Mazda Training manual - part 81

Dynamic Driving Safety Systems 

Fundamentals 

Yaw Moment 

• 

The yaw moment around the vehicle’s vertical axis is caused by different longitudinal 
forces acting on the left and right side of the vehicle, or different lateral forces acting at 
the front and rear axles. Yaw moments are required to turn the vehicle when cornering. 
Undesired yaw moments can occur when a vehicle rotates too strongly around the yaw 
axis. 

 

Longitudinal Force 

• 

During driving, accelerating, decelerating, and braking,  the longitudinal force acts in the 
driving direction of the vehicle. 

 

Lateral Force 

• 

The lateral force, that is applied to the vehicle by wind and cornering, acts sideways on 
the vehicle. 

 

Vertical Force 

• 

The vertical force is the weight that is transmitted vertically by a tire. It depends on the 
vehicle’s gross weight, the vehicle’s centre of gravity, and other dynamic influences. 

 
 

Curriculum Training 

01-3 

Fundamentals 

Dynamic Driving Safety Systems 

Coefficient of Friction 

• 

The frictional force is additionally affected by the coefficient of friction, which differs 
according to the materials and the surfaces rubbing against each other.  

• 

The illustration shows that less force is necessary to push the larger weight across iced 
tarmac. It can be easily seen that the force required is much less than the vertical force 
due to the object’s gross weight. 

• 

The relationship between the frictional force and the vertical force is the coefficient of 
friction μ: 

Frictional force

μ=

Vertical force 

 

 

L2003_01004 

 

A  Small weight on tarmac 

2  Frictional force 

B  Heavy weight on iced tarmac 

3  Vertical force 

1  Necessary force to push the object 

   

 

01-4 Curriculum 

Training 

Dynamic Driving Safety Systems 

Fundamentals 

• 

The illustration shows the relationship between the tire downforce and the friction on a 
vehicle. 

 

 

L2003_01017 

 

1  Linear velocity of the vehicle 

3  Frictional force 

2 Tire 

downforce 

  

 
• 

The table shows some sample values for the coefficient of friction between a tire and the 
road surface at various conditions. 

 

Vehicle speed 
Tire condition

New

Worn

New

Worn

New

Worn

Dry road

0,85

1

0,8

0,95

0,75

0,9

Rain (depth of water approx. 0.2 mm

0,65

0,5

0,6

0,2

0,55

0,2

Heavy rain (depth of water approx. 1 mm)

0,55

0,4

0,3

0,1

0,2

0,1

Puddles (depth of water approx. 2 mm)

0,5

0,25

0,05

0

0

0

Icy road

0,3

< 0.1

< 0.1

< 0.1

< 0.1

< 0.1

50 km/h

90 km/h

130 km/h

L2003_T01001

 

 
 
 

Curriculum Training 

01-5 

Fundamentals 

Dynamic Driving Safety Systems 

Wheel slip 

• 

The wheel speed is, depending on the driving conditions, more or less different to the 
actual vehicle speed (what is the theoretical wheel speed). The difference between the 
theoretical and the actual wheel speed is the wheel slip. 

• 

The circumferential speed of a driven wheel is higher than the vehicle speed during 
accelerating, and the circumferential speed of a braked wheel is less than the vehicle 
speed.  

• 

The relationship between the speed difference (between vehicle speed and wheel 
speed) and the vehicle speed is the wheel slip 

λ: 

Vehicle speed - wheel speed

λ =  

Vehicle speed 

 * 100 

 

• 

The wheel slip 

λ is calculated as a percentage. A fully locked wheel during driving, or a 

spinning wheel while the vehicle is stationary has a slip of 100 % while a wheel rotating 
with the vehicle speed has a slip of 0 %. 

• 

The correct wheel slip is very important for the stability and driveability of a vehicle. 
Since the most force can be transmitted with a wheel slip of approximately 20 %, the 
ABS keeps the wheel slip between approximately 15…20 % in order to achieve a short 
braking distance while maintaining high driving stability and steerability of the vehicle. 

 

 

L2003_01005 

 

1  Circumferential wheel speed  

2  Vehicle speed  

 

01-6 Curriculum 

Training