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THE IMPACT OF SPEED INCONSISTENCY ON DRIVING SAFETY
Biljana Vukoje, B.Sc. CE University of Split, Faculty of Civil Engineering, Architecture and Geodesy
E-mail: [email protected]
Prof. Dražen Cvitanić, PhD. CE University of Split, Faculty of Civil Engineering, Architecture and Geodesy
E-mail: [email protected]
1. Introduction The geometric features of the road play a significant role in driving safety considering the fact that accidents often occur on horizontal curves. One of the main reasons for accident occurrence is the lack of geometric design consistency in terms of maintaining the desired travel speed which results in road alignment does not fit the drivers' expectations. A consistent road design ensures coordinated succesive elements producing harmonized driver behaviour with no surprising events. Drivers tend to select speeds with respect to their own perception of the road and those values do not match the design speeds. Beside the succesive elements consistency, a good road design must establish the balance of superelevation and side friction values in curves with the actual driving speeds. The most commonly used indicator of the speed distribution in curves is operating speed which represents the speed below which 85% of drivers operate. Although numerous operating speed studies have been conducted, most of them were based on spot speeds with certain assumptions providing incomplete information about the actual speeds. The limitations of the existing models indicate the need for more detailed analysis of actual driver behaviour and the inclusion of real speeds in the design process. The free flow speed analysis is presented in this paper, with speeds recorded on a segment of the state road D1 in Dalmatia region of Croatia using a new GPS based metodology. This metodology allows the continuous speed data collection and gives an accurate picture of drivers' behaviour. Operating speed prediction model for horizontal curves was determined based on the speed data on 10 km long road segment, with horizontal curve radius and the approach speed as independent variables. The model validation was made with the data from 1 km long segment of the road. The values of the operating speeds were compared to the road's design speed and the differences between side friction values (demand, supply and design) were also made. The deviations between side friction factors point to the need for improving the road design guidelines in terms of harmonizing the values of design speed with actual speeds of most drivers in order of safety. Key-words: design speed, operating speed, consistency, GPS, horizontal curve, side friction factor
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2. Speeds, superelevation and side friction design values
2.1. The design speed The design speed concept is the basis of all road design guidelines. According to this concept, the design speed is determined based on the road and terrain category. It is used to determine the minimum values of road alignment elements, among which the most important one is the determination of minimum radius of horizontal curve. The minimum radius of horizontal curvature Rmin (m) for design speed Vd (km/h) is determined from the equation of vehicle stability in the curve for the maximum permissible superelevation emax (%) and design side friction factor fRdesign:
( )
2
127min
max
=+
d
Rdesign
VR
e f (1)
In this way, the safe driving speed is provided in curves with minimum radius, while road segments with flatter curves allow higher driving speeds. Most guidelines recommend the application of minimum radius only in exceptional situations and designers are encouraged to adopt higher speeds. Subsequentelly, alignments created on design speed concept may generate operating speeds that fluctuate considerably along different road sections, especially if guidelines which define no upper limit value of curve radii were applied. Speed variability has been the cause of many accidents. Few studies (Lamm et al. 1995, Lamm et al. 1989, Fink et al. 1995) show that accident rates at curves with small radii are up to 5 times higher when compared to accident rates on straight road sections. Since it has been established that the design speed concept has a lot of deficiencies, over past decades many researchers in different parts of the world have conducted numerous investigations focusing on the relationship between the design and the actual (operating) speed in curves. In response to these investigations, road design guidelines of many countries have started to use the operating speed.
2.2. The operating speed The operating speed is usually taken as 85% of the speed distribution on a particular road segment, i.e. it is the speed below which 85% of drivers actually drive. The inclusion of operating speed in the design procedure allows estimation of speed changes between adjacent elements as well as more realistic distribution of superelevation in curves with large radius. Many factors affect the free flow speed of vehicles. It has been established that radii of horizontal curves have the greatest impact on the free-flow speed of passenger cars. This free flow speed is much less influenced by the grade, radius of curvature and shape of the vertical elements of the cross section. The most recent overview of the operating speed models in various parts of the world is given in (Hassan et al. 2011). Several studies have shown that the free flow speed in curves R<500 m is mostly influenced by the curvature of the road and approach speed (i.e. speed at which vehicle approaches a curve), as shown in Figure 1. This figure shows that, for the same values of curve radius, the 85th percentile speed in curve differs significantly depending on the speed at which drivers approach the curve. Thus for the radius of 120 m, 85th percentile speed changes from 50 to more than 80 km/h depending on the approach speed (60 to 100 km/h).
Figure 1 Relationship between operati
2.3. Superelevation The superelevation rate is directed toward the center of motion. There are practical upper limits are related to weather conditions(urban or rural roads) and the pomorstva, prometa i veza, Republika Hrvatska, 2001maximum superelevation rate of 72001) allow the use of five different maximum superelevationaccording to different prevailing conditions in various states of the USA.
2.4. Side friction factor Croatian guidelines for road design wereyears 1973 and 1984 (Forschungsgesellschaft für Straßen “Straßenentwurf“, 1973, 1984). Npavement conditions, were made in fTmax as a function of speed were determined based on the 95th friction. When one drives in a curve, the lateral hence the available values of tangential frictionvalue of tangential friction coefficient is:
2 2
max= −
Tdesign T Rdesignf f f
where fRdesign is the design side friction factor. supply fR,max) is the value established when values are much lower than the limiting values, calculated according to:
0 925max
.= ⋅ ⋅Rdesign Tf n f
where 0.925 represents the ratio of maximum available friction in the radial and tangential directions due to the tire characteristics andrural roads, n is 0.5, which ensures that tangential direction. The same principle is applied in Croatiaguidelines in which the coefficient This side friction factor value is sufficiently small compared to the limiting (skidding) value, but still large enough to make the drivers feel accelerate.
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Relationship between operating speed, curve radius and the approach speed 1999)
The superelevation rate is directed toward the center of horizontal curve to support motion. There are practical upper limits for superelevation in horizontal curves. The limiting values
weather conditions (frequency and amount of snow and ice), adjacent land use (urban or rural roads) and the percentage of slow vehicles. Croatian guidelinespomorstva, prometa i veza, Republika Hrvatska, 2001), as most European countriesaximum superelevation rate of 7% for rural roads. On the other hand, USA guidelines
allow the use of five different maximum superelevation values (4, 6, 8, 10 and 12according to different prevailing conditions in various states of the USA.
Croatian guidelines for road design were made on the basis of German guidelines datiForschungsgesellschaft für Straßen - und Verkehrswesen, Arbeitsgruppe
Numerous measurements of tangential friction factors, for various pavement conditions, were made in Germany and diagrams of limiting friction (skidding) values
as a function of speed were developed. The value of fTmax (longitudinal friction supply) percentile of the distribution of all recorded skidding values of
friction. When one drives in a curve, the lateral component of the friction of tangential friction are reduced. Therefore, the
value of tangential friction coefficient is:
is the design side friction factor. The maximum side friction factoris the value established when the skidding starts. For safety
values are much lower than the limiting values, calculated according to:
0.925 represents the ratio of maximum available friction in the radial and tangential characteristics and n is the utilization ratio of the available friction. For
is 0.5, which ensures that 89% of the total friction remains available The same principle is applied in Croatia, but it is based on older German
in which the coefficient n = 0.6. This side friction factor value is sufficiently small compared to the limiting (skidding) value, but
drivers feel a slight discomfort as a "warning"
speed, curve radius and the approach speed (Bonneson
to support the turning horizontal curves. The limiting values
(frequency and amount of snow and ice), adjacent land use uidelines (Ministarstvo
ost European countries, apply On the other hand, USA guidelines (AASHTO
values (4, 6, 8, 10 and 12%),
guidelines dating from the und Verkehrswesen, Arbeitsgruppe
umerous measurements of tangential friction factors, for various diagrams of limiting friction (skidding) values
(longitudinal friction supply) is percentile of the distribution of all recorded skidding values of
component of the friction is also activated and the design (permitted)
(2)
The maximum side friction factor (side friction safety reasons, the design
(3)
0.925 represents the ratio of maximum available friction in the radial and tangential the utilization ratio of the available friction. For
remains available in the , but it is based on older German
This side friction factor value is sufficiently small compared to the limiting (skidding) value, but is as a "warning" advising them not to
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Side friction limiting values used in the USA guidelines are based on researches conducted more than 70 years ago, which were based on driver comfort (Barnett 1936). Although the USA and European approaches for determining the lateral friction design values significantly differ from one another, the design side friction values for rural roads with speeds greater than 70 km/h are quite similar (Figure 2).
Figure 2 Maximum design side friction factors recommended by several highway agencies
(Cvitanić et al. 2012)
3. Croatian guidelines for the horizontal alignement Croatian guidelines for the road design define the following terms: 1. Design speed (Vd) is the maximum speed for which safety is guaranteed along entire road
section, 2. Project speed (Vp) is the maximum expected speed in free flow conditions that can be
achieved with sufficient safety on a particular part of the road segment depending on its horizontal and vertical characteristics.
Project speed is determined by equation (1) as a function of applied curve radius or the largest applied longitudinal grade (smaller value is chosen), Table 1. Table 1 Determination of the project speed with respect to horizontal curve radius
Vp (km/h) 30 40 50 60 70 80 90 100 110 120 130
R (m) 25 45 75 120 175 250 350 450 600 750 850
Croatian guidelines define the project speed as a criterion for determining superelevation and stopping sight distance. They also provide consistency criteria, namely: 1. The difference between project and design speed within a section should be less than 20 km/h, 2. The maximum difference in the project speed within section should be less than 15 km/h.
4. Data collection One of the most important tools in the road design is speed and it is very important to properly define the relevant speed. Project speed defined by Croatian guidelines for the road design is theoretical value and the question is how much are the values of project speeds consistent with real speeds of most drivers. To answer this question, an experimental investigation was done. This investigation refers to drivers’ speed behaviour on two-lane state roads in Croatia. The data were recorded on a segment of the state road D1 in Dalmatia region of Croatia (Figure 3) using an
0,00
0,05
0,10
0,15
0,20
0,25
10 20 30 40 50 60 70 80 90 100 110 120 130 140
f R
Vp (km/h)
Croatia Germany USA
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innovative GPS based device Performance Box. Performance box allows measuring speed, position, acceleration and hedaing ten times a second. The data were collected on 27 km long road segment which consists of horizontal curves with radii varying from 80 to 1000 m. The test driver sample consisted of 15 people with passanger cars of different types and ages. Numerous speed studies have been developed in order to determine operating speed model in horizontal curves, but most of them were based on spot speeds and certain assumptions about drivers’ speed behaviour. Previous speed reserches were based on the assumption that the speed remains constant throughout a curve and that the critical speeds are at the specific locations of a roadway. The lowest speeds along the horizontal curves and highest speeds along tangents are considered to be the critical speeds for analysis. In previous researches speeds were mostly collected at the middle point of horizontal curves and tangents, using radar gun or similar device. Compared to previous spot-speed studies, GPS based data collection methodology has a lot advantages. GPS allows determination of locations and values of critical speeds on tangents and horizontal curves and enables determination of drivers’ path radii, on which the side friction demand depands.
Figure 3 Analyzed segment of the state road D1
In this study, the values of speeds and radii relevant for analysis, V85 and R15, are determined based on data collected from 15 individual drivers (Proso 2013, Vrsalović 2013). The 85th percentile speed V85 is the speed below which 85% of drivers actually drive. The path radii of 15% of drivers are smaller than the 15th percentile radius R15.
5. Analysis and Results The data collected in this study (Table 2) were used for 3 types of analysis:
- Relationship between project and operating speed - Comparison between side friction factors - Determination of operating speed model in horizontal curves
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Table 2 Horizontal curve radii, approach speeds and operating speeds in curves of 44 horizontal curves
Ordinal
number of the
curve
R (m)
Vapproach85 (km/h)
V85 (km/h)
Ordinal
number of the
curve
R (m)
Vapproach85 (km/h)
V85 (km/h)
R1 158 83,24 75,24 R23 266 81,17 83,25
R2 147 80,65 74,37 R24 86 84,16 73,60
R3 143 75,79 71,15 R25 197 73,60 76,19
R4 121 73,15 70,14 R26 83 78,78 67,46
R5 114 73,02 72,99 R27 101 67,76 66,35
R6 803 90,21 99,08 R28 121 77,40 74,59
R7 101 102,39 73,36 R29 470 81,03 84,86
R8 101 75,40 69,66 R30 845 95,56 93,99
R9 108 75,56 73,10 R31 263 90,66 92,70
R10 101 73,95 70,72 R32 597 97,10 95,87
R11 117 76,42 72,24 R33 297 95,87 88,42
R12 353 78,75 82,43 R34 121 85,71 78,46
R13 307 84,73 82,44 R35 200 89,21 88,19
R14 155 82,44 76,96 R36 100 80,52 75,33
R15 107 76,96 70,16 R37 200 81,78 84,17
R16 167 70,16 78,46 R38 179 88,38 88,72
R17 347 82,55 80,53 R39 402 92,23 94,93
R18 243 91,69 85,03 R40 243 94,31 88,42
R19 106 86,16 70,84 R41 180 91,55 83,42
R20 161 71,40 72,81 R42 253 90,28 93,00
R21 183 78,67 80,83 R43 1013 99,47 97,51
R22 172 83,05 81,17 R44 613 100,96 99,07
5.1. Disparity between project and operating speed The analyzed segment of the road D1 has been designed as a 2nd category state road with design speed of 60 km/h. The values of project speeds in horizontal curves were determined according to Croatian guidelines, for a 2nd category road and actual radii. The actual curve radii on horizontal curves were determined from the road surveying which was made in 2006 by Hrvatske ceste (company for managing, constructing and maintaining of state roads in Croatia). The comparison of the operating and project speeds is shown in Figure 4. It can be seen that the operating speed is greater than the project speed in all curves with radii smaller than about 300 m.
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Figure 4 Operating and project speeds in horizontal curves
Operating and project speeds in horizontal curves of the analyzed road segment are presented in Figure 5. Each point on the figure represents the 85th percentile speed determined from the collected data and appropriate project speed for a horizontal curve. The diagonal line indicates equal operating and project speeds. All the curves with project speeds less than about 90 km/h had operating speeds that exceeded the project speed. The project speed is lower than the operating speed which results in insufficient values of stopping sight distances and superelevations optimal for a comfortable ride. Very important elements of the road from a safety point of view are determined based on speeds much lower than actual speeds which may be the cause of accident.
Figure 5 Operating and project speeds in horizontal curves
30
40
50
60
70
80
90
100
110
120
130
1400
20
0
40
0
60
0
80
0
10
00
Sp
ee
d V
(km
/h)
Radius R (m)
Vk85 Vr
50
60
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100
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130
140
50
60
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90
10
0
11
0
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0
Op
era
tin
g s
pe
ed
V8
5 (k
m/h
)
Project speed Vp (km/h)
85V
pV
8
5.2. Side friction demand, supply and design
Differences between operating and project speeds result in exceeding the limiting values of side friction. The side friction demand factors (fRd) are calculated for actual superelevations in horizontal curves and relevant radii and speeds (V85 and R15). The actual radii and superelevations on horizontal curves were determined from the road surveying made by Hrvatske ceste. The side friction demands are compared to the side friction supply (fRmax) and design side friction factors (fRdesign). The comparison is presented in Figure 6.
Figure 6 Relationship between side friction demand, supply and design factors
The side friction demands exceed design side friction factors in all curves and they are higher than the peak side friction supply values in almost all curves. This point to the danger of skidding, especially in poor driving conditions such as wet and dirty pavement and worn tires.
5.3. Operating speed model for horizontal curves Because of the importance of using the operating speed models, this paper describes procedure for determining the curve speed model and procedure of the model validation. The model was developed with a multiple regression procedure based on data collected on 10 km long segment of state road D1, with horizontal curve radius (R) and the approach speed (Vapproach) as independent variables. The model validation was made with the data from 1 km long segment of the road. Data from 44 horizontal curves (80 m < R < 1000 m) were used for model determination and from 4 curves (170 m < R < 300 m) were used for model validation. Based on the collected data and using a multiple linear regression, the following model was developed:
85 85
ˆ 0, 023 0, 471 35, 443= ⋅ + ⋅ +approach
V R V (4)
The coefficient of determination of the model is equal to 0,761. The accuracy of the model was also expessed by the mean absolute percentage error, defined by the formula:
85 85
85
ˆ100%
−= ⋅
V VMAPE
V
(5)
The overall mean absolute percentage error (MAPE) for the data from 10 km long segment is 4,2% and the maximum MAPE is 17,2%.
0,000
0,050
0,100
0,150
0,200
0,250
0,300
0,350
0,400
0,450
0,500
30
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90
10
0
11
0
12
0
13
0
Sid
e f
rict
ion
fa
cto
r f R
SpeedV (km/h)
fR,d fR,max fR,designfRd fRdesign fRmax
9
Operating speeds derived from the collected data (85
V ) and model predicted speeds (85
V̂ ) in
horizontal curves are shown in Figure 7. It should be noted that the model fits the data well.
Figure 7 Operating and model predicted speeds in horizontal curves
After the regression model is made, it is necessary to examine the quality and the validity of the results. The validation of the speed prediction equation for horizontal curves (4) was performed by comparing the model predicted speeds to field observed speeds from the 1 km long segment of the road. The MAPE values for the validation data is 4,6% and the maximum value is 6,3%. The MAPE values for the data from 10 km long segment (model data) were compared to the values for the data from 1 km long segment of the road (validation data), which is presented in Figure 8.
Figure 8 The values of mean absolute percentage error for the model data and validation data
The MAPE values for validation data are similar to the MAPE values for model data what means that, according to radii and approach speeds, the model predicts accurately the curve speed choice of the driving population.
6. Conclusions This paper presented an experimental investigation of the drivers' speed behaviour on horizontal curves of two-lane state roads in Croatia. It was found that the operating speed is greater than the project speed in curves with radii smaller than 300 m. On curves with project speed less than about 90 km/h, operating speeds are in excess of the project speeds. Differences between operating and project speeds result in exceeding design side friction factors and peak side friction supply values. These findings indicate the need for changes in the existing road design, mostly in terms of harmonization the relevant speeds that are used in the road design with actual speeds of most drivers.
0
20
40
60
80
100
120
R1
=
1
58
R2
=
1
47
R3
=
1
43
R4
=
1
21
R5
=
1
14
R6
=
8
03
R7
=
1
00
R8
=
1
01
R9
=
1
08
R1
0 =
1
01
R1
1 =
1
17
R1
2 =
3
53
R1
3 =
3
07
R1
4 =
1
55
R1
5 =
1
07
R1
6 =
1
67
R1
7 =
3
47
R1
8 =
2
43
R1
9 =
1
06
R2
0 =
1
61
R2
1 =
1
83
R2
2 =
1
72
R2
3 =
2
66
R2
4 =
8
6
R2
5 =
1
97
R2
6 =
8
3
R2
7 =
1
01
R2
8 =
1
21
R2
9 =
4
70
R3
0 =
8
45
R3
1 =
2
63
R3
2 =
5
97
R3
3 =
2
97
R3
4 =
1
20
R3
5 =
2
00
R3
6 =
1
00
R3
7 =
2
00
R3
8 =
1
79
R3
9 =
4
02
R4
0 =
2
43
R4
1 =
1
80
R4
2 =
2
53
R4
3 =
10
13
R4
4 =
6
13
Sp
ee
d V
(km
/h)
Ordinal number and radius of the curve R (m)
Vk,85 V^k,85
02468
101214161820
R1
=
1
58
R2
=
1
47
R3
=
1
43
R4
=
1
21
R5
=
1
14
R6
=
8
03
R7
=
1
00
R8
=
1
01
R9
=
1
08
R1
0 =
1
01
R1
1 =
1
17
R1
2 =
3
53
R1
3 =
3
07
R1
4 =
1
55
R1
5 =
1
07
R1
6 =
1
67
R1
7 =
3
47
R1
8 =
2
43
R1
9 =
1
06
R2
0 =
1
61
R2
1 =
1
83
R2
2 =
1
72
R2
3 =
2
66
R2
4 =
8
6R
25
= 1
97
R2
6 =
8
3R
27
= 1
01
R2
8 =
1
21
R2
9 =
4
70
R3
0 =
8
45
R3
1 =
2
63
R3
2 =
5
97
R3
3 =
2
97
R3
4 =
1
20
R3
5 =
2
00
R3
6 =
1
00
R3
7 =
2
00
R3
8 =
1
79
R3
9 =
4
02
R4
0 =
2
43
R4
1 =
1
80
R4
2 =
2
53
R4
3 =
10
13
R4
4 =
6
13
R6
5 =
3
04
R6
6 =
1
70
R6
7 =
2
90
R6
8 =
2
25
Me
an
ab
solu
te p
erc
en
tag
e e
rro
r
MA
PE
(%
)
Ordinal number and radius of the curve R (m)
MAPE (model) MAPE (validation)
85V̂
85V
10
REFERENCES AASHTO (American Association of State Highway and Transportation Officials) (2001), A Policy on Geometric Design of Highway and Streets, Washington, D.C. Barnett, J. (1936) Safe Side Friction Factors and Superelevation Design, Highway Research Board, Proc., Vol. 16, pp. 69–80 Bonneson, J.A. (1999) Side Friction and Speed as Controls for Horizontal Curve Design, Journal of Transportation engineering, Vol 125/6, pp 473-479 Cvitanić, D., Vukoje, B., Breški, D. (2012) Methodes for Ensuring Consistency of Horizontal Alignment Elements, Građevinar 64, pp. 385-393 Fink, K. L.; Krammes, R. A. (1995) Tangent Length and Sight Distance Effects of Accident Rates at Hhorizontal Curves on Rural Two-lane Highways, Transportation Research Board, Washington DC Forschungsgesellschaft für Straßen - und Verkehrswesen, Arbeitsgruppe “Straßenentwurf“, Die Richtlinien für die Anlage von Straßen – Teil: Linienführung (kurz RAS-L), (1973, 1984, 1995) Germany Hassan, Y., Sarham, M., Dimaiuta, M., Donnell, E., Himes, S., Porter, R., Psarianos, B., García, A., Perco, P. y Taylor, M. (2011) Modeling Operating Speed: Synthesis Report, Transportation Research Circular number E-C151, Transportation Research Board Lamm, R., Guenther, A.K., Choueiri, E.M. (1995) Safety Module for Highway Geometric Design, Transportation Research Record 1512, 7 – 15 Lamm, R., Choueriri, E.M., and Mailaender, T. (1989) Accident Rates on Curves as Infleunced by Highway Design Eelements, Proc. Roads safety in Europe, pp. 33-54, Sweden Ministarstvo pomorstva, prometa i veza, Republika Hrvatska (2001) Pravilnik o osnovnim uvjetima kojima javne ceste izvan naselja i njihovi elementi moraju udovoljavati sa stajališta sigurnosti prometa (NN 110/01), Zagreb Proso, A. (2013) Free Ride Dependence on Geometric Characteristics of the Road Route, diploma thesis Vrsalović, M. (2013) The Impact of Radius of Movement and Operating Speed of Vehicles on the Radial Resistance to Sliding in the Curves, diploma thesis
