vehicle dynamics - rizayana · 1. turbulent air flow around vehicle body (85%) 2. friction of air...
TRANSCRIPT
CE
E 3
20
Win
ter 2
006
Outline
1. Resistance a. Aerodynamic b. Rolling c. Grade
2. Tractive Effort 3. Acceleration 4. Braking Force 5. Stopping Sight Distance (SSD)
CE
E 3
20
Win
ter 2
006
Main Concepts
• Resistance • Tractive effort • Vehicle acceleration • Braking • Stopping distance
grla RRRmaF +++=
CE
E 3
20
Win
ter 2
006
Resistance
Resistance is defined as the force impeding vehicle motion 1. What is this force? 2. Aerodynamic resistance 3. Rolling resistance 4. Grade resistance
grla RRRmaF +++=
CE
E 3
20
Win
ter 2
006
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
ρ=
3
2VACP fDRa
ρ=
sec5501 lbfthp ⋅
=from National Research Council Canada
CE
E 3
20
Win
ter 2
006
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 resistance 5. Simplifying approximation:
WfR rlrl =
⎟⎠
⎞⎜⎝
⎛ +=147
101.0 VfrlWVfP rlrlR =
sec5501 lbfthp ⋅
=
CE
E 3
20
Win
ter 2
006
Grade Resistance Rg
gg WR θsin=gg θθ tansin ≈
gg WR θtan=Gg =θtan
WGRg =
For small angles,
θg Wθg
Rg
CE
E 3
20
Win
ter 2
006
Available Tractive Effort
The minimum of: 1. Force generated by the engine, Fe
2. Maximum value that is a function of the vehicle’s weight distribution and road-tire interaction, Fmax
( )max,mineffort tractiveAvailable FFe=
CE
E 3
20
Win
ter 2
006
Engine-Generated Tractive Effort
• Force
• Power
rMF de
eηε 0=
( )π2
minsec60
rpm engine550
lbft torquesec
lbft550 hp ×
⎟⎠
⎞⎜⎝
⎛×
⋅=⎟
⎠
⎞⎜⎝
⎛ ⋅
Fe = Engine generated tractive effort reaching wheels (lb)
Me = Engine torque (ft-lb)ε0 = Gear reduction ratioηd = Driveline efficiency
r = Wheel radius (ft)
CE
E 3
20
Win
ter 2
006
Vehicle Speed vs. Engine Speed
( )0
12ε
π irnV e −=
V = velocity (ft/s)r = wheel radius (ft)
ne = crankshaft rpsi = driveline slippageε0 = gear reduction ratio
CE
E 3
20
Win
ter 2
006
Maximum Tractive Effort
• Front Wheel Drive Vehicle
• Rear Wheel Drive Vehicle
• What about 4WD?
( )
LhLhfl
WF
rlf
µ
µ
−
−
=1
max
( )
LhLhflW
Frlr
µ
µ
+
+
=1
max
CE
E 3
20
Win
ter 2
006
Vehicle Acceleration
• Governing Equation
• Mass Factor (accounts for inertia of vehicle’s rotating parts)
maRF mγ=−∑
200025.004.1 εγ +=m
CE
E 3
20
Win
ter 2
006
Example
A 1989 Ford 5.0L Mustang Convertible starts on a flat grade from a dead stop as fast as possible. What’s the maximum acceleration it can achieve before spinning its wheels? µ = 0.40 (wet, bad pavement)
1989 Ford 5.0L Mustang Convertible
Torque 300 @ 3200 rpmCurb Weight 3640
Weight Distribution Front 57% Rear 43%Wheelbase 100.5 in
Tire Size P225/60R15 Gear Reduction Ratio 3.8
Driveline efficiency 90%Center of Gravity 20 inches high
CE
E 3
20
Win
ter 2
006
Braking Force
• Front axle
• Rear axle
( )[ ]L
fhlWF rlrbf
++=
µµmax
( )[ ]L
fhlWF rlfbr
+−=
µµmax
CE
E 3
20
Win
ter 2
006
Braking Force
• Ratio
• Efficiency
( )( ) rear
frontfhlfhlBFRrlf
rlr =+−
++=
µ
µ
µη maxgb =
CE
E 3
20
Win
ter 2
006
Braking Distance
• Theoretical – ignoring air resistance
• Practical
• Perception
• Total
( )( )grlb
b
fgVVS
θµη
γ
sin2
22
21
±+
−=
⎟⎟⎠
⎞⎜⎜⎝
⎛±
−=
Ggag
VVd2
22
21
pp tVd 1=
ps ddd +=
aVVd
2
22
21 −=
For grade = 0
CE
E 3
20
Win
ter 2
006
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+
⎟⎟⎠
⎞⎜⎜⎝
⎛±
=
CE
E 3
20
Win
ter 2
006
Stopping Sight Distance (SSD)
from ASSHTO A Policy on Geometric Design of Highways and Streets, 2001
Note: this table assumes level grade (G = 0)
CE
E 3
20
Win
ter 2
006
SSD – Quick and Dirty
( )( ) ( )
( ) aVVVV
GgagVVd
222
221
22
21 075.1
2.11075.1
2.111
247.1
02.322.112.322047.1
2==××=
+×
−×=
±
−=
1. Acceleration due to gravity, g = 32.2 ft/sec2
2. There are 1.47 ft/sec per mph
3. Assume G = 0 (flat grade)
ppp VttVd 47.147.1 1 =××=
V = V1 in mph a = deceleration, 11.2 ft/s2 in US customary units tp = Conservative perception / reaction time = 2.5 seconds
ps VtaVd 47.1075.12
+=
CE
E 3
20
Win
ter 2
006
Primary References
• Mannering, F.L.; Kilareski, W.P. and Washburn, S.S. (2005). Principles of Highway Engineering and Traffic Analysis, Third Edition). Chapter 2
• American Association of State Highway and Transportation Officals (AASHTO). (2001). A Policy on Geometric Design of Highways and Streets, Fourth Edition. Washington, D.C.