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Road Vehicle Performance. CEE 320 Anne Goodchild. Outline. Resistance Aerodynamic Rolling Grade Tractive Effort Maximum Tractive Effort Engine Generated Tractive Effort Acceleration Braking Stopping Sight Distance. Review. Force (N): influence that tends to change motion - PowerPoint PPT Presentation
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CEE
320
Fall
2008
Road Vehicle Performance
CEE 320Anne Goodchild
CEE
320
Fall
2008
Outline
1. Resistancea. Aerodynamicb. Rollingc. Grade
2. Tractive Effort1. Maximum Tractive Effort2. Engine Generated Tractive Effort
3. Acceleration4. Braking
1. Stopping Sight Distance
CEE
320
Fall
2008
Review
• Force (N): – influence that tends to change motion– mass (kg) * acceleration (m/s2)
• Torque (Nm):– infleunce that tends to change rotational motion– Force * lever arm
• Work (Nm):– Force * distance
• Power (Nm/s):– Rate of doing work (work/time)
Units matter!
CEE
320
Fall
2008
Primary Opposing Forces• Resistance (N): Force impeding vehicle motion• Tractive Effort (N): Force available at the roadway
surface to perform work
CEE
320
Fall
2008
Primary Opposing Forces• Resistance (N): Force impeding vehicle motion• Tractive Effort (N): Force available at the roadway
surface to perform work
CEE
320
Fall
2008
Sum forces on the vehicle
grla RRRmaF
CEE
320
Fall
2008
Aerodynamic Resistance Ra
Composed of:1. Turbulent air flow around vehicle body (85%)2. Friction of air over vehicle body (12%)3. Vehicle component resistance, from radiators
and air vents (3%)
2
2VACR fDa
from National Research Council Canada
CEE
320
Fall
2008
CEE
320
Fall
2008
Power required to overcome Ra
• Power– work/time – force*distance/time– Ra*V
3
2VACP fDRa
sec5501 lbfthp
CEE
320
Fall
2008
Rolling Resistance Rrl
Composed primarily of 1. Resistance from tire deformation (90%)2. Tire penetration and surface compression ( 4%)3. Tire slippage and air circulation around wheel ( 6%)4. Wide range of factors affect total rolling resistance5. Simplifying approximation:
WfR rlrl
147101.0 Vfrl
CEE
320
Fall
2008
Power required to overcome rolling resistance
• On a level surface at maximum speed we could identify available hp
WVfP rlrlR
sec5501 lbfthp
CEE
320
Fall
2008
Grade Resistance Rg
Composed of – Gravitational force acting on the vehicle– The component parallel to the roadway
gg WR sin
gg tansin
gg WR tanGg tan
WGRg
For small angles,
θg W
θg
Rg
G=grade, vertical rise per horizontal distance (generally specified as %)
CEE
320
Fall
2008
Available Tractive Effort
The minimum of:1. Force generated by the engine, Fe2. Maximum value that is a function of the
vehicle’s weight distribution and road-tire interaction, Fmax
max,mineffort tractiveAvailable FFe
CEE
320
Fall
2008
Engine-Generated Tractive Effort
• Force
rMF de
e 0
Fe = Engine generated tractive effort reaching wheels (lb)
Me = Engine torque (ft-lb)
ε0 = Gear reduction ratio
ηd = Driveline efficiency
r = Wheel radius (ft)
CEE
320
Fall
2008
Engine Generated Tractive Effort: Power
10002
2speed engine torquetime
torquepower
eee
nMP
Pe in kW
5502 ee
enMhP
hPe in hp
CEE
320
Fall
2008
Vehicle Speed vs. Engine Speed
0
12
irnV e
V = velocity (ft/s)r = wheel radius (ft)ne = crankshaft rps
i = driveline slippageε0 = gear reduction ratio
CEE
320
Fall
2008
DiagramRa
Rrlf
Rrlr
ma
Wθg
Fbf
Fbr
h
h
lf
lrL
θg
Wf
Wr
CEE
320
Fall
2008
Maximum Tractive Effort
• Front Wheel Drive Vehicle
• Rear Wheel Drive Vehicle
= coefficient of road adhesion
LhL
hflW
F
rlf
1
max
LhL
hflWF
rlr
1
max
CEE
320
Fall
2008
Tractive Effort Relationships
CEE
320
Fall
2008
CEE
320
Fall
2008
Typical Torque-Power Curves
CEE
320
Fall
2008
Vehicle Acceleration
• Governing Equation
• Mass Factor (accounts for inertia of vehicle’s rotating parts)
maRF m
200025.004.1 m
CEE
320
Fall
2008
Braking
• Maximum braking force occurs when the tires are at a point of impending slide.– Function of roadway condition– Function of tire characteristics
• Maximum vehicle braking force (Fb max) is– coefficient of road adhesion () multiplied by
the vehicle weights normal to the roadway surface
CEE
320
Fall
2008
Braking Force
• Front axle
• Rear axle
L
fhlWF rlrbf
max
L
fhlWF rlf
br
max
CEE
320
Fall
2008
Braking Force
• Maximum attainable vehicle deceleration is g
• Maximum obtained when force distributed as per weight distribution
• Brake force ratio is this ratio that acheives maximum braking forces
CEE
320
Fall
2008
Braking Force
• Ratio
• Efficiency
rear
frontfhlfhlBFRrlf
rlrrf
max
maxg
b
We develop this to calculate braking distance – necessary for roadway design
CEE
320
Fall
2008
Braking Distance• Theoretical
– Assumes effect of speed on coefficient of rolling resistance is constant and calculated for average of initial and ending speed
– Ignores air resistance
– Minimum stopping distance given braking efficiency• For population of vehicles, what do you assume about rolling
resistance, coefficient of adhesion, and braking efficiency?
grlb
b
fgVVS
sin2
22
21
CEE
320
Fall
2008
Braking Distance• Practical
• For 0 grade
Ggag
VVd2
22
21
aVVd
2
22
21
typically assume a = 11.2 ft/sec2
CEE
320
Fall
2008
Response time• Perception time
• Total stopping distance
pp tVd 1
ps ddd
CEE
320
Fall
2008
Stopping Sight Distance (SSD)
• Worst-case conditions– Poor driver skills– Low braking efficiency– Wet pavement
• Perception-reaction time = 2.5 seconds• Equation
rtVG
gag
VSSD 1
21
2
CEE
320
Fall
2008
Stopping Sight Distance (SSD)
from ASSHTO A Policy on Geometric Design of Highways and Streets, 2004
Note: this table assumes level grade (G = 0)