Picture of the Day
Picture of the Day
Lecture Outline
In addition to cornering, other effects can cause
longitudinal and lateral load transfer-page 684 in text)
1. Driving-Longitudinal
2. Grade-Longitudinal
3. Crests/Dips-Longitudinal
4. Aerodynamic-Longitudinal
5. Banking-Lateral
BONUS!! Engine Torque Reaction
General Solution Steps
1. Calculate forces
2. Resolve forces around the ground axis
system
3. Balance moments and forces with wheel
loads
Driving
Longitudinal
• Caused by inertial forces
• Driving forces caused by braking and
accelerating
• Intuitively see this when driving
Driving
Longitudinal
Step 1-Calculate Forces
Fx Ax
h
b a
Δw
Δwx - Change in Wheel Load
Fx – Inertial Force
Driving
Longitudinal
Step 2-Resolve Forces:
• Forces already resolved around appropriate axis system
Step 3-Balance Forces
Fx Ax
h
b a
Moments about
Δw front tire
Driving
Longitudinal
• When using equations car CG can shift as the
springs flex
Fx Ax
h
b a
Grade
Longitudinal
• Grade means hill steepness
• Changes the overall total load
• Changes the front-rear distribution
• Grade and tractive/braking forces can be
combined
• Grade has the effect of turning weight into
tractive/braking forces
Grade
Longitudinal
Step 1-Calculate Forces
w
FF θ
FR
Fx – Inertial Force
FF-Front Tire Force
FR-Rear Tire Force
w -Weight
Grade
Longitudinal
Step 2-Resolve Forces
w
X
FF θ
FR Z
Resolve Weight Force: Resolve Inertial Force:
These are already along
the ground axis system
Grade
Longitudinal
Step 3-Balance Forces w
O
x
FF θ
FR z
Crests/Dips
Longitudinal
• Cresting a hill changes wheel loads
• Depends on radius of hill and vehicle
speed
• Essentially the same as flat grade, 2
exceptions
1. Centrifugal forces reduce wheel loading
2. Differences in road curvature causes
different normal wheel load forces
• Factor 2 is usually ignored
Crests
Longitudinal
Step 1-Calculate Forces
w
Angular
θ Acceleration
AR
Weight
Force
Inertia
Force
Crests
Longitudinal
Step 2-Resolve Forces
w Angular Already
θ Acceleration Resolved
Weight
X o Force
Inertia Already
Z Force Resolved
Step 3-Balance Forces
• Why subtract centrifugal force for a crest?
Like a roller coaster, feel weightless at the top of a hill
Crests
Longitudinal
w
θ
X o
Z
Dips
Longitudinal
w
• A dip is analogous to
a crest, but centrifugal
forces are applied in
the opposite direction
θ
Aerodynamic
• SAE Aerodynamic axis system is located
on the ground plane equidistant from the
tires
– Means only pitch, roll and lift effects are
considered
• Calculated using a moment balance
• More an exercise in fluid dynamics than
RVD
Banking
Lateral
• Considering only the steady state case
– No Driving/Braking forces
• Usually seen on corners, although most
roads slightly banked to shed water
• Causes lateral load transfer
Banking
Lateral
Step 1-Calculate Forces
w
α
FL
FR
Centrifugal Force Gravity Force Wheel Reactions
Banking
Lateral
Step 2-Resolve Forces:
F’z F’y
FL w
FR
Centrifugal Force Gravity Force
Banking
Lateral
Step 3-Balance Forces
Summing the forces yields:
With the normal and lateral forces, the moments on the vehicle can be
balanced around the tires to find the left and right wheel loads.
The lateral load transfer from banking also causes longitudinal load
transfer. (page 687)
Banking
Lateral
• ΔWf and ΔWR are positive for an increase
in load on the outside wheels
Outside Wheel w
BONUS
Engine Torque Reaction
• For front engine, rear
Summing the Forces and Moments
wheel drive
• Weight shifts to left
wheel
ME
Substituting for Fl
w
FL FR
So Fr is always less for positive ME and slips first!
Example Problem
A 2800 lb car with a 100
in wheelbase and 60 in
front and rear tracks
has 56% front weight,
53% left weight and 50
lb of diagonal load.
Calculate the wheel
loads.
Example Problem
Solving 4 linear equations and 4 unknowns is easiest using
matrices
Invert Matrix to find:
Banking
Lateral
• Solution has three steps
1. Calculate force
2. Resolve force around ground axis system
3. Balance moments and forces with wheel
loads
Φ
w