Vehicle dynamics is a complicated analytical and experimental technology that is used to study and understand the responses of a vehicle in various in-motion situations.  In the driver education field, it is not necessary to deal with the specifics of this technology but rather with some of the basic physical principles involved in it.  The following principles will be discussed in this unit.


I.                   Kinetic Energy

II.                Centrifugal Force

III.             Inertia

IV.              Friction

V.                 Traction


There is no intent to give a complete technical definition of each principle but to present them in a manner that will be useful in understanding why a vehicle acts as it does.




Kinetic energy is a term that describes the energy a vehicle has due to its mass and speed.  Its formula is simple, yet tells a great deal.


            Kinetic energy = ½ (mass) x (velocity)2


This shows that the kinetic energy of the vehicle increases as the square of the velocity.  This means that if speed is doubled, the energy increases four times.  This energy increase causes no problem unless it must be dissipated or redirected quickly.


One way kinetic energy can be dissipated very quickly is when the vehicle strikes a solid object.  In this case, when the speed is doubled, four times the energy is available to damage the vehicle and injure its passengers.  The kinetic energy of a 4,000 pound vehicle traveling at 100 mph is equal to 1.36 million foot pounds – enough to lift a 175 pound man 1.5 miles.  To stop this vehicle tremendous energy must be dissipated.  This can be accomplished by impact or by the brakes.  Stopping distance is related to the square of velocity; therefore, 30 mph requires four times the distance to stop than 15 mph.  Many drivers never think of the consequences of increased speed but they should be aware of the risks involved.




When a vehicle turns, centrifugal force acts on the vehicle and tries to push it to the outside of the curve.  The formula is:


            Centrifugal Force = (mass) X (velocity)2/ radius of turn


This shows that centrifugal force increases as the square of velocity.  Also, at a given speed, small (tight) radius turns produce more force than large radius turns.  Large amounts of centrifugal force require equally large amounts of counteracting force from the tires if the vehicle is to remain on the road.  The tires can be thought of as strings from each end of the vehicle to the center of the turn.  If the centrifugal force is higher than the tires can counteract, one or both of the strings break.  The vehicle will then leave the turn.




Inertia is the resistance to change the direction or velocity of a body, either at rest or in motion.  In this case, it is related to changing the heading, or direction, of a vehicle; that is, changing from straight ahead driving to a turn.


The importance of inertia and weight distribution as they relate to driving is that they affect the amount of time required to make a transition from straight to turning or vice versa.  Although these changes with the usual loading of a vehicle are not large, a driver should recognize the unusual loading of a vehicle, such as the placing of a large load on the tailgate of a station wagon (or the addition of a heavy load on the vehicle roof) will cause changes in the way the vehicle drives and adjustments should be made in driving accordingly.


Since inertia dictates that a body in motion will continue to move in a straight line, a force must be applied to cause a vehicle to turn.  This force is called Centripetal force, and is a result of tires stretching to pull the car from a straight path.  Centripetal force must exceed centrifugal force for the vehicle to turn.




A.                 Pitch – the force felt in acceleration or braking movement around (Horizontal axis) of vehicle

B.                 Roll – the force felt in cornering, side to side movement (Lateral axis) of the vehicle

C.                 Yaw – the force felt in a spin movement around (Vertical axis) of the vehicle




A very important handling concept, which dictates the willingness of a car to change directional position if called Polar Moment of Inertia.  “Poles of inertia” are just another way of saying “center of weight concentration”.  The “moment” in this concept is determined by the front-to-rear location of the center of gravity.  The car turns (changes direction) about its center of gravity in a corner so the further away the centers of weight concentration are located from the center of gravity (which is their common center), the bigger the “moment”.


A high polar moment of inertia is present when the weight concentrations are heavy and are far apart.  The low polar moment of inertia is found when weight concentrations are light and are close together.  In other words, it is easier to steer a vehicle with a low polar moment of inertia.


A vehicle with a low polar moment of inertia gives a quick response to steering commands.  A vehicle with a high polar moment has high directional stability (meaning it resists changing its direction).




Friction is defined as the resistance to motion between two surfaces.  There are four basic types of friction.


A.                Static – the holding force between two surfaces at rest

B.                Sliding – the resistance to motion between two surfaces which are moving across each other

C.                Rolling – the resistance to motion of a rolling object like a ball, cylinder or wheel

D.                Internal – the resistance to motion within elastic objects (tires get warm from internal friction as they flex)


The amount of friction between two surfaces depends upon:


1)                  substance of material

2)                  roughness of the surfaces

3)                  amount of force pushing the surfaces together

4)                  presence of lubricants


The amount of friction between two surfaces is called coefficient of friction.




The term coefficient of friction is defined as the maximum force that can be created by a tire on a given road surface condition, divided by the weight on the tire.  Its formula is:


                                        Maximum Force Available

Coefficient of Friction = Weight on the Tire




Maximum Force Available = Coefficient of Friction X the Wheel Load Weight


Thus, the maneuvering ability of a vehicle on a dry road depends primarily upon road surface and vehicle weight.  On a wet road, other factors such as tire condition must also be considered.


As the vehicle accelerates or slows down more rapidly, or as the vehicle corners at faster speeds, it demands greater traction forces from the tire-road combination.  The tire and road combination will produce these forces up to the friction limit.




Traction is defined as the adhesive friction of the tire to the road surface.  There are three traction forces:


1)                 Driving Traction – To accelerate the vehicle

2)                 Braking Traction – To slow or stop the vehicle

3)                 Cornering Traction – To turn the vehicle


At any time traction force becomes greater than the coefficient of friction the vehicle will go out of control.


A driver has the potential for exerting three forces.  For any given situation, there is a level of friction (coefficient) available for exerting these forces, and therefore, maneuvering the vehicle.  When a driver exerts either a braking or acceleration force while at the same time exerting a cornering force, you must add the forces when considering the available friction.  In other words, the sum of driving or braking traction and cornering traction must not exceed the friction limit, or the vehicle will go out of control.  Whenever possible, avoid braking or accelerating while cornering.  This allows all available friction to be used in cornering.


A spinning tire cannot provide full driving traction when accelerating.  If a driver causes drive wheel spinning when cornering, the vehicle may go out of control.


A locked tire provides no cornering traction and reduced braking traction.  When a driver locks the wheels in a corner, there will be no response to the steering input.  During braking, the maximum coefficient of friction; therefore, maximum braking ability, is when the driver applies the brakes at a level of 15% slippage.

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