There are safety concerns when sharp curves are combined with steep grades. The presentation shows the results on friction deficiencies resulting when vehicles accommodate such road sections

1. Stergios Mavromatis, Assistant Professor
Technological Educational Institute of Athens
stemavro@teiath.gr
Basil Psarianos, Professor
National Technical University of Athens
psari@survey.ntua.gr
Pavlos Tsekos, Research Associate
Technological Educational Institute of Athens
tg09038@teiath.gr
Giorgos Kleioutis, Research Associate
Technological Educational Institute of Athens
gkleioutis@teiath.gr
Evaggelos Katsanos, Research Associate
National Technical University of Athens
rs05064@central.ntua.gr

2.  Vehicle Industry
 evolves technological improvements for vehicle stability
ABS
EBD
ESP
 Road Design Practice
 vehicle dynamics simplified
point mass
many parameters ignored
 vehicle type
 vehicle mass and position of gravity center
 vehicle’s motion is examined independently in the tangential
and lateral direction of travel
 heavy vehicles dynamics

3. )e+f(127
V
=R
maxperm,R
2
min
where
Rmin : minimum curve’s radius (m)
V : vehicle speed – usually design speed (km/h)
emax : maximum superelevation rate (%/100)
m : vehicle’s mass
fR,perm: permissible side friction factor as a portion of peak friction
 Parameters Ignored
 actual demand of lateral friction
 roadway’s longitudinal profile
 vehicle dynamics
e.g. loading, driving configuration, horse-power supply

4.  Point Mass Model
 adopted in current practice
 Bicycle Model
 simulates the vehicle by an axle in steady state
cornering conditions
 Transient Formulation of the Bicycle Model
 utilized in cases of variable steering inputs
(e.g. lane changes)
 Full Multi–Body Vehicle Simulation
 used mostly by the automotive industry for vehicle
stability prediction
lflr
L/R
L
fα
rα
fθ
β
L/R
m V
R
2
V
Vf
Vr
R

5.  Determine the Safety Hazard
 passenger cars in tractive mode
 sharp horizontal curves
combined with steep
longitudinal grades
 Examine Point Mass
Model’s Adequacy
to Assess
Vehicle Motion

6.  Field Measurements
on Road Section
 road geometry elements
 tire – road adhesion values
 speed data vs driven distance
 Correlate Vehicle
Performance against
Existing Vehicle Dynamics
Model

7.  Divided Urban Ring Road in Athens
 Steep Graded and Sharp Curved
Road Section


8.  Road Section Surveyed
via Laser Scanner

9.  Road Section Surveyed
via Laser Scanner
 median of 1.50m

10.  Road Section Surveyed
via Laser Scanner
 median of 1.50m
 independent road
geometries representing
vehicle paths
(offset 4.00m from axis)
per vehicle’s
direction of travel

11. cross - slope
e (%)
0,00 0,00
14,62 R=○○ 2,50
14,62
13,10 A=16,90 2,50 - 5,50 35,78 6,50
27,72 43,73 8,49
48,65 R=21,80 5,50 79,51 11,00
76,37
3,51 A=8,74 2,50 - 5,50
79,87
32,02 R=○○ 2,50
111,90 111,90
upgrade section
horizontal
station (m)
distance
between (m)
horizontal geometry
(A,R) (m)
vertical
station (m)
distance
between (m)
vertical geometry
(K) (m) grade between (%)
32,39
11,92
10,87
35,78
cross - slope
e (%)
0,00 0,00
18,99
18,99 12,00
16,76
4,10 A=11,05 2,50 - 5,00
20,85
68,16 R=29,80 5,00
89,01
15,30 A=21,35 2,50 - 5,00 89,54 6,50
104,31
13,71 R=○○ 2,50
118,02 118,02
16,76 R=○○ 2,50
downgrade section
horizontal
station (m)
distance
between (m)
horizontal geometry
(A,R) (m)
vertical
station (m)
distance
between (m)
vertical geometry
(K) (m) grade between (%)
70,55 -6,58
28,48
-9,54
-11,04

12.  Test Vehicle
 C class passenger car, FWD
(KIA, Proceed)
 ABS equipped

13.  Test Vehicle
 C class passenger car, FWD
(KIA, Proceed)
 ABS equipped
 Measuring Device
 Accelometer, (Vericom, VC4000)

14.  Test Vehicle
 C class passenger car, FWD
(KIA, Proceed)
 ABS equipped
 Measuring Device
 Accelometer, (Vericom, VC4000)
 Dry Pavement
 Runs
(performed by the same driver)
 braking (friction)
 driving in tractive mode
(speed vs distance)

15.  Time, Speed and Distance Data

16.  Time, Speed and Distance Data
 Friction Data
 braking runs on tangent sections
and constant grade
 drag factor
drag = f + s
where
f: braking friction coefficient
s: roadway’s grade value (%/100)
[(+) for upgrades, (-) for downgrades]

17. 0.62 0.64
0.70 0.690.68
0.75 0.74
0.800.81
0.64
0.81
0.73
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
s= 13,0%
KIA
s= -10,7%
KIA
s= 7,0%
AUDI
s= -7,0%
AUDI
faverage
fmax
max drag
upgrade downgrade
s=13,0%
KIA
s=-10,7%
KIA
s=7,0% s=-7,0%
AUDI AUDI

18.  Parameters Correlated
 vehicle technical characteristics
vehicle speed, wheel drive, sprung and unsprung mass
and its position of gravity center, aerodynamic drag,
vertical lift, track width, wheel-base, roll center, vertical
suspension stiffness, cornering stiffness, etc.

19.  Parameters Correlated
 vehicle technical characteristics
vehicle speed, wheel drive, sprung and unsprung mass
and its position of gravity center, aerodynamic drag,
vertical lift, track width, wheel-base, roll center, vertical
suspension stiffness, cornering stiffness, etc.
 road geometry
grade, superelevation rate,
horizontal radius
 tire friction

20.  Four - Wheel Model
 Actual Wheel Load
due to
Lateral Load Transfer
 Alteration of
Lateral Force
on each Wheel

21.  Vehicle Examined at Impending Skid
 Vehicle Speed Variation as a Function of Driven
Distance
 Variation of Vehicle Dynamic Parameters
 acceleration, horse power utilization, lateral –
longitudinal friction values for every wheel, etc.
 Definition of Vsafe (dv/dt=0)

22. 0.00
0.50
1.00
1.50
2.00
2.50
10
20
30
40
50
60
0 10 20 30 40 50 60 70 80 90 100 110 120
dv/dt(m/sec2)
V(km/h)
distance (m)
run1
run2
run3
run4
V
dv/dt
R=oo A=16.90 R=21.80 A=8.74 R=oo
Vsafe

23. 0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
0
10
20
30
40
50
60
70
80
0 10 20 30 40 50 60 70 80 90 100 110 120
dv/dt(m/sec2)
V(km/h)
distance (m)
run1
run2
run3
run4
V
dv/dt
R=oo A=11.05 R=29.80 A=21.35 R=oo
Vsafe

24. 0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0 10 20 30 40 50 60 70 80 90 100 110 120
friction
distance (m)
fMAX
fTfo model
fRfo model
fTfi model
fRfi model
fR pm
fRri modelR=oo A=16.90 R=21.80 A=8.74 R=oo

25. 0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0 10 20 30 40 50 60 70 80 90 100 110 120
friction
distance (m)
fMAX
fTfo model
fRfo model
fTfi model
fRfi model
fR pm
fRri modelR=oo A=11.05 R=29.80 A=21.35 R=oo

26. 49
53
77
86
0
10
20
30
40
50
60
70
80
90
s = 8% s = -8% s = 8% s = -8%
V(km/h)
R=30m R=80m

27. 0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
acceleration(m/sec2)
horsepowerutilizationn(%)
distance (m)
n (%)
dv/dt
R=oo A=11.05 R=29.80 A=21.35 R=oo

28.  Friction Values
 Braking Performance of Vehicles
Equipped with ABS,
on Steep Grades
average braking performance
is actually the same
peak friction coefficients higher
on downgrades
 Possible Explanation
steep upgrades subject to more
intense road distortion

29.  Determination of Vsafe (model)
Correlation against Field Measurements
 model provides accurate results
vehicle drifting on certain upgrade runs
 driver’s discomfort reported on downgrades
 Critical Wheel for Skidding
 inner to the curve
 inner front prevails

30.  Point – Mass Model Accuracy in fR
 better approximation on upgrade
sections
downgrade section demand greater
portion of lateral friction
 point mass model model usually
underestimates the actual friction
requirements especially
on steep grades

31.  Steep Upgrade Road Segments
More Critical
at Impending Skid Conditions
 portion of friction is engaged
in the longitudinal direction
of travel causing less friction
availability in the
lateral direction

32.  Vehicle’s Acceleration Safety
Performance at Curve Entrance
 vehicles equipped with excessive
amounts of horse power rates must
be driven very conservatively in
sharp horizontal curves combined
with steep vertical grades
 previous research findings
confirmed
highlight the increased risk
associated with such alignment
combinations

33.  Investigation in Entire Vehicle Fleet
(SUVs, Heavy Vehicles, etc.)
 Analyse in More Detail
the Interaction between Driver – Vehicle
on Sharp Curves and Steep Grades
 determine appropriate
horizontal and vertical
alignment combinations