. Doe, or J.Robert Doe). List author's affiliation if it differs
from the performing organization.
8- Performing Organization Report Number. Insert if performing organization wishes to assign (his number.
9. Performing Organization Nome and Address, dive name, street, city, state, and zip rode. List no more than two levels of
an organisational hierarchy. Display the name of the organization exactly as it should appear in Government indexes such
as USGRDR-I.
10. Project Toik Work Unit Number. I'se the protect, task and work unit numbers under which the report was prepared.
11. Contract Grant Number. Insert <. onfr.u t IT grant number under which report "was prepared.
12- Sponsoring Agency Nome and Address. ln< lu.je y.ip code.
13. Type of Report and Period Covered. Iiii.iu.ite interim, final, etc., and, if applicable, dates covered.
14. Sponsoring Agency Code. Leave blank. :>-,.-
15. Supplementary Notes. Knter information not included c Iscwherc but useful, such as: Prepared in cooperation with . . .
Translation of ... (-"resented at <. onfcri-nre ol . . . To he published in ... Supersedes . . . Supplements
lo. Abstract. Include a brief (JOO words or less) factual summary of the most significant information contained in the report.
If the report contains a significant bibliography or literature survey, mention it here.
17. Key Words and Document Analysis, (a). Descriptors. Select from the Thesaurus of Kngineering and Scientific Terms the
proper authorized terms that identify the major concept of the research and are sufficiently specific and precise to be used
as index entries for cataloging.
(b). Identifiers and Open-Ended Terms. Use identifiers for project names, code names, equipment designators, etc. Use
open-ended terms written in descriptor form for those subjects for which no descriptor exists.
(c). COSATI Field/Group. Field and Croup .assignments are to be,taken from the 1965 COSATI Subject Category List.
Since the majority of documents are multidisc iplinary in nature^ the primary Field/Group assignment(s) will be the specific
discipline, area of human endeavor, or type of physical object. The application(s) will be cross-referenced with secondary
Field/Group assignments that will follow the primary posting(s). c.
18. Distribution Statement. Denote rcleasability to the public or limitation for reasons other than security for example "Re-
lease unlimited". Cite any availability to the public, with address and price.
19 & 20. Security Classification. Do not submit classified reports to the National Technical
21. Number of Pages. Insert the total number of pages, including this one and unnumbered pages, but excluding distribution
list, if any. ',
22. Price. Insert the price set by the National Technical Information Service or the Government Printing Office, if known.
FORM NTIS-35 (REV. 3-72) USCOMM-OC I48S2-P72
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