For motorized vehicles, such as automobiles,

aircraft An aircraft is a vehicle that is able to flight, fly by gaining support from the Atmosphere of Earth, air. It counters the force of gravity by using either Buoyancy, static lift or by using the Lift (force), dynamic lift of an airfoil, or in ...

, and

watercraft Any vehicle used in or on water as well as underwater, including boats, ships, hovercraft and submarines, is a watercraft, also known as a water vessel or waterborne vessel. A watercraft usually has a propulsive capability (whether by sai ...

, vehicle dynamics is the study of vehicle motion, e.g., how a vehicle's forward movement changes in response to driver inputs, propulsion system outputs, ambient conditions, air/surface/water conditions, etc. Vehicle dynamics is a part of

engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...

primarily based on

classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classi ...

Factors affecting vehicle dynamics

The aspects of a vehicle's design which affect the dynamics can be grouped into drivetrain and braking, suspension and steering, distribution of mass, aerodynamics and tires.

Drivetrain and braking

Automobile layout The powertrain layout of a motorised vehicle such as a car is often defined by the location of the engine and drive wheels. Layouts can roughly be divided into three categories: front-wheel drive (FWD), rear-wheel drive (RWD) and four-wheel driv ...

(i.e. location of engine and driven wheels) *

Powertrain A drivetrain (also frequently spelled as drive train or sometimes drive-train) is the group of components that deliver mechanical power from the prime mover to the driven components. In automotive engineering, the drivetrain is the components o ...

* Braking system

Suspension and steering

Some attributes relate to the

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

of the suspension,

steering Steering is a system of components, linkages, and other parts that allows a driver to control the direction of the vehicle. Introduction The most conventional steering arrangement allows a driver to turn the front wheels of a vehicle using ...

and

chassis A chassis (, ; plural ''chassis'' from French châssis ) is the load-bearing framework of an artificial object, which structurally supports the object in its construction and function. An example of a chassis is a vehicle frame, the underpar ...

. These include: * Ackermann steering geometry *

Axle track In automobiles (and other wheeled vehicles which have two wheels on an axle), the axle track is the distance between the hub flanges on an axle. Wheel track, track width or simply track refers to the distance between the centerline of two wheels ...

Camber angle Camber angle is one of the angles made by the wheels of a vehicle; specifically, it is the angle between the vertical axis of a wheel and the vertical axis of the vehicle when viewed from the front or rear. It is used in the design of steering a ...

Caster angle 250px, θ is the caster angle, the red line is the pivot line, and the grey area is the tire. 250px, Front suspension of a race car, the caster angle is formed by the line between upper and lower ball joint. The caster angle or castor angle is t ...

* Ride height *

Roll center The roll center of a vehicle is the notional point at which the cornering forces in the suspension are reacted to the vehicle body. There are two definitions of roll center. The most commonly used is the geometric (or kinematic) roll center, wher ...

Scrub radius The scrub radius is the distance in front view between the king pin axis and the center of the contact patch of the wheel, where both would theoretically touch the road. It can be positive, negative or zero. The kingpin axis also known as steeri ...

* Steering ratio * Toe * Wheel alignment *

Wheelbase In both road and rail vehicles, the wheelbase is the horizontal distance between the centers of the front and rear wheels. For road vehicles with more than two axles (e.g. some trucks), the wheelbase is the distance between the steering (fron ...

Distribution of mass

Some attributes or aspects of vehicle dynamics are purely due to

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...

and its distribution. These include: *

Center of mass In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may ...

Moment of inertia The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular accele ...

* Roll moment * Sprung mass *

Unsprung mass The unsprung mass (colloquially unsprung weight) of a vehicle is the mass of the suspension, wheels or tracks (as applicable), and other components directly connected to them. This contrasts with the sprung mass (or weight) supported by th ...

Weight distribution Weight distribution is the apportioning of weight within a vehicle, especially cars, airplanes, and trains. Typically, it is written in the form ''x''/''y'', where ''x'' is the percentage of weight in the front, and ''y'' is the percentage in ...

Aerodynamics

Some attributes or aspects of vehicle dynamics are purely

aerodynamic Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dyn ...

. These include: * Automobile drag coefficient * Automotive aerodynamics * Center of pressure *

Downforce Downforce is a downwards lift force created by the aerodynamic features of a vehicle. If the vehicle is a car, the purpose of downforce is to allow the car to travel faster by increasing the vertical force on the tires, thus creating more grip ...

* Ground effect in cars

Tires

Some attributes or aspects of vehicle dynamics can be attributed directly to the

tire A tire (American English) or tyre (British English) is a ring-shaped component that surrounds a Rim (wheel), wheel's rim to transfer a vehicle's load from the axle through the wheel to the ground and to provide Traction (engineering), t ...

s. These include: * Camber thrust * Circle of forces *

Contact patch Contact patch is the portion of a vehicle's tire that is in actual contact with the road surface. It is commonly used in the discussion of pneumatic (i.e. pressurized) tires, where the term is used strictly to describe the portion of the tire’s ...

* Cornering force * Ground pressure * Pacejka's Magic Formula * Pneumatic trail * Radial Force Variation *

Relaxation length Relaxation length is a property of pneumatic tires that describes the delay between when a slip angle is introduced and when the cornering force reaches its steady-state value. It is also described as the distance that a tire rolls before the later ...

Rolling resistance Rolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body (such as a ball, tire, or wheel) rolls on a surface. It is mainly caused by non-elastic effects; that is, not all the energy ...

* Self aligning torque *

Skid __NOTOC__ Skid or Skids may refer to: * Skid, a type of pallet * Skid (aerodynamics), an outward side-slip in an aircraft turn * Skid (automobile), an automobile handling condition where one or more tires are slipping relative to the road * Skid ...

* Slip angle *

Slip (vehicle dynamics) In (automotive) vehicle dynamics, slip is the relative motion between a tire and the road surface it is moving on. This slip can be generated either by the tire's rotational speed being greater or less than the free-rolling speed (usually describ ...

Spinout Spinout or Spin Out may refer to: * Corporate spin-off, also known as a spin-out, a type of corporate action where a company turns a portion of itself into a separate business *Spinout (driving), failure when braking Entertainment * ''Spinout (fi ...

* Steering ratio * Tire load sensitivity

Vehicle behaviours

Some attributes or aspects of vehicle dynamics are purely

dynamic Dynamics (from Greek δυναμικός ''dynamikos'' "powerful", from δύναμις ''dynamis'' "power") or dynamic may refer to: Physics and engineering * Dynamics (mechanics) ** Aerodynamics, the study of the motion of air ** Analytical dyn ...

. These include: * Body flex * Body roll * Bump Steer * Bundorf analysis *

Directional stability Directional stability is stability of a moving body or vehicle about an axis which is perpendicular to its direction of motion. Stability of a vehicle concerns itself with the tendency of a vehicle to return to its original direction in relation ...

* Critical speed *

Noise, vibration, and harshness Noise, vibration, and harshness (NVH), also known as noise and vibration (N&V), is the study and modification of the noise and vibration characteristics of vehicles, particularly cars and trucks. While noise and vibration can be readily measured ...

* Pitch * Ride quality * Roll * Speed wobble * Understeer, oversteer, lift-off oversteer, and

fishtailing Fishtailing is a vehicle handling problem which occurs when the rear wheels lose traction, resulting in oversteer. This can be caused by low friction surfaces (sand, gravel, rain, snow, ice, etc.). Rear-drive vehicles with sufficient power can ...

* Weight transfer and load transfer * Yaw

Analysis and simulation

The dynamic behavior of vehicles can be analysed in several different ways. This can be as straightforward as a simple spring mass system, through a three- degree of freedom (DoF) bicycle model, to a large degree of complexity using a multibody system simulation package such as

MSC ADAMS MSC ADAMS (Automated Dynamic Analysis of Mechanical Systems) is a Multibody simulation, multibody dynamics simulation software system. It is currently owned by MSC Software, MSC Software Corporation. The simulation software solver runs mainly on Fo ...

Modelica Modelica is an object-oriented, declarative, multi-domain modeling language for component-oriented modeling of complex systems, e.g., systems containing mechanical, electrical, electronic, hydraulic, thermal, control, electric power or process- ...

. As computers have gotten faster, and software user interfaces have improved, commercial packages such as CarSim have become widely used in industry for rapidly evaluating hundreds of test conditions much faster than real time. Vehicle models are often simulated with advanced controller designs provided as software in the loop (SIL) with controller design software such as

Simulink Simulink is a MATLAB-based graphical programming environment for modeling, simulating and analyzing multidomain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block libraries. It offers t ...

, or with physical hardware in the loop (HIL). Vehicle motions are largely due to the shear forces generated between the tires and road, and therefore the tire model is an essential part of the math model. In current vehicle simulator models, the tire model is the weakest and most difficult part to simulate.Rachel Evans
Quantum leaps
', Automotive Testing Technology International, September 2015, p.43 quote from MTS' Mark Gillian: "''From an OEM perspective, thermal modelling may be overkill but the tire models are still the weak point of any vehicle model''" The tire model must produce realistic shear forces during braking, acceleration, cornering, and combinations, on a range of surface conditions. Many models are in use. Most are semi-empirical, such as the Pacejka Magic Formula model. Racing car games or simulators are also a form of vehicle dynamics simulation. In early versions many simplifications were necessary in order to get real-time performance with reasonable graphics. However, improvements in computer speed have combined with interest in realistic physics, leading to

driving simulator Driving simulators are used for entertainment as well as in training of driver's education courses taught in educational institutions and private businesses. They are also used for research purposes in the area of human factors and medical r ...

s that are used for vehicle engineering using detailed models such as CarSim. It is important that the models should agree with real world test results, hence many of the following tests are correlated against results from instrumented test vehicles. Techniques include: * Linear range constant radius understeer * Fishhook *

Frequency response In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of s ...

* Lane change * Moose test * Sinusoidal steering * Skidpad * Swept path analysis