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Forces on Vehicle
Total Tractive Force
1. Rolling Resistance Force (Frr)
2. Aerodynamic drag force (Faero)
3. Hill climbing Force (Fhc)
4. Acceleration Force (Fxi)
1. Linear Acceleration Force
2. Angular acceleration force
Rolling Resistance Force
It is one of the forces that act to oppose the motion of a vehicle.
The Coefficient is a function of the Tire material, structure, temp, pressure, tread
geometry, road roughness, material, presence & absence of liquids on the road.
- This value varies with SPEED.
- Tire pressure increases its value decreases
Frr = µrr m.g
µrr - Rolling Resistance Constant
m - Mass of the Vehicle
g - Gravitational acceleration constant
Below are few Rolling resistance Constant depending upon road surface type:
Car tires on Concrete/asphalt = 0.013
Car tires on rolled gravel = 0.02
Tar Macadam = 0.025
Unpaved Road = 0.05
Field = 0.1 - 0.35
Truck Tires on concrete or asphalt = 0.006 - 0.01
Wheels on Rail = 0.001 - 0.002
Aerodynamic Drag Force
• The force on an object that resists its motion through an air is called drag.
• Drag is a force that acts parallel to and in the same direction as the airflow.
• Aerodynamic drag increases with the square of speed.
Fad = ½ρCdAv2 Newtons
ρ – Air Density kg/m3
A – Frontal Area m2
Cd – Drag Coefficient
v - Velocity of the Vehicle m/s
Low Pressure
High Pressure
Hill Climbing Force
Rise / Run
Fhc = m.g.Sin θ
Acceleration Force
1. Linear Acceleration force (Fla) = m.a
2. Angular Acceleration force (Fωa)
I - moment of inertia
G – Gear Ratio
a - Acceleration
r – Radius of tire
- Efficiency of gear
Fωa
Drag Coefficient constant Typical Values
Trucks Road Trains = 0.8 - 1.5
Buses = 0.6 - 0.7
Modified Buses/car = 0.3 - 0.4
Motorcycles = 0.6 - 0.7
Total Power Required
Total Power P = Fte . v
Fte Total Tractive Power = Frr + Fad + Fhc + Fla + Fwa
Rolling Resistance Force Frr = µrr m.g
- µrr - Rolling Resistance Constant
- m - Mass of the Vehicle
- g - Gravitational acceleration constant
Aerodynamic Drag Force Fad = ½ρCdAv2 Newtons
- ρ – Air Density kg/m3
- A – Frontal Area m2
- Cd – Drag Coefficient
- v - Velocity of the Vehicle m/s
Hill Climbing Force Fhc = m.g.Sin θ
Linear Acceleration Force (Fla) = m.a
Angular Acceleration Force Fωa
- I - moment of inertia
- G – Gear Ratio
- a - Acceleration
- r – Radius of tire
- - Efficiency of gear
EV Rating(2kw)
Parameters
Notations
Value
Units
Weight
m
1,000.00
Kg
Width
W
1.00
m
Height
H
1.50
m
Rolling
Resistance
µrr
0.02
Air Density
ƥ
1.25
kg/m2
Drag
Coefficient
Cd
0.30
gravitational
Force
g
9.80
Speed in km
40.00
kpmh
Frontal Area
A
1.50
m2
Velocity
v
11.11
m/sec
Velocity = kpm -> m/s
= 40 * 1000/3600
Tractive Force = Rolling Resistance Force + Aerodynamic drag force
Fte (Total Tractive Power) = Frr + Fad
Tractive Force (Fte) = 170.15 Nm
Total Power = Total Tractive Force x Velocity
Total Power P = Fte . v
Total Power for 40Km (P) = 1,890.53 Watts