Ergonomics
ISSN: 0014-0139 (Print) 1366-5847 (Online) Journal homepage: http://www.tandfonline.com/loi/terg20
Driver-Vehicle Behaviour in Restricted-Path Turns M. C. GOOD & P. N. JOUBERT To cite this article: M. C. GOOD & P. N. JOUBERT (1977) Driver-Vehicle Behaviour in RestrictedPath Turns, Ergonomics, 20:3, 217-248, DOI: 10.1080/00140137708931624 To link to this article: http://dx.doi.org/10.1080/00140137708931624
Published online: 25 Apr 2007.
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Date: 06 November 2015, At: 03:27
ERGONOMICS, 1977, VOL. 20, No.3, 217-248
Driver-Vehicle Behaviour in Restricted-Path Turns By AL C. GOOD and P. N. JOUBERT
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Department of Mcchnnlcul Engineering, University of Melbourne An experiment was conducted in which drivers negotiated a test course containing thirteen low-speed curves with well-defined lateral boundaries [rest.r-iot.ed-pn.t.h tUTUS), but were free to select their speed of travel. No evidence is found t.hnf the , preferred ynw rate' behuvicur exhibited in free-path turns is relevant to restrictedpath driving. The results indicate that the maximum lateral acceleration developed was tho major determinant of speed selection on a given radius cur-ve, tho level adopted docreasing with increased curve radius. The deviations of the vehicle paths from the sot-out curves arc examined in detail. The effect of experimental instructions designed to elicit' normal' and' stressed' driving strategies is also investigated. The data obtained o.ppear to provide the first comprehensive collection of detailed information on driver-vehicle behaviour O\'C(' a range of curve geomotries.
Introduction Accident data indicate a possible mismatch between tile elements of the driver-vehicle-road system on road curves, particularly for sharp radius, low-speed curves. For example, the review of accident studies by Loisch and Associates (1971) shows a sharp increase in the accident rate for radii less than 200 m. Also, while a major reduction in highway accident rates is effected by control of access, the low-speed curves of the consequent interchange loops and ramps remain relatively hazardous in comparison with the mainline freeway curves. Considering the economio and social importance of highway systems, there have been remarkably few detailed investigations of the response of drivers and vehicles to the geometric properties of road curves. The relatively comprehensive studies of the variation of spot speeds with curve radius made by Taragin (1954), Emmerson (HlG9, 1(70) and the Department of Main Roads, New South Wales (1!J69) indicate that superelevation (banking) has little effect on driver speed-selection on open-highway curves, but reveal different forms of relationship between speed and radius. The effect of curve geometry on the variation of speed through a curve has reeeivecllittle study since Taragin concluded that" drivers of free-moving passenger ears do not change their speeds appreciably after entering a horizontal curve even when the curvature is as sharp as 15 deg. [116 m radius]". Most design Policies are based on the assumption that vehicle speeds are constant on curves. However, there is evidence (e.g. Tharp and Harr 1965, Holmquist 1970, Neuhardt et (II. 1(71) that Taragin's conclusion is not universally valid. The prevailing method of determining minimum curve radii, R, for various design speeds, V, is to make use of an assumed comfortable and safe relationship between the unbalanced lateral acceleration, {ly= V2/R (or 'side friction factor " f = (ly/Y), and speed. Following this approach, several investigators (e.g. Ritchie 1972, Herrin and Neuhardt HJ74) have attempted to draw conclusions about individual driver stratcgies fromf- V relationships arrived at by averaging over a large number of drivers. It will be shown in this paper that such data, although useful for design purposes, cannot be representative of 1.
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individual behaviour, and the subsequent speculation about driver strategies is fruitless. A detailed review of these, and other aspects of empirical studies of driver-vehicle behaviour has been made recently by Good (1975 a). It is shown that such data are particularly lacking for low-speed road curves, where the highest lateral friction demands are made. Good, Rolls and Joubert (1969) found that, when free to choose their own curved paths without lateral constraints, drivers developed paths which could be characterized by a ' preferred yaw rate " r = V /R, which was independent of the forward speed of the vehicle, but increased logarithmically with the prescribed deviation angle of the turn,.p. The authors observed that the results of these free-path turn experiments may have particular relevance to the design of low-speed curves for intersections and interchanges. This was because the' psychological context' of both situations appeared to be similar, and the wide runge of lateral accelerations developed in the free turns could only be ncoommodated in designs for low-speed curvea, for which large superelevations oould be furnished and high levels of side-friction developed. Also, from the very limited observations that have been made of driver-vehicle behaviour on interohange ramps (Gray and Kauk 1968, Takebe 1968), there is evidence which suggests that there may be some situations in which driver behaviour is similar to that revealed in the free-path tests. In view of these considerations it was decided to perform experiments in which drivers would be required to negotiate a number of low-speed curves with well-defined lateral boundaries (restricted-path turns) but were free to select their speed of travel. The objective was to see whether there was any similurlty between the driver-vehicle behaviour in this situation, and that exhibited when the vehicle speed was defined by the experimenter but there were no lateral constraints (free-path turns). Specifically the following experimental hypotheses, based on the free-path turn behaviour, were to be tested: Hypothcsis I:
On circular curves (with spiral transitions at each end) of different minimum radius but the same deviation angle, drivers will seleot a speed and curvature distribution (within the defined boundaries) such that the maximum vehiele yaw rate is the same for each curve.
Hypothcsis II: On curves with the same rnmnnum radius, but different deviation angles, the maximum ynw rate developed by the driver will increase approximately linearly with the logarithm of the deviation angle. In addition, the detailed distributions of speed, curvature, yaw rate and lateral aoocloration were to be observed to see how closely they corresponded with the usual design assumptions of (a) constant speed, and (b) a vehicle path coincident with the centreline of the road. Failing confirmation of the experimental hypotheses, the objective was to determine the criteria governing the selection of the speed and curvature distributions in restricted-path turns. Relevant to the criteria employed by drivers is likely to be their motivation for driving. It is possible that the criteria governing unhurried, relaxed driving are different from those employed when the objective is to make a trip in
Driver-Vehicle Behaviour in Restricted-Path T'urn»
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minimum time, consistent with some tolerable level of risk. Accordingly, it was decided to investigate the effect of experimental instructions which would encourage (a) normal, comfortable driving, or (b) a driving strategy aimed at minimizing a cost function which involved penalties for both increased trip time and encroachment on the boundaries of the restricted path.
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2.
Methods
2.1. Selection of Ourve Geometries Two requirements of the experiment were that the geometry of the restrictedpath curves should be precisely known, and that the geometric parameters should be varied over a sufficient range to allow confirmation or rejection of the experimental hypotheses. It was also necessary that the driver-vehicle behaviour should be determined, as far as possible, by the curve geometry and the experimental instructions alone, without interference from other vehicles or extraneous environmental factors. These requirements effectively ruled out the use of public roads for the experiments. It was not feasible to construct a set of superelevated test curves. Hence, the experiments had to be performed on horizontal surfaces, and the selection of radii and deviation angles which would allow the free-path behaviour to be exhibited had to be made within tills constraint. The only suitable test site available was the North-South runway, and associated taxiways, of an unopened section of Melbourne Airport. The geometry of the test site further rcstricted the available choices of radii and angles. To allow adequate exploration of the effects of radius and deviation angle on driver-vehicle behaviour, five levels of each variable were selected for the test curves. However, only 13 of the possible 25 combinations were used, as shown in Table 1. The five 18 rn radius curves would allow the free-turn behaviour expressed in hypothesis II to be exhibited without excessive lateral accelerations. The five 1·57 rad curves allowed testing of hypothesis 1. The remaining four curves allowed the interactions between radius and angle to be investigated. Table 1.
Numbers assigned to tho curves used in experiment
Radius m
(ft)
0·52
(30) 18·3 38·1 53·3 76·2 115·8
(60) (125) (175) (250) (380)
Deviation angle red (dog.) 2·62 1·57 3·14 (!l0) ( 150) ( 180)
1 6
2 7
11
10 12
3 8
4
4·71 (270) 5
9
13
The main objective of the experiment was to investigate the effects of minimum radius and overall deviation angle on driver-vehicle behaviour. However, plain circular curves without curvature transitions were considered unsuitable as test curves, because difficulties associated with the lack of transitions could have had an overriding effect on the observed behaviour. On the other hand, introduction of curvature transitions increases thc number of independent variables describing the geometry of the curve. Rather than
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increase the number of experiments considerably by replications with different transition lengths, this dilemma was resolved by providing each curve with tmnsitions of a length recommended for its particular radius in the intersection curve Policy of the American Association of State Highway Officials [AASHO] (I!Hi5). As the Policy of the National Association of Australian State Road Authoritics (UJ70) recommends the AASHO values as suitable for minimum design, thc transition Icngths provided for each radius curve, in thc experimcnts, were probably close to those experienced by the subjects in everyday driving. Tn the absence of other information for restricted-path driving, the 1\AS HO values rcpresent perhaps the most authoritati ve guide to ' appropriate' trunsition lengths for each radius. The length of transition curve provided for each radius is shown ill Table 2, together with the AASHO design values of side friction factor and radial jerk. As the AASHO transitions for 18 and :~8 m radii consume more than 0·2(; fad of deviation angle, the 0·52 rad curves for thosc radii wore made all-transitional. A standard 3'(;6 m (12 ft) lane width was used for all ourvcs,
Table 2.
Design chnrnctcrist.ica of experimental curves according to AASHO (1965) intersection curve Policy Radius R,m
Trunalt.ion length
L.
In
Design speed V, kmh- 1
Sidc-Frict.ion factor J
1;·3' 20·3t
26·6 35·1
0·304
7H·2
21-!) 23·5
39·7 45,)
115-8
26·5
52·8
0·232 0·210 0·189
18·:1
38·1 53·3
Radial jerk
0·254
0,1119- 2
1·271·19t 1·15 1·10 1·02
•.F'or 0·52 rad ull.transit.icnnl curve: L=9'58, 0=2·30 n.ll-t.rnnait.ionn.l curve: L= 11)·9. C= }·21
t For 0·52 rod
2.2. Snbjects Fourteen males and two females aoted as subjects. Their ages ranged from 21 to 5:~ yr (mean age 31 yr). They had held driving licences from 1 to 35 yr (mean 10'5) and usually drove from 1500 to 50000 km pCI' ycar (mean 10000). Four subjcets were professional driving instructors, the remainder being amuteur drivers. 2.3. Test Vchicle and Instrumentation The test vehicle was a 1969 Ford Falcon 500 station sedan, fitted with automatic transmission, with the following particulars: Weight, unladen, 1450 kg; wheelbase, 281!l mm ; track, 1473 mm ; overall length, 4834 mm; overall width, 1875 mm. Tyre pressures were set so that the yehiele characteristic speed, determined using the fixed-steer angle technique described by Bundorf (1967), WI1S approximately 65 krnhr '. The vehicle was instru mcnted to measure the sprung mass lateral acceleration at a point close to the vehicle centre of gravity, sprung mass yaw rate and forward speed. All instrumentation signals were filtered and attenuated for recording on a light-beam recording oscillograph.
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2.4. '1'he Driving Task The test curves were set out on a large, flat airport, remote from terminal buildings, so that the requirement of a similar environment for each curve was fairly well satisfied. The curves were delineated by 2 litre-size square plastic bottles, painted in brilliant colours to enhance visibility. Curve markers on a given curve were of uniform colour, so that curves could be identified to the subjects by their colour, from considerable distances away. A 30 m long tangent section was set out at each end of the curves to introducc the 3·66 m lane width. To increase the realism of the task, the curves wcre made part of a continuous course, which included relatively long stretches of straight road, and took approximately half an hour to traverse completely. A different test course was defined for each subject by selecting a sequence of curves to be driven through. In an attempt to reduce serial effects the selection of thc starting point for the course, and the selection of each successive curve from those physically accessible, were made randomly (but subject to a latin square constraint). Each curve was driven through at least once as a left turn and as a right turn, 2.5. Experimental Instructions As stated in the Introduction, one objective of the experiment was to observe the effect on driver behaviour of requiring a trade-off between travel time and comfort or level of risk. The experiment was planned so that each subject drove through the test course twice. The sequence of cnrvcs for a given subject was the same for both trials. On the first trial, all subjects were asked to drive normally and comfortably. For the second trial, the subjects were assigned to one of two groups: Group A drivers (Subjects I-G, 15 and 16) were given the same instructions as before, and functioned as a control group. Group B drivers (Subjects 7-14), the experimental group, were informed that they were under moderate pressure of time, that a schedule had been worked out for them to keep, and that they would be kept up to elate with how they were progressing by being informed of the change in their score, and their accumulated total score, immediately after each curve was traversed. The f:,'TOUp B drivers were not told the criteria which determined whether their score increased, decreased or remained the same. It was left to the subject to learn the nature of the cost function as he progressed through the courso. That human operators are capable of modifying their behaviour to optimize on tho basis of a learnt criterion has been demonstrated in tracking studies (Obermayer et (II. 19(6). A speed limit of 90 kmh- 1 was imposed over the whole course for both trials. Hence it was clear to the subjects that they would have to reduce the timc taken to negotiate the curves in order to satisfy the time pressure. It was originally intended that the group B drivers' scores be manipulated in the following manner: If the time taken to traverse a curve during the second trial was reduced by more than 20% when compared with the first-trial time, the score was to be increased by 1. If the reduction in curve traverse time was less than 20%, no change would be made in the score. The score would be rcduced by 1 for every ti 1110 the vehicle touched one of the curve markers used to delineate the course. However, experience with the first two subjects who were subjected
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111. G. Gooil anil P. N. Joubert
to this schedule showed that the penalties for high-risk driving were insufficient. The subjects were able to build up their score rapidly, by driving at speeds which produced (for the two passengers) extremely uncomfortable lateral accelerations, but at which they retained sufficient control of the vehicle to avoid muny encroachments on the curve boundaries. For the third subject tested, the critcria were modified thus: If the reduction in curve traverse time was less than ]0%, no change was made in the score; for reductions between ] 0 and 20 % the score was increased by L; for reductions greater than 20 % the score was reduced by I. Also, the penalty for touching a curve marker was increased to 5 score points. Even this modification appeared unsuccessful in discouraging abnormally uncomfortable driving. For the final five subjects the 10 und 20% limits were reduced to 5 and 15%, respectively. The scoring critcrin are summarized in Table :1. 'I'oblc
Subject no. 7,8 !l
10-14
n.
Scoring criteria for group B drivers
Percentage reduction in curve traverse time required for score change of +1 -I 0-20% >20% 0-10% 10-20% >20% 0-5% G-l!i% >15%
°
Score change per curve marker hit -1
-5 -5
2.6. Daln Annlysis The raw data from the experiments consisted of approximately 1000 osoillogmph records of the signals from the speed, yaw rate and lateral acceleration transducers. Because of the large volume of data, and the desire to examine the data in a number of different ways, the signal traces were digitized at 0'5 s intervals, to enable analyses to be performed with a digital computer. This time interval was selected in a trade-off between accurate digital representation of the analogue signal, and practical limitations of time and effort in performing the conversion. For a circular curve with spiral transitions at each end, the yaw rate and lateral acceleration records for a constant speed vehicle can be expected to be roughly trapezoidal in shape. If a trapezium shape were' fitted' to the data, the slopes of the entry and exit transition lines, and the height of the central plateau section, would provide convenient parameters with which to characterize the overall driver-vehicle behaviour on the curve. These parameters could then bc compared with the values assumed in design of curves, and used to check the validity of the experimental hypotheses. However, in the present tests there was no requirement that the curves be traversed at constant speed. Also, Leeming and Black (1950) found that some of their lateral acceleration records had an ' anomalous' shape, referred to here as a ' quadrilateral shape', in whioh thc central plateau section had a non-zero slope. Hence, to provide pnrumeters representative of the gross levels of lateral jerk, maximum yaw rate, ctc., used in the present experiments, quadrilateral shapes were fitted to the yaw rate and lateral acceleration records, using a least-squares fit procedure described by Good and Joubert (1975 a). Figure 1 illustrates the notation used and the parameters derived from the curve fits, using an example of an
Drioer- Vehicle Behaviour in Restricted-Path 7'1Lms
223
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Yj
Figure I.
Definition sketch for quudt'ilntcru.l cur-ve fit.t.ing analysis of 'ymv rate and Iatorul nccolcrutiou records.
actual yaw rnte record. In some cases, a triangular (all-transitional) shape provided the best fit to the data. Apart from the gross measures derived from quadrilateral curve fits, maximum instantaneous values of the variubles were also investigated. In addition, computer programs were written to plot the variation of speed, yn,w rate, lateral ncoeleration and path curvature with distance along the curve, so that the detailed shapes of these distributions could be compared across, for example, su bjects and directions of turn. Path distance was calculated by integrating the forward speed, but thc instantaneous path curvature could only be estimated approximately from thc yaw rate r and speed V, using K=::r/V, (1) because the vehicle sideslip angular velocity S was not known. In a steady stn.te turn, of course, equation (1) is exact. The error in tbe curvature calculatcd from this equation would generally only be appreciable ncar tile entry and exit to the curve where the curvature was small and transient motions relatively large. The curvatures of interest, however, wero in the central rcgion of the curve where sideslip velocities would be relat! vcly small. Nevertheless, high frequency oscillations in the oalculuted curvature distributions should be viewed with some caution-see Section 3.8.
3. Results and Discussion Test of Experimental Hypotheses A number of pnrametcrs could be used to represent the' maximum vehicle yaw rate ' mentioned in the experimental hypotheses. A variable representative of the overall level of yn,w rate developed is the entry height R 2 (at the end of the entry transibion ), derived from the quadrilnteral curve fit. The variation of this quantity with curvature and deviation angle is shown in Figure 2. Tbe datil, plotted are averages over the first trials of all 16 subjects :~. I.
ERG.
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M: C. Good and P. N. Joubert
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and over both directions of turn. It is clear that, apart from the two alltransitional 0·52 rad curves, the deviation angle had no effect on the yaw rates developed, contrary to hypothesis II. Also, the yaw rate increased with ourvature of the restricted-path, contrary to hypothesis I. Thus neither of tho experimental hypotheses was confirmed. The varlution of YI1W rate with curvature shown in :Figure 2 is approximately linear, especially in the range of radii from UG m to :l8 m, but there appears to be a levelling-off at higher curvatures. The lower yaw rates on the alltransitional 0·52 rad curves resulted from drivers selecting vehicle paths, within the Iuteru! constraints, with smaller minimum curvatures than the centre-line curvature; that is, they 'cut the corner', maintaining lateral accelerations consistent with the other curves. as will be shown later.
(a)
-
~ 0.1 ook-----!---+--~-~--~-~
6
Figure 2. Val'io.tion of entry yaw rate R 2 with (a) curvature and (b) deviation angle of restricted path. Plot.ted points are averages over all first trials. Full lines represent regression of ilion curvature for individual data. (a) 0, Deviation angle 0·52 rad; \}' ],57 red, 0.2'62 rnd: 6. 3·14 rud: 4·71 rnd . (b) 0, Radius 18 In; 'V. 38 In; 0, 53 In; 6. 76 In;
C>.110m.
C>.
Driver- Vehicle Behaviour in Restricted-Path Turns
225
A linear regression was fitted to the individual data which are represented by means in Figure 2, but excluding those for the 18 m radius, 0·52 rad curve. Including the deviation angle as an independent variable made no significant reduction in variance (F 1.375 =0,707). The regression of yaw rate on curvature is shown in Figure 2. The proportion of the total variance accounted for by this regression was 82% . ,
.6
I
I
,
r-
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.4
-
-,
.2 l-
-e
r-
"e
0
I
I
I
1
2
3
.6
I
~
I
I
(m-') I
I
-
r-
w
Ar-
B
0 0
~
§
-
6
6
I
0
ij
'iJ
f-- @
0
@
-
f-- 0
.2r-
@
I
'·75
I
I
I
I
5·24
3-49
Deviation angle
Figure 3.
6
5
4
102/R
0
)0-
-
-
Curvature
.-)(
-
-
\J \J
~
~o
'"
0 0
~
~
e
0 0
~
-
Y'
(rad)
Example of entry yaw rate data for first trial of individual subject (Subject 4). Symbols as for Figure 2.
The conclusions drawn above, regarding the relationship between the entry yaw rate R 2 and curvature and deviation angle, hold also for other variables such as the maximum instantaneous yaw rate r max' the exit yaw rate R 3 , the mean central yaw rate R m = (R 2 + R 3)f2, or the maximum fitted yaw rate Rmax=max (R 2 , R 3 ) · Similar behaviour was also observed on the second trials of Group B drivers, who were under a time-cost incentive. Although the general level of yaw rate was higher than in the first trials, reflecting the increased vehicle speeds, the general form of the relationship was the same. The behaviour of individual subjects was also consistently similar to the averaged behaviour. Figure 3 shows a typical case. While the scatter in the
220
M. O. Good and P. N. Joubert
data for a given subject was generally small, there were naturally individual differences between subjects. These differences are most conveniently investigated using regressions of R 2 on curvature for the first trial of each subject. The variance accounted for by the individual regressions was typically nr. %. 'I'ho individual regression coefficients differed significantly (for Group A: F 7,172 = (j.(j, p
u
Ftgurc 10.
DISTANCE Diat.r-ibut.ioua of speed, lateral acceleration, yaw rate and curvature for first trials of (a) Subject 10 und (b) all subjects on 18 m radius, 3·14 red curve.
Driver- Vchicle Belunriour in Restricted-Path Turns
235
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The present corner cutting behaviour was consistent with Emmerson's (l !WO) observations of vehicles on rural highway curves, from which he found that, " m~tny cars on curves of radius less than 500 ft (152 Ill) sought to increase the curvature [sic] of their path by cutting the curve corner". In the present experiment the opportunity for significant corner cutting was restricted to tho 0·.52 rad curves, because of the restrictive :HHi m lane width. The asyrnmetry of the curvature distributions was consistent with the observations of Leeming and Black (1950) and Cysewski (HJ49).
'!-r-
,±Ih
(B)
(A)
, , , 'c-
~
..
~,
.... " .. ~ ..
~)~
.'
-
'~"."
'~.'::
'
,'
.
1,~,m,:,:i'''''~lii,m~:,'~:i:':i,l~~i ~--.--LU
j ·0'5 r8d8- 1
O, Road curvature find superolcvot.ion. A final report, on experiments on comfort and driving practice. Procccdinqs of the t netitution oj Munieipal Engineers, 76, 522-53!J. LEISCH, J. E., and Assocrxrns, 1971, Alignment. In Traffic Control and Roadlcay ElementsTheir Relationship to Highway Safety. (Sydney: HIGHWAY Usnns FEI1EHA'fWN son SAF~~TY AND 1\IOllILITY.) Chapter 12. l\IcLEA1'l", J". R.; 1974, Driver behaviour on curves-e-n review. A uetrotian Road Research; 5, 76-H I. ~lGLEAS", J. R., and HOFFMANN, E. H., 1071, Analysis of drivers' oont.rol movements, Human Factors, 13, 407-418. N"ATroNAL ASSOCIATION OF AUSTRALIAN STAT!':: HOAD AUTJlOHITlES, lU70, Guide to Traffic Engineering Practice. (Sydney: NAASHA.) l
Driver-Vehicle Behaviour in Restricted-Path Turns
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.J. 13., HlmHIN, G. D., and .ROCKWELL, T. H" 1971, Demonstration of a test-driver technique to nSBoBS tho effects of roadway geometries and development all speed selection. Department. of t nduetrial Engineering, Ohio State University, Project EEB 326B Report. O,mHJ\lAYlm, It, W., \VEBSTER, H. 13., and Mucxr.xn, F. A., 1966, Studies in opt.irna.l behaviour in manual oont.rot systems: The effect of four performance criteria in compensatory ratecontrol tracking. Proceedinqs of the Second Annual ]l,TASA-University Conference on NI;;UIIAltDT,
J,lfamwl Control.
HITCllm, 1\'1. L., IH72, Choico of speed in driving through curves as a function of advisory speed Hod curve signs. Human Factors, 14, 533-538. SNI,;pgCOH, G. \V., 1956, Statistical Methode, 5t,h edition. (Ames: IOWA STATE UNIVERSITY
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PH1·;,ss.)
'1',\I
ISSN: 0014-0139 (Print) 1366-5847 (Online) Journal homepage: http://www.tandfonline.com/loi/terg20
Driver-Vehicle Behaviour in Restricted-Path Turns M. C. GOOD & P. N. JOUBERT To cite this article: M. C. GOOD & P. N. JOUBERT (1977) Driver-Vehicle Behaviour in RestrictedPath Turns, Ergonomics, 20:3, 217-248, DOI: 10.1080/00140137708931624 To link to this article: http://dx.doi.org/10.1080/00140137708931624
Published online: 25 Apr 2007.
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Date: 06 November 2015, At: 03:27
ERGONOMICS, 1977, VOL. 20, No.3, 217-248
Driver-Vehicle Behaviour in Restricted-Path Turns By AL C. GOOD and P. N. JOUBERT
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Department of Mcchnnlcul Engineering, University of Melbourne An experiment was conducted in which drivers negotiated a test course containing thirteen low-speed curves with well-defined lateral boundaries [rest.r-iot.ed-pn.t.h tUTUS), but were free to select their speed of travel. No evidence is found t.hnf the , preferred ynw rate' behuvicur exhibited in free-path turns is relevant to restrictedpath driving. The results indicate that the maximum lateral acceleration developed was tho major determinant of speed selection on a given radius cur-ve, tho level adopted docreasing with increased curve radius. The deviations of the vehicle paths from the sot-out curves arc examined in detail. The effect of experimental instructions designed to elicit' normal' and' stressed' driving strategies is also investigated. The data obtained o.ppear to provide the first comprehensive collection of detailed information on driver-vehicle behaviour O\'C(' a range of curve geomotries.
Introduction Accident data indicate a possible mismatch between tile elements of the driver-vehicle-road system on road curves, particularly for sharp radius, low-speed curves. For example, the review of accident studies by Loisch and Associates (1971) shows a sharp increase in the accident rate for radii less than 200 m. Also, while a major reduction in highway accident rates is effected by control of access, the low-speed curves of the consequent interchange loops and ramps remain relatively hazardous in comparison with the mainline freeway curves. Considering the economio and social importance of highway systems, there have been remarkably few detailed investigations of the response of drivers and vehicles to the geometric properties of road curves. The relatively comprehensive studies of the variation of spot speeds with curve radius made by Taragin (1954), Emmerson (HlG9, 1(70) and the Department of Main Roads, New South Wales (1!J69) indicate that superelevation (banking) has little effect on driver speed-selection on open-highway curves, but reveal different forms of relationship between speed and radius. The effect of curve geometry on the variation of speed through a curve has reeeivecllittle study since Taragin concluded that" drivers of free-moving passenger ears do not change their speeds appreciably after entering a horizontal curve even when the curvature is as sharp as 15 deg. [116 m radius]". Most design Policies are based on the assumption that vehicle speeds are constant on curves. However, there is evidence (e.g. Tharp and Harr 1965, Holmquist 1970, Neuhardt et (II. 1(71) that Taragin's conclusion is not universally valid. The prevailing method of determining minimum curve radii, R, for various design speeds, V, is to make use of an assumed comfortable and safe relationship between the unbalanced lateral acceleration, {ly= V2/R (or 'side friction factor " f = (ly/Y), and speed. Following this approach, several investigators (e.g. Ritchie 1972, Herrin and Neuhardt HJ74) have attempted to draw conclusions about individual driver stratcgies fromf- V relationships arrived at by averaging over a large number of drivers. It will be shown in this paper that such data, although useful for design purposes, cannot be representative of 1.
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u. O. Good and P.
N. Joubert
individual behaviour, and the subsequent speculation about driver strategies is fruitless. A detailed review of these, and other aspects of empirical studies of driver-vehicle behaviour has been made recently by Good (1975 a). It is shown that such data are particularly lacking for low-speed road curves, where the highest lateral friction demands are made. Good, Rolls and Joubert (1969) found that, when free to choose their own curved paths without lateral constraints, drivers developed paths which could be characterized by a ' preferred yaw rate " r = V /R, which was independent of the forward speed of the vehicle, but increased logarithmically with the prescribed deviation angle of the turn,.p. The authors observed that the results of these free-path turn experiments may have particular relevance to the design of low-speed curves for intersections and interchanges. This was because the' psychological context' of both situations appeared to be similar, and the wide runge of lateral accelerations developed in the free turns could only be ncoommodated in designs for low-speed curvea, for which large superelevations oould be furnished and high levels of side-friction developed. Also, from the very limited observations that have been made of driver-vehicle behaviour on interohange ramps (Gray and Kauk 1968, Takebe 1968), there is evidence which suggests that there may be some situations in which driver behaviour is similar to that revealed in the free-path tests. In view of these considerations it was decided to perform experiments in which drivers would be required to negotiate a number of low-speed curves with well-defined lateral boundaries (restricted-path turns) but were free to select their speed of travel. The objective was to see whether there was any similurlty between the driver-vehicle behaviour in this situation, and that exhibited when the vehicle speed was defined by the experimenter but there were no lateral constraints (free-path turns). Specifically the following experimental hypotheses, based on the free-path turn behaviour, were to be tested: Hypothcsis I:
On circular curves (with spiral transitions at each end) of different minimum radius but the same deviation angle, drivers will seleot a speed and curvature distribution (within the defined boundaries) such that the maximum vehiele yaw rate is the same for each curve.
Hypothcsis II: On curves with the same rnmnnum radius, but different deviation angles, the maximum ynw rate developed by the driver will increase approximately linearly with the logarithm of the deviation angle. In addition, the detailed distributions of speed, curvature, yaw rate and lateral aoocloration were to be observed to see how closely they corresponded with the usual design assumptions of (a) constant speed, and (b) a vehicle path coincident with the centreline of the road. Failing confirmation of the experimental hypotheses, the objective was to determine the criteria governing the selection of the speed and curvature distributions in restricted-path turns. Relevant to the criteria employed by drivers is likely to be their motivation for driving. It is possible that the criteria governing unhurried, relaxed driving are different from those employed when the objective is to make a trip in
Driver-Vehicle Behaviour in Restricted-Path T'urn»
219
minimum time, consistent with some tolerable level of risk. Accordingly, it was decided to investigate the effect of experimental instructions which would encourage (a) normal, comfortable driving, or (b) a driving strategy aimed at minimizing a cost function which involved penalties for both increased trip time and encroachment on the boundaries of the restricted path.
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2.
Methods
2.1. Selection of Ourve Geometries Two requirements of the experiment were that the geometry of the restrictedpath curves should be precisely known, and that the geometric parameters should be varied over a sufficient range to allow confirmation or rejection of the experimental hypotheses. It was also necessary that the driver-vehicle behaviour should be determined, as far as possible, by the curve geometry and the experimental instructions alone, without interference from other vehicles or extraneous environmental factors. These requirements effectively ruled out the use of public roads for the experiments. It was not feasible to construct a set of superelevated test curves. Hence, the experiments had to be performed on horizontal surfaces, and the selection of radii and deviation angles which would allow the free-path behaviour to be exhibited had to be made within tills constraint. The only suitable test site available was the North-South runway, and associated taxiways, of an unopened section of Melbourne Airport. The geometry of the test site further rcstricted the available choices of radii and angles. To allow adequate exploration of the effects of radius and deviation angle on driver-vehicle behaviour, five levels of each variable were selected for the test curves. However, only 13 of the possible 25 combinations were used, as shown in Table 1. The five 18 rn radius curves would allow the free-turn behaviour expressed in hypothesis II to be exhibited without excessive lateral accelerations. The five 1·57 rad curves allowed testing of hypothesis 1. The remaining four curves allowed the interactions between radius and angle to be investigated. Table 1.
Numbers assigned to tho curves used in experiment
Radius m
(ft)
0·52
(30) 18·3 38·1 53·3 76·2 115·8
(60) (125) (175) (250) (380)
Deviation angle red (dog.) 2·62 1·57 3·14 (!l0) ( 150) ( 180)
1 6
2 7
11
10 12
3 8
4
4·71 (270) 5
9
13
The main objective of the experiment was to investigate the effects of minimum radius and overall deviation angle on driver-vehicle behaviour. However, plain circular curves without curvature transitions were considered unsuitable as test curves, because difficulties associated with the lack of transitions could have had an overriding effect on the observed behaviour. On the other hand, introduction of curvature transitions increases thc number of independent variables describing the geometry of the curve. Rather than
1J1. C. Good and P: N . Joubert
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220
increase the number of experiments considerably by replications with different transition lengths, this dilemma was resolved by providing each curve with tmnsitions of a length recommended for its particular radius in the intersection curve Policy of the American Association of State Highway Officials [AASHO] (I!Hi5). As the Policy of the National Association of Australian State Road Authoritics (UJ70) recommends the AASHO values as suitable for minimum design, thc transition Icngths provided for each radius curve, in thc experimcnts, were probably close to those experienced by the subjects in everyday driving. Tn the absence of other information for restricted-path driving, the 1\AS HO values rcpresent perhaps the most authoritati ve guide to ' appropriate' trunsition lengths for each radius. The length of transition curve provided for each radius is shown ill Table 2, together with the AASHO design values of side friction factor and radial jerk. As the AASHO transitions for 18 and :~8 m radii consume more than 0·2(; fad of deviation angle, the 0·52 rad curves for thosc radii wore made all-transitional. A standard 3'(;6 m (12 ft) lane width was used for all ourvcs,
Table 2.
Design chnrnctcrist.ica of experimental curves according to AASHO (1965) intersection curve Policy Radius R,m
Trunalt.ion length
L.
In
Design speed V, kmh- 1
Sidc-Frict.ion factor J
1;·3' 20·3t
26·6 35·1
0·304
7H·2
21-!) 23·5
39·7 45,)
115-8
26·5
52·8
0·232 0·210 0·189
18·:1
38·1 53·3
Radial jerk
0·254
0,1119- 2
1·271·19t 1·15 1·10 1·02
•.F'or 0·52 rad ull.transit.icnnl curve: L=9'58, 0=2·30 n.ll-t.rnnait.ionn.l curve: L= 11)·9. C= }·21
t For 0·52 rod
2.2. Snbjects Fourteen males and two females aoted as subjects. Their ages ranged from 21 to 5:~ yr (mean age 31 yr). They had held driving licences from 1 to 35 yr (mean 10'5) and usually drove from 1500 to 50000 km pCI' ycar (mean 10000). Four subjcets were professional driving instructors, the remainder being amuteur drivers. 2.3. Test Vchicle and Instrumentation The test vehicle was a 1969 Ford Falcon 500 station sedan, fitted with automatic transmission, with the following particulars: Weight, unladen, 1450 kg; wheelbase, 281!l mm ; track, 1473 mm ; overall length, 4834 mm; overall width, 1875 mm. Tyre pressures were set so that the yehiele characteristic speed, determined using the fixed-steer angle technique described by Bundorf (1967), WI1S approximately 65 krnhr '. The vehicle was instru mcnted to measure the sprung mass lateral acceleration at a point close to the vehicle centre of gravity, sprung mass yaw rate and forward speed. All instrumentation signals were filtered and attenuated for recording on a light-beam recording oscillograph.
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221
2.4. '1'he Driving Task The test curves were set out on a large, flat airport, remote from terminal buildings, so that the requirement of a similar environment for each curve was fairly well satisfied. The curves were delineated by 2 litre-size square plastic bottles, painted in brilliant colours to enhance visibility. Curve markers on a given curve were of uniform colour, so that curves could be identified to the subjects by their colour, from considerable distances away. A 30 m long tangent section was set out at each end of the curves to introducc the 3·66 m lane width. To increase the realism of the task, the curves wcre made part of a continuous course, which included relatively long stretches of straight road, and took approximately half an hour to traverse completely. A different test course was defined for each subject by selecting a sequence of curves to be driven through. In an attempt to reduce serial effects the selection of thc starting point for the course, and the selection of each successive curve from those physically accessible, were made randomly (but subject to a latin square constraint). Each curve was driven through at least once as a left turn and as a right turn, 2.5. Experimental Instructions As stated in the Introduction, one objective of the experiment was to observe the effect on driver behaviour of requiring a trade-off between travel time and comfort or level of risk. The experiment was planned so that each subject drove through the test course twice. The sequence of cnrvcs for a given subject was the same for both trials. On the first trial, all subjects were asked to drive normally and comfortably. For the second trial, the subjects were assigned to one of two groups: Group A drivers (Subjects I-G, 15 and 16) were given the same instructions as before, and functioned as a control group. Group B drivers (Subjects 7-14), the experimental group, were informed that they were under moderate pressure of time, that a schedule had been worked out for them to keep, and that they would be kept up to elate with how they were progressing by being informed of the change in their score, and their accumulated total score, immediately after each curve was traversed. The f:,'TOUp B drivers were not told the criteria which determined whether their score increased, decreased or remained the same. It was left to the subject to learn the nature of the cost function as he progressed through the courso. That human operators are capable of modifying their behaviour to optimize on tho basis of a learnt criterion has been demonstrated in tracking studies (Obermayer et (II. 19(6). A speed limit of 90 kmh- 1 was imposed over the whole course for both trials. Hence it was clear to the subjects that they would have to reduce the timc taken to negotiate the curves in order to satisfy the time pressure. It was originally intended that the group B drivers' scores be manipulated in the following manner: If the time taken to traverse a curve during the second trial was reduced by more than 20% when compared with the first-trial time, the score was to be increased by 1. If the reduction in curve traverse time was less than 20%, no change would be made in the score. The score would be rcduced by 1 for every ti 1110 the vehicle touched one of the curve markers used to delineate the course. However, experience with the first two subjects who were subjected
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222
111. G. Gooil anil P. N. Joubert
to this schedule showed that the penalties for high-risk driving were insufficient. The subjects were able to build up their score rapidly, by driving at speeds which produced (for the two passengers) extremely uncomfortable lateral accelerations, but at which they retained sufficient control of the vehicle to avoid muny encroachments on the curve boundaries. For the third subject tested, the critcria were modified thus: If the reduction in curve traverse time was less than ]0%, no change was made in the score; for reductions between ] 0 and 20 % the score was increased by L; for reductions greater than 20 % the score was reduced by I. Also, the penalty for touching a curve marker was increased to 5 score points. Even this modification appeared unsuccessful in discouraging abnormally uncomfortable driving. For the final five subjects the 10 und 20% limits were reduced to 5 and 15%, respectively. The scoring critcrin are summarized in Table :1. 'I'oblc
Subject no. 7,8 !l
10-14
n.
Scoring criteria for group B drivers
Percentage reduction in curve traverse time required for score change of +1 -I 0-20% >20% 0-10% 10-20% >20% 0-5% G-l!i% >15%
°
Score change per curve marker hit -1
-5 -5
2.6. Daln Annlysis The raw data from the experiments consisted of approximately 1000 osoillogmph records of the signals from the speed, yaw rate and lateral acceleration transducers. Because of the large volume of data, and the desire to examine the data in a number of different ways, the signal traces were digitized at 0'5 s intervals, to enable analyses to be performed with a digital computer. This time interval was selected in a trade-off between accurate digital representation of the analogue signal, and practical limitations of time and effort in performing the conversion. For a circular curve with spiral transitions at each end, the yaw rate and lateral acceleration records for a constant speed vehicle can be expected to be roughly trapezoidal in shape. If a trapezium shape were' fitted' to the data, the slopes of the entry and exit transition lines, and the height of the central plateau section, would provide convenient parameters with which to characterize the overall driver-vehicle behaviour on the curve. These parameters could then bc compared with the values assumed in design of curves, and used to check the validity of the experimental hypotheses. However, in the present tests there was no requirement that the curves be traversed at constant speed. Also, Leeming and Black (1950) found that some of their lateral acceleration records had an ' anomalous' shape, referred to here as a ' quadrilateral shape', in whioh thc central plateau section had a non-zero slope. Hence, to provide pnrumeters representative of the gross levels of lateral jerk, maximum yaw rate, ctc., used in the present experiments, quadrilateral shapes were fitted to the yaw rate and lateral acceleration records, using a least-squares fit procedure described by Good and Joubert (1975 a). Figure 1 illustrates the notation used and the parameters derived from the curve fits, using an example of an
Drioer- Vehicle Behaviour in Restricted-Path 7'1Lms
223
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Yj
Figure I.
Definition sketch for quudt'ilntcru.l cur-ve fit.t.ing analysis of 'ymv rate and Iatorul nccolcrutiou records.
actual yaw rnte record. In some cases, a triangular (all-transitional) shape provided the best fit to the data. Apart from the gross measures derived from quadrilateral curve fits, maximum instantaneous values of the variubles were also investigated. In addition, computer programs were written to plot the variation of speed, yn,w rate, lateral ncoeleration and path curvature with distance along the curve, so that the detailed shapes of these distributions could be compared across, for example, su bjects and directions of turn. Path distance was calculated by integrating the forward speed, but thc instantaneous path curvature could only be estimated approximately from thc yaw rate r and speed V, using K=::r/V, (1) because the vehicle sideslip angular velocity S was not known. In a steady stn.te turn, of course, equation (1) is exact. The error in tbe curvature calculatcd from this equation would generally only be appreciable ncar tile entry and exit to the curve where the curvature was small and transient motions relatively large. The curvatures of interest, however, wero in the central rcgion of the curve where sideslip velocities would be relat! vcly small. Nevertheless, high frequency oscillations in the oalculuted curvature distributions should be viewed with some caution-see Section 3.8.
3. Results and Discussion Test of Experimental Hypotheses A number of pnrametcrs could be used to represent the' maximum vehicle yaw rate ' mentioned in the experimental hypotheses. A variable representative of the overall level of yn,w rate developed is the entry height R 2 (at the end of the entry transibion ), derived from the quadrilnteral curve fit. The variation of this quantity with curvature and deviation angle is shown in Figure 2. Tbe datil, plotted are averages over the first trials of all 16 subjects :~. I.
ERG.
Q
224
M: C. Good and P. N. Joubert
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and over both directions of turn. It is clear that, apart from the two alltransitional 0·52 rad curves, the deviation angle had no effect on the yaw rates developed, contrary to hypothesis II. Also, the yaw rate increased with ourvature of the restricted-path, contrary to hypothesis I. Thus neither of tho experimental hypotheses was confirmed. The varlution of YI1W rate with curvature shown in :Figure 2 is approximately linear, especially in the range of radii from UG m to :l8 m, but there appears to be a levelling-off at higher curvatures. The lower yaw rates on the alltransitional 0·52 rad curves resulted from drivers selecting vehicle paths, within the Iuteru! constraints, with smaller minimum curvatures than the centre-line curvature; that is, they 'cut the corner', maintaining lateral accelerations consistent with the other curves. as will be shown later.
(a)
-
~ 0.1 ook-----!---+--~-~--~-~
6
Figure 2. Val'io.tion of entry yaw rate R 2 with (a) curvature and (b) deviation angle of restricted path. Plot.ted points are averages over all first trials. Full lines represent regression of ilion curvature for individual data. (a) 0, Deviation angle 0·52 rad; \}' ],57 red, 0.2'62 rnd: 6. 3·14 rud: 4·71 rnd . (b) 0, Radius 18 In; 'V. 38 In; 0, 53 In; 6. 76 In;
C>.110m.
C>.
Driver- Vehicle Behaviour in Restricted-Path Turns
225
A linear regression was fitted to the individual data which are represented by means in Figure 2, but excluding those for the 18 m radius, 0·52 rad curve. Including the deviation angle as an independent variable made no significant reduction in variance (F 1.375 =0,707). The regression of yaw rate on curvature is shown in Figure 2. The proportion of the total variance accounted for by this regression was 82% . ,
.6
I
I
,
r-
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.4
-
-,
.2 l-
-e
r-
"e
0
I
I
I
1
2
3
.6
I
~
I
I
(m-') I
I
-
r-
w
Ar-
B
0 0
~
§
-
6
6
I
0
ij
'iJ
f-- @
0
@
-
f-- 0
.2r-
@
I
'·75
I
I
I
I
5·24
3-49
Deviation angle
Figure 3.
6
5
4
102/R
0
)0-
-
-
Curvature
.-)(
-
-
\J \J
~
~o
'"
0 0
~
~
e
0 0
~
-
Y'
(rad)
Example of entry yaw rate data for first trial of individual subject (Subject 4). Symbols as for Figure 2.
The conclusions drawn above, regarding the relationship between the entry yaw rate R 2 and curvature and deviation angle, hold also for other variables such as the maximum instantaneous yaw rate r max' the exit yaw rate R 3 , the mean central yaw rate R m = (R 2 + R 3)f2, or the maximum fitted yaw rate Rmax=max (R 2 , R 3 ) · Similar behaviour was also observed on the second trials of Group B drivers, who were under a time-cost incentive. Although the general level of yaw rate was higher than in the first trials, reflecting the increased vehicle speeds, the general form of the relationship was the same. The behaviour of individual subjects was also consistently similar to the averaged behaviour. Figure 3 shows a typical case. While the scatter in the
220
M. O. Good and P. N. Joubert
data for a given subject was generally small, there were naturally individual differences between subjects. These differences are most conveniently investigated using regressions of R 2 on curvature for the first trial of each subject. The variance accounted for by the individual regressions was typically nr. %. 'I'ho individual regression coefficients differed significantly (for Group A: F 7,172 = (j.(j, p
u
Ftgurc 10.
DISTANCE Diat.r-ibut.ioua of speed, lateral acceleration, yaw rate and curvature for first trials of (a) Subject 10 und (b) all subjects on 18 m radius, 3·14 red curve.
Driver- Vchicle Belunriour in Restricted-Path Turns
235
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The present corner cutting behaviour was consistent with Emmerson's (l !WO) observations of vehicles on rural highway curves, from which he found that, " m~tny cars on curves of radius less than 500 ft (152 Ill) sought to increase the curvature [sic] of their path by cutting the curve corner". In the present experiment the opportunity for significant corner cutting was restricted to tho 0·.52 rad curves, because of the restrictive :HHi m lane width. The asyrnmetry of the curvature distributions was consistent with the observations of Leeming and Black (1950) and Cysewski (HJ49).
'!-r-
,±Ih
(B)
(A)
, , , 'c-
~
..
~,
.... " .. ~ ..
~)~
.'
-
'~"."
'~.'::
'
,'
.
1,~,m,:,:i'''''~lii,m~:,'~:i:':i,l~~i ~--.--LU
j ·0'5 r8d8- 1
O, Road curvature find superolcvot.ion. A final report, on experiments on comfort and driving practice. Procccdinqs of the t netitution oj Munieipal Engineers, 76, 522-53!J. LEISCH, J. E., and Assocrxrns, 1971, Alignment. In Traffic Control and Roadlcay ElementsTheir Relationship to Highway Safety. (Sydney: HIGHWAY Usnns FEI1EHA'fWN son SAF~~TY AND 1\IOllILITY.) Chapter 12. l\IcLEA1'l", J". R.; 1974, Driver behaviour on curves-e-n review. A uetrotian Road Research; 5, 76-H I. ~lGLEAS", J. R., and HOFFMANN, E. H., 1071, Analysis of drivers' oont.rol movements, Human Factors, 13, 407-418. N"ATroNAL ASSOCIATION OF AUSTRALIAN STAT!':: HOAD AUTJlOHITlES, lU70, Guide to Traffic Engineering Practice. (Sydney: NAASHA.) l
Driver-Vehicle Behaviour in Restricted-Path Turns
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.J. 13., HlmHIN, G. D., and .ROCKWELL, T. H" 1971, Demonstration of a test-driver technique to nSBoBS tho effects of roadway geometries and development all speed selection. Department. of t nduetrial Engineering, Ohio State University, Project EEB 326B Report. O,mHJ\lAYlm, It, W., \VEBSTER, H. 13., and Mucxr.xn, F. A., 1966, Studies in opt.irna.l behaviour in manual oont.rot systems: The effect of four performance criteria in compensatory ratecontrol tracking. Proceedinqs of the Second Annual ]l,TASA-University Conference on NI;;UIIAltDT,
J,lfamwl Control.
HITCllm, 1\'1. L., IH72, Choico of speed in driving through curves as a function of advisory speed Hod curve signs. Human Factors, 14, 533-538. SNI,;pgCOH, G. \V., 1956, Statistical Methode, 5t,h edition. (Ames: IOWA STATE UNIVERSITY
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PH1·;,ss.)
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