L5

04/08/26 Tue 9:07am

EV Component Sizing

Dr.P.Rangarajan

Why Proper Sizing Matters?

• Ensures optimal performance, efficiency, and durability
• Matches power delivery to driving demands
• Helps manage energy use and heat generation

Main Components to Size:

• Electric Motor - Delivers required torque and speed
• Battery Pack - Stores and supplies energy for driving range and performance
• Power Electronics - Manages Power flow between battery and motor
• Drive train - Transfers motor output to wheels efficiently

EV Vs Ice Powertrain Sizing

• ICE: Focus on engine displacement and fuel efficiency
• EV: Emphasis on motor power, battery capacity and energy efficiency

Unique EV Challenges

• Must deliver instantaneous power for quick acceleration
• Sustain power for cruising and uphill driving
• Enable regenerative breaking for energy recovery
• Require thermal management to avoid overheating and ensure reliability

Vehicle Dynamics

Understanding the Forces that move an Electric Vehicle:
Rolling Resistance: Opposition to motion due to tire deformation and road surface interaction

Aerodynamic Drag: Air resistance acting against the vehicles motion

Grade Force: Component of weight acting along the road on an incline

Inertial Force: Force required to accelerate the vehicle and its mass

Step by Step Procedures:

1. Rolling Resistance Analysis for Electric Vehicle Applications

1.Understand the Rolling Resistance Formula

The rolling resistance force is calculated using:

$$F_{rr}={\mu }_r\times m\times g\times \cos \theta$$

Note

For a flat road, $\theta =0^{\circ }$
Since $\cos 0^{\circ }=1$,
the equation simplifies to $F_{rr}=\mu \times m\times g$

Symbol	Description	Unit
$F_{rr}$	Rolling Resistance Force	N
${\mu }_r$	Rolling Resistance Coefficient	-
$m$	Vehicle Mass	kg
$g$	Gravitational Acceleration (9.81)	$m/s^2$
$\theta$	Road Inclination Angle	degrees

2. Understand the Physical Origin of Rolling Resistance

Cause	Contribution
Tyre deformation (Rubber Hysteresis)	$\approx 90\%$
Road surface indentation	$\approx 5\%$
Wheel Bearing friction	$\approx 5\%$

1. Tyre Deformation

• Front portion compresses
• Rear portion expands
• Rubber is not perfectly elastic
• Energy is lost as heat every rotation
• This phenomenon is called hysteresis loss.

2. Road Surface Indentation

• Soft road surface deform under vehicle weight.
• Examples: Gravel, Sand, Mud
• Energy is spent deforming the road.

3. Bearing Friction

• Wheel bearings rotate continuously.
• Mechanical friction inside bearings also consumes energy

3. Select the Rolling Resistance Coefficient (${\mu }_r$)

Surface	${\mu }_r$ Value
Smooth Asphalt (Passenger Car)	0.010 - 0.015
EV Low Rolling Resistance Tyre	0.007 - 0.012
Gravel	0.020 - 0.035
Sand	0.050 - 0.150
Steel Rail	0.001 - 0.003

Observation

Lower ${\mu }_r$ means
→ less energy loss
→ higher vehicle efficiency
→ longer EV driving range

4. Collect Vehicle Parameters

Example: Tata Nexon EV

• Vehicle Mass, $m=1510kg$
• Rolling Resistance Coefficient, ${\mu }_r=0.012$
• Gravitational Acceleration, $g=9.81m/s^2$
• Road: Flat road ($\theta =0^{\circ }$)

5. Substitute the Values

using the equation $F_{rr}={\mu }_r\times m\times g$
and upon substitution

$$F_{rr}=0.012{\times }_{1}510\times 9.81$$

6. Calculate Rolling Resistance Force

Calculate vehicle weight
$1510\times 9.81=14813.1N$
Now,
$F_{rr}=0.012\times 14813.1$
$F_{rr}=177.7N$
Final Rolling Resistance Force
$\boxed{F_{rr}=177.7N}$

7. Calculate Rolling Resistance Power

$$P_{rr}=F_{rr}\times v$$

Symbol	Meaning
$P_{rr}$	Rolling Resistance Power
$F_{rr}$	Rolling Resistance Force
$v$	Vehicle Speed

8. Convert Vehicle Speed

Vehicle speed = 100 km/h
Convert to m/s
$v=\frac{100\times 100}{3600}$

$$\boxed{v=27.78m/s}$$

9. Calculate Rolling Resistance Power

Substitute

$$P_{rr}=177.7\times 27.78$$ $$P_{rr}=4937W$$

Convert to kilowatts

$$\boxed{P_{rr}=4.94kW}$$

10. Interpretation

At 100 km/h,
Rolling resistance consumes $\boxed{4.94kW}$ of battery power continuously. This energy is permanently lost while driving.

11. Compare with Aerodynamic Drag (at 100 km/h)

Force	Power Required
Rolling Resistance	4.94 kW
Aerodynamic Drag	11.5 kW
Observation: at high speeds, aerodynamic drag requires more than twice the power needed to overcome rolling resistance.

12. Effect of Speed on Rolling Resistance

• The rolling resistance force remains nearly constant because vehicle mass is constant and tyre coefficient changes very little with speed.
• However, the power increases directly with speed because
  $P_{rr}=F_{rr}\times v$.
• If speed doubles, rolling resistance power also doubles.
• Rolling resistance power is linearly proportional to vehicle speed.

13. Rolling Resistance VS Aerodynamic Drag

Vehicle Speed	Dominant Resistance
0 - 40 km/h	Rolling Resistance
40 - 60 km/h	Rolling Resistance $\approx$ Aerodynamic Drag
Above 100 km/h	Aerodynamic Drag Dominates

[! Key Insight]

• Below approximately 60 km/h, rolling resistance is generally greater than aerodynamic drag.
• Above 100 km/h, aerodynamic drag becomes the dominant resistive force and consumes significantly more battery power.

14. Factors Affecting ${\mu }_r$ (Rolling Resistance Coefficient)

Factor	Effect
Low Tyre Pressure	10% pressure drop → 3 - 5% increase in ${\mu }_r$
Cold Temperature	Approximately 20% increase in ${\mu }_r$ during cold start
Tyre Compound	Silica-based “green” tyres reduce ${\mu }_r$ by 15 - 25%

2. Aerodynamic Drag - the $v^2$ Force and $v^3$ Power Law