EFFECT OF ROADWAY FRICTION}? ON VEHICLE OPERATING CHARACTERISTICS Thesis I0: 1110 Degree cf M. S. MICHIGAN STATE UNIVERSITY Edwin T. Kaneko “I960 LIBRAR Y 0-169 This is to certify that the thesis entitled Effect of Roadway Frictions on Vehicle Operating Characteristics presented by Edwin T. Kaneko has been accepted towards fulfillment of the requirements for M.S. degree in Civil Engineering ./7«7 ” I f// I /L, Y C’l/t/L 1,-1 ' Major professor / July 7, 1960 EFFECT OF ROADI-FAY FRICTIONS ON VEHICLE OPERATING CHARACTERISTICS BY Edwin T. Eaneko A THESIS Submitted to the College of Engineering Michigan State University of Agriculture and Applied Science In partial fulfillment of the requirements for the degree of I‘IASTER OF SCIENL‘E IN CIVIL ENGINEERING Department of Civil Engineering June 1960 TABLE OF CONTENTS Chapter , Page I IN'FRODUCTION O O O O O O O O O O O O O O O O O O 1 1. Purpose of Study . . . . . . . . . . . . . 1 2. Justification of Problem . . . . . . . . . l 3. Scope and Limitation of Study . . . . . . 2 4. Definition of Technical Words Used . . . . 3 II. REVIEW OF LITERATURE . . . . . . . . . . . . . . 5 1. Literature on Determination of Travel Time and Fuel Consumption . . . . . . 5 III 0 bTETIVIOD OF STUDY 0 O O O O O O O O C O O O O O O O 10 Design of Experiment . . . . . . . . . . . 10 Location of Study Site . . . . . . . . . . 12 Description of Instrumentation . . . . . . 13 Procedure of Field Work .. . . . .. . . 19 . Dates of Study . . . . . . . . . . . . . . 24 UIJ-‘KNNH 0 IV. lIiNJAXLYSIS OF DATA 0 o o o o o o o o o o o o o o o 25 1. Method of Analysis . . . . . . . . . . . . 25 2. Results of Analysis . . . . . . . . . . . 27 V. CONCLUSIONS AND RECOMMENDATIONS . . . . . . . . . 35 BI BLI CERXXPHY O O O C O O O O O O O O O O 0 C O O 48 .AEPEMDIX .A O O O O O O O O O O O O O O O O O O O 38 APPENDIX B . . . . . . . . . . . . . . . . . . . 42 Table II III IV 1A 13 28 LIST OF TABLES Description of Test Routes Keefer's Multiple Regression Equation . . Statistical Data for Multiple Regression Equation . . . . Correlation Between Travel Time and Frictional Characteristics Correlation Between Fuel Consumption and Fricational Characteristics Sample Data For Travel Time and Fuel Consumption . . Output Data from K2-135 Using Table 2A As Input . . . . Output Data from KZM Page 14 29 32 4O 45 46 Figure LIST OF FIGTRES Design of Experiment . . Speed and Delay Meter . Statistical Instrument . Speed and Delay Chart . Fifth Wheel . . . . . . Intervalometer Camera . Typical Location of Volume Recorders Page 11 16 16 18 2O 20 22 ARSTRACT Equations for predicting mean travel time and mean fuel con- sumption from certain roadway and traffic flow frictional character- istics are developed in this study. Statistical methods of multiple regression are used to develop these formulae from a large series of test runs made on urban multilane roadways. A total of 1,159 test runs were made with a specially equipped test vehicle to obtain average travel time and average fuel consump— tion data for each test run, along with volume, practical capacity, posted speed limit, and other physical and geometrical features. Mathmatical equations are developed for estimating mean travel time and mean fuel consumption for each direction of roadway. The formulae are in the form of multiple regression equations with mean travel time and mean fuel consumption as the dependent variable and roadway and traffic flow frictional characteristics as the inde— pendent variables. A total of ten roadway and traffic flow independent variables are originally considered, but only three variables are found to have a significant influence upon mean travel time and two upon mean fuel consumption. The multiple regression equations developed are: Y1 = 4.2479 - .0469}:3 + .6306}:4 + .1664X5 e Y2e = 5.1307 + .5734x4 + .1375xS The notations of the equations are to be interpreted as follows: Yle = Estimated mean travel time Y = Estimated mean fuel consumption 2e X3 = Posted speed limit in miles per hour X4 = Volume/capacity X5 = Number of signals per mile. The first equation accounts for 78% of the total variation in mean travel time, and the second equation accounts for 48% of the total variation in mean fuel consumption. CHAPTER I INTRODUCTION 1. PURPOSE The purpose of this study is threefold: (1) determine and evaluate the roadway frictions that resist the flow of vehicular traffic; (2) statistically illustrate that vehicle operating char- acteristics are related to the roadway friction; (3) develop math- matical equations which may be used to compute the vehicle operating characteristics for a given roadway. The equation is based on the theory of least square deviation and is in the form of multiple regression with operating characteristics as the criterion variable and frictional characteristics as the independent variables. 2. JUSTIFICATION OF PROBLEM The concept that the adequacy of a facility may be determined by evaluating certain vehicle operating characteristics has found its use in numerous traffic engineering studies. As a result, the measurement of vehicle operating characteristics on our streets and highways is becoming increasingly important. The primary application is based on the premise that the adequacy of a street or highway is reflected by its ability to serve the user safely, conveniently, and economically. It is believed that certain vehicle operating charac- teristics and accident records may be used for the quantitative eval- uation or measure of the three yardsticks: safety, economy, and con- venience of operating a vehicle on a traffic moving facility. At the present, the quantitative evaluation of the three yardsticks is a rather laborious and expensive task. It involves careful investiga- tion of accident records and numerous measurements of vehicle operating characteristics requiring considerable amount of special instrumen- tation. Consequently, an easier and more economical method of evalu- ating the three yardstick is desirable. The development of statistical equations which is done in this study is an attempt to simplify the determination of vehicle operating characteristics. Several studie31'2'3have indicated that certain motor vehicle operating characteristics are related to some physical, geometrical, and operational features of a roadway. If this rela- tionship is strong enough it must be possible to develop statistical equations with a reasonable degree of reliability on the basis of known physical features which are comparatively easy to measure. Such equations will be very useful for economic studies where travel time and fuel economy are factors considered. A further application would be traffic operational studies in which the effects of changes in road- way frictional characteristics on vehicle operating characteristics could be estimated. 3. SCOPE AND LIMITATION OF STUDY The study is confined to two selected vehicle operating charac- teristics: (1) average travel time and (2) average fuel consumption rate. The test sections under study are on multilane roadways with four or more lanes located in an urban area. The test sections are level, tangent, uniform throughout a three-quarter to one mile length in regard to basic geometries, traffic volume, traffic and parking con- trols, and adjacent land use. Furthermore, the vehicle under study is a passenger-car Operated during the daylight hours under favorable weather conditions. 4. DEFINITIONS OF TERMS USED Traffic Flow Frictions. Resistances against the smooth flow of vehicular traffic are primarily due to the four basic types of traffic frictions.“5 The term traffic friction as used in this study refers to the following classifications and their respective definitions: 1. Intersectional friction, caused by right angle movements at intersections. 2. Marginal friction,, caused by interferences along the outer edges of the moving traffic stream. 3. Medial friction, caused by conflicts in the middle of the road between opposing streams of traffic. 4. Internal stream friction, caused by vehicles moving in the same directions. Travel Time. Total time required to traverse a given distance. Fuel Consumption. Total amount of fuel required to traverse a given distance. Practical Capacity. The maximum number of vehicles that can pass a given point on a lane or roadway, during one hour, without the traffic denstty being so great as to cause unreasonable delay, hazard, or restriction to the drivers' freedom to maneuver under the prevailing roadway and traffic conditions. Intersectional Practical Capacity. Maximum volume that can enter the intersection from that approach, during one hour, with most of the drivers being able to clear the intersection without waiting for more than one complete signal cycle. Statistic. A value computed entirely from the sample data. Parameter. Any measurable characteristic of the universe or population. Friction point. A friction point is defined as: (1) any inter— section at grade. If the opposing approaches of an intersection are offset by more than one-hundred feet, two friction points are assessed.. (2) Any railroad crossing at grade. (3) Special speed zones within the section such as for a hospital or school. Equivalent volume. Total volume of traffic in terms of passenger vehicle assuming that each commerical vehicle is the equivalent of two passenger cars. QMFERII REVIEW OF THE LITERATURE Knowledge of the fundamental vehicle operating characteristics of motor vehicles is an essential feature in the development of stan- dards and specifications for highway design, traffic operations, and for the design of the vehicle itself in order to provide for the safe, convenient, and economical transportation of persons and goods. To meet this end a continued effort has been expended by numerous researchers with the assistance of industry and government. I. LITERATURE ON DETERMINATION OF TRAVEL TIME AND FUEL COI‘BUMPTION In the last ten years or so much information on travel time and fuel consumption has been determined for various types of roadways. This was made possible primarily by the develOpment of the General Motors Statistical Instrument. The initial study utilizing this equip- ment was conducted in 1950 and the results were reported by Messrs. Carmichael and Haley.6 Subsequent studies utilizing this instrument 1'2'3’7’8’9 A later travel time determination device have been undertaken. is the speed and delay recorder which was developed by the Automatic Signal Division of Eastern Industries for the Bureau of Highway Traffic at Yale University.10 Besides these mechanical devices, the License Plate Matching method for determining travel time on a given route had been developed. This method is neither simple nor economical but a . reliable standard,11 well suited to test the validity of other methods. A more recent method of computing travel time on a given section of roadway by sampling a relative small portion of the total traffic flow was developed in England by Wardrop and Charlesworth.12 This method is proposed for measuring traffic speeds and volumes by observations made from a moving vehicle. The observers in a test car driven in the traffic stream record their travel times, count opposing traffic, and keep a count of overtaking and overtaken vehicles. From these obser- vations, the mean travel time and number of vehicles passing along a street can be obtained. The equation is in the form: E = tw '.X q I mean travel time tw = travel time of observer when traveling with the stream y = number of vehicles that overtakes the observer minus the number that he overtakes in the section t = travel time of the observer when traveling against traffic stream. x = number of vehicles met in traffic stream A study to test the feasibility of the Wardrop-Charlesworth es- timated mean travel time equation was undertaken by Mortimer.13 Ten urban streets, approximately a half mile in length, containing a signi- ficant difference in traffic volumes and land use were selected as the test section. A total of 90 vehicles runs per section between the hours of 10:00 a.m. and 3:00 p.m. over a period of five days were made. The five hour period was selected on the hypothesis that traffic flow on urban streets during these hours is uniform. The average travel time of traffic as determined by the Matching License Plate method on the basis of a 20 per cent sample was used as control. The study showed that the average error of estimate was -2.9 miles per hour with stan- dard deviation equal to 1.8 miles per hour. It was concluded that on high volume sections or on section where turning-off and stopping are minimized, the Wardrop-Charlesworth Equation should give' an unbiased estimate of travel time. Keefer14 developed a series of equations to determine average speed for four types of roadway. The development of these equations is based on the statistical method of multiple regression where four- teen independent variables were correlated with the dependent variable, average speed, and thosesignificantly correlated used for the develop- ment of the multiple regression equations. The sample data for travel time and volume were determined by the moving vehicle. The limited application for Keefer's equation is pointed out. In some cases, the signs of the regression coefficient are contrary to logical expecta— tions, for example, increasing friction points would 23: be expected to correspond with increasing speed as illustrated by equation three and four (refer to Table II). In other cases the coefficient of determina- tion, R2, and the standard error of estimate, 33’ (Refer Table III) indicates that the combination of independent variables selected for the equation did not explain a significant amount of the variability in speed. This is illustrated by equations (2) and (3) which has a value of .24 and .47 respectively for the coefficient of determination (R2). TABLE II KEEPER'S MULTIPLE REGRESSION EQUATION Type of Highway Multiple Regression Equation Expressway Rural Urban with parking (1) (2) (3) Urban without parking (4) 14 14 " + 2.72 - 14.35 + .34 x1 + .75 x5 - 1.69 x -5.64 + 1.03 V + .0008 X [\1 10 60041 ~ .27 X1 + .21 X4 - .67 X5 -.004 X10 —.006 7 X10 - -23.14 + .60 X1 ~ .02 X2 - .10 X3 X5 + .32 X - 1085 X7 - .003 X 6 13 *The notations of these equations >< I! Posted speed limit are to be interpreted as follows: X = percent commercial vehicles X = One-half total surface width X4 = Divider width X5 = Fsiction points per half mile X6 = Average percent green X7 = Signals/mile >< ll 8 Volume/10' moving lane X = Volume/10' moving lane/Hour of green X = Equivalent Volume/10' moving lane/Hour of green >4 ll X13= Total volume 14= Average speed Equivalent volume TABLE III STATISTICAL DATA FOR MULTIPLE REGRESSION EQUATION Equation R R2 SE No. of Runs No. of Routes (l)* .876 .7665 14.171 MPH 216 5 (2) .4884 .2386 :15.8428 MPH 232 10 (3) .685 .4684 14.0601 MPH 868 37 (4) .921 .8489 1 2.8995 MPH 119 7 *refer to Keefer's multiple regression equation in Table II. No publication was found which discussed the estimate of fuel consumption on the basis of roadway and traffic frictional characteris- tics. CHAPTER III METHOD OF STUDY 1. DESIGN OF FIELD EXPERIMENT The purpose of the field experiment is to obtain sample vehicle operating characteristics by the use of a specially instrumented research vehicle on selected test sections of roadways in urban areas. The ultimate aim in the selecting of test routes is to obtain streets that are homogeneous physically and geometrically throughout the test length. Furthermore, it is desired to select a number of test routes, each varying in the amount of friction. Using the selected routes as test streets, a research vehicle is used to obtain vehicle Operating characteristics while driving with normal traffic. Due to the various possible combinations of traffic flow friction that exist in varying degrees it is necessary to arbitrarily select various combinations and degrees of traffic friction. As a result a diagram depicting the various possible combinations of traffic flow friction was developed and an attempt made in the field to select test routes to satisfy the combinations. Figure 1 illustrates the design of the field experiment. The amount of marginal friction is divided into three degrees; none, moderate, and heavy. Test routes with control of access are classified as having no marginal friction; streets with residential and commerical drives, and cross streets as 11 mmDQE m.._>>3 505.25.— «I: 3938 no? o« .92 3.2.35 ,3 5158. use: I: 9:53 come a“ done .. 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Eon «-3 39.58 Jo no? «« 63 noon.» 3 cocoon .33 78 ha 0 AW: on on an - so ago.— uoouum ..< so a , Eon BE 50 noun—136mg Hg 15 maintained. This consisted of oil change, greasing and checking of the battery, water, and tires. An initial motor tune up was done prior to the beginning of field testing, and no further tuneup was done. It is assumed that the overall performance of the test vehicle during the test period did not appreciably change, and that the operating charac- teristics of the selected test vehicle represent an average performance. Three principal instruments are used in this study to obtain the desired vehicle operating characteristics of the test vehicle while driving through the selected routes. The basic factors measured and recorded are; time, distance, number of brake applicatiorsarxd units of fuel consumed. The first instrument utilized is the modified speed and delay meter.7 This instrument is installed on the right front floor of the research vehicle (Figure 2) in a position to be of access to the driver or another operator. Three connections are required between the instrument and test car. These are as follows: 1. A flexible cable connected to the speedometer gear box, 2. A power cable connected to the d—volt battery system of the test car, 3. A connection to the foot-brake rear light switch,and 4. A connection is made to a fuel metering device, statistical instrument, which will be described later. The modified Speed and delay meter consists essentially of a constant. speed graphical chart and seven recording pens (Figure 4). The speed of the chart was set at three (3) inches per minute after numerous trial studies to determine the most suitable rate. The seven recording pens are labeled from.A.to F with the exception of the speed profile pen, and are connected either mechanically or electrically to their respective SPFEF AND DELAY METER FIGURE 2 ._ ._ .«s. I “thaw-«o «w --..o STATISTICAL I“3TRUKBNT h FIGURE 3 ,- wwemwwwwm- ,- » .4. I/ 17 sources. Pen "A" designating time in six second increments is one of the two time recording pens. Pen "B" records time in one minute increments. By the use of both pens, it is possible to determine time to the nearest second. Pen "C" is a distance marker which records distance in increments of either 200 or 400 feet. The next pen, not labeled, is the speed profile pen which plots a continuous instantaneos speed profile of the test vehicle. Since the horizontal scale of the chart represents time the slope of this speed profile indicates acceler- ation or deceleration. Further, maximum and minimum speeds are indica- ted. Pen "D" is a code pen which may be used for numerous purposes. In this study the pen was used to code the starting and terminating points of a selected test route. This is done by actuating a button. Pen "E" which is connected to the rear foot-brake light system marks the number, location on a route, and duration of each brake application. Pen "F" records each unit of fuel consumed. The unit used in this study is 0.00132 gallons per marker. Each test run on a selected route is represented by a speed and delay chart approximately six inches in length. The second instrument used in this study is the General Motors Statistical Instrument.6 (Figure 3) Although several operating char- acteristics of the test vehicle were measured, only the fuel recording portion is utilized for this study. This instrument was rigidly installed on the rear floor of the test vehicle and connected to three sources: 1. A cable drive to the speedometer gear box, 2. A connec- tion to the test car fuel system, and 3. A power cable connection to the battery system. The fuel measuring portion of this instrument con- mmmxmdéz MHDZE mZO \lmawxa<2 OZOUmm x_m m H A P MP. W M M / ‘ ,/Lr M ;.H. -II T 4 / .y a. .. : 1 v. O 0 8-0m 0—0 om-o¢Q_wno¢nom N_Q ownom MJ_\ 0N6. W_ 9-0 w on . 3:65 ommam v _ M . 8 w _ W 1963.60 N_ K‘ .os+o<.+caou 30 - - - y . .. o h -- - , , _ Q0 modem .52 b: M1 3on .32 uw d \ 25... 3.0.5 -+ 00 : y \ I V, dQloxotm .de MIA N oEFvoaaospm \“Auhfi \ 25... 3+3 : l om . -. - - oo. \ 53035 W _\ .02 Si N d «u _ Q cozoom +3... 0 y : KKQM.\\UQ VCO\U\\%\ \OQEQ cmu3+ofi hr\0 \KKUXxV +OOL+m ON. \ om. w \ \ MOOU 4652,42 i y i - 2“ u e PPR; :L._r meter tr. m a: ,1 A ; mZOJq (}I Analyzation of the films for detailed route characteristics was done with the aid of a Perceptoscope. This instrument is essentially a time and motion projector 24 suitable for this type of work. It may be operated at several speeds, ranging from one frame per second to twenty-four frames per second (ordinary moving picture speed). Additional features are the single frame advance, reverse, and hold at any frame. The practical capacity as defined by the Highway Capacity Manual17 is determined for each test route direction. The field work consists of a physical route inventory and recording of traffic opera— tional restrictive characteristics that are required for capacity determination. Intersectional practical capacity for a test route was determined at the intersection where the combined effect of those factors which tend to lower capacity is greatest. 5. DATES 0F TEST SECTION STUDY The data for this study is a part of a project entitled "Quality of Traffic Flow" that was carried out by the Highway Traffic Safety Center, Michigan State University, in cooperation with the Michigan State Highway Department and the U.S. Bureau of Public Roads. The field work was undertaken during the Summer months, June to . September, of 1957 by a research team of which the writer was one of the members. Table I is a summary of the dates of test route study. CHA: ER IV (NKLYEIS CF DATA 1. ‘MIITEIU’D CF AMLYSIS The vehicle operating characteristics for a given roadway are not exactly the same for all vehicles. Automobiles and more so the~drivers do not function exactly alike but vary, depending upon a large number of factors. As a result, the operating characteristics when determined for a given route are not exact but are in a range of a statistical nature which must he correctly interpreted to be meaningful. In the case of this study which is a relatively large collection of field sample data it is necessary to bring out the essential relations from a mass of data. The use of statistical methods is employed in this study to correlate and analyze the selected vehicle operating characteristics and the route frictional characteristics on various types of streets and highways. The method of treatment of the multi-variate data is based on the statistical method of multiple regression.29 The primary objective is to develop an equation where one variable, the criterion or dependent variable, can be computed from known values of other selected variables called the independent or predictor variables. The general equation is in the form: A = Y - b1 X1 - b2 X2 ~ b3 X7 - b4 X4 - b5 X5 26 whoro Y is tho criterion vsrisblo and tho X's sro tho indopondont vsri- sblos. Determination of the "b” vsluos, roforrod to ss psrtisl rogrossion coefficients is bosod on tho thoory of losst squsro donations"0 Tho osoontisl fostuno of tho thoory is thst tho on of tho squsro's of tho dovistion botwoon tho sctusl critorion vorisblo. Y, and tho vsluo conputod by tho oqustion is minim. Thus it is roquirod to nininiso th orrors of ostinstion snd this losds by tho Isthod of losst squsros to "p” sinultsnoous oqustions whoro ”p” oqusls tho nunbor of indopondont vsrisblos solootod. For thisstudypfivo indopondont vsrisblos sro soloctod sud tho fivo silultsnoous linosr oqnstions sro givon bolow: b1 g :12 9 b2 gxlxz o b3gxl :3 o b‘gxl x‘ 4» b5 1x1 :5 ngl y b1 (:2 x1 4 b2 gxzz 4 b3 £32 x3 + b‘gxz x4 + b5fi‘2 x, Otxz y b1 £13 :1 4» b2 gr, :2 4- b3 gxsz + bags:3 x‘ o 1’55}; :5 Its, y b1 gar“ x1 + ”2‘34 :2 + b3 £12 :3 o b4gx‘2 4 b5 11‘ :5 Ifix‘ y b1 3:, :1 o h2g1:5 x2 + bme5 :3 + b‘ t}, :4 + b52232 '8’ y Tho indopondont vsrisblos sro soloctod on tho basis of linosr cornistion analysis.” Gonorslly sposking, tho rolisbility of tho um ultiplo rogrossion oqustion will dopond upon tho soloction of tho indo- pondout vsrisblos thst sro significantly corrolstod with tho dopondont vsrioblo snd losst corrolstod with othor indopondont vsrisblos. Thoro- foro, tho linosr corrolstion botwoon tho soloctod vsrisbloo snd sll poosiblo indopondont vsrisblos sro dotsrlinod. 'l‘ho finsl nultiplo rogrossion oqustion includos only thoso thst sro significantly corrolstod. Sovorsl Isthods for tho solution of tho fivo sinultsnoous limsr oqustions sro invostigstod. Linosr oqustions with two or throo unknowns, con bo solvod by tho diroct spplicstion of olonontsry Iothods involving 27 successive elimination of the unknowns without any difficulty. As the number of unknowns increases, the process becomes extremely laborious. To counteract this, several tabular methods for solving first degree equations are available. One of the most versatile and commonly used is the Modified Doolittle Method2O whereby the solution is derived through matrix algebra. This method continues to require a series of time consuming systematic computations which are generally done with the aid of a desk calculator. To minimize computing time, the simultaneous linear equations for this study are solved with the aid of MISTIC,21 a high speed digital computer which is available at the Computer Laboratory of Michigan State University. The following prepared programs are used with their respective parameters: K2 - 135, M3 - M, K2 - M, and M—13. The program descriptions and a schematic diagram of the data computing process used for this study is included in the appendix. The effectiveness of thecnuation developed is determined by the method of partioning the total sums of squares22 and the test of sig- nificance, "F", for the multiple correlation coefficient at the 95% level of significance. The significance test, "t",22 for the partial regression coefficients, "b", is also made. 2. RESULTS OF ANALYSIS A total of 1,179 test runs were made in both directions on the twenty-five test sections. Each direction of travel is treated as a sample totaling therefore fifty samples with an average of twenty-three test runs per sample. Two vehicle operating characteristics "average i‘ fl“._fl_ travel time: and "average fuel consumption", are determined for each test run. These test runs are made under conditions of non-peak and peak hour volumes. The average of the total test runs for a test route direction is treated as a smple operating characteristic. With the exception of volume-capacity ratio the frictional characteristics are assumed constant for a given test route direction. Isa...” _ J“ ,lgf’ The volume-capacity ratio is determined for each test run and the average of the total runs per test route direction is used as the sample statistic. The sample vehicle operating characteristics, average travel time, "Y1", and average fuel consumption, "Y2", are treated as the dependent variables. The roadway and traffic flow frictional charac- teristics are the independent variables. They are: percent commercial frontage (X1), percent parking (X2), posted speed limit (X3), volume- capacity ratio (X4), and signalized intersections per mile (X5). The equation relating the independent variable, "Y", to the independent variables, "X's", is developed by the statistical method of multiple regression.22 Detailed procedures for this method are given in Appendix B. Average Travel Time Average travel time is the average time that is required by a given vehicle to traverse a unit length. It is also the reciprocal of speed. The linear correlation coefficient is computed between average travel time and each of the five roadway and traffic frictional charac- teristics. The results of these computations are shown in Table IV. TABLE IV CORRELATION BE 'IWEEN TRAVEL TIME AND FRICTIONAL CHARACTERISTICS x1 x2 x3 x4 x5 Y1 X1 1.0 iii? x2 0.78 1.0 ' ~a x3 -.34 . -.26 1.0 x4 .63 0.60 -.30 1.0 ; x5 .65 .63 -.63 .71 1.0 «J Y1 .54 .49 -.72 .67 .82' 1.0 In interpreting this table, a positive correlation indicates that travel time increases with increase in friction, whereas a negative correlation indicates that travel time increases with a decrease in friction. Per- fect correlation between the factors would be indicated by a value of one and no correlation by a value of zero. Travel time is Positively correlated with four of the independent variables. The exception is posted speed limit, X for which the 3. correlation is negative. The highest linear correlation is between travel time and number of signals per mile (+.82) and the lowest is between travel time and percent parking (+.49). From the zero order or linear correlation matrix given in Table IV, the multiple regression equation and multiple correlation coefficient is computed by solving five simultaneous equations with five unknowns. The multiple regression equation developed for travel time is: (1) YIe = 4.19 - .0018X1 - .00056x - .0464x + .6537x + .1763x 2 3 4 5 Ry 12345 = .8839 R2 = .7814 *The notations of this equation are to be interpreted as follows: Yle = Estimated mean travel time in hundreths of hours per mile X1 = Percent commercial frontage- X2 = Percent parking X3 = Posted speed limit in miles per hour X4 = Volume-capacity ratio X5 = Signals per mile The partial regression coefficients, (b-values) indicate the respective weight given to the independent variables in the regression equation. It is noted that the partial regression coefficients for X1 and X2 are relatively small and it may be that in the population they are zero. To test this hypothesis the "t" test is made on all partial regression coefficients. The multiple correlation coefficient, R, indicates the correlation between the value computed by the regression equation and the actual value, while R2 indicates the effectiveness of the regression equation or the proportion of variation which is attribu- ted to the five selected independent variables. Significance test is made for the "R" value and it is found to be significantly different from zero. It is found that "b1", and "b2" are not significant and are therefore omitted. A second equation for travel time, "Yle"’ is set up using the remaining three independent variables. The equation is: (2) Yle = 4.2479 - .0469X3 + .6306}:4 + .1664X5 R = .8833 R2 = .7803 Standard Error = .0569 31 The ”t" test for significance of the pertisl regression co- efficients,"b'e". indicetes thet b3, b‘, b ere significently differ- 5 ent In. sero, end "R” is found to be highly significent. It is noted thet tb effectiveness, R2. of the second regression equetioe hes slightly decreesed with the "11" end "12" independent veriebles removed firm the equetion. The R2 velue tor theitirst equetion besed on five independent verieblee is .7814 which indicetes thet 78.14 per cent of the verietion in eeen trevel tine is ettributed to the five selected independent veriehles. The respective weights of the eccounteble verietion is indiceted by the ”b” velues. The R2 velue for the second equetion besed on the three significent independent veriebles is .7803. Th snell reduction of only .0011 indicetes that the two independent veriebles b1 end b2 do not contribute significently to the regression equetion. Ilininetion of the first two independent veriebles results in en incresse of the b3 helm end e decreese for b4 end b5, in equetion (2). no equetion indicetes thet for eeoh unit incresse of posted speed linit (x3) neen trevel tine decreeeed by .05 units, ‘ while unit incresse of volue-cepecity ratio incresses neen trevel tine by .63 end the unit incresse of signels/nile incresses neen trevel tine by .lzunits. The stenderd error (88), for equetion (2) is found to be .0569, i.e. the probebility is .95 thet the populetion of trevel the, given everege velues of 13, lg, 15. is between 21. - 28.! end 21. 4- 2S.E. Aversg: P_u_e_l_ ConsEption Averege fuel consueption is the everege mount, of. gesoline con- sued' by e given vehicle in treversing e nile of roedwey. The units are hundreths of gallon per mile of travel. The average fuel consumption per test direction is correlated with the selected roadway and traffic flow characteristics. This is illustrated in Table V. Interpretations of this table is similar to Table IV. TABLE V CORRE ATION RETWEEN FUEL CONSUMPTION AND FRICTIONAL CHARACTERISTICS x x x xZ x Y 1 2 3 : 5 2 XI 1.0 x2 .78 1.0 x3 -.34 -.26 1.0 x4 .63 .60 —.30 1.0 x5 .65 .63 -.63 .71 1.0 Y2 .40 .38 -.22 .<3 .64 1.0 Fuel consumption is positively correlated with four of the five independent variables, while the remaining variable, posted speed limit, is negatively correlated. It is noted that in all cases, the correlation between fuel consumption and the independent variables are less than the correlations between travel time and the independent variables. From the zero order correlation matrix in Table V, the multiple regression equation and the multiple correlation coefficient is computed for fuel consumption. The regression equation for fuel consumption is: = 5.5169 — .000831 - .00101. + .02041. + 4850\5 + 4387K II. q ;—.12§A5 .7179 R .519- a *The notations for the equation are to be interpreted as follows; A ., ll 12‘ estimated average fuel consumption in hundreths of gallons of gasoline per mile — percent cremorcial frontage x2 : :qrcent parking e o , O ‘ m X; : posted speed ilHlt in miles per hour % 1 .. ° ! ‘ ‘ X, = voiuie—capaCitj ratio X5 = signals per mile Pf, It is noted that the partial regression Coefficients "b's" for £1, X2, and x3 are relatively small and the actual population coefficients may be zero. The 't" test is made to test the hypothesis that population partial regreSSion coefficients are zero and therefore negfligible at the 95% level of significance. The results indicate that X1, x; and x3 do not significantly contribute to the equation. The multiple Correlation, 2, is found to be .7179 and the effective- ness of the equation, (22) is .5155. This indicates that 51.55 percent of the variation in mean fuel consumption is attributable to the five independent variables while the remaining 48.45 percent is due to factors not considered. This is Considerably lower t Cn the basis of the test of signifiCanee for 91, h“, and H., .L 4 the first three independent variahles are removed and new multiple regression equation is computed using two independent variables, a, and Pig. The equation is; R = .6913 R2 = .4780 The notation of this equation is to be interpreted as follows: Y e = Estimated fuel consumption expressed in hundreths of a gallon a mile A4 = Volume capacity ratio X5 = Number of signals per mile It is noted that with two independent variables, the partial regression coefficient for X4 has increased and the coeffiCient for X5 has decreased. The proportion of the variability ettributed to the independent variables has also decrezsei from .5155 to .4780. The standard error for equation (4) is found to be .0634. CHEPTIZL’. V CFIT‘ULUQlONS AND RECOFWE ‘ATIUNS Conclusions. 1. It is found in this tudv that mean travel time and - m.en fuel consumption are significantly related to some physical, geometrical, and traffic flow frictional characteristics. The rela- tionships can be determined by multiple regression equations. 2. Seventy-eight percent of the variability in mean travel time is controlled by three variables, namely: posted speed limit (X3), ratio of volume/capacity (X4) and number of signals per mile (X5). The remaining twenty-two percent of the variability is due to other factors. 3. The formul'2 for predicting mean travel time is: Y = 4.25 - .0469." + .6306Xé + .1664? 3 5 The notations are to be interpreted as: Y1 = Estimated mean travel time in .Ol hours/mile J = Posted speed limit in N.P.H. K4 = Ratio of volume/capacity Xr = rumber of sionals er mile ) t) The suggested range of applications for the above formula is 25 MPH < x ( 40 Inn 3 .00 ( X5<5.50 36 Within the above range, the maximum standard error is i .13 or i 7.3 percent at the 95 percent level of confidence. 4. Forty-eight percent of the variability in mean fuel consump- tion is controlled by two variables, namely: ratio of volume/capacity (K4), and number of signals per mile (X5). The remaining proportion is due to other factors. F7“? 5 :i 5. The formula for predicting mean fuel consumption is: 1 . i‘q 2 " Z ‘ l'xr Y2e 5.1507 + .57r4x4 + .1375“.5 The notations are to be interpreted as: _ Y2e = Estimated mean fuel consumption in .01 Gallons/mile g‘j 5) XA = Ratio of volume/capacity x3 :- I'm-bar of signals par .11. The suggested range of applications for the above formula HI U} u .50 < :24 < 1.25 .00 < x5 < 3.50 Within the above range, the mayimum standard error is 1 .19 which would work out to te : 3.0 percent at the 95 percent level of significance. Recommendations. Continued study of the method of predicting travel time and fuel consumption is urged. The technique of multiple regression equations is well suited for this approach and with the aid of MISTIC, up to 38 independent variables may be studied, for which prepared programs are available. The effectiveness (R2) of the regression equations may be improved by a better sampling method. Instead of using samples averaged per direction as the unit data, samples averaged per hour or per testing period may be a more suitable unit. This will be advantageous for predictors such as percent parking, and ratio of volume/capacity. A further improvement may be forthcoming if a weighted capacity is used for a test route instead of selecting the most restrictive point for the capa- city determination. c‘il .a i I“ my. ‘ F APPENDICES APPENDIX A - SOURCE OF RAW DATA APPENDIX B - MULTIPLE CORRELATION TECHNIQUE APPENDIX A SOURCE OF RAW DATA APPENDIX A Source of Raw Data The basic field data for this study is a part of a project entitled, "Quality of Traffic Flow" which was undertaken by the Highway Traffic Safety Center, Michigan State University, in coopera- tion with the United States Bureau of Public Roads, and the Michigan State Highway Department. The field data was collected by a research team of which the writer was a member. The complete data is filed with the Highway Traffic Safety Center. Tables IA is the basic data used for this study. 39 _ 1“— my TABLE 1A SAMPLE DATA FOR TRAVEL TIME AND FUEL COBBUMPTION 40 X1 12 x3 x4 X5 Y1 Y2 +000 +000 +55 +071 +00 +0216 +0543 +000 +000 +55 +056 +00 +0208 +0625 +000 +000 +55 +064 +00 +0230 +0558 +000 +000 +55 +071 +00 +0212 +0595 +000 +000 +35 +054 +00 +0272 +0487 +000 +010 +35 +043 +00 +0271 +0483 +000 +000 +40 +056 +00 +0268 +0531 +000 +010 +40 +051 +00 +0260 +0512 +000 +010 +35 +024 +00 +0271 +0505 +000 +010 +35 +020 +00 +0274 +0520 +000 +000 +35 +041 +00 +0267 +0458 +000 +000 +35 +047 +00 +0265 +0462 +000 +000 +35 +120 +10 +0362 +0584 +025 +025 +35 +120 +10 +0334 +0546 +000 +010 +35 +042 +12 +0308 +0505 +000 +010 +35 +062 +12 +0319 +0529 +030 +050 +35 +109 +18 +0326 +0584 +100 +075 +35 +126 +18 +0343 +0561 +075 +100 +35 +080 +10 +0311 +0507 +100 +100 +35 +074 +10 +0318 +0500 +000 +000 +35 +126 +18 +0340 +0584 +000 +000 +35 +143 +18 +0326 +0617 +000 +000 +25 +078 +42 +0390 +0617 +060 +025 +25 +097 +42 +0434 +0564 +100 +100 +35 +126 +45 +0458 +0636 +100 +100 +35 +134 +45 +0434 +0689 +100 +100 +30 +137 +39 +0421 +0628 +100 +100 +30 +133 +39 +0446 +0613 +000 +000 +35 +059 +00 +0268 +0478 +025 +000 +35 +054 +00 +0277 +0546 +050 +000 +40 +035 +00 +0277 +0515 +075 +000 +40 +020 +00 +0284 +0526 +000 +000 +35 +054 +12 +0363 +0546 +000 +000 +35 +057 +12 +0364 +0568 +100 +000 +30 +119 +21 +0383 +0598 +100 +000 +30 +105 +21 +0369 +0555 +075 +010 +35 +101 +22 +0325 +0595 +100 +025 +35 +096 +22 +0347 +0581 +090 +100 +35 +086 +26 +0357 +0632 +100 +100 +35 +097 +26 +0326 +0606 +100 +100 +30 +142 +27 +0485 +0649 +100 +050 +30 +163 +27 +0454 +0628 +000 +000 +25 +064 +16 +0442 +0625 +000 +000 +25 +050 +16 +0480 +0694 +025 +050 +100 +075 +100 +100 +000 +000 +100 +075 +100 +100 TABLE 1A (CONT.) +25 +25 +25 +25 +30 +30 +068 +085 +104 +095 +176 +167 +37 +37 +49 +49 +50 +50 +0444 +0444 +0358 +0348 +0537 +0537 +0628 +0588 +0621 +0483 +0632 +0704 41 APPENDIX MULTIPLE REGRESSION TECHNIQUE AND MISTIC PROGIUMS USED 43 APP ENDIX B Multiple Correlation Technique To evaluate the individual and joint contributions of the five selected frictional characteristics upon travel time and fuel consumption the multiple correlation technique is used. This method is designed to provide an estimate of the over—all relationship between several factors and a given factor. In this study the given factor is travel time or fuel consumption. The multiple correlation technique provides two pieces of important information. First, it provides a multiple correlation (R) which expresses the extent of association between the estimated value and the actual value. R can vary from 0 to l. The better the equation, the larger "R" becomes. The squared value (R2) of the multiple regression coefficient expresses the proportion of the variability that can be attributed to the independent variables. The second important result is the developmentcf a multiple regression equation, which is a statement of the theoretical contribu- tion of the various frictional elements to travel time or fuel con- sumption. The effectiveness of the equation depends on the independent variables selected. Selection of the independent variables is based upon the linear relationship between the dependent and each independent variable. The quantitative measure of this relationship is given by the correlation coefficient (r). This term is also referred to as zero-order correlation 44 or Pearsonian Correlation Coefficient and the equation is shown below: (2 =£XY -£X£Y q A LN“? - (£101le 6‘ - (e304) N = Sample size ix = Sum of X values £Y = Sum of Y values (X2 = Sum of squared K values p» "L, Sum of Squared Y values '9 r3 n Sum of X and Y cross products As shown above the mathematics is quite elementary buttime consuming therefore the MISTIC, a high speed computer is used. The data is prepared in a specified form and fed as input with a prepared routine, K2-l35, which comput,s: 1. Correlation coefficients 2. Means 3. Standard deviations 4. Variances 5. Covariances A sample output from program K2-l35 is shown in TABLE 18. With the proper scaling factors observed, the means, standard deviations, and correlation coefficients are all that is necessary to proceed with the development of the correlation coefficient and the multiple regression equation. The standard procedure is to use the modified Doolittle22 method to solve the equation but this becomes tedious especially with three or more independent variables.' The MISTTC is again used for this purpose. The correlation matrix (Table 18) is the input data and the 45 TABLE 1B OUTPUT DATA FROM K2-135 USING TABLE 2A AS INPUT Correlation Mean Standard Variance-Covariance Matrix Deviation Matrix +10000000 +04310000 +04451842 +00198189 +03190000 +O4l93912 +07793574 +34600000 +07337574 +00145511 +10000000 +08604000 +03953882 +00175889 +18160000 +168016l9 -0343663O +03470600 +00824513 —00112260 -02639965 -00081240 +10000000 +005384OO +06313329 +00111127 +06005970 +00099592 -02998217 —00086984 +1000C000 +00156332 +06488181 +00485304 +06306664 +00444396 -O6305486 -OO77736O +07064311 +00469293 +10000000 +02822944 +05402964 +00019832 +04871071 +00016844 ~07224484 ~00043707 +06673866 +OOO21757 +08163847 +00113095 +10000000 +00006798 N program used is M3-M. This program forms a square symetric correlation matrix from the triangular form that is output from K2-135. The output from M3-M is immediately input into another program, KZAM, which computes the "R" value and the "beta weights". (Table 28) Since the "beta weights" are in a standardized form they must be multiplied by the ratio 46 of criterion standard deviation and the respective independent variable standard deviations which are available in TABLE l-B. TABLE 2B OUTPUT DATA FROM KZM R Betas 4’.88395448 -.01018115 -.41301093 +.31350134 +.3593203O The "b" values are then computed as follows with the aid of a desk calculator; b 1 Beta (Standard Deviation of D/(Standard Deviationcffixl) b -.010181 .824513 = —.0018 1 ._____._ 44.51842 COMPU'ER .IABORATORY K 2 (135) TITLE Product Moment Correlations, Means, Standard Deviations, Variances and Covariances TYPE Entire Program DURATION Input: .7(n2 + 4n + 2 + l0 k)s milliseconds Computation: 53.3n2 + 60.2n milliseconds Output: 25 p1n(n+1) milliseconds - for correlation matrix 25(1 + p2)(5+n)n milliseconds - for mean, standard deviation and variance - co- variance matrices where s =- sample size n a number of variables 1: . number of characters per row of the measurement p1 - Eager of characters with which each correlation coefficient is punched. p2 = umber of characters with which each mean, standard deviation, variance and covariance is to be punched. METHOD OF USE The program is read into the memory in the usual way followed by the parameter tape and lastly the data tape. Some computing is done after each row of the measurement matrix has been read into the memory. Since the correlation and variance-covariance matrices are symetric, it is necessary to print only half the off-diagonal elements. The lower off-diagonal and diagonal elements are printed out row by row (this is equivalent, however, to printing out the upper off-diagonal and diagonal elements column by column). First the correlation matrix is punched out, scaled down by a factor of ten, followed by an N. Next the mean and standard deviations appear in two ‘ parallel columns. Finally, the variance-covariance matrix is punched out. A new problem can be begun by reading in new parameters. CAPACITY Thirty-eight variables; there is no limit on the number of observations. -e- K 9 (13? PUNCHING 01" m TAPES For every problem four parameters are necessary. They are as follows: 1. Let "s" be the sample size. Put sS on the parameter tape. 2. Let "n" be the number of variables. Put an on the parameter tape. 3. Let "f" be the number of decimal places to which the correlation matrix is to be printed. Put f? on the parmeter tape. If no print out is desired, 1‘ - 0. 4. let '2 " be the number of decimal places to which the means, standard deviations and variance-covariance matrices are to be printed. Put ,2 L on the parameter tape. If no print out is desired, Q - 0. Each observation (which must lie in the range -l s x .- i) is punched as a sign followed by up to .12 decimal digits. The character "N" must be punched after each row of the measurement matrix. LETHOD USED The product moment correlation coefficient is a measure of the degree of relation of two variables. It may be shown to range between +1 and -1. This program computes the matrix of product moment correlations between each pair of a set of variables. The product manent correlation coefficient may be written in terms of the observed data, as ik-EW-S") r- - _ _,,, W (.2... (x-x)2 215' - y)“]1/2 _ For computational convenience this can be rewritten in terms of x, y, my, and s as '- ‘3' Ica(135 “in“ ZXZV (to £28-