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Vehicle Dynamics - Lesson Summary

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This chapter attempts to compute how much power is required to drive a vehicle and how much energy is required to carry out a trip from one place to another. To do this, we need to understand a few things about the vehicle. The gross weight of the vehicle, that is the weight of the vehicle plus the weight of the passengers, road conditions, and how wind resistance impacts the vehicle. To do such calculations, we need to understand the impact Aerodynamic Drag, Rolling Resistance, Uphill Resistance, and Acceleration has on a vehicle.

Aerodynamic Drag, or wind resistance, is the force that pushes the car back, or acts against the car, as the car moves forward.

Drag = 1/2*p*Cd*A*v2


Rolling Resistance is the force that pushes the car down as the car moves forward, it acts on the car due to friction created by the conditions of the road, vehicle wheels, and vehicle weight.

Rolling Resistance = m*g*μ*cosθ

Gradient Resistance is the force that pushes the car down as the car moves uphill.

Gradient Resistance = m*g*sinθ

A vehicle needs Traction Power, Ptrac (in Watts), applied for it to move and accelerate.

Traction power in Internal Combustion Engines comes from petrol or diesel engines.
Traction power in EVs comes from a battery through motors and its controllers.

The traction power creates a Force (Ftrac) on the vehicle to move forward.

Ptrac = Ftrac*v (where v is velocity in m/sec)

The resulting Torque T (in Newton-Meters Nm) on the vehicle wheel created by the force is:

T = Ftrac*rwheel(wheel radius in meters)

Torque and Speed (referred to as rpm) are the fundamental parameters of a motor or an engine, and vehicle rpm is obtained from v=rpm*2π*rwheel/60

Ftrac = Acceleration Force + Aerodynamic Drag + Rolling Resistance + Gradient Resistance

The Energy consumed by a vehicle in motion is the integration of Traction Power

Energy = ∫ Ptrac dt in Watt-sec and is converted to kWh by 3.6

A drive train is to be designed to provide adequate force and torque force at different speeds to overcome drag, rolling resistance, gradient resistance, and to provide the right acceleration for pick up.

The purpose of a drive cycle is to determine how much energy a vehicle will consume per kilometer. This concept of energy efficiency in Electric Vehicles is measured in Kilo-Watt hours over kilometer (kWh/km). Different countries have different drive cycles to account for different driving conditions.

In a battery-powered electric vehicle, regenerative braking is the conversion of the vehicle's kinetic energy into chemical energy stored in the battery, where it can be used later to drive the vehicle. The Regeneration Efficiency has to be taken into account when calculating the results of a drive cycle. In real-world applications, regeneration efficiencies are between 30% to 40%.

Other inefficiencies will cause an energy loss due to power dissipation as heat. Therefore, thermal insulation needs to be designed to cater for that.

Batteries in electric vehicles operate at 85% capacity, and at 80% as the battery ages, this too has to be taken into account when designing a vehicle’s power requirements.