Investigation of Vehicle Motion on sharp Horizontal Curves combined with steep longitudinal Grades

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
tg09038@teiath.gr
Giorgos Kleioutis, Research Associate
gkleioutis@teiath.gr
Evaggelos Katsanos, Research Associate
National Technical University of Athens
rs05064@central.ntua.gr

 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

)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

 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

 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

 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

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

 Road Section Surveyed
via Laser Scanner

via Laser Scanner
 median of 1.50m

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

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

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

 Test Vehicle
(KIA, Proceed)
 ABS equipped
 Measuring Device
 Accelometer, (Vericom, VC4000)

 Test Vehicle
(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)

 Time, Speed and Distance Data

 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]

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

 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.

 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

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

 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)

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

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

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

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

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

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

 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

 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

 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

 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

 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

 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

Investigation of Vehicle Motion on sharp Horizontal Curves combined with steep longitudinal Grades

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Investigation of Vehicle Motion on sharp Horizontal Curves combined with steep longitudinal Grades