This document contains lecture slides for a CEE320 Vehicle Dynamics course. It covers topics such as resistance forces that impede vehicle motion like aerodynamic, rolling, and grade resistance. It also discusses tractive effort, vehicle acceleration, braking forces, and stopping sight distance. Formulas and examples are provided for calculating forces, acceleration, braking distance, and stopping sight distance. Key concepts are defined including resistance, tractive effort, and the relationships between engine torque, gear ratios, and vehicle speed.
5. CEE320
Winter2006
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
2
VACR fDa
ρ
=
3
2
VACP fDRa
ρ
=
sec
5501
lbft
hp
⋅
=
from National Research Council Canada
6. CEE320
Winter2006
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
V
frlWVfP rlrlR =
sec
5501
lbft
hp
⋅
=
8. CEE320
Winter2006
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,minefforttractiveAvailable FFe=
13. CEE320
Winter2006
Maximum Tractive Effort
• Front Wheel Drive Vehicle
• Rear Wheel Drive Vehicle
• What about 4WD?
( )
L
h
L
hfl
W
F
rlf
µ
µ
−
−
=
1
max
( )
L
h
L
hfl
W
F
rlr
µ
µ
+
+
=
1
max
16. CEE320
Winter2006
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 rpm
Curb 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
22. CEE320
Winter2006
SSD – Quick and Dirty
( )
( ) ( )
( ) a
VV
V
V
Ggag
VV
d
22
2
22
1
2
2
2
1
075.1
2.11
075.1
2.11
1
2
47.1
02.322.112.322
047.1
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 Vt
a
V
d 47.1075.1
2
+=
24. CEE320
Winter2006
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.
Editor's Notes
Power is in ft-lb/sec
Rolling resistance = 2 components
Hysteresis = energy loss due to deformation of the tire
Adhesion = bonding between tire and roadway
Low profile tires reduce r and increase tractive effort
Torque and HP always cross at 5252 RPM. Why? Look at the equation for HP
For 4WD
Fmax = μW (if your 4WD distributes power to ensure wheels don’t slip, which is common)
For a front wheel drive car, sum moments about the rear tire contact point:
-Rah – Wsinθh + Wcosθlr + mah - WfL = 0
cosθ = about 1 for small angles encountered
-Rah – Wsinθh + Wlr + mah - WfL = 0
WfL = -Rah – Wsinθh + Wlr + mah
WfL = + Wlr – Wsinθh – Rah + mah
Wf = (lr/L)W + (h/L)(-Wsinθ – Ra + ma)
But… Wsinθ = Rg
Substituting: Wf = (lr/L)W + (h/L)(-Rg – Ra + ma)
We know that… F = ma + Ra + Rrl + Rg Therefore, -F + Rrl = -ma – Ra– Rg
Wf = (lr/L)W + (h/L)(-F + Rrl)
Now, Fmax = μWf and Rrl = frlW
Substituting: Fmax = μ((lr/L)W + (h/L)(-Fmax + frlW))
Simplifying: Fmax + (μh/L)Fmax = μ((lr/L)W + (h/L)(frlW))
Fmax(1 + μh/L) =( μW/L)((lr + hfrl)
Tire size
P = passenger car
1st number = tire section width (sidewall to sidewall) in mm
2nd number = aspect ratio (sidewall height to width) in tenths (e.g. 60 = 0.60)
3rd number = wheel diameter
Practical comes from V22 = V12 + 2ad (basic physics equation or rectilinear motion)
a = 11.2 ft/sec2 is the assumption
This is conservative and used by AASHTO
Is equal to 0.35 g’s of deceleration (11.2/32.2)
Is equal to braking efficiency x coefficient of road adhesion
γb = 1.04 usually