- Email: [email protected]
Geometric and environmental effects on speeds of 2-lane highways
0191-x07/83 $3.00 + .oo e; 1983 Pergamon Press Ltd.
Tronspn Rex -A Vol. 17A. No. 4. pp. 315 325, 1983 Printed in Great Bntain.
GEOMETRIC AND ENVIRONMENTAL EFFECTS ON SPEEDS OF 2-LANE HIGHWAYS SAM Department
YACAR
of Civil Engineering,
and
MICHEL
University (Rrcriwd
VAN
of Waterloo,
13 April
AERDE
Ontario,
Canada
N2L 3Gl
1982)
Abstract--A study of the effects of various geometric and environmental factors on the speeds for 2-lane rural highways was performed in Ontario, Canada using 1980 data which had been collected by means of the Radar-Platoon technique. Over 5000 5-min periods of data, collected at 35 different locations, were used to estimate the effects of the various contributing local factors. Each of these contributing factors was formulated as the exponentially smoothed average of the geometric properties up to 1500 m upstream. To control for varying traffic volumes, the speeds used for estimating the geometric effects were those corresponding to main direction volumes of 900 passenger car units (pcu) per hour and opposing volumes of about 300pcu/hr. A multiple linear regression model related measured speeds to the upstream influencing properties of the highway. Land use adjacent to the road, and legal speed limit, were found to have the most significant impacts on speed. Grade, access from other roads, and lane width, followed in that order. The above significant factors explained 85:; of the across-sites variation in speed, leaving relatively small residual errors. Road curvature, presence of an extra lane, sight distance, center line markings and lateral obstructions were not found to have statistically significant effects on speed. Stronger statistical relationships could be obtained for both the above significant and insignificant factors, by testing these factors over wider ranges than those available on Ontario’s highways, as Ontario uses relatively high and uniform design standards. For example, gradients were limited to less than 3%, and radius of curvature to greater than 1400m. INTRODUCTION
and Coombe (197 I), in a study of a greater variety of geometric features, again found curvature to be the dominant factor. Duncan (1974) found that at low volumes speeds are strongly affected by hilliness and bendiness, but not by carriageway width. Duncan’s formula for freespeeds on 2-lane highways accounts for nearly 80% of the variance of the free speed, after correcting for traffic flow. Using 1963 data, Troutbeck (1976) found that neither pavement width nor shoulder width significantly affect free speeds of cars and trucks. This same study found grade, for all vehicle types, and sight distance, for just passenger cars, to be the most significant factors for predicting free speeds. Leong (1968), using similar data, found that in general, an increase in gradients, either upgrade or downgrade, decreased speeds, while increases in pavement width, shoulder width and sight distance, increased speeds. Turner et ul. (1982) found that the conversion of a shoulder to an additional travel lane could be expected to increase average speed of a 2-lane highway by about 5’:/, for volumes exceeding 150 veh/hr. The effect of landuse adjacent to the highway is significant, according to Galin (1981), who found that speeds in agricultural and wooded areas are higher than in low-density residential areas. He also found that the speed at a site was affected by the trip distance from its origin to that site. While the above works tended to emphasize the effects on free speeds, this paper addresses the effects of geometric and environmental factors at a practical medium-to-high flow rate, represented by 900 pcu/hr in the mainline direction and 300 pcu/hr in the opposing direction. It is in this range of traffic volumes
O’Flaherty
speeds depend upon traffic volumes, and the many geometric and environmental conditions on and adjacent to the roadway. An earlier paper by Van Aerde and Yagar (1983) examined the former, while this paper considers the latter. The effects of roadway conditions on average speed, at a mainline volume of 900 pcu/hr and an opposing volume in the range of 300 pcu/hr are studied, as this is considered to be a typical demand at which geometric improvements are often considered in order to improve service levels. Geometric factors relate to the roadway design, while e&ironmental factors consider other conditions surrounding the roadway, such as landuse and speed limit. Both the roadway design factors and these other environmental conditions are often collectively referred to simply as geometric factors. Highway
EARLIER
ESTIMATES
ENVIRONMENTAL
OF
EFFECTS
GEOMETRIC/ ON
SPEEDS
The effect of geometric properties on the operating characteristics of 2-lane highways has been the subject of a number of studies. Much of the earlier work in this area is reviewed by Oppenlander (1966) and has been incorporated into the first two editions of the U.S. Highway Capacity Manual (1950, 1965). The HCM has been the most commonly used design standard since that time, but changing traffic and vehicle characteristics have left much of it outdated. More recent works have addressed specific aspects of the relationship between speed and the geometric properties of the roadway. The majority of this research has dealt with the effects of geometries on free speeds. McLean (1981), in a study of 120 curve sites, found a strong effect of curvature on speed. TRA Vol. 17 No. .+E
315
316
SAM YAGAR
and
MICHEL VAN AERDE
that upgrading of 2-lane highways is usually considered. Also, most of the previous research used instantaneous geometric properties as the factors influencing spot speeds, while speeds are largely dependent upon upstream geometric characteristics. This is especially true on 2-lane facilities, as the restriction on passing opportunities tends to build up platoons over prolonged stretches of road. This paper attempts to account for upstream geometric factors by using a smoothed average of the geometric properties over a 1500-m stretch upstream of the sites where spot speeds were monitored.
lane, access, shoulder width to nearest obstruction, sight distance, centre line marking, and speed limit. The approximate ranges of the above geometric factors, as found in the data base, are summarized in Table 1. These values represent average values over the entire 1500-m upstream stretch as opposed to any instantaneous values within that upstream stretch. The effects of all of these factors are described qualitatively in this paper, whether they were found significant or not, as one is interested in knowing both the significant and insignificant factors. The estimated levels of statistical significance can also aid the synthesis of future studies.
DATA
FACTOR FOR WEIGHTING UPSTREAM GEOMETRIC/ENVIRONMENTAL PROPERTIES
DECAY
The previous paper by Van Aerde and Yagar (1983) described the data bank that was acquired at 35 Ontario locations. These speeddvolume data were analyzed, along with the geometric conditions at each of the 35 study locations, to determine the effects of geometric properties on the speeds of 2-lane rural highways. For each location, the volumeespeed data were plotted to obtain an estimate of the average speed at a mainline volume of 900 pcu/hr, and an opposing direction volume of about 300pcu/hr. In this way, the traffic volumes were essentially controlled while the geometric/environmental factors were varied, so that the marginal effects of the geometric/environmental effects could be studied quite simply. FACTORS
WHICH
WERE
The speeds at a location depend upon conditions for some distance upstream, with the closer geometrics having the greater impacts. Therefore a “decay factor” was applied to model the effects of each of the geometric conditions up to 1500m upstream of each study location. The effect of any geometric condition is represented by means of a decay factor which reduces in the upstream direction, until at some point little identifiable influence remains. Theoretically, this factor decays geometrically from an initial value of 1, at the data collection site, to a value approaching zero at an infinite distance upstream. This ideal format is illustrated in Fig. 1. For practical purposes the section from 0 to 1500 m upstream of the location was divided into 10 sections, each 150 m long. The set of geometric conditions within each section was given 90% of the weight accorded to the adjacent upstream section. This configuration is illustrated in Table 1. The choice of 150-m increments, a maximum upstream distance of 1500 m and a 0.9 decay factor were based on judgment and on local and practical consid-
CONSIDERED
The geometric properties, which were thought to affect operating speeds and also available in sufficient variety to be analyzed, are discussed below in general terms. The actual values of these properties for the locations of interest are listed in detail by Yagar and Van Aerde (1981). The factors considered are curvature, gradient or slope, lane width, landuse, extra
WEIGHT
0. 2 0. 0 0
150
300
450
600
750
900
1050 1200 1350 1500 DISTANCE UPSTREAM IN
Fig. I. Graphical illustration
i 1650 1800 HETRES
of ideal decay factor.
Table I. Range of average upstream geometric properties among the 35 Ontario data collection sites 1
-
road
-
slope
or
-
lane
width
-
adJacent
-
access
-
extra
-
lateral
-
centre
-
sight legal
curvature grade
0
to
-3%
to
3.3
from
other
lane obstructlon
line speed
roads
degrees
to
3.8 100
%
type
1 to
type
none
to
45
4 %
none
to to
minor continuous
to
infinite
solid
limit
500 80
m
km/h
to __~
90 ~~__.
per
%
to
markings
distance
m
0
landuse
4 +2
Ill
passing
km/h
10 10 m
1
317
Geometric and environmental effects on speeds of 2-lane highways WEIGHT
y-----l___ 0. 0.
_
2 0
I 0
150
300
450
600
750
900
1650
1200
DISTANCE
1350
1500
UPSTREAM
1650 IN
ll300
METRES
Fig. 2. Graphical illustration of actual decay factor.
erations. They are subject to review and can be appropriately modified to adapt to the specific accuracy requirements of any given application. The sum of the decay factors for I = O-10 is 6.87. To combine the influences at the upstream sections, one merely adds their weighted effects, and normalizes by dividing by 6.87. FORMULATION
OF GEOMETRIC
FROM THE GEOMETRIC
FACTORS
PROPERTIES
In order to regress the speed measurements upon the upstream geometric properties the latter must all be represented quantitatively. The attributes of each factor must be reflected appropriately, providing an approximately linear relationship between the transformed factor and the measured speed. The following section describes how, based on the above, each of the geometric factors was formulated from its relevant geometric properties for the purposes of the analysis described herein.
(1) Curvature The curvature at each upstream section was measured as the maximum rate of curvature in that
section, expressed in degrees per 100 m. Negative values were used to indicate curvature to the left and positive values to indicate curvature to the right. The following formats were considered: (a) The effect of a curve modelled as linearly dependent upon the rate of curvature but independent of the direction of curvature. (b) The effect of a curve treated as linearly dependent upon rate of curvature and also dependent upon direction of curvature. (c) The effect of a curve expressed as a non-linear function of curvature. (2) Grade Vehicles tend to accelerate downhill and decelerate when going uphill, unless the driver compensates. The impact of road gradient was analyzed based on each of the following types of models: (a) Effect on speed proportional to absolute grade, increasing downhill and decreasing uphill as per Fig. 3(a). (b) Different linear increase/decrease in speed for down and uphill grade, as per Fig. 3(b). (c) Linear decrease in speed for deviations from an
downhill
uphill
(b)
Fig. 3. (a) Combined
grade
factor
for uphill and downhill. (b) Grade factor most grade” mode1 for uphill and downhill.
sensitive
to uphill.
(c) “Optimum
318
SAM
YAGAK
and
MICHEL
VAN
AERDE
SPEED DE;:;;”
- ~~-~~_>-----~
A=3.
Fig. 4. Ideal and simplified
“ideal”
or “optimum”
downhill
grade,
model
as per Fig.
3(c). (d) Combined effects of grade and length, or grade and presence of lateral obstructions. (3) Lane width ,factor The passage of vehicles requires a minimum lane width. Any additional width beyond this minumum allows one to drive faster and/or with a greater measure and perception of safety. This type of behaviour can be most accurately modelled by a decaying function (e.g. exponential), as shown in Fig. 4. The exponential model is not easily transformed into a simple speed prediction model, as it requires the calibration of two coefficients. However, the small range of lanewidths encountered in the data set permitted a linear approximation to the exponential form, as illustrated by the range from A to B in Fig. 4. Lane width.was therefore treated as a linear factor with an ideal lane width of 4 m. The coefficient of the lane width factor then determines the rate at which the speed would decrease for each metre by which land width falls short of 4 m. Although the choice of 4 m was arbitrary, the use of a different value would not change the value of this rate coefficient. Only the default speed cqrresponding to an arbitrarily defined generic road would be affected. (4) Land use Land use is defined to be a factor which land adjoining the section of highway driveways, and not otherwise. The land therefore represents the fraction (weighted according to distance upstream) of road
Table
Decay
2.
DISTANCE
(in
3m
8=3.0m
Lane
Width
width
min.
is set if the has access use factor inversely on which
factor
UPSTREAM
metres 0
1
weights
for the effect of lanewidth
land use was present in the 1500-m upstream stretch. The effect of access driveways interacting with a two-lane highway can be broken down into two components: (a) The actual or potential entering and exiting of vehicles onto or off the highway will tend to slow down the traffic as other vehicles are held up during the time the turning vehicle decelerates or accelerates. (b) The driver’s cognizance of and attention to the adjacent land use, such as reading of billboards, or attention to the activities of children. (5) Extru lane The extra lane factor represents the fraction of upstream stretch during which an extra lane or fully paved shoulder was available. The presence of an extra lane can increase the operating speed of a highway in the following ways: (a) An extra lane (or a paved shoulder) provides an extra margin of safety which can promote higher speeds. (b) The extra lane also allows passing of slow vehicles which might otherwise inhibit the normal traffic flow, such as heavy vehicles on an uphill section, farm equipment on a rural road, or an entering or exiting vehicle. (6) Access ,jhctor Access is distinguished from Land use in that the former considers road intersections, which are public, while the latter considers driveways, which are generally private. Access thus considers trip continuations rather than origins and/or destinations. There are a variety of means of gaining access to a two lane highway and the nature of the access
for upstream STATION I 0
150
1
300
2
450
3 4
600
on speed
geometric
conditions WEIGHT C.9) XSI 1 09 0 0
I 81 73
0. 66
750
5
0
900
6
1050
7
0. 53 0. 48
1200
e
0. 43
1350 1500
9
0. 39
10
59
Geometric
and environmental
Table 3. Access types and corresponding 1 WEIGHT 1
TYPE
0
-
1 2 3 4
-
319
effects on speeds of 2-lane highways
weights used
OF ACCESS
I
access by any roads minor road (usually gravel) high speed ramp merge ma.jor road (paved with no sccel/deceleration controlled intersection (traffic signals) no
ramps)
governs the severity of its speed impact. For the purposes of this study the different types of access were divided into the categories described in Table 3. The weights assigned to the various access types increase with the severity but no attempt has been made to quantitatively reflect the relative severity of the various types of access as the Ontario data file did not contain sufficient variety in access data. Rather, the weights given in Table 3 were adopted. It is conceded that these weights are really a rank ordering. However, after much deliberation a “better” set of weights could not be determined. It is also noted that the access factor will generally be significantly less than one, as accesses of the above type are not found within 100 m of one another, and more than one major access or 2 minor road accesses within 1500 m is very uncommon.
The ideal road was assumed to have an ideal sight distance of 1500 m and the sight distance factor was formulated as the difference between the actual sight distance and the ideal of 1500 m. The benefit of sight distances greater than 1500 m were not considered.
(7) Lateral obstruction Provision of a shoulder, rather than an abrupt obstruction or curb, gives the driver an extra margin of safety which should tend to promote higher speeds. The lateral obstruction factor included in the model represents the distance to the end of the shoulder or to the nearest object or curb, whichever is less. Whenever the distance to an object is small one would have a small positive obstruction factor and the speed should be reduced. Conversely, a greater distance, as indicated by a greater obstruction factor, would increase the speed.
(10) Speed limit The speed limit can directly inhibit the speeds of the faster vehicles when the road geometries might otherwise permit higher speeds. Higher limits also tend to reflect better designs causing speeds to be correlated with the posted limits. The speed limit factor used in the model represents its marginal effect on speeds, after the other geometric factors have been accounted for. Using a speed limit of 90 km/hr as a reference, the speed limit factor was formulated as the difference between that reference and the posted limit. Its coefficient represents the reduction in average speed due to speed limits below 90 km/hr.
(8) Sight distance The lack of adequate sight distance should tend to decrease the operating speed on a two lane highway, as faster vehicles are prevented from passing slower ones. Longer sight distance also gives the driver an opportunity to see what is ahead providing the platoon leader with a longer perception and reaction time and promoting higher speeds.
(9) Centre line For the purposes of this speed prediction model, all the centreline markings are classified as either allowing passing or not allowing passing in the direction that is being monitored. Sections allowing passing were given a value of 0 for the passing factor, and those not allowing passing were given a value of 1. Thus, the coefficient provided by the regression model for this factor would directly estimate the speed reduction penalty which occurs if passing is not allowed.
SUMMARY
OF GEOMETRIC
FACTORS
Roads in Ontario are generally designed using relatively uniform design standards. As a result, the variation of the geometric variables that were studied was in some cases not as great as might be expected in other parts of the world. The coefficients calibrated in
Table 4. Ranges considered for the upstream average geometric factors Min Curvature factor in degrees per 100 m Average Uphill grade as a positive X Average Downhill grade as a negative X Net summation of up-down hill grades as a X Lane width less than ideal of 4 metres Fraction of extra lane in upstream stretch Severity of access onto upstream stretch Fraction of landuse in upstream stretch Average distance to obstruction in metres Sight distance short of 1500 metres Indicator of centre line passing provision Speed Limit Less than 9Okm/h reference
0. 00 0. 00 0.
00
-3. 06 0. 20 0. 00 0. 00 0. 00 1. 75 326 0. 00 0. 0
Ilax 4. OS 2. OS -3.26 1. 72 0. 70 0. 44 0. 73 1. 00 5. 00 1034 1.00 10 0 -_
Mean 0. S5 0. 60 -0. 67 -0.07 0. 38 0. 06 0. 16 0. 19 4:34 553 0. 44 8. 14
SAM YAGARand MICHELVAN
320
this study should therefore be considered in view of the averages and ranges of the various geometric factors. These are summarized in Table 4. SPEED PREDICTION MODEL
(1) Simple correlution matrix Table 5 presents the simple correlation matrix for the geometric/environmental factors which were considered, along with the corresponding probability of each pair of factors not being correlated. The following factors were considered: = Average speed as measured at data collection sites. = Speed limit penalty (90 km/hr-Posted Limit). = Curvature factor expressed as degrees per 100m. = Average Uphill grade quoted as a positive 7;. = Average Downhill grade quoted as a negative ‘4. = Lane width less than ideal of 4 m.
SPDLIM CURVE UPHILL DOHILL WIDTH
Table *et*
CDRRELATIDN
AVER
5. Correlation
COEFF*CIENTS
FOR
XLANE
= Fraction of occurrence of extra lane in upstream stretch. = Severity of access onto the upstream stretch. = Fraction of land use present in upstream stretch. = Average distance to nearest obstruction in metres. = Sight distance short of 1500 m. = Indicator of centre line passing provision. = Net summation of up and down hill grades as a %.
ACCESS LANDUSE
A speed prediction model was formulated and calibrated through the use of regression analysis. The simple correlation matrix of the above factors, and the statistical parameters of the regression model are presented in Tables 5 and 6 respectively. Table 7 lists the speed predictions of the model and compares them to the speeds that were actually observed at each of the locations.
AVER
AERDE
matrix
THE
SPDLIM
OBSTR SIGHT CENTRE SLOPE
(2) Multiple linear regression model Several multiple linear regression models were considered. The stability of each model was tested by adding and subtracting marginal variables using a step-wise approach. A final model is presented in Table 6 along with its statistical significance indicators. This model explains 85% of the original variation in the measured speeds, based on 5 significant geometric factors and a constant representing the expected speed for neutral geometric conditions. The factors used in the final model were statistically significant at the 0.05 level and causally acceptable; the latter signifying correct sign and reasonable magnitude. The rejected parameters are illustrated for academic interest. The estimates quoted for each of these rejected parameters were obtained from separate regression models, each of which contained the corresponding rejected parameter and all of the
for geometric/environmental
GEcmETAIC
WIDTH
FACTORS
XLANE 0 04 8017
CONSIDERED
ACCESS -0
25 1446
AVER
1 00 0000
-0 73 000 1
-0 47 .0047
SPDLIM
-0 74 0001
1 DO 0000
0 15 3849
015 3766
022 2051
D 18 2993
0 31 0687
0 31 0740
CURVE
“WILL
DOHILL
WIDTH
XLANE
ACCESS
013 4459
-002 .91m
10 30 0749
0 12 4904
-0 28 09-L
0 36 0289
-0 35 .,0386
0 50 ,002,
0. 15 .3891
-0. 37 0291
0 49 0028
0 64 0001
0 44 0083
-0 30 .0791
0 26 1391
-0 81 0001
0. 31 ,071L
-0 07 6863
-0. 24 ,584
0 27 ,169
0 13 4480
0 54 .0007
0 02 .91&b
0 38 0234
-0.43 0108
0 19 26353
-0. 10 5802
0 38 0243
-0 31 0717
0 09 6081
0 0, 9611
0 03 8.520
0 01 9390
0 IE 2938
-0 20 2574
0 57 0003
037 0285
-012 5027
-0 47 0047
0 15 3849
1 00 0000
-0 07 6820
0 12 .4759
0 04 8017
0 13 3766
I 00 0000
0. 56 0003
-0
0 SC OOOJ
100 0000
-014 4089
0 31 .0627
0 31 0716
-0
11 5167
-0 14 .4089
OBSTR
-0 02 9223
0
07 6863
0
54 0007
0.
SIGHT
0 20 2460
-0 30 0749
24 1584
0 02 9166
-0
-0 19 2856
0 12 4944
0 27 ,165 0. 13 4480
SLOPE
D 38 .0260
0 16 3646
-0. 60 0002
CENTRE
0 32 Ot.27
-0.13 .4953
I ANDUSE
-0
24 1656
38 0760
-0 00 9970
-0
-0
-0 11 5189
0 64 0001
-0 Bl 0001
19 2653
CENTRE
0 20 2460
-004 81.52
0 12 4759
SIGHT
-0 02 9223
003 BB93
0 22 .2051
rlODEL***+
OQSTR
-0 03 8579
25 ,446
THE
-0 60 0002
0 24 1690
-0
IN
LANDUSE
-0 20 2451
-0.07 6828
factors
11 3167
1 00 0000 0. 09 .6081
1
00 0000
10 5802
0 01 961 I
0 38 0234
0 38 0243
0 03 0620
0 37 0307
-0 43 0100
-0 31 0717
0 01 9390
-025 1489
-0 20 2370
-0
-0.19 2856
30 2378
0
1
-0
00
37 0307 45
SLOPE -0
24 lb56
-0 00 9970 -0
-0
11 5189
25 1489
0069
0 01 9350
-0 45 0069
1 00 0000
0 09 6016
001 9350
0 09 6016
1 00 0000
0000
Geometric and environmental effects on speeds of 2-lane highways Table PARAMETER
93. factor
lane
-
width
landuse access
factor
speed
T
limit
0001
1.
12
3.74
0008
0.
48
2.
31
65
-
2.54
.0205
4.92
0001
1. 68
-
8.0
-
3.18
0035
2.
52
-
0.7
-
6.
.OOOl
0.
10
in
estimate multiples
of
of
Sums
Squares
Model Total
829 151 1010
Variable
Dependent
0. Dep.
of
Standard
of
REJECTED
Variable of
Variation
Parameters
PARAt’lETERS
Curvature
factor
Extra
Lane
Sight
Distance Line
Obstruction
factor factor
IMPACTS
OF
FACTORS
ESTIMATE +
0.45
+
6.2 0.06
factor
-
3.
ON
SPEED
(1) Curvature A simple linear term was introduced as a first approximation of the curvature factor, with right and
28
0.
0275
Model
Final PR
>
----
T
3480
0.3
The final statistical model for predicting speeds on 2-lane highways as a function of geometric and environmental factors has been described above. A more detailed discussion of each of the factors is presented below with our findings for each compared to those in the literature.
00
.2493 .9208
-
GEOMETRIC/
85
2.
from
-
(3) Speed prediction and residuals Table 7 lists a summary of the average upstream geometric/environmental properties, corresponding speed predicted by the model, observed average speed, and residuals for each location. OF
ReJected
factor
significant parameters. It is noted that the obstruction factor appeared statistically significant, but in the wrong direction.
ENVIRONMENTAL
83.
Deviation
Coefficient
Properties
----
MAGNITUDE
R-Squared Mean
OF
SQUARES
34
of
parameter
----
SUM
OF
INDICATOR
DISCUSSION
Model
5
Properties
Centre
for
29
Corrected
----
the
parameter
FREEDOM
Error
value
dev.
for
estimated
DEGREES
OF
DEVIATION
parameter
std.
level
the
of
of of
Significance CPP~P
Analysis
SOURCES
56
regression
Statistical
----
ERROR
-
83.
Standard
----
STD.
-
Significance
-
:T:
5.7
Multiple
IT:
>
8.3
-
ERROR-
PR
VALUE
-
-
>
for speed prediction
-
T-VALUE STD.
-
3
1.8
ESTIMATE PR
model
ESTIMATE
intercept grade
6. Final
321
5
9818
.0049
lefthand curvature carrying the same weight. The curvature factor had a coefficient of 0.45 with a standard error of 0.47 and did not prove significant for the given data set. It was not incorporated into the geometric speed prediction model because its coefficient was found to be insignificant and of the wrong sign. Since the approximation as a linear term did not show statistical significance, more elaborate combinations and variations of the curve factor were not considered, as a much higher level of significance would be required to calibrate these terms. The lack of significance of the curvature factor is in contrast with the findings from other sources. Duncan (1974) and O’Flaherty and Coombe (1971) found that speeds at low flows were strongly affected by bendiness in the upstream section, while McLean (1981) and numerous others established similar relationships for speeds and instantaneous curvature. This discrepancy could be due to the lack of a sufficient variety of severe curves in Ontario. Also, the effect of curvature might have been hidden in
322
SAM YAGAK and
MICHEL
Table 7. Gcometric,:environmental
~~___
LANE
LAND
WIDTH
USE
AEKDE
properties and speed predictions
EXTRA
---_SPEED----
UP
DOWN
OBS
0. 0
0. 4
89
90.5
0
0. 0
91
90.8
+o.
0. 2
0. 0
87 94
89. 5 93.0
-2 5 +1.0
0. 0
0. 8
95
93.3
+1.7
0.0
1.2
94
93.
3. 9
87
84.0
83
83.
79
83.5
SPEED
TION
LIMIT
4OOSl
90
3
0. 0
0.8
00
0. 8
4oos2
90
38
0.0
07
00
0. 0
400%
90
38
0.0
02
0. 0
1.9
1300
400Nl
90
3. 5
0. 0
0. 5
0. 0
1. 8
400N2
90
3. 8
0. 0
0. 7
0.
0
400N3
90
3. 8
0. 0
1. 0
0. 0
0.7
35Sl
00
36
0.0
01
0. 4
3
3x4
80
3. 6
0. 0
0. 4
0. 0
1.4
0812
3585
80
3. 6
0. 0
0. 5
0. 2
0. 0
0. 5
1. 6
LINE
CURVA
-GRADE-
LOCA
5
CENTRE
VAN
LANE
TURE
1
0
5
0.
6
1
PRED
RES -1.5
4
+O.
-0.
80
36
0.4
00
0. 2
3. 0
2. 4
0. 8
84
79.4
+4.
00
34
0. 0
0. 8
0. 0
3. 4
1. 5
1. 0
82
82.3
-0.3
3SN4
80
37
0. 0
0. 4
0. 0
0. 0
1. 4
1. 3
80
82.
3SN5
80
3. 6
0. 0
0. 5
0. 2
0.0
0.2
1.0
82
81.7
80
36
0. 7
0. 6
0. 0
0. 0
0. 4
0. 2
79
78.0
80
37
1.0
1.0
0. 0
0. 0
0. 0
0
3
76
76.
1
7El
80
3.8
00
0. 9
0.
0. 0
0. 4
0.
7E2
80
3. 8
0. 0
0. 5
0. 0
1
0.0
7E3
80
38
0. 7
0. 0
0.8 0.1
0.0 1.2
0. 6
2.
2
-2.
+1
0
-0.
5
1
+2.
79
79.8
86
83.
-0.8
81 84
84.0 83. 4
-3.0 +O. 6
85
84
+1.0
81
84.5
-3.5
83
79.8
+3
3
86
84.
+l.
2 g
7E4
80
3.8
0. 7
0. 0
7ES
80
3.8
04
0. 5
0. 0
00
0.313
7Wl
00
3. 8
0. 0
0. 9
0. 0
0. 0
5
7W2
80
3.8
00
0. 3
0. 0
09
0. 5 0 2 10.1
7w3
80
3. 8
0. 2
0.5
00
0. 0
0.2
5
7w4
80
30
03
0.7
02
0.0
0
1.2
79
81.4
-2.
7w5
80
38
00
OS
00
2. 0
1. 1
0. 6
82
83.6
-1.6
85Sl
80
36
0.0
08
00
0. 0
0. 4
0.
1
82
84.0
ass2
80
3. 6
0.0
09
00
0. 7
0. 5
0. 2
86
84.
00
0. 4
0. 2
77
75.8
+1.2
0. 6
78
79.4
-1.4
6
0
8
1
-2.
0 9
8553
80
3
3
0. 8
0.4
00
80
3. 3
0. 4
0. 4
0. 0
0. 2
0. 3
8555
80
33
01
06
0. 0
1. 5
0. 9
0. 4
78
77.
8SNl
80
3. 6
0. 0
0. 6
0. 0
2. 8
0.
0. 3
84
82.7
+1.3
8SN2
80
36
00
1. 0
0. 0
0. 0
0. 0
0. 3
88
84.7
+3
8SN3
80
33
06
01
00
0. 8
0. 8
0. 0
73
73.5
-0.5
8SN4
80
33
0. 4
0.2
00
0. a
0. 8
0. 3
75
76.7
8SNS
80
33
0. 7
0. 6
0. 0
0. 0
0. 4
0.
76
76.
Speed
Limit
Lane
Width
Land
Ure
Centre Extra
Line Lane
curvature Grade Speed
OBS
Speed
PRED
Speed
RES
:
Legal
speed
limit
quoted
in
1
4
9
+l.
8554
1
2
5
2. 6 00
0
6
+0.3
0. 3 03
1
3
-4.5
35N3
6Sl
6
+3.0 2
35Nl
652
2
+0
6 3
-1.7 6
-0.
6
km/h
: Width of lane in direction of travel in metres : Landuse adJacent to highway, quoted as a fraction : Legally permitted passing, quoted as = fraction : Additional Lane provision, quoted as a fraction : Average degree of curvature in degrees per iOOm : Up and downhill gradientsquoted as a percent : Speed in km/h as observed at data collection site : Speed predlcticn based on the geometric properties : Difference between the observed and predicted speed
some of the other factors because of its colinearity with speed limit, sight distance, landuse, grade and the centre line markings. (2) Grade Initially a single linear grade factor was introduced, as per Fig. 3(a), which yielded a coefficient of - 1.80 and a standard error of 0.48. This implies that the operating speed at a location is expected to increase/decrease by approx. 1.8 km/hr for each I’:,, of grade when going downhill/uphill respectively. This is in keeping with the treatment of saturation flows by Webster and Cobbe (1966), where capacity increases by 3% for each 1% of downhill grade and decreases at the same rate for uphill grades. The level of sophistication of the grade factor model was increased by relaxing the restriction that down and uphill sections contribute the same absolute value to the operating speed. This was accom-
plished by introducing separate terms for positive grade and for negative grade as per Fig. 3(b). When considered separately, an average uphill grade of 1% was found to decrease the average speed by 1.3 km/hr, while a similar downhill grade increased the average speed by 2.2 km/hr. This indicates that speeds are more sensitive to downhill grades than to uphill grades. It should be noted however that the data were restricted to average positive and negative grades of 0.60 and 0.67% respectively with corresponding maxima of 2.00 and 3.26%. The relative statistical significance of the separate up and downhill factors and the combined factor are shown in Table 8. The choice between the use of the combined factor or the two separate factors depends upon the availability of data and the desired level of accuracy. An “optimum grade” model, as per Fig. 3(c), was also investigated but was not found significant. Can-
323
Geometric and environmental effects on speeds of 2-lane highways
Table 8. Comparison of combined and independent grade factors ESTIMATE Combined
Grade
Factor
Separate Separate
Uphill Factor Downhill Factor
didate “optimum” grades of 0.5. 1.0, 1.5, 2.0 and 2.5 were investigated. The effect of grades on speed is found significant by most sources but the variability in the format of the grade factors makes comparisons sometimes difficult. Linear relationships have been used by Leong (1968), quadratic relationships by Troutbeck (1976) and average hilliness function by Duncan (1974). Leong (1968) and Troutbeck (1976) found, for grades ranging from + 10% to - IO%, that uphill and severe downhill sections decrease the speed of passenger cars. While a decrease in speed for uphill grades is supported by our findings, the limited range of Ontario data did not allow a test of severe down grades. The topography of the Ontario locations was not conducive to comparing single long continuous uphill sections to aggregations of several shorter uphill sections. Similarly, the special distinction between trucks and passenger cars was not critical for the shorter and less steep uphill sections encountered in Southern Ontario. Specifically, Taylor et ul. (1972) suggest that, based on simulation techniques, the proportion of trucks in the flow does not significantly affect speeds for gradients below3’:,:. The combined effect of grades with curvature or obstructions could not be investigated, as the required variety of geometric combinations was not available.
For the practical range of lane widths from 3.3 to 3.8 m it was found that the operating speed of a given location is decreased by approx. 5.7 km/hr for each meter of reduction in lane width. The coefficient of - 5.67 and standard error of 2.3 1 indicate a reasonably high level of statistical significance. In accordance with the shape of Fig. 4, it is speculated that the speed reduction rate for lane widths less than 3.3 m will be even greater, and that for lane widths larger than 3.8 m this rate will be less. The effect of lane width on the speed of 2-lane highways is not always found significant by other sources. A significant positive effect of lane width is found in the HCM (1965), and by Leong (1968) but not by Duncan (1974) or Troutbeck (I 976).
(4) Lunrl USP The presence of landuse along the 1500 m of road leading up to the location was found, on the average,
STANDARD
ERROR
-1.80
0.
48
-1. 27 2. 16
0. 63 0. 67
to decrease speeds by approx. 8.3 km/hr, with a standard error of 1.7. The size of the land use coefficient and the corresponding small standard error indicate statistically, that land use is one of the most important and significant factors influencing speeds on 2-lane rural highways. The effect of land use on the average speed of 2-lane highways has often been ignored in the past but recently more emphasis has been put on its study. Opiela et al. (1976), studied the effect of abutting landuse and found that more intense land use slightly lowers the speed/volume curve for volumes beyond SOOveh/hr. Galin (1981) also found that speeds in agricultural and wooded areas are higher than in low-density residential areas. Based on this supporting evidence it is hypothesized that the statistical significance of adjacent land use, as found in this study, does imply that it is one of the major factors influencing speeds on 2-lane highways.
(5) Extra he The extra lane factor was found to be only marginally significant based on the Ontario data, as indicated by a coefficient of 6.23 and a standard error of 5.28. The suggested speed increase of 6.23 km/hr appears to be of the right order of magnitude but more locations with a greater variety of extra lane conditions need to be investigated before this value can be used with a significant amount of confidence. It is interesting to note that upgrading a 2-lane highway to a 4-lane highway is analogous to adding an extra lane. It could therefore be argued that the increase in speed due to the upgrading of a highway from 2 to 4 lanes would be approx. 6 km/hr. Turner et ul. (1982) found that the conversion of the shoulder of two lane highways to an additional travel lane would increase average speed by about 5’:;. For an average speed of 80 km/hr, this corresponds to an increase of 4 km/hr.
(6) Accrss The coefficient for the access factor had a magnitude of - 8.03, with a standard error of 2.52. This indicates that the operating speed of a two lane highway would drop by approx. 8 km/hr for each unit of severity of access, as defined previously. Despite the high coefficient value the access factor, by which it is multiplied to determine speed reduction, is small, as discussed previously.
SAM YAGAR
324 The use of the factor is illustrated
and
by the following
MICHEL VAN AERDE
examples:
(1) A ramp merge at an upstream speed decrease = coefficient x weight = S.Okm/hr x 2 = 1.4 km/hr.
distance of 750 m. x decay x normalization x 0.59 x (l/6. 86)
(2) A traffic light at an upstream distance of 450 m. speed decrease = coefficient x weight x decay x normalization = 8.0 km/hr x 4 x 0.73 x (l/6. 86) = 3.4 km/hr. (3) A gravel road access at an upstream distance of 1500 m. speed decrease = coefficient x weight x decay x normalization = 8.0 km/hr x 1 x 0.35 x (l/6. 86) = 0.4 km/hr. The impact of left hand turns from a two-lane highway is much more severe than that of right hand turns from the same highway, as a left hand turn requires an acceptable gap in the opposing traffic flow. The effect of the access in this case depends upon the number of left turners and the opposing volume as described by Van Aerde and Yagar (198 I).
positive effect on faster vehicles, as represented by the 85th and 97.5th percentile. However, truck speeds were not found to be affected, for any speed percentile. Leong (1968) found sight distance to be as important for trucks as for passenger cars, and estimated a speed increase of 0.25 kmjhr per 100 m of increased sight distance.
(7) Lateral obstruction Most two-lane highways today have sufficient pavement and shoulder widths, except for restricted widths on some bridges and in areas with large accumulations of snow. These latter special conditions were not considered in our data. More common potential lateral clearance problems have been addressed by Inglis (1979) but severe lateral obstructions of these types were also rare and minor at our study locations. As a result, the regression analysis found the coefficient for lateral obstruction to be unstable (and of the incorrect sign) and the lateral obstruction factor was removed from the regression. The effect on speed, of distance to nearest obstruction, is not clear in the literature. Some sources, such as HCM (1965) and Leong (1968) acknowledge an increase in speed for wider shoulders but other sources, such as Troutbeck (1976) and O’Flaherty and Coombe (1971), find no significant effect on speed. Due to these discrepancies, the effect of minor variation in shoulders is thought to be minimal. Any further study of this factor would need to have data at the extreme low clearance end as well as at some greater clearances.
(9) Centre line Centre line had a coefficient of -0.0560 and a standard error of 2.43, which indicates it was totally insignificant. This was not due to a lack of required range in data but perhaps due to the fact that centre line markings are selected based on the amount of curvature, grade, and sight distance. Any speed impact of the centre line markings could therefore already be reflected by these other factors with which it was found colinear.
(8) Sight distance The coefficient of sight distance was found to be insignificant as shown by its estimate of - 0.0003 and its standard error of 0.0030. The lack of significance can be due to a lack of variety in the data or it might simply indicate that the influence of sight distance is an order of magnitude smaller than that of some of the other geometric factors. Other sources have found sight distance to be a significant factor, but often they question the correlation with curvature and hilliness. Troutbeck (1976) found sight distance to have a
(IO) Speed limit Speed Limit was found to have a coefficient of -0.67 and a standard error of 0.10. This indicates that the speed at a location decreases by about 0.7 km/hr for every 1 km/hr by which 90 km/hr exceeds the posted legal speed limit. The effect of legally posted speed limits is generally not incorporated in speed prediction models even though a large number of studies have been conducted on the enforcement of speed limits. While it is noted that speed limits are set in accordance with the level of design of the highway and certain environmental factors, many highways are designed for higher than legal speeds, and drivers are guided by the posted speed limit as well as geometric factors. On Highway 400 a smooth transition from a 4-lane section, with a speed limit of 100 km/hr, to a 2-lane section, with a speed limit of 90 km/hr, takes place approx. 4 km upstream of the data collection site 400Nl. The higher upstream speed limit still has a residual impact 4 km downstream, as illustrated in Fig. 5. The data indicate that the half-life is about 4 km, so that the transition will be about half completed at site 400N1. The use of an effective speed limit of 95 km/hr was substantiated by the resulting
Geometric
and environmental
325
effects on speeds of 2-lane highways
Effective Speed Limit
----
4
km
Fig. 5. Effect of smooth
Distance upstream
correct
speed prediction for the location. Similar analysis was used at other sites. It is noted that the speed limit of 90 km/hr would be used strictly for site 4OOSl as the south bound speed limit is 90 km/hr for a long distance north of 400SI. Further discussion of this effect is not warranted in this paper but may be treated in a future paper.
CONCLUSIONS (1) For the variety of conditions studied in Ontario, land use and speed limit were found to have greater impacts on speeds of 2-lane rural highways than geometric design factors. Seventy percent of any variation in speed limit was reflected directly in operating speeds, while adjacent landuse decreased speeds by about 8 km/hr. (2) Although less pronounced, gradient, access to highways, and lane width were also statistically significant. It was found that each percent of upgrade reduced speeds by about 2 km/hr, while downgrades increased speeds at this same rate. The coefficient of reduced speed due to access from other roads was about 8 km/hr, although the net access factor would generally result in a speed reduction which was just a fraction of this 8 km/hr. The sensitivity of speed to lane width was 6 km/hr per m. (3) Road curvature, presence of an extra lane, sight distance, centre lane markings and lateral obstructions were not found to have statistically significant effects on speed.
REFERENCES Duncan N. C. (1974) Rural speed/flow relations. TRRL Rep. 651. Galin D. (1981) Speeds on two-lane rural roads-a multiple regression analysis. Trajic Engng Control 22(8/9), 453.
Upstream
speed limit transition.
Highway Capacity Manual (1950) U.S. Dept. of Commerce. Bureau of Public Roads. Highway Capacity Manual (1965) U.S. Highway Res. Bd., Spec. Rep. 87. Inglis P. F. (Ed.) (1979) Treatment of Roadside Hazards. RTAC, Ottawa. Leong H. J. W. (1968) Distribution and trend of free speeds on two-lane two-way rural highways in New South Wales. Proc. ARRB. 4, Part 1, 791-814. McLean J. R. (1981) Driver speed behaviour and rural road alignment design, Traffic Engng Control 22(4), 208. O’Flaherty C. A. and Coombe R. D. (1971) Speeds on level rural roads: a multivariate approach. Traffic Engng Control 13( l-3). Opiela K., Datta T. D. and Randolph D. (1976) Study of location bias in speed-volume relationships for two-lane arterial roadways. TRR 615, 18-19. Onoenlander J. C. (1966) Variables influencing soot speed ‘characteristics. HRB .?pec. Rep. 89. - . ’ Taylor M. A. P., Miller A. J. and Ogden K. W. (1972) Aspects of traffic flow on grades. ARRB Proc. 6, Part 3, 2322248. Troutbeck R. J. (1976) Analysis of free speeds. ARRB Proc. 8, Session 23, 40. Turner D. S., Rogness R. 0. and Fambro D. B. (1982) Shoulder upgrading alternatives to improve the operational characteristics of two-lane highways. TRB Mreting, Jan. Washington, D.C. Van Aerde M. and Yagar S. (1981) Quantitative estimates of capacities and levels of service for 2-lane highways. Final Report to Ontario Ministry of Transportation and Communications, 188 pp., July. Van Aerde M. and Yagar S. (1982) Efficient provision of a large data bank for speeds on 2-lane highways. Presented to RTAC Ann. Con/, Hzlifax, Sept. Van Aerde M. and Yagar S. (1983)Volume effects on speeds of 2-lane highways in Ontario. Transpn Res. 17A, No. (4), 301-313. Yagar S. and VanAerde M. (1981) Field studies on 2-lane highways: volume/capacity relationships. Final Report to Ontario Ministry of Transportation and Communications, 266 pp., February. Yagar S. and VanAerde M. (1982) Radar-platoon technique for efficient and complete speed measurements. TRR 841, 36-41. Webster F. V. and Cobbe B. M. (1966) Traffic signals. Road Research Paper 56, London.
Tronspn Rex -A Vol. 17A. No. 4. pp. 315 325, 1983 Printed in Great Bntain.
GEOMETRIC AND ENVIRONMENTAL EFFECTS ON SPEEDS OF 2-LANE HIGHWAYS SAM Department
YACAR
of Civil Engineering,
and
MICHEL
University (Rrcriwd
VAN
of Waterloo,
13 April
AERDE
Ontario,
Canada
N2L 3Gl
1982)
Abstract--A study of the effects of various geometric and environmental factors on the speeds for 2-lane rural highways was performed in Ontario, Canada using 1980 data which had been collected by means of the Radar-Platoon technique. Over 5000 5-min periods of data, collected at 35 different locations, were used to estimate the effects of the various contributing local factors. Each of these contributing factors was formulated as the exponentially smoothed average of the geometric properties up to 1500 m upstream. To control for varying traffic volumes, the speeds used for estimating the geometric effects were those corresponding to main direction volumes of 900 passenger car units (pcu) per hour and opposing volumes of about 300pcu/hr. A multiple linear regression model related measured speeds to the upstream influencing properties of the highway. Land use adjacent to the road, and legal speed limit, were found to have the most significant impacts on speed. Grade, access from other roads, and lane width, followed in that order. The above significant factors explained 85:; of the across-sites variation in speed, leaving relatively small residual errors. Road curvature, presence of an extra lane, sight distance, center line markings and lateral obstructions were not found to have statistically significant effects on speed. Stronger statistical relationships could be obtained for both the above significant and insignificant factors, by testing these factors over wider ranges than those available on Ontario’s highways, as Ontario uses relatively high and uniform design standards. For example, gradients were limited to less than 3%, and radius of curvature to greater than 1400m. INTRODUCTION
and Coombe (197 I), in a study of a greater variety of geometric features, again found curvature to be the dominant factor. Duncan (1974) found that at low volumes speeds are strongly affected by hilliness and bendiness, but not by carriageway width. Duncan’s formula for freespeeds on 2-lane highways accounts for nearly 80% of the variance of the free speed, after correcting for traffic flow. Using 1963 data, Troutbeck (1976) found that neither pavement width nor shoulder width significantly affect free speeds of cars and trucks. This same study found grade, for all vehicle types, and sight distance, for just passenger cars, to be the most significant factors for predicting free speeds. Leong (1968), using similar data, found that in general, an increase in gradients, either upgrade or downgrade, decreased speeds, while increases in pavement width, shoulder width and sight distance, increased speeds. Turner et ul. (1982) found that the conversion of a shoulder to an additional travel lane could be expected to increase average speed of a 2-lane highway by about 5’:/, for volumes exceeding 150 veh/hr. The effect of landuse adjacent to the highway is significant, according to Galin (1981), who found that speeds in agricultural and wooded areas are higher than in low-density residential areas. He also found that the speed at a site was affected by the trip distance from its origin to that site. While the above works tended to emphasize the effects on free speeds, this paper addresses the effects of geometric and environmental factors at a practical medium-to-high flow rate, represented by 900 pcu/hr in the mainline direction and 300 pcu/hr in the opposing direction. It is in this range of traffic volumes
O’Flaherty
speeds depend upon traffic volumes, and the many geometric and environmental conditions on and adjacent to the roadway. An earlier paper by Van Aerde and Yagar (1983) examined the former, while this paper considers the latter. The effects of roadway conditions on average speed, at a mainline volume of 900 pcu/hr and an opposing volume in the range of 300 pcu/hr are studied, as this is considered to be a typical demand at which geometric improvements are often considered in order to improve service levels. Geometric factors relate to the roadway design, while e&ironmental factors consider other conditions surrounding the roadway, such as landuse and speed limit. Both the roadway design factors and these other environmental conditions are often collectively referred to simply as geometric factors. Highway
EARLIER
ESTIMATES
ENVIRONMENTAL
OF
EFFECTS
GEOMETRIC/ ON
SPEEDS
The effect of geometric properties on the operating characteristics of 2-lane highways has been the subject of a number of studies. Much of the earlier work in this area is reviewed by Oppenlander (1966) and has been incorporated into the first two editions of the U.S. Highway Capacity Manual (1950, 1965). The HCM has been the most commonly used design standard since that time, but changing traffic and vehicle characteristics have left much of it outdated. More recent works have addressed specific aspects of the relationship between speed and the geometric properties of the roadway. The majority of this research has dealt with the effects of geometries on free speeds. McLean (1981), in a study of 120 curve sites, found a strong effect of curvature on speed. TRA Vol. 17 No. .+E
315
316
SAM YAGAR
and
MICHEL VAN AERDE
that upgrading of 2-lane highways is usually considered. Also, most of the previous research used instantaneous geometric properties as the factors influencing spot speeds, while speeds are largely dependent upon upstream geometric characteristics. This is especially true on 2-lane facilities, as the restriction on passing opportunities tends to build up platoons over prolonged stretches of road. This paper attempts to account for upstream geometric factors by using a smoothed average of the geometric properties over a 1500-m stretch upstream of the sites where spot speeds were monitored.
lane, access, shoulder width to nearest obstruction, sight distance, centre line marking, and speed limit. The approximate ranges of the above geometric factors, as found in the data base, are summarized in Table 1. These values represent average values over the entire 1500-m upstream stretch as opposed to any instantaneous values within that upstream stretch. The effects of all of these factors are described qualitatively in this paper, whether they were found significant or not, as one is interested in knowing both the significant and insignificant factors. The estimated levels of statistical significance can also aid the synthesis of future studies.
DATA
FACTOR FOR WEIGHTING UPSTREAM GEOMETRIC/ENVIRONMENTAL PROPERTIES
DECAY
The previous paper by Van Aerde and Yagar (1983) described the data bank that was acquired at 35 Ontario locations. These speeddvolume data were analyzed, along with the geometric conditions at each of the 35 study locations, to determine the effects of geometric properties on the speeds of 2-lane rural highways. For each location, the volumeespeed data were plotted to obtain an estimate of the average speed at a mainline volume of 900 pcu/hr, and an opposing direction volume of about 300pcu/hr. In this way, the traffic volumes were essentially controlled while the geometric/environmental factors were varied, so that the marginal effects of the geometric/environmental effects could be studied quite simply. FACTORS
WHICH
WERE
The speeds at a location depend upon conditions for some distance upstream, with the closer geometrics having the greater impacts. Therefore a “decay factor” was applied to model the effects of each of the geometric conditions up to 1500m upstream of each study location. The effect of any geometric condition is represented by means of a decay factor which reduces in the upstream direction, until at some point little identifiable influence remains. Theoretically, this factor decays geometrically from an initial value of 1, at the data collection site, to a value approaching zero at an infinite distance upstream. This ideal format is illustrated in Fig. 1. For practical purposes the section from 0 to 1500 m upstream of the location was divided into 10 sections, each 150 m long. The set of geometric conditions within each section was given 90% of the weight accorded to the adjacent upstream section. This configuration is illustrated in Table 1. The choice of 150-m increments, a maximum upstream distance of 1500 m and a 0.9 decay factor were based on judgment and on local and practical consid-
CONSIDERED
The geometric properties, which were thought to affect operating speeds and also available in sufficient variety to be analyzed, are discussed below in general terms. The actual values of these properties for the locations of interest are listed in detail by Yagar and Van Aerde (1981). The factors considered are curvature, gradient or slope, lane width, landuse, extra
WEIGHT
0. 2 0. 0 0
150
300
450
600
750
900
1050 1200 1350 1500 DISTANCE UPSTREAM IN
Fig. I. Graphical illustration
i 1650 1800 HETRES
of ideal decay factor.
Table I. Range of average upstream geometric properties among the 35 Ontario data collection sites 1
-
road
-
slope
or
-
lane
width
-
adJacent
-
access
-
extra
-
lateral
-
centre
-
sight legal
curvature grade
0
to
-3%
to
3.3
from
other
lane obstructlon
line speed
roads
degrees
to
3.8 100
%
type
1 to
type
none
to
45
4 %
none
to to
minor continuous
to
infinite
solid
limit
500 80
m
km/h
to __~
90 ~~__.
per
%
to
markings
distance
m
0
landuse
4 +2
Ill
passing
km/h
10 10 m
1
317
Geometric and environmental effects on speeds of 2-lane highways WEIGHT
y-----l___ 0. 0.
_
2 0
I 0
150
300
450
600
750
900
1650
1200
DISTANCE
1350
1500
UPSTREAM
1650 IN
ll300
METRES
Fig. 2. Graphical illustration of actual decay factor.
erations. They are subject to review and can be appropriately modified to adapt to the specific accuracy requirements of any given application. The sum of the decay factors for I = O-10 is 6.87. To combine the influences at the upstream sections, one merely adds their weighted effects, and normalizes by dividing by 6.87. FORMULATION
OF GEOMETRIC
FROM THE GEOMETRIC
FACTORS
PROPERTIES
In order to regress the speed measurements upon the upstream geometric properties the latter must all be represented quantitatively. The attributes of each factor must be reflected appropriately, providing an approximately linear relationship between the transformed factor and the measured speed. The following section describes how, based on the above, each of the geometric factors was formulated from its relevant geometric properties for the purposes of the analysis described herein.
(1) Curvature The curvature at each upstream section was measured as the maximum rate of curvature in that
section, expressed in degrees per 100 m. Negative values were used to indicate curvature to the left and positive values to indicate curvature to the right. The following formats were considered: (a) The effect of a curve modelled as linearly dependent upon the rate of curvature but independent of the direction of curvature. (b) The effect of a curve treated as linearly dependent upon rate of curvature and also dependent upon direction of curvature. (c) The effect of a curve expressed as a non-linear function of curvature. (2) Grade Vehicles tend to accelerate downhill and decelerate when going uphill, unless the driver compensates. The impact of road gradient was analyzed based on each of the following types of models: (a) Effect on speed proportional to absolute grade, increasing downhill and decreasing uphill as per Fig. 3(a). (b) Different linear increase/decrease in speed for down and uphill grade, as per Fig. 3(b). (c) Linear decrease in speed for deviations from an
downhill
uphill
(b)
Fig. 3. (a) Combined
grade
factor
for uphill and downhill. (b) Grade factor most grade” mode1 for uphill and downhill.
sensitive
to uphill.
(c) “Optimum
318
SAM
YAGAK
and
MICHEL
VAN
AERDE
SPEED DE;:;;”
- ~~-~~_>-----~
A=3.
Fig. 4. Ideal and simplified
“ideal”
or “optimum”
downhill
grade,
model
as per Fig.
3(c). (d) Combined effects of grade and length, or grade and presence of lateral obstructions. (3) Lane width ,factor The passage of vehicles requires a minimum lane width. Any additional width beyond this minumum allows one to drive faster and/or with a greater measure and perception of safety. This type of behaviour can be most accurately modelled by a decaying function (e.g. exponential), as shown in Fig. 4. The exponential model is not easily transformed into a simple speed prediction model, as it requires the calibration of two coefficients. However, the small range of lanewidths encountered in the data set permitted a linear approximation to the exponential form, as illustrated by the range from A to B in Fig. 4. Lane width.was therefore treated as a linear factor with an ideal lane width of 4 m. The coefficient of the lane width factor then determines the rate at which the speed would decrease for each metre by which land width falls short of 4 m. Although the choice of 4 m was arbitrary, the use of a different value would not change the value of this rate coefficient. Only the default speed cqrresponding to an arbitrarily defined generic road would be affected. (4) Land use Land use is defined to be a factor which land adjoining the section of highway driveways, and not otherwise. The land therefore represents the fraction (weighted according to distance upstream) of road
Table
Decay
2.
DISTANCE
(in
3m
8=3.0m
Lane
Width
width
min.
is set if the has access use factor inversely on which
factor
UPSTREAM
metres 0
1
weights
for the effect of lanewidth
land use was present in the 1500-m upstream stretch. The effect of access driveways interacting with a two-lane highway can be broken down into two components: (a) The actual or potential entering and exiting of vehicles onto or off the highway will tend to slow down the traffic as other vehicles are held up during the time the turning vehicle decelerates or accelerates. (b) The driver’s cognizance of and attention to the adjacent land use, such as reading of billboards, or attention to the activities of children. (5) Extru lane The extra lane factor represents the fraction of upstream stretch during which an extra lane or fully paved shoulder was available. The presence of an extra lane can increase the operating speed of a highway in the following ways: (a) An extra lane (or a paved shoulder) provides an extra margin of safety which can promote higher speeds. (b) The extra lane also allows passing of slow vehicles which might otherwise inhibit the normal traffic flow, such as heavy vehicles on an uphill section, farm equipment on a rural road, or an entering or exiting vehicle. (6) Access ,jhctor Access is distinguished from Land use in that the former considers road intersections, which are public, while the latter considers driveways, which are generally private. Access thus considers trip continuations rather than origins and/or destinations. There are a variety of means of gaining access to a two lane highway and the nature of the access
for upstream STATION I 0
150
1
300
2
450
3 4
600
on speed
geometric
conditions WEIGHT C.9) XSI 1 09 0 0
I 81 73
0. 66
750
5
0
900
6
1050
7
0. 53 0. 48
1200
e
0. 43
1350 1500
9
0. 39
10
59
Geometric
and environmental
Table 3. Access types and corresponding 1 WEIGHT 1
TYPE
0
-
1 2 3 4
-
319
effects on speeds of 2-lane highways
weights used
OF ACCESS
I
access by any roads minor road (usually gravel) high speed ramp merge ma.jor road (paved with no sccel/deceleration controlled intersection (traffic signals) no
ramps)
governs the severity of its speed impact. For the purposes of this study the different types of access were divided into the categories described in Table 3. The weights assigned to the various access types increase with the severity but no attempt has been made to quantitatively reflect the relative severity of the various types of access as the Ontario data file did not contain sufficient variety in access data. Rather, the weights given in Table 3 were adopted. It is conceded that these weights are really a rank ordering. However, after much deliberation a “better” set of weights could not be determined. It is also noted that the access factor will generally be significantly less than one, as accesses of the above type are not found within 100 m of one another, and more than one major access or 2 minor road accesses within 1500 m is very uncommon.
The ideal road was assumed to have an ideal sight distance of 1500 m and the sight distance factor was formulated as the difference between the actual sight distance and the ideal of 1500 m. The benefit of sight distances greater than 1500 m were not considered.
(7) Lateral obstruction Provision of a shoulder, rather than an abrupt obstruction or curb, gives the driver an extra margin of safety which should tend to promote higher speeds. The lateral obstruction factor included in the model represents the distance to the end of the shoulder or to the nearest object or curb, whichever is less. Whenever the distance to an object is small one would have a small positive obstruction factor and the speed should be reduced. Conversely, a greater distance, as indicated by a greater obstruction factor, would increase the speed.
(10) Speed limit The speed limit can directly inhibit the speeds of the faster vehicles when the road geometries might otherwise permit higher speeds. Higher limits also tend to reflect better designs causing speeds to be correlated with the posted limits. The speed limit factor used in the model represents its marginal effect on speeds, after the other geometric factors have been accounted for. Using a speed limit of 90 km/hr as a reference, the speed limit factor was formulated as the difference between that reference and the posted limit. Its coefficient represents the reduction in average speed due to speed limits below 90 km/hr.
(8) Sight distance The lack of adequate sight distance should tend to decrease the operating speed on a two lane highway, as faster vehicles are prevented from passing slower ones. Longer sight distance also gives the driver an opportunity to see what is ahead providing the platoon leader with a longer perception and reaction time and promoting higher speeds.
(9) Centre line For the purposes of this speed prediction model, all the centreline markings are classified as either allowing passing or not allowing passing in the direction that is being monitored. Sections allowing passing were given a value of 0 for the passing factor, and those not allowing passing were given a value of 1. Thus, the coefficient provided by the regression model for this factor would directly estimate the speed reduction penalty which occurs if passing is not allowed.
SUMMARY
OF GEOMETRIC
FACTORS
Roads in Ontario are generally designed using relatively uniform design standards. As a result, the variation of the geometric variables that were studied was in some cases not as great as might be expected in other parts of the world. The coefficients calibrated in
Table 4. Ranges considered for the upstream average geometric factors Min Curvature factor in degrees per 100 m Average Uphill grade as a positive X Average Downhill grade as a negative X Net summation of up-down hill grades as a X Lane width less than ideal of 4 metres Fraction of extra lane in upstream stretch Severity of access onto upstream stretch Fraction of landuse in upstream stretch Average distance to obstruction in metres Sight distance short of 1500 metres Indicator of centre line passing provision Speed Limit Less than 9Okm/h reference
0. 00 0. 00 0.
00
-3. 06 0. 20 0. 00 0. 00 0. 00 1. 75 326 0. 00 0. 0
Ilax 4. OS 2. OS -3.26 1. 72 0. 70 0. 44 0. 73 1. 00 5. 00 1034 1.00 10 0 -_
Mean 0. S5 0. 60 -0. 67 -0.07 0. 38 0. 06 0. 16 0. 19 4:34 553 0. 44 8. 14
SAM YAGARand MICHELVAN
320
this study should therefore be considered in view of the averages and ranges of the various geometric factors. These are summarized in Table 4. SPEED PREDICTION MODEL
(1) Simple correlution matrix Table 5 presents the simple correlation matrix for the geometric/environmental factors which were considered, along with the corresponding probability of each pair of factors not being correlated. The following factors were considered: = Average speed as measured at data collection sites. = Speed limit penalty (90 km/hr-Posted Limit). = Curvature factor expressed as degrees per 100m. = Average Uphill grade quoted as a positive 7;. = Average Downhill grade quoted as a negative ‘4. = Lane width less than ideal of 4 m.
SPDLIM CURVE UPHILL DOHILL WIDTH
Table *et*
CDRRELATIDN
AVER
5. Correlation
COEFF*CIENTS
FOR
XLANE
= Fraction of occurrence of extra lane in upstream stretch. = Severity of access onto the upstream stretch. = Fraction of land use present in upstream stretch. = Average distance to nearest obstruction in metres. = Sight distance short of 1500 m. = Indicator of centre line passing provision. = Net summation of up and down hill grades as a %.
ACCESS LANDUSE
A speed prediction model was formulated and calibrated through the use of regression analysis. The simple correlation matrix of the above factors, and the statistical parameters of the regression model are presented in Tables 5 and 6 respectively. Table 7 lists the speed predictions of the model and compares them to the speeds that were actually observed at each of the locations.
AVER
AERDE
matrix
THE
SPDLIM
OBSTR SIGHT CENTRE SLOPE
(2) Multiple linear regression model Several multiple linear regression models were considered. The stability of each model was tested by adding and subtracting marginal variables using a step-wise approach. A final model is presented in Table 6 along with its statistical significance indicators. This model explains 85% of the original variation in the measured speeds, based on 5 significant geometric factors and a constant representing the expected speed for neutral geometric conditions. The factors used in the final model were statistically significant at the 0.05 level and causally acceptable; the latter signifying correct sign and reasonable magnitude. The rejected parameters are illustrated for academic interest. The estimates quoted for each of these rejected parameters were obtained from separate regression models, each of which contained the corresponding rejected parameter and all of the
for geometric/environmental
GEcmETAIC
WIDTH
FACTORS
XLANE 0 04 8017
CONSIDERED
ACCESS -0
25 1446
AVER
1 00 0000
-0 73 000 1
-0 47 .0047
SPDLIM
-0 74 0001
1 DO 0000
0 15 3849
015 3766
022 2051
D 18 2993
0 31 0687
0 31 0740
CURVE
“WILL
DOHILL
WIDTH
XLANE
ACCESS
013 4459
-002 .91m
10 30 0749
0 12 4904
-0 28 09-L
0 36 0289
-0 35 .,0386
0 50 ,002,
0. 15 .3891
-0. 37 0291
0 49 0028
0 64 0001
0 44 0083
-0 30 .0791
0 26 1391
-0 81 0001
0. 31 ,071L
-0 07 6863
-0. 24 ,584
0 27 ,169
0 13 4480
0 54 .0007
0 02 .91&b
0 38 0234
-0.43 0108
0 19 26353
-0. 10 5802
0 38 0243
-0 31 0717
0 09 6081
0 0, 9611
0 03 8.520
0 01 9390
0 IE 2938
-0 20 2574
0 57 0003
037 0285
-012 5027
-0 47 0047
0 15 3849
1 00 0000
-0 07 6820
0 12 .4759
0 04 8017
0 13 3766
I 00 0000
0. 56 0003
-0
0 SC OOOJ
100 0000
-014 4089
0 31 .0627
0 31 0716
-0
11 5167
-0 14 .4089
OBSTR
-0 02 9223
0
07 6863
0
54 0007
0.
SIGHT
0 20 2460
-0 30 0749
24 1584
0 02 9166
-0
-0 19 2856
0 12 4944
0 27 ,165 0. 13 4480
SLOPE
D 38 .0260
0 16 3646
-0. 60 0002
CENTRE
0 32 Ot.27
-0.13 .4953
I ANDUSE
-0
24 1656
38 0760
-0 00 9970
-0
-0
-0 11 5189
0 64 0001
-0 Bl 0001
19 2653
CENTRE
0 20 2460
-004 81.52
0 12 4759
SIGHT
-0 02 9223
003 BB93
0 22 .2051
rlODEL***+
OQSTR
-0 03 8579
25 ,446
THE
-0 60 0002
0 24 1690
-0
IN
LANDUSE
-0 20 2451
-0.07 6828
factors
11 3167
1 00 0000 0. 09 .6081
1
00 0000
10 5802
0 01 961 I
0 38 0234
0 38 0243
0 03 0620
0 37 0307
-0 43 0100
-0 31 0717
0 01 9390
-025 1489
-0 20 2370
-0
-0.19 2856
30 2378
0
1
-0
00
37 0307 45
SLOPE -0
24 lb56
-0 00 9970 -0
-0
11 5189
25 1489
0069
0 01 9350
-0 45 0069
1 00 0000
0 09 6016
001 9350
0 09 6016
1 00 0000
0000
Geometric and environmental effects on speeds of 2-lane highways Table PARAMETER
93. factor
lane
-
width
landuse access
factor
speed
T
limit
0001
1.
12
3.74
0008
0.
48
2.
31
65
-
2.54
.0205
4.92
0001
1. 68
-
8.0
-
3.18
0035
2.
52
-
0.7
-
6.
.OOOl
0.
10
in
estimate multiples
of
of
Sums
Squares
Model Total
829 151 1010
Variable
Dependent
0. Dep.
of
Standard
of
REJECTED
Variable of
Variation
Parameters
PARAt’lETERS
Curvature
factor
Extra
Lane
Sight
Distance Line
Obstruction
factor factor
IMPACTS
OF
FACTORS
ESTIMATE +
0.45
+
6.2 0.06
factor
-
3.
ON
SPEED
(1) Curvature A simple linear term was introduced as a first approximation of the curvature factor, with right and
28
0.
0275
Model
Final PR
>
----
T
3480
0.3
The final statistical model for predicting speeds on 2-lane highways as a function of geometric and environmental factors has been described above. A more detailed discussion of each of the factors is presented below with our findings for each compared to those in the literature.
00
.2493 .9208
-
GEOMETRIC/
85
2.
from
-
(3) Speed prediction and residuals Table 7 lists a summary of the average upstream geometric/environmental properties, corresponding speed predicted by the model, observed average speed, and residuals for each location. OF
ReJected
factor
significant parameters. It is noted that the obstruction factor appeared statistically significant, but in the wrong direction.
ENVIRONMENTAL
83.
Deviation
Coefficient
Properties
----
MAGNITUDE
R-Squared Mean
OF
SQUARES
34
of
parameter
----
SUM
OF
INDICATOR
DISCUSSION
Model
5
Properties
Centre
for
29
Corrected
----
the
parameter
FREEDOM
Error
value
dev.
for
estimated
DEGREES
OF
DEVIATION
parameter
std.
level
the
of
of of
Significance CPP~P
Analysis
SOURCES
56
regression
Statistical
----
ERROR
-
83.
Standard
----
STD.
-
Significance
-
:T:
5.7
Multiple
IT:
>
8.3
-
ERROR-
PR
VALUE
-
-
>
for speed prediction
-
T-VALUE STD.
-
3
1.8
ESTIMATE PR
model
ESTIMATE
intercept grade
6. Final
321
5
9818
.0049
lefthand curvature carrying the same weight. The curvature factor had a coefficient of 0.45 with a standard error of 0.47 and did not prove significant for the given data set. It was not incorporated into the geometric speed prediction model because its coefficient was found to be insignificant and of the wrong sign. Since the approximation as a linear term did not show statistical significance, more elaborate combinations and variations of the curve factor were not considered, as a much higher level of significance would be required to calibrate these terms. The lack of significance of the curvature factor is in contrast with the findings from other sources. Duncan (1974) and O’Flaherty and Coombe (1971) found that speeds at low flows were strongly affected by bendiness in the upstream section, while McLean (1981) and numerous others established similar relationships for speeds and instantaneous curvature. This discrepancy could be due to the lack of a sufficient variety of severe curves in Ontario. Also, the effect of curvature might have been hidden in
322
SAM YAGAK and
MICHEL
Table 7. Gcometric,:environmental
~~___
LANE
LAND
WIDTH
USE
AEKDE
properties and speed predictions
EXTRA
---_SPEED----
UP
DOWN
OBS
0. 0
0. 4
89
90.5
0
0. 0
91
90.8
+o.
0. 2
0. 0
87 94
89. 5 93.0
-2 5 +1.0
0. 0
0. 8
95
93.3
+1.7
0.0
1.2
94
93.
3. 9
87
84.0
83
83.
79
83.5
SPEED
TION
LIMIT
4OOSl
90
3
0. 0
0.8
00
0. 8
4oos2
90
38
0.0
07
00
0. 0
400%
90
38
0.0
02
0. 0
1.9
1300
400Nl
90
3. 5
0. 0
0. 5
0. 0
1. 8
400N2
90
3. 8
0. 0
0. 7
0.
0
400N3
90
3. 8
0. 0
1. 0
0. 0
0.7
35Sl
00
36
0.0
01
0. 4
3
3x4
80
3. 6
0. 0
0. 4
0. 0
1.4
0812
3585
80
3. 6
0. 0
0. 5
0. 2
0. 0
0. 5
1. 6
LINE
CURVA
-GRADE-
LOCA
5
CENTRE
VAN
LANE
TURE
1
0
5
0.
6
1
PRED
RES -1.5
4
+O.
-0.
80
36
0.4
00
0. 2
3. 0
2. 4
0. 8
84
79.4
+4.
00
34
0. 0
0. 8
0. 0
3. 4
1. 5
1. 0
82
82.3
-0.3
3SN4
80
37
0. 0
0. 4
0. 0
0. 0
1. 4
1. 3
80
82.
3SN5
80
3. 6
0. 0
0. 5
0. 2
0.0
0.2
1.0
82
81.7
80
36
0. 7
0. 6
0. 0
0. 0
0. 4
0. 2
79
78.0
80
37
1.0
1.0
0. 0
0. 0
0. 0
0
3
76
76.
1
7El
80
3.8
00
0. 9
0.
0. 0
0. 4
0.
7E2
80
3. 8
0. 0
0. 5
0. 0
1
0.0
7E3
80
38
0. 7
0. 0
0.8 0.1
0.0 1.2
0. 6
2.
2
-2.
+1
0
-0.
5
1
+2.
79
79.8
86
83.
-0.8
81 84
84.0 83. 4
-3.0 +O. 6
85
84
+1.0
81
84.5
-3.5
83
79.8
+3
3
86
84.
+l.
2 g
7E4
80
3.8
0. 7
0. 0
7ES
80
3.8
04
0. 5
0. 0
00
0.313
7Wl
00
3. 8
0. 0
0. 9
0. 0
0. 0
5
7W2
80
3.8
00
0. 3
0. 0
09
0. 5 0 2 10.1
7w3
80
3. 8
0. 2
0.5
00
0. 0
0.2
5
7w4
80
30
03
0.7
02
0.0
0
1.2
79
81.4
-2.
7w5
80
38
00
OS
00
2. 0
1. 1
0. 6
82
83.6
-1.6
85Sl
80
36
0.0
08
00
0. 0
0. 4
0.
1
82
84.0
ass2
80
3. 6
0.0
09
00
0. 7
0. 5
0. 2
86
84.
00
0. 4
0. 2
77
75.8
+1.2
0. 6
78
79.4
-1.4
6
0
8
1
-2.
0 9
8553
80
3
3
0. 8
0.4
00
80
3. 3
0. 4
0. 4
0. 0
0. 2
0. 3
8555
80
33
01
06
0. 0
1. 5
0. 9
0. 4
78
77.
8SNl
80
3. 6
0. 0
0. 6
0. 0
2. 8
0.
0. 3
84
82.7
+1.3
8SN2
80
36
00
1. 0
0. 0
0. 0
0. 0
0. 3
88
84.7
+3
8SN3
80
33
06
01
00
0. 8
0. 8
0. 0
73
73.5
-0.5
8SN4
80
33
0. 4
0.2
00
0. a
0. 8
0. 3
75
76.7
8SNS
80
33
0. 7
0. 6
0. 0
0. 0
0. 4
0.
76
76.
Speed
Limit
Lane
Width
Land
Ure
Centre Extra
Line Lane
curvature Grade Speed
OBS
Speed
PRED
Speed
RES
:
Legal
speed
limit
quoted
in
1
4
9
+l.
8554
1
2
5
2. 6 00
0
6
+0.3
0. 3 03
1
3
-4.5
35N3
6Sl
6
+3.0 2
35Nl
652
2
+0
6 3
-1.7 6
-0.
6
km/h
: Width of lane in direction of travel in metres : Landuse adJacent to highway, quoted as a fraction : Legally permitted passing, quoted as = fraction : Additional Lane provision, quoted as a fraction : Average degree of curvature in degrees per iOOm : Up and downhill gradientsquoted as a percent : Speed in km/h as observed at data collection site : Speed predlcticn based on the geometric properties : Difference between the observed and predicted speed
some of the other factors because of its colinearity with speed limit, sight distance, landuse, grade and the centre line markings. (2) Grade Initially a single linear grade factor was introduced, as per Fig. 3(a), which yielded a coefficient of - 1.80 and a standard error of 0.48. This implies that the operating speed at a location is expected to increase/decrease by approx. 1.8 km/hr for each I’:,, of grade when going downhill/uphill respectively. This is in keeping with the treatment of saturation flows by Webster and Cobbe (1966), where capacity increases by 3% for each 1% of downhill grade and decreases at the same rate for uphill grades. The level of sophistication of the grade factor model was increased by relaxing the restriction that down and uphill sections contribute the same absolute value to the operating speed. This was accom-
plished by introducing separate terms for positive grade and for negative grade as per Fig. 3(b). When considered separately, an average uphill grade of 1% was found to decrease the average speed by 1.3 km/hr, while a similar downhill grade increased the average speed by 2.2 km/hr. This indicates that speeds are more sensitive to downhill grades than to uphill grades. It should be noted however that the data were restricted to average positive and negative grades of 0.60 and 0.67% respectively with corresponding maxima of 2.00 and 3.26%. The relative statistical significance of the separate up and downhill factors and the combined factor are shown in Table 8. The choice between the use of the combined factor or the two separate factors depends upon the availability of data and the desired level of accuracy. An “optimum grade” model, as per Fig. 3(c), was also investigated but was not found significant. Can-
323
Geometric and environmental effects on speeds of 2-lane highways
Table 8. Comparison of combined and independent grade factors ESTIMATE Combined
Grade
Factor
Separate Separate
Uphill Factor Downhill Factor
didate “optimum” grades of 0.5. 1.0, 1.5, 2.0 and 2.5 were investigated. The effect of grades on speed is found significant by most sources but the variability in the format of the grade factors makes comparisons sometimes difficult. Linear relationships have been used by Leong (1968), quadratic relationships by Troutbeck (1976) and average hilliness function by Duncan (1974). Leong (1968) and Troutbeck (1976) found, for grades ranging from + 10% to - IO%, that uphill and severe downhill sections decrease the speed of passenger cars. While a decrease in speed for uphill grades is supported by our findings, the limited range of Ontario data did not allow a test of severe down grades. The topography of the Ontario locations was not conducive to comparing single long continuous uphill sections to aggregations of several shorter uphill sections. Similarly, the special distinction between trucks and passenger cars was not critical for the shorter and less steep uphill sections encountered in Southern Ontario. Specifically, Taylor et ul. (1972) suggest that, based on simulation techniques, the proportion of trucks in the flow does not significantly affect speeds for gradients below3’:,:. The combined effect of grades with curvature or obstructions could not be investigated, as the required variety of geometric combinations was not available.
For the practical range of lane widths from 3.3 to 3.8 m it was found that the operating speed of a given location is decreased by approx. 5.7 km/hr for each meter of reduction in lane width. The coefficient of - 5.67 and standard error of 2.3 1 indicate a reasonably high level of statistical significance. In accordance with the shape of Fig. 4, it is speculated that the speed reduction rate for lane widths less than 3.3 m will be even greater, and that for lane widths larger than 3.8 m this rate will be less. The effect of lane width on the speed of 2-lane highways is not always found significant by other sources. A significant positive effect of lane width is found in the HCM (1965), and by Leong (1968) but not by Duncan (1974) or Troutbeck (I 976).
(4) Lunrl USP The presence of landuse along the 1500 m of road leading up to the location was found, on the average,
STANDARD
ERROR
-1.80
0.
48
-1. 27 2. 16
0. 63 0. 67
to decrease speeds by approx. 8.3 km/hr, with a standard error of 1.7. The size of the land use coefficient and the corresponding small standard error indicate statistically, that land use is one of the most important and significant factors influencing speeds on 2-lane rural highways. The effect of land use on the average speed of 2-lane highways has often been ignored in the past but recently more emphasis has been put on its study. Opiela et al. (1976), studied the effect of abutting landuse and found that more intense land use slightly lowers the speed/volume curve for volumes beyond SOOveh/hr. Galin (1981) also found that speeds in agricultural and wooded areas are higher than in low-density residential areas. Based on this supporting evidence it is hypothesized that the statistical significance of adjacent land use, as found in this study, does imply that it is one of the major factors influencing speeds on 2-lane highways.
(5) Extra he The extra lane factor was found to be only marginally significant based on the Ontario data, as indicated by a coefficient of 6.23 and a standard error of 5.28. The suggested speed increase of 6.23 km/hr appears to be of the right order of magnitude but more locations with a greater variety of extra lane conditions need to be investigated before this value can be used with a significant amount of confidence. It is interesting to note that upgrading a 2-lane highway to a 4-lane highway is analogous to adding an extra lane. It could therefore be argued that the increase in speed due to the upgrading of a highway from 2 to 4 lanes would be approx. 6 km/hr. Turner et ul. (1982) found that the conversion of the shoulder of two lane highways to an additional travel lane would increase average speed by about 5’:;. For an average speed of 80 km/hr, this corresponds to an increase of 4 km/hr.
(6) Accrss The coefficient for the access factor had a magnitude of - 8.03, with a standard error of 2.52. This indicates that the operating speed of a two lane highway would drop by approx. 8 km/hr for each unit of severity of access, as defined previously. Despite the high coefficient value the access factor, by which it is multiplied to determine speed reduction, is small, as discussed previously.
SAM YAGAR
324 The use of the factor is illustrated
and
by the following
MICHEL VAN AERDE
examples:
(1) A ramp merge at an upstream speed decrease = coefficient x weight = S.Okm/hr x 2 = 1.4 km/hr.
distance of 750 m. x decay x normalization x 0.59 x (l/6. 86)
(2) A traffic light at an upstream distance of 450 m. speed decrease = coefficient x weight x decay x normalization = 8.0 km/hr x 4 x 0.73 x (l/6. 86) = 3.4 km/hr. (3) A gravel road access at an upstream distance of 1500 m. speed decrease = coefficient x weight x decay x normalization = 8.0 km/hr x 1 x 0.35 x (l/6. 86) = 0.4 km/hr. The impact of left hand turns from a two-lane highway is much more severe than that of right hand turns from the same highway, as a left hand turn requires an acceptable gap in the opposing traffic flow. The effect of the access in this case depends upon the number of left turners and the opposing volume as described by Van Aerde and Yagar (198 I).
positive effect on faster vehicles, as represented by the 85th and 97.5th percentile. However, truck speeds were not found to be affected, for any speed percentile. Leong (1968) found sight distance to be as important for trucks as for passenger cars, and estimated a speed increase of 0.25 kmjhr per 100 m of increased sight distance.
(7) Lateral obstruction Most two-lane highways today have sufficient pavement and shoulder widths, except for restricted widths on some bridges and in areas with large accumulations of snow. These latter special conditions were not considered in our data. More common potential lateral clearance problems have been addressed by Inglis (1979) but severe lateral obstructions of these types were also rare and minor at our study locations. As a result, the regression analysis found the coefficient for lateral obstruction to be unstable (and of the incorrect sign) and the lateral obstruction factor was removed from the regression. The effect on speed, of distance to nearest obstruction, is not clear in the literature. Some sources, such as HCM (1965) and Leong (1968) acknowledge an increase in speed for wider shoulders but other sources, such as Troutbeck (1976) and O’Flaherty and Coombe (1971), find no significant effect on speed. Due to these discrepancies, the effect of minor variation in shoulders is thought to be minimal. Any further study of this factor would need to have data at the extreme low clearance end as well as at some greater clearances.
(9) Centre line Centre line had a coefficient of -0.0560 and a standard error of 2.43, which indicates it was totally insignificant. This was not due to a lack of required range in data but perhaps due to the fact that centre line markings are selected based on the amount of curvature, grade, and sight distance. Any speed impact of the centre line markings could therefore already be reflected by these other factors with which it was found colinear.
(8) Sight distance The coefficient of sight distance was found to be insignificant as shown by its estimate of - 0.0003 and its standard error of 0.0030. The lack of significance can be due to a lack of variety in the data or it might simply indicate that the influence of sight distance is an order of magnitude smaller than that of some of the other geometric factors. Other sources have found sight distance to be a significant factor, but often they question the correlation with curvature and hilliness. Troutbeck (1976) found sight distance to have a
(IO) Speed limit Speed Limit was found to have a coefficient of -0.67 and a standard error of 0.10. This indicates that the speed at a location decreases by about 0.7 km/hr for every 1 km/hr by which 90 km/hr exceeds the posted legal speed limit. The effect of legally posted speed limits is generally not incorporated in speed prediction models even though a large number of studies have been conducted on the enforcement of speed limits. While it is noted that speed limits are set in accordance with the level of design of the highway and certain environmental factors, many highways are designed for higher than legal speeds, and drivers are guided by the posted speed limit as well as geometric factors. On Highway 400 a smooth transition from a 4-lane section, with a speed limit of 100 km/hr, to a 2-lane section, with a speed limit of 90 km/hr, takes place approx. 4 km upstream of the data collection site 400Nl. The higher upstream speed limit still has a residual impact 4 km downstream, as illustrated in Fig. 5. The data indicate that the half-life is about 4 km, so that the transition will be about half completed at site 400N1. The use of an effective speed limit of 95 km/hr was substantiated by the resulting
Geometric
and environmental
325
effects on speeds of 2-lane highways
Effective Speed Limit
----
4
km
Fig. 5. Effect of smooth
Distance upstream
correct
speed prediction for the location. Similar analysis was used at other sites. It is noted that the speed limit of 90 km/hr would be used strictly for site 4OOSl as the south bound speed limit is 90 km/hr for a long distance north of 400SI. Further discussion of this effect is not warranted in this paper but may be treated in a future paper.
CONCLUSIONS (1) For the variety of conditions studied in Ontario, land use and speed limit were found to have greater impacts on speeds of 2-lane rural highways than geometric design factors. Seventy percent of any variation in speed limit was reflected directly in operating speeds, while adjacent landuse decreased speeds by about 8 km/hr. (2) Although less pronounced, gradient, access to highways, and lane width were also statistically significant. It was found that each percent of upgrade reduced speeds by about 2 km/hr, while downgrades increased speeds at this same rate. The coefficient of reduced speed due to access from other roads was about 8 km/hr, although the net access factor would generally result in a speed reduction which was just a fraction of this 8 km/hr. The sensitivity of speed to lane width was 6 km/hr per m. (3) Road curvature, presence of an extra lane, sight distance, centre lane markings and lateral obstructions were not found to have statistically significant effects on speed.
REFERENCES Duncan N. C. (1974) Rural speed/flow relations. TRRL Rep. 651. Galin D. (1981) Speeds on two-lane rural roads-a multiple regression analysis. Trajic Engng Control 22(8/9), 453.
Upstream
speed limit transition.
Highway Capacity Manual (1950) U.S. Dept. of Commerce. Bureau of Public Roads. Highway Capacity Manual (1965) U.S. Highway Res. Bd., Spec. Rep. 87. Inglis P. F. (Ed.) (1979) Treatment of Roadside Hazards. RTAC, Ottawa. Leong H. J. W. (1968) Distribution and trend of free speeds on two-lane two-way rural highways in New South Wales. Proc. ARRB. 4, Part 1, 791-814. McLean J. R. (1981) Driver speed behaviour and rural road alignment design, Traffic Engng Control 22(4), 208. O’Flaherty C. A. and Coombe R. D. (1971) Speeds on level rural roads: a multivariate approach. Traffic Engng Control 13( l-3). Opiela K., Datta T. D. and Randolph D. (1976) Study of location bias in speed-volume relationships for two-lane arterial roadways. TRR 615, 18-19. Onoenlander J. C. (1966) Variables influencing soot speed ‘characteristics. HRB .?pec. Rep. 89. - . ’ Taylor M. A. P., Miller A. J. and Ogden K. W. (1972) Aspects of traffic flow on grades. ARRB Proc. 6, Part 3, 2322248. Troutbeck R. J. (1976) Analysis of free speeds. ARRB Proc. 8, Session 23, 40. Turner D. S., Rogness R. 0. and Fambro D. B. (1982) Shoulder upgrading alternatives to improve the operational characteristics of two-lane highways. TRB Mreting, Jan. Washington, D.C. Van Aerde M. and Yagar S. (1981) Quantitative estimates of capacities and levels of service for 2-lane highways. Final Report to Ontario Ministry of Transportation and Communications, 188 pp., July. Van Aerde M. and Yagar S. (1982) Efficient provision of a large data bank for speeds on 2-lane highways. Presented to RTAC Ann. Con/, Hzlifax, Sept. Van Aerde M. and Yagar S. (1983)Volume effects on speeds of 2-lane highways in Ontario. Transpn Res. 17A, No. (4), 301-313. Yagar S. and VanAerde M. (1981) Field studies on 2-lane highways: volume/capacity relationships. Final Report to Ontario Ministry of Transportation and Communications, 266 pp., February. Yagar S. and VanAerde M. (1982) Radar-platoon technique for efficient and complete speed measurements. TRR 841, 36-41. Webster F. V. and Cobbe B. M. (1966) Traffic signals. Road Research Paper 56, London.