3- AUTOMOTIVE LATERAL DYNAMICS, Rev. A

Brian Paul Wiegand, B.M.E., P.E.
1
AUTOMOTIVE DYNAMICS and DESIGN

AUTOMOTIVE DYNAMICS,LATERAL
There are a number of automotive performance aspects
which are associated with motions in the lateral
direction: maneuver ( & ),
, and . With regard to maneuver,
the which can be attained
in turning is an important index of
performance and safety; the lateral acceleration point
at which roll-over can occur is generally at a level
significantly greater than this maximum lateral
acceleration. However, the level at which rollover could
occur is still an important . Before
attaining a steady-state condition, a turning maneuver
must first go through a phase, which is also a
matter of some significance. Lastly, there is the matter
of , which has to do with the lateral
tire traction force balance front-to-rear, and the
of the vehicle tires due to
those forces.
AUTOMOTIVE DYNAMICS and DESIGN 2

An automobile undergoing directional change is in general
plane motion: translation + rotation. Here the radius of the
turn is considered large enough that the forces producing
acceleration are to be considered purely lateral in
orientation:

For this case, the principle of “dynamic equilibrium”
requires the following relationships between forces,
moments, and the accelerations produced thereby:
TRANSLATIONAL:
ROTATIONAL:
Consider for the moment only the steady-state
condition of constant angular velocity (“ ”);
in this state the equations become…

In the lateral force equation substitute “ ” for “m”
and “ ” for “ ”:
In the moments about the CG equation substitute “ ” for
“ ”:
Substitute this expression for “ ” in the force
equation and do a little manipulation:

Now solve for “ ”, and “ ”, then substitute “ ” for
“ ”, “ ” for “ ”, and “ ” for “ ”:
So, for steady-state turning the lateral tire traction
force(s) at each axle need only equal the weight load at
each axle times the lateral acceleration in g’s. However,
the generation of those tire forces is a bit more complex
than might first be supposed; the matter is not simply a
case of applying Coulomb’s friction law…

Automobiles produce all primary direction
controlling forces at the tire/road interface. This
force generation is not in accord with Coulomb’s
Friction Law: “ ”. Because of the nature of
rubber pneumatic tires, the traction force (“ ”) and
normal load (“ ”) relation is nonlinear. Empirical
studies show that for a tire the lateral traction
coefficient “ ” is itself a function of the normal
load:
The coefficients “ ” and “ ” are particular to the
type of tire concerned.

The “ ” coefficient is the
basic coefficient of
traction; it is dependent
upon the type of tire
material / road surface,
and directly proportional
to the magnitude of the
contact area. The “ ”
coefficient is a measure
of the decrease of
contact area due to tire
distortion under lateral
load:

Combining the lateral traction
coefficient and Coulomb’s
law by substitution for “ ”
results in the normal
load/potential lateral force
relationship
Graphically, this function may
be depicted for a “typical” set
of coefficient values as

A lateral
traction
force at the
tire / road
contact area
not only
causes
“curl-up”
distortion of
the tire in
the
plane, but
also…
…causes a
distortion in
the
plane
resulting in
what is
erroneously
called the
“ ”,
but here is
called the
“
”…

The
“ ”
relation, for a
particular
normal load/
tire/inflation
pressure,
looks as per
the depiction

The lateral force generation potential for an axle is
essentially only a matter of adding the lateral force
generation potentials of the tires:
In the static case the normal loads would be equal, “
”. However, in a turning situation a “weight
transfer” occurs which alters the lateral force
generation potential by decreasing the normal load on
the tire closest to the turn center and increasing, by
an equivalent amount, the normal load on the tire
furthest from the turn center.

This situation may be depicted as follows:

From the information given in the figure expressions
for the normal loads at the inner and outer tires may be
determined:
The quantity “ ” is the “weight transferred”.

Substituting “ ” and “ ” into the “ ” equation
produces the axle lateral traction force potential taking
“weight transfer” into account:

From that equation, further equations for the maximum
axle lateral acceleration limits of slide and overturn can
be determined:

A plot of traction potential vs. lateral load illustrates the
situation:

The “ ” and “ ”
points are given
directly by the means
of the appropriate
equations. Observe
what happens when
these equations are
plotted vs. increasing
axle weight load (with
no change in vertical
c.g.):

Plotting those same
equations vs. the
center of gravity
height produces:

A conventional vehicle has two axles in tandem. The
static portion of vehicle weight that can be assigned to
each axle equation is determined from the total vehicle
weight and the longitudinal center of gravity:

Using the same
values for axle
weight (2000 lb),
track, and tire
coefficients the
effect of varying
the longitudinal
on the
maximum lateral
acceleration
(slide) may be
visualized:

For a conventional automotive configuration
(rear drive, same type & size tires/wheels all
around) obtaining a maximum lateral
acceleration level favors an even longitudinal
weight distribution. However, directional
stability favors a forward bias, while
acceleration and braking favor a rear bias.
The longitudinal weight distribution of a
particular vehicle depends upon the vehicle’s
design intent (family car, race car, sporty
road car, etc.)

2o14 Chevrolet Corvette Stingray
Weight Distribution Frt/Rr: 49.5%/50.5%
Tires Frt/Rr: 245/35R19 / 285/30R20
2013 F1 (typical, per FIA regulations)
Wt Distribution Frt/Rr: 45.5-46.7% / 54.5-53.3%
Tires Frt/Rr: 245/660R13 / 325/660R13
1980 Ford Fiesta S
Weight Distribution Frt/Rr: 63.0%/37.0%
Tires Frt/Rr: 155/80R12 / 155/80R12

The two-axle model for static “weight transfer”
between axles as used so far was highly simplified;
there was no consideration of the effects resulting
from the presence of a suspension in a dynamic
situation. By design, a suspension allows for
deflection under load, and consequently there is
some deflection under longitudinal loads (dive,
squat) and some deflection under lateral loads
(roll). The deflection under lateral loads modifies
the “weight transfer” results from that obtained
using the previous simple moment balance
equations.

The suspension type and dimensions determines the
location of the roll center at either front or rear axle
line. The line delineated by connecting the two roll
centers constitutes the “ ” about which the
sprung mass will rotate under lateral load:

To illustrate the matter, consider this depiction of the
roll axis and c.g. situation of a 1980 Ford Fiesta S (1.1
liter, European version) in a “4 up” condition:

Some simple weight accounting was used to establish
the sprung weight and its c.g. coordinates:
Note the unsprung mass c.g. is assumed to be at mid-
wheelbase longitudinally, at centerline laterally, and at
the rolling radius height of the 155SR12 tires.

Looking at the vehicle cross-section through the
sprung c.g., the situation is as depicted:

The roll angle “ ” of the sprung mass under a 0.5 g
lateral acceleration “ ” can be determined from the
fact that the roll resistance (roll angle “ ” times the
roll stiffness “ ”) has to equal the roll moment
(lateral force “ ” times the roll moment arm “ ”) at
equilibrium:
Into this simple equation plug all the necessary
parameters and solve for “ ”:

However, the roll angle determination not quite so simple. The roll
height “ ” decreases by an amount “ ” during the rolling action,
which would tend to make the roll angle “ ” less than 3.9 degrees,
but the rolling also moves the sprung mass laterally by an
amount “ ”, which would tend to make the roll angle “ ” more than
the 3.9 degrees:

There is further complication in that the unsprung
masses at the front and rear axles also make their
contributions to the sprung roll moment as transmitted
through their linkages (if the suspension is of an
independent type, otherwise the unsprung mass
moments are absorbed internally). From this fact, a more
complex reality may be expressed by the equation:
The symbolism in this equation is as follows…

= The sprung mass roll angle, degrees.
= The total vehicle roll resistance, lb-ft/deg.
= The weight of the sprung mass, lb.
= The lateral acceleration, g’s.
= The sprung mass roll moment arm, ft.
= The front axle unsprung mass weight, lb.
= The front axle unsprung mass vertical c.g.
(approx. the rolling radius), ft.
= The rear axle unsprung mass weight, lb.
= The rear axle unsprung mass vertical c.g.
(approx. the rolling radius), ft.

Even with all this complication, the resulting value
for the roll angle will still just be approximate as
matters such as free surface effect of liquids,
lateral shift of the unsprung mass c.g.(s), and
various secondary deflections (including shift of
the RC’s in roll) are still unaccounted for.
However, the roll angle value as determined may
have all the accuracy that is needed for early
design studies. A simple iterative spreadsheet
solution yields , which is reasonable,
but probably a bit low considering certain effects
still were not taken into account.

Now that the roll angle “ ” has been estimated, the
normal loads “ ” and “ ”, can be determined at the front
and rear axles. First, consider the IFS which is a
MacPherson strut type:
Rolled sprung mass
normal load equations:

Plugging the appropriate values into the new sprung
equations produces the following results:
If the previous simple equations were used, i.e. if roll
stiffness was not considered, the results would have
been:
Nif = (1241.7/2)–(12(4.3)218.3)/52.52)–2138.4(0.5)7.28(48.8)/(90×52.2)= 326.0 lb
Nof = (1241.7/2)+(12(4.3)218.3/52.52)+2138.4(0.5)7.28(48.8)/(90×52.2)= 915.7 lb

Now that the front axle has been considered, let’s turn our
attention to the rear axle, which is non-independent of the
dead beam type:
Rolled sprung mass
normal load equations:

Plugging the appropriate values into the new sprung
equations produces the following results:
If the previous simple equations were used, i.e. if roll
stiffness was not considered, the results would have
been:
Nir = (1057.7/2)-(12(4.3)154.9/52.01)-2138.4(0.5)7.52(41.2)/(90×52.01) = 304.4 lb
Nor = (1057.7/2)+(12(4.3)154.9/52.01)+2138.4(0.5)7.52(41.2)/(90×52.01) = 753.3 lb

Note that without roll, the little Fiesta’s normal loads
in a 0.5g maneuver would have been much more
even front-to-rear on the heavily loaded outside
wheels. The effect of the Fiesta’s relative roll
stiffnesses, which is the result of the spring rates
and moment arms, is to have much more of the roll
moment resisted by the front suspension than by the
rear. Consequently, when roll is taken into account
the Fiesta’s normal loads are much more skewed
toward the front outer wheel. This is by design; the
suspension roll centers (roll axis only slightly down
towards front), spring rates (greater roll stiffness at
front), and tracks were chosen for this effect.

Speaking of lateral
performance in the
current context of
roll is a natural
lead-in to the
subject of “roll
gain”. Roll gain is
the steady state
equilibrium amount
of roll, usually in
degrees, per lateral
acceleration, in g’s,
as illustrated:

The subject of roll gain is closely inter-related with the
topic of transient response in maneuver; there are a
number of aspects to the subject of transient response of a
vehicle in maneuver, and roll gain is just one such aspect.
There is also an angular acceleration “ ” associated with
the transient condition at the initiation or termination of a
turn (or with the application of the accelerator or brakes in
a turn, or with a turn of varying radius). The yaw inertia of
the vehicle “ ” times this angular acceleration represents
an inertial moment which must be equaled by moments
generated by forces at the tires in order for the transition
from straight ahead to turning to occur…

In the above equation, “ ” is the case when the
vehicle is initiating a turning maneuver. When the
vehicle comes out of the turning maneuver there will
be a less intense shorter lived reversal of this
situation, i.e., “ ”. Then, as is often the case in
slaloms, chicanes, or lane changing maneuvers, a
turning action in the opposite direction may
commence causing a situation of “ ” once
again, only now the forces will be pointing in the
direction opposite from before!

With all this fluxing of forces and moments
inflicted upon a damped spring-mass system
it should not be surprising that there would
be some oscillatory behavior observable. A
plot of vehicle yaw velocity “ ” versus time
“ ” for the transient phase at the
commencement of a turn leading up to a
steady state condition illustrates such yaw
oscillation behavior and its two phases, “rise”
and “decay”, which sum to the total vehicle
“response time”:

For the same specific vehicles as noted in the previous
figure, the over-plot of transient responses is illustrated
by:

Just as the or “ ” is an important factor
in the pitch motion of the sprung mass, the or
“ ” (a.k.a. “ ”) is an important factor in the
yaw motion of the entire vehicle as it determines an
“oscillation center” ( ) about which the vehicle will
initially tend to pivot. The value of this important
yaw motion factor has three possibilities:

Each of these possibilities corresponds to a certain
physical reality with a particular location for the
oscillation center:

(1) As soon as the front wheels begin to steer the tendency
to pivot about the will generate lateral reaction forces
at the rear tires in the same direction as when the steady
state condition is reached;
(2) The tendency to pivot about the rear axle means that
steering angle input at the front wheels will not
immediately generate lateral reaction forces at the rear
tires; .
(3) As the front wheels begin to steer the pivot about the
will generate reaction forces at the rear tires in opposite
direction from steady state condition; there will be a
reversal of forces from transient to steady state.
.

The transient condition has terminated and the
steady state has begun when the sprung mass
has attained some constant roll angle, the
vehicle has reached some constant yaw
velocity (no yaw acceleration), and the
associate fluctuation of traction forces at the
tires has ceased. This is the condition
generally sought while circling the
circumference of that test course known as
the “skidpad”.

A
common
skidpad
in plan
view

As noted earlier, rollover seldom occurs for modern
passenger cars as the slide point is generally reached
first. However, this does not mean that rollover is not a
concern. Although rollover was involved in less than 3%
of passenger vehicle accidents in the US for 2009,
rollover was involved in about 35% of all fatalities
(23,437 total fatalities, 8,296 roll-over fatalities). Of the
8,296 fatalities about 66% failed to wear seatbelts, with
many resultant ejections from the vehicle. However, that
leaves 34% who were properly belted in, yet who fail to
survive anyway, which still represents a disconcertingly
large proportion of all fatalities at about 12%.
(Highway Loss Data Institute, Insurance Institute for Highway Safety, “Rollover and
Roof Strength”, ‘www.iihs.org’, March 2011, pg. 1).

Therefore, even though rollover is unlikely, it still merits serious
concern. The NHTSA used to (NCAP 2001-2003) rate vehicles for
rollover resistance based solely on a mathematically derived figure
of merit called the “Static Stability Factor” ( ). The is
exactly the same as “ ” as calculated by the previous rigid
model equation:
Where:
= A figure numerically equal to the lateral
acceleration for overturn (in “g’s”).
= The average vehicle track width, front plus rear
divided by two.
= The vehicle center of gravity height above the
ground plane.

The can’t be a totally accurate means of comparison
between vehicles for reasons touched on earlier: under lateral
inertial load a rolling movement of the sprung mass will occur
through some angle “ which will reduce the “ ” by some
amount “ ” and cause the sprung weight to shift laterally by
some amount “ ”, all of which is among a number of
suspension dependent changes which will render the real
overturn point somewhat less than “ ”. Still, while the
difference between the actual “ ” and the is
significant, the is simple to determine and exhibits a
strong statistical correlation with the incidence of roll-over
accidents, as determined by NHTSA statistical analysis. Since
2004 the NHTSA has been using the combined results of the
calculation plus the “Fishhook” test for new vehicle
rollover resistance ratings.

The “Fishhook” name comes from the shape of the
path taken by the vehicle during the test. The
Fishhook invokes the rollover tendency of a vehicle
by approaching as close as possible to actual
rollover through a rather harsh maneuver. The
Fishhook uses steering inputs that approximate the
steering a panicked driver might use to regain lane
position after dropping two wheels off the roadway
onto the shoulder, but is performed on a level
pavement with a rapid initial steering input followed
by an over correction. The original version of this
test was developed by Toyota, and variations of it
were adopted by Nissan and Honda.

NHTSA’s test version includes roll rate measurement in order to
time the counter-steer to coincide with the maximum roll angle each
vehicle takes in response to the initial steering input. The test
utilizes an automated steering system programmed with inputs
intended to compensate for differences in vehicle steering gear
ratio, wheelbase, and stability properties. To begin, the vehicle is
driver controlled in a straight line. The driver releases the throttle,
coasts to the target speed, which starts around 35 mph (56 kph) and
is increased in 5 mph (8 kph) increments for each run (until
“termination” is achieved), and then activates the auto-pilot which
commences the maneuver. The test runs conclude when a
“termination” condition is achieved involving two inch or greater lift
of the vehicle’s “inside” tires (fail), or if the vehicle completes the
final run at maximum speed of 50 mph/80 kph without lift (pass). If
needed, further testing is undertaken to confirm the exact speed at
which lift occurs, and that the lift point is repeatable.

Vehicle directional stability is a subject that was
initially developed for, and by, the aircraft industry
starting from that industry’s earliest days. Although
the advent of the automobile preceded the airplane, it
would be more than 35 years before the science of
stability would even start to be applied to ground
vehicles. Stability as it pertains to a vehicle can have
many aspects, mainly yaw (directional) stability, roll
stability, and pitch stability. The emphasis of this
course segment on lateral acceleration narrows the
focus to just directional stability and roll stability, and
to a limited extent the latter has already been dealt
with.

What held back the development of directional
stability theory as applied to automobiles was the
lack of information regarding tire behavior. The
behavior of an airplane in flight is determined by
aerodynamic forces, and the effort to understand
such forces was present at the very dawn of the
airplane; Orville and Wilber Wright built a wind
tunnel to study aero effects long before their first
airplane ever left the ground. The behavior of
automobiles is predominantly determined by tire
behavior, and the first tire testing machine was
possibly the rotating steel drum tire tester of
Becker, Fromm, and Maruhn circa 1930.

Those German researchers generated tire data as a
prerequisite for their investigation of the great
automotive problem of the time: steering “shimmy”.
In this they were following up on the French
researcher George Broulheit who had identified the
tire characteristic of “slip angle” in his investigation
relating to shimmy. A notable follower in the
footsteps of these Europeans was R.D. Evans of the
Goodyear Tire and Rubber Company who continued
the investigation of the physical properties of tires
via another drum tire tester.

The war years of 1939-1945 brought most research into tire
and automotive behavior to a halt. However, in Germany at
Junkers Aircraft the researchers Von Schlippe and Dietrich
developed a simple structural model of the pneumatic tire
which after the war would tie in with the research of Dr. A.W.
Bull and (later) S. A. Lippmann at US Rubber. Essentially
this had to do with the lag time of drift angle formation after
application of a side force being a function of the distance
rolled, and hence of velocity and time. They found that, for
highway speeds and small drift angles, the transient phase
of the tires adjusting to the lateral forces could be neglected
and the modeling of vehicle behavior for just the steady
state condition would still have broad validity. This made
possible all the subsequent steady state modeling
investigations into vehicle directional stability.

One of the first to attempt a mathematical analysis of
automotive stability was Prof. Yves Rocard of the
Sorbonne in 1954. Prof. Rocard’s model was 4-wheeled
but rigid; no weight transfer or roll effects were
included. In 1955 M.A. Julien and G.J. Arnet presented
a paper based on an analysis of a less simplified model
in that it separated the vehicle into a sprung and an
unsprung mass. Maurice Olley at General Motors had
begun research into the “shimmy” problem in the early
1930’s, and by the 1950’s he and his GM compatriots
had progressed to major revelations regarding
automotive stability, benefiting greatly from the tire
work of Evans, Bull, Gough, and others.

Also around this 50’s period William F. Milliken, David
W. Whitcomb, and Leonard Segel of the Cornell
Aeronautical Laboratory would do a great deal to
advance the understanding of tire behavior and
automotive directional stability, including the
construction of the AF-CAL on-road tire tester. The
stability model utilized by the CAL investigators was a
four wheel model of sprung and unsprung masses, so
the effects of lateral “weight transfer” and roll were
accounted for, and steady-state conditions prevailed.
Tire drift angle and other functions were linearized
such that the stability analysis results were valid only
up to about 0.3 to 0.4 g’s.

Since the heady period of the 1950’s many new approaches to
understanding automotive directional stability have been taken.
Mathematical vehicle modeling and empirical tire research, utilizing
newer and ever more realistic test machines, would continue, but
computer simulations would come to play an ever more prominent role.
At first the computer simulations were largely through the use of analog
devices intended to serve in validation of theory, and vice versa.
However, analog computers were limited in capability, and were to be
replaced by more versatile digital machines. Since early digital machines
were typically slower than analogs, for a while in the early 1970’s hybrid
computers found favor. As the computational speed and other
characteristics of digital computers rapidly improved they came to
dominate the simulation world, initially as just mainframes but ultimately
also as “personal computers”. The change in platforms also coincided
with corresponding changes in simulation software; specific purpose
built software was to a large extent supplanted by general multipurpose
dynamic simulation and finite element analysis (FEA) codes.

The result has been a modern plethora of highly
detailed and complex modeling attempts. A full
understanding would involve a long exposition
involving a good deal of higher math and complex
algorithms which are beyond the scope of this
course (and beyond this instructor’s capability as
well). Therefore, this course will address the
subject through a simple “analysis” that will cover
most automotive cases, especially passenger cars,
and arrive at a limited result with the limitations as
fully identified as possible.

The greatest single complicating factor with regard to
automotive directional stability is that an automobile must be
“dynamically” stable, not just “statically” stable. The defining
difference between those two conditions is that a “statically”
stable system may show the accepted stable state
characteristic of returning to equilibrium position after the
application of a disturbance input, but in returning may
“overshoot” the equilibrium position and then execute a
reverse correction back to the equilibrium point once again,
which results in an even greater overshoot, and so on.
Although the system initially exhibits what would be regarded
as stable behavior, that is not the full story; that initial behavior
degenerates into an ever increasing series of oscillations
ultimately leading to a loss of control. Such a system is
statically stable, but dynamically unstable.

Consider the case of a vehicle traveling in a straight
line on a level (slightly crowned) road just before
encountering a “disturbance” such as a sudden change
in the road crown (highly exaggerated) resulting in a
lateral (with respect to the vehicle) component of the
weight vector acting through the c.g. (disturbance force
“ ”):

The essence of automotive directional stability may be gleaned from
the illustrative example just given of the three vehicles of varying weight
distribution. However, such an “explanation” falls far short of an
authentic analysis. Such an analysis begins with an assessment of the
geometry of a vehicle undergoing a slight turning action, either as the
result of a lateral disturbance force or an input from the steering wheel.
From the geometry of the situation the differential equations of
motion are written as if the vehicle were a free body moving in space, but
generally in only 2-DOF (1 translational, 1 rotational); these equations
consist of the summation of forces in the lateral direction, and the
summation of moments about the vehicle c.g., in accord with the concept
of “Dynamic Equilibrium”. The analysis leading to the following
discussion was essentially (other modeling results may have been
blended in) based upon the “bicycle model”; the geometry of which is
presented as follows…

The resulting differential equations are solved in accord with the
appropriate classical math methodology. Depending on the
complexity of the model, the resulting expressions may include:
1. “ ” ( ) is expressed in radians or degrees
and is a stability indicator.
2. “ ” ( ) provides a means of comparing
designs with respect to the degree of understeer present.
3. “ ” ( ) is a speed at which an oversteering
vehicle can switch from initially controllable (slight oversteer) to
very unstable (high oversteer) behavior.
4. “ ” ( ), as required at the front wheels
to make a steady-state turn of radius “ ” is another measure of
under/over steer.
5. “ ” ( ) is a determinant like “ ” for classifying a
vehicle condition as stable (understeering).

“ ” ( ), a.k.a. “Understeer
Gradient”, expressed in radians or degrees, presents a
more general way of classifying a vehicle’s stability
condition than comparing specific drift angle values
“ ” and “ ”. If a vehicle is stable (understeering, US)
then “ ”, if neutral (NS) then “ ”, or if
unstable (oversteering, OS): “ ”. This coefficient
can take various forms, of which one of the simpler is:

“ ” ( ) provides a means of
comparing designs with respect to the degree of
understeer present. Mathematically, it is the speed at
which the steering angle “ ” to make a turn of radius
“ ” is equal to “ ” (that is, the steering angle is
twice that determined by the low speed “Ackermann”
steering geometry “ ”):
(Note that the 57.3 is the number of degrees per radian; it is a units
conversion factor…)

“ ” ( ) is a speed at which an
oversteering vehicle can switch from initially
controllable (slight oversteer) to very unstable (high
oversteer) behavior:
(Note that the system of units conversion factor “57.3” is now
negative; this is in recognition of the fact that an oversteering
vehicle will have a negative “ ”. Since an understeering vehicle
does not have a negative “ ” this particular stability factor is not
applicable (“…there is no critical speed for an understeer car…a
neutral steer car does not have a real critical speed…”).)

“ ” ( ), as required at the front
wheels to make a steady-state turn of radius “ ” is
another measure of under/over steer (the smaller the
angle the less the degree of understeer):
An alternative formulation might be given as:

“ ” ( ) is a determinant like “ ” for
classifying a vehicle’s directional stability nature: “
” is stable (understeering), “ ” is neutral, and
“ ” is unstable (oversteering). Specifically, the
SM is a dimensionless fraction that relates the LCG
placement to the “Neutral Steer Point” (NSP) for that
condition ( ):

• FOR
AUTOMOTIVE LATERAL ANALYSIS HAS BEEN
WRITTEN BY THE INSTRUCTOR (TBD) WHICH,
PLUS A COPY OF “
” WILL
BE

3- AUTOMOTIVE LATERAL DYNAMICS, Rev. A

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3- AUTOMOTIVE LATERAL DYNAMICS, Rev. A