## Vehicle Dynamics

#### Longitudinal Acceleration

The acceleration of a vehicle depends on the net force acting on it. The basic equation for longitudinal acceleration is:

Where:

: Net force acting on the vehicle (N) : Total mass of the vehicle (kg) : Acceleration (m/s²)

Longitudinal acceleration is calculated as:

### Resistive Forces to Motion

#### Aerodynamic Drag

Where:

: Coefficient of aerodynamic drag (dimensionless) : Frontal area of the vehicle (m²) : Air density (kg/m³) : Speed of the vehicle (m/s)

#### Rolling Resistance

Where:

: Coefficient of rolling resistance (dimensionless) : Acceleration due to gravity (9.81 m/s²)

#### Slope Resistance (or Gradient)

Where:

: Angle of inclination of the slope (rad)

### Vehicle Motion Equation (Sum of Forces)

The sum of all forces acting on a vehicle gives the net force:

#### Maximum Speed of the Vehicle

The maximum speed can be found when the traction force

Solving for speed:

## Transmission and Powertrain

#### Gear Ratio

The gear ratio for a gear system can be calculated as:

Where:

: Number of teeth on the driving gear : Number of teeth on the driven gear

#### Power at the Wheels

The power available at the wheels is related to torque and angular velocity:

Where:

: Power (W) : Torque (N·m) : Angular velocity (rad/s)

#### Torque

The torque at the wheels is related to the torque at the engine through the gear ratio:

Where:

: Efficiency of the transmission

## Vehicle Aerodynamics

### Aerodynamic Drag

Aerodynamic drag is the main resistive force acting on a vehicle at high speeds. The formula has been provided but is broken down into the following factors:

#### Drag Coefficient

Depends on the shape and aerodynamic design of the vehicle.

#### Frontal Area

Effective area facing air resistance.

#### Lift Force

Some vehicles generate lift or aerodynamic load due to their design. This force is calculated similarly to drag:

Where:

: Lift coefficient.

## Braking

#### Braking Force

The total braking force that a vehicle can exert is given by the following equation:

Where:

: Coefficient of friction between the tire and the road. : Normal force on the tires, which equals the weight of the vehicle on flat surfaces.

#### Braking Distance

The distance required to stop a vehicle from an initial speed

## Suspension and Tires

#### Natural Frequency of the Suspension

The natural frequency of a suspension is important for the comfort and stability of the vehicle. It is calculated as:

Where:

: Spring constant (N/m) : Suspended mass (kg)

#### Load on Tires

The vertical load on a tire can be calculated as:

Where:

: Distance from the center of mass to the front axle. : Distance from the center of mass to the rear axle. : Wheelbase.

## Power and Fuel Consumption

#### Required Power

The power required to move a vehicle at constant speed is determined by the total resistive forces:

Where:

: Speed of the vehicle (m/s)

#### Specific Fuel Consumption (SFC)

Where:

: specific fuel consumption (kg/W·h) : mass flow rate of fuel (kg/h) : engine power (W)

#### Thermal Efficiency

Where:

: useful power (W) : chemical power of the fuel (W)

#### Range

Where:

: range of the vehicle (km) : energy stored in the tank (J or Wh) : fuel consumption per km (L/km)