The document discusses various forces of resistance that act on a moving vehicle, including aerodynamic drag, rolling resistance, and grade resistance. It provides formulas to calculate these forces and examines how they vary with factors like vehicle mass, speed, tire type, and road conditions. The document also addresses inertial forces like those due to acceleration and rotational inertia. It explores how these resisting forces impact vehicle performance and engine demand.

1. Resistance Forces on A Vehicle
P M V Subbarao
Professor
Mechanical Engineering Department
Estimation of Vehicle Demands….

2. Resistance Forces on A Vehicle
• The major components of the resisting forces to motion
are comprised of :
• Acceleration forces (Faccel = ma & I forces)
• Aerodynamic loads (Faero)
• Gradeability requirements (Fgrade)
• Chassis losses (Froll resist ).
g
rr
aero
accel F
F
F
F
F 




3. Force System on A Rolling Wheel

4. Road Conditions & Rolling Resistance
4

5. Rolling Resistance
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
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
g
V
M
C
=
P rr
rr 


Mg
Frr  Mg
C
F rr
rr 

6. Standard Formula for Rolling Resistance
V
M
C
)
10
(2.72
=
P
V
M
C
3600
9.81
=
P
rr
3
-
rr
rr
rr













where:
P = power (kW)
Crr = coefficient of rolling resistance
M = mass (kg)
V = velocity (KpH)








147
1
01
.
0
V
Crr

7. Contact Type Crr
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

8. Effect of Road Condition on Crr
8

9. Rolling Resistance And Drag Forces Versus Velocity

10. Grade Resistance
Composed of
– Gravitational force acting on the vehicle
g
g mg
F 
sin

g
g 
 tan
sin 
g
g mg
F 
tan

G
g 

tan
mgG
Fg 
For small angles,
θg mg
θg
Fg

11. Total Vehicular Resistance at Constant Velocity
AR = air resistance [N]
RR = rolling resistance [N]
GR = gradient resistance [N]
TR = total resistance [N]

12. Resistance
Vehicle Speed
Steady State Demand Curve

13. Vehicle Speed vs. Engine Speed
 
o
crank
G
i
rN
V



60000
1
2
V = velocity , km/hr
r = wheel radius, m
Ncrank = crankshaft rpm
i = driveline slippage
GO = Overall gear reduction ratio

14. Typical Engine Torque-Power Curves @ SS

15. Steady State Demand Vs Available Effort
15

16. Inertial or Transient Forces
• Transient forces are primarily comprised of acceleration
related forces where a change in velocity is required.
• These include:
• The rotational inertia requirements (FI ) and
• the translational mass (Fma).
• If rotational mass is added to a translating vehicle, it adds not
only rotational inertia but also translational inertia.

17. Inertial Resistance
17
a
m
=
F vehicle
eff
IR 

 a
m
m
=
F eq
vehicle
IR 

where:
FIR = inertia resistance [N]
meff-vehicle = Vehicle mass + Equivalent mass of rotating parts [kg]
a = car acceleration [m/s2],
(from 0 to 100 km/h in: 6 s (4.63 m/s2), 18 s (1.543 m/s2))
mvehicle = Vehicle mass [kg]
meq = Equivalent mass of rotating parts [kg]

18. 18

19. = angular acceleration k = radius of gyration
Equivalent Mass of Rotating Parts
Torque due to any rotating part (ex. Wheel)


wheel
wheel
wheel
i I
=
dt
d
I
=
T
wheel
2
wheel k
m
=
r
a
=
tire
vehicle
wheel

wheels and axles = 78% of total polar inertia
propeller shaft = 1.5%
Engine = 6%
Flywheel and clutch =14.5%

20. Therefore the equivalent mass of all rotational parts including losses is
represented as:
 
2
2
2
2
2
2
&
wheel
gb
f
mt
clutch
flywheel
e
wheel
f
f
propeller
wheel
axles
wheel
eq
r
G
G
I
I
I
r
G
I
r
I
m













21. Required Torque & Power at Wheels
wheel
vehicle
demand
wheel
p
T



wheel
vehicle
demand
wheel
N
p
T

2
60 


wheel
mt
engine
wheel
N
p
T


2
60 












f
gb
engine
mt
engine
wheel
G
G
N
p
T


2
60











f
gb
engine
mt
engine
wheel
G
G
N
p
P



2
60
mt
f
gb
engine
wheel G
G
T
T 




wheel
mt
f
gb
engine
wheel
wheel
TE
r
G
G
T
r
T
F






Tractive Effort demanded by a vehicle):

22. Vehicle Dynamics Model

23. Transmission System Model

24. Torque Requirements Model

25. Engine Model

26. Pune Urban Drive Cycle

27. Engine RPM during Urban Driving Cycle

28. Engine Fuel Consumption During Urban Driving
Cycle

29. Kinetic Energy Available during Braking per Driving
Cycle
-20000
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
0 200 400 600 800 1000 1200 1400 1600
42382.8 79296.9
22501.6 53078.1
9407.5 35019.5
2538.6 36748.7
4921.9 11812.9
29754.2 179702.1
29393.3 145894.5
9071.9 148095.7
97748.6 179691.7
18132.9 21710.0
29393.3
1204149.7
12041kJ

30. Inertial Energy in A Sub Cycle Duration : 450 to 475
sec
0
5000
10000
15000
20000
25000
30000
35000
445 450 455 460 465 470 475 480
Time in seconds
Inertial
Energy,
J

31. Inertial Energy in A Sub Cycle Duration :1105 to 1139
sec
-20000
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
1020 1040 1060 1080 1100 1120 1140

32. Fuel Savings due to Idling Logic

33. Idling Engine During Braking : Fuel
Consumption

34. Fuel Consumption over Pune Drive Cycle

35. Braking Methods Vs Fuel Economy
• A planned gradual stop, say at a traffic light where you would
prefer saving fuel over engine braking - you may press the clutch
and / or shift to neutral and brake simultaneously.
• Caveat - if you are using fuel cut-off, you need not shift to
neutral or press clutch. Just use clutch to avoid engine stalling.
• Slowing down to slightly lower speeds, say while abandoning an
overtaking maneuver - Clutch is not required as long as you don't
drop too low on engine speed.
• Panic braking from high speed to stop or very slow speed - don't
touch the clutch even if you risk stalling the engine and use
maximum engine braking.

36. • Stop-and-go braking like in bumper to bumper traffic - press
clutch and brake to avoid engine stalling.
• Track / rally circuit - brakes first and eyes on tachometer. As
soon as you close on in-gear idle (which you should know
better than your birthday if you are racing), press the clutch
and downshift gears. Re-engage clutch as soon as you have
finished shifting.
• Coasting downhill - brakes first and use clutch only to shift
gears.

37. Braking Vs Safety
• The driver is trying to achieve two things by braking
Slow down the vehicle or bring it to stop within a desirable
time span so that everyone is safe
• As long as the first one is achieved, avoid engine stall
• If you do not apply clutch while braking, vehicle gets more
braking assistance due to engine resistance.

38. You are trying to slowdown the vehicle from say
80kmph or more for a normal stop
• At 80kmph or more you would normally be driving in top gear.
• Your engine is not going to stall in the same gear till you come
down to say 40kmph.
• In this case apply brake without clutch till you reach that speed
and then move to the lower gear(usually 4th) and release the
clutch.
• Keep braking till you reach around 25 kmph and apply clutch
and bring the vehicle to stop.
• The second part is applicable if you were driving at less than say
50kmph.
• You don't need to change the gear.
• Keep applying the brakes and apply clutch when you feel engine
running too slow.

39. Emergency stop/slowdown at any speed
• Just apply brake without clutch.
• You need maximum braking even at the cost of engine
stalling.
• Even if you are at a very high speed (100kmph or more),
lowering the gear is not a great idea.
• Disengaged clutch (even if it is for very short duration) would
lower your total braking effectiveness.

40. Driving downhill
• Lower the gear to a comfortable one (usual theory advises the
same gear in which you would go uphill at the same place.
• However my experience say it would be too slow, you may
want to run in the next higher gear) and apply brakes without
clutch.
• This will help to avoid over heating of your brakes.

41. Braking N Safety
• In general, if we're talking normal driving situations the rule of
thumb you should follow is to keep the car in gear for the most
amount of time.
• Downshifting is good, but most people do not downshift when
stopping.
• This can either just be laziness, but it's also driven by the fact
that when you need to slow down reasonably fast you might
just not have enough time to row through the gears.
• Best way to do is, brake in gear until the car about the slowest
speed for whatever gear it is in, then clutch in, go into neutral
and keep braking further.