VehicleDynamics_Forces accting,Balance equation

Vehicle dynamics

1. Vehicle Dynamics

2. Resistance Forces on A Vehicle
•The major components of the resisting forces to motion are
comprised of :
•Aerodynamic Drag (F
w)
•Rolling Resistance (F
r)
•Grading resistance (F
g)

4. Modeling of Aerodynamic Resistance on A
Vehicle
Aerodynamic Drag Force depends on:
•Air Density (ρ)
•Cross Sectional Area of Vehicle (A)
•Velocity (v)
C
D
-aerodynamic drag coeff.
Typically between 0.30 and 0.35., More for SUVs

6. Road Conditions & Rolling Resistance

7. Rolling Resistance
•Rolling Resistance mostly affected by:
•1. Composition, type and tire condition consisting of inflation
pressure, tire tread, the type of rubber
•2. Composition and type of road
•3. Sliding speed in tire-road contact
•4. Existence of external agents (rain, ice, snow etc.)

8. Model to Estimate Rolling Resistance
The magnitude of this force is Approximated as:
Rolling resistance of a vehicle is proportional to the component of
weight normal to the surface of travel
MgF
rr MgCF
rrrr


9. Contact Type
C
rr
Steel wheel on rail 0.0002...0.0010
Car tire on road 0.010...0.035
Car tire energy safe 0.006...0.009
Tube 22mm, 8 bar 0.002
Race tyre 23 mm, 7 bar 0.003
Touring 32 mm, 5 bar 0.005
Tyre with leak protection 37 mm, 5
bar / 3 bar
0.007 / 0.01
Typical Values of Coefficient of Rolling
Resistance







147
101.0
V
C
rr

10. Effect of Road Condition on C
rr

11. Rolling Resistance And Drag Forces Versus
Velocity on A Good Road

12. Grade Resistance
Composed of Gravitational force acting on the vehicle
gg
mgF sin
ggtansin
gg
mgF tan
For small angles,

θg mg
θg
Fg
The slope of the flyover ramp is calculated on the basis of a 1:20
gradient, on the basis of a truck.
However, a slope of 1:10 would provide comfortable access for
cars.

18. Dynamic Equation
Dynamic Equation of vehicle motion along with longitudinal direction :
Total Tractive EffortTotal resistive forcesAcceleration