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<title>Vehicle dynamics</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Vehicle dynamics</span></span>

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<p><b>Vehicle dynamics</b> is the study of <a href="Vehicle" title="Vehicle">vehicle</a> 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 <a href="Engineering" title="Engineering">engineering</a> primarily based on <a href="Classical_mechanics" title="Classical mechanics">classical mechanics</a>.

It may be applied for <a href="Motorized_vehicles" class="mw-redirect" title="Motorized vehicles">motorized vehicles</a> (such as automobiles), <a href="Bicycle_and_motorcycle_dynamics" title="Bicycle and motorcycle dynamics">bicycles and motorcycles</a>, <a href="Flight_dynamics" title="Flight dynamics">aircraft</a>, and <a href="Ship#hydrodynamics" title="Ship">watercraft</a>.

</p>

<div class="mw-heading mw-heading2"><h2 id="Factors_affecting_vehicle_dynamics">Factors affecting vehicle dynamics</h2></div>

<p>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.

</p>

<div class="mw-heading mw-heading3"><h3 id="Drivetrain_and_braking">Drivetrain and braking</h3></div>

<ul><li><a href="Automobile_layout" class="mw-redirect" title="Automobile layout">Automobile layout</a> (i.e. location of engine and driven wheels)</li>

<li><a href="Powertrain" title="Powertrain">Powertrain</a></li>

<li><a href="Braking_system" class="mw-redirect" title="Braking system">Braking system</a></li></ul>

<div class="mw-heading mw-heading3"><h3 id="Suspension_and_steering">Suspension and steering</h3></div>

<p>Some attributes relate to the <a href="Geometry" title="Geometry">geometry</a> of the <a href="Suspension_(vehicle)" class="mw-redirect" title="Suspension (vehicle)">suspension</a>, <a href="Steering" title="Steering">steering</a> and <a href="Rolling_chassis" title="Rolling chassis">chassis</a>. These include:

</p>

<ul><li><a href="Ackermann_steering_geometry" title="Ackermann steering geometry">Ackermann steering geometry</a></li>

<li><a href="Axle_track" title="Axle track">Axle track</a></li>

<li><a href="Camber_angle" title="Camber angle">Camber angle</a></li>

<li><a href="Caster_angle" title="Caster angle">Caster angle</a></li>

<li><a href="Ride_height" title="Ride height">Ride height</a></li>

<li><a href="Roll_center" title="Roll center">Roll center</a></li>

<li><a href="Scrub_radius" title="Scrub radius">Scrub radius</a></li>

<li><a href="Steering_ratio" title="Steering ratio">Steering ratio</a></li>

<li><a href="Wheel_alignment" title="Wheel alignment">Wheel alignment</a></li>

<li><a href="Wheelbase" title="Wheelbase">Wheelbase</a></li></ul>

<div class="mw-heading mw-heading3"><h3 id="Distribution_of_mass">Distribution of mass</h3></div>

<p>Some attributes or aspects of vehicle dynamics are purely due to <a href="Mass" title="Mass">mass</a> and its distribution. These include:

</p>

<ul><li><a href="Center_of_mass" title="Center of mass">Center of mass</a></li>

<li><a href="Moment_of_inertia" title="Moment of inertia">Moment of inertia</a></li>

<li><a href="Roll_moment" title="Roll moment">Roll moment</a></li>

<li><a href="Sprung_mass" title="Sprung mass">Sprung mass</a></li>

<li><a href="Unsprung_mass" title="Unsprung mass">Unsprung mass</a></li>

<li><a href="Weight_distribution" title="Weight distribution">Weight distribution</a></li></ul>

<div class="mw-heading mw-heading3"><h3 id="Aerodynamics">Aerodynamics</h3></div>

<p>Some attributes or aspects of vehicle dynamics are purely <a href="Aerodynamics" title="Aerodynamics">aerodynamic</a>. These include:

</p>

<ul><li><a href="Automobile_drag_coefficient" title="Automobile drag coefficient">Automobile drag coefficient</a></li>

<li><a href="Automotive_aerodynamics" title="Automotive aerodynamics">Automotive aerodynamics</a></li>

<li><a href="Center_of_pressure_(fluid_mechanics)" title="Center of pressure (fluid mechanics)">Center of pressure</a></li>

<li><a href="Downforce" title="Downforce">Downforce</a></li>

<li><a href="Ground_effect_in_cars" class="mw-redirect" title="Ground effect in cars">Ground effect in cars</a></li></ul>

<div class="mw-heading mw-heading3"><h3 id="Tires">Tires</h3></div>

<p>Some attributes or aspects of vehicle dynamics can be attributed directly to the <a href="Tire" title="Tire">tires</a>. These include:

</p>

<ul><li><a href="Camber_thrust" title="Camber thrust">Camber thrust</a></li>

<li><a href="Circle_of_forces" title="Circle of forces">Circle of forces</a></li>

<li><a href="Contact_patch" title="Contact patch">Contact patch</a></li>

<li><a href="Cornering_force" title="Cornering force">Cornering force</a></li>

<li><a href="Ground_pressure" title="Ground pressure">Ground pressure</a></li>

<li><a href="Pacejka" class="mw-redirect" title="Pacejka">Pacejka's Magic Formula</a></li>

<li><a href="Pneumatic_trail" title="Pneumatic trail">Pneumatic trail</a></li>

<li><a href="Radial_Force_Variation" class="mw-redirect" title="Radial Force Variation">Radial Force Variation</a></li>

<li><a href="Relaxation_length" title="Relaxation length">Relaxation length</a></li>

<li><a href="Rolling_resistance" title="Rolling resistance">Rolling resistance</a></li>

<li><a href="Self_aligning_torque" title="Self aligning torque">Self aligning torque</a></li>

<li><a href="Slip_angle" title="Slip angle">Slip angle</a></li>

<li><a href="Slip_(vehicle_dynamics)" title="Slip (vehicle dynamics)">Slip (vehicle dynamics)</a></li>

<li><a href="Spinout_(driving)" class="mw-redirect" title="Spinout (driving)">Spinout</a></li>

<li><a href="Steering_ratio#Alternate_definition" title="Steering ratio">Steering ratio</a></li>

<li><a href="Tire_load_sensitivity" title="Tire load sensitivity">Tire load sensitivity</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Vehicle_behaviours">Vehicle behaviours</h2></div>

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</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Car_handling" class="mw-redirect" title="Car handling">Car handling</a></div>

<p>Some attributes or aspects of vehicle dynamics are purely <a href="Analytical_dynamics" class="mw-redirect" title="Analytical dynamics">dynamic</a>. These include:

</p>

<li><a href="Bump_Steer" class="mw-redirect" title="Bump Steer">Bump Steer</a></li>

<li><a href="Bundorf_analysis" title="Bundorf analysis">Bundorf analysis</a></li>

<li><a href="Directional_stability" title="Directional stability">Directional stability</a></li>

<li><a href="Oversteer" class="mw-redirect" title="Oversteer">Critical speed</a></li>

<li><a href="Noise%2C_vibration%2C_and_harshness" title="Noise, vibration, and harshness">Noise, vibration, and harshness</a></li>

<li><a href="Flight_dynamics_(aircraft)" class="mw-redirect" title="Flight dynamics (aircraft)">Pitch</a></li>

<li><a href="Ride_quality" title="Ride quality">Ride quality</a></li>

<li><a href="Speed_wobble" title="Speed wobble">Speed wobble</a></li>

<li><a href="Understeer" class="mw-redirect" title="Understeer"> Understeer, oversteer</a>, <a href="Lift-off_oversteer" title="Lift-off oversteer">lift-off oversteer</a>, and <a href="Fishtailing" title="Fishtailing">fishtailing</a></li>

<li><a href="Weight_transfer" title="Weight transfer">Weight transfer and load transfer</a></li>

<div class="mw-heading mw-heading2"><h2 id="Analysis_and_simulation">Analysis and simulation</h2></div>

<p>The dynamic behavior of vehicles can be analysed in several different ways.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> This can be as straightforward as a simple <a href="Tuned_mass_damper" title="Tuned mass damper">spring mass</a> system, through a three-<a href="Degrees_of_freedom_(mechanics)" title="Degrees of freedom (mechanics)">degree of freedom</a> (DoF) bicycle model, to a large degree of complexity using a <a href="Multibody_system" title="Multibody system">multibody system simulation</a> package such as <a href="MSC_Software" title="MSC Software">MSC ADAMS</a> or <a href="Modelica" title="Modelica">Modelica</a>. 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 <a href="Electronic_stability_control" title="Electronic stability control">advanced controller</a> designs provided as software in the loop (SIL) with controller design software such as <a href="Simulink" title="Simulink">Simulink</a>, or with physical hardware in the loop (HIL).

</p><p>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.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> 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 <a href="Pacejka" class="mw-redirect" title="Pacejka">Pacejka</a> Magic Formula model.

</p><p><a href="Sim_racing" title="Sim racing">Racing car games or simulators</a> 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 <a href="Driving_simulator" title="Driving simulator">driving simulators</a> that are used for vehicle engineering using detailed models such as CarSim.

</p><p>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.

</p><p>Techniques include:

</p>

<ul><li><a href="Bundorf_analysis" title="Bundorf analysis">Linear range constant radius understeer</a></li>

<li>Fishhook</li>

<li><a href="Frequency_response" title="Frequency response">Frequency response</a></li>

<li><a href="Lane_change" class="mw-redirect" title="Lane change">Lane change</a></li>

<li><a href="Moose_test" title="Moose test">Moose test</a></li>

<li>Sinusoidal steering</li>

<li><a href="Skidpad" title="Skidpad">Skidpad</a></li>

<li>Swept path analysis</li></ul>

<div role="note" class="hatnote navigation-not-searchable">Further information: <a href="Performance_driving_techniques" title="Performance driving techniques">Performance driving techniques</a></div>

<ul><li><a href="Automotive_suspension_design" class="mw-redirect" title="Automotive suspension design">Automotive suspension design</a></li>

<li><a href="Automobile_handling" title="Automobile handling">Automobile handling</a></li>

<li><a href="Hunting_oscillation" title="Hunting oscillation">Hunting oscillation</a></li>

<li><a href="Multi-axis_shaker_table" class="mw-redirect" title="Multi-axis shaker table">Multi-axis shaker table</a></li>

<li><a href="Vehicular_metrics" title="Vehicular metrics">Vehicular metrics</a></li>

<li><a href="4-poster" title="4-poster">4-poster</a></li>

<li><a href="7_post_shaker" title="7 post shaker">7 post shaker</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFElkadyElmarakbi,_Ahmed2012" class="citation journal cs1">Elkady, Mustafa; Elmarakbi, Ahmed (26 September 2012). <a rel="nofollow" class="external text" href="https://nrl.northumbria.ac.uk/37363/1/Elkady%2C%20Elmarakbi%20-%20Modelling%20and%20analysis%20of%20vehicle%20crash%20system%20integrated%20with%20different%20VDCS%20under%20high%20speed%20impacts%20OA.pdf">"Modelling and analysis of vehicle crash system integrated with different VDCS under high speed impacts"</a> <span class="cs1-format">(PDF)</span>. <i>Central European Journal of Engineering</i>. <b>2</b> (4): <span class="nowrap">585–</span>602. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2012CEJE....2..585E">2012CEJE....2..585E</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2478%2Fs13531-012-0035-z">10.2478/s13531-012-0035-z</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:109017056">109017056</a>.</cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Rachel Evans <i><a rel="nofollow" class="external text" href="https://www.vi-grade.com/dynatc/attachments-0542-361e/Automotive%20Testing%20Technology%20oct2015.pdf">Quantum leaps</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20211123234058/https://www.vi-grade.com/dynatc/attachments-0542-361e/Automotive%20Testing%20Technology%20oct2015.pdf">Archived</a> 2021-11-23 at the <a href="Wayback_Machine" title="Wayback Machine">Wayback Machine</a></i>, Automotive Testing Technology International, September 2015, p.43 quote from <a href="MTS_Systems_Corporation" title="MTS Systems Corporation">MTS</a>' Mark Gillian: "<i>From an OEM perspective, thermal modelling may be overkill but the tire models are still the weak point of any vehicle model</i>"</span>

</li>

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<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li><cite id="CITEREFEgbertNyborgPacejka1987" class="citation journal cs1">Egbert, Bakker; Nyborg, Lars; <a href="Hans_B._Pacejka" title="Hans B. Pacejka">Pacejka, Hans B.</a> (1987). <a rel="nofollow" class="external text" href="http://www.theoryinpracticeengineering.com/resources/tires/pacejka87.pdf">"Tyre modelling for use in vehicle dynamics studies"</a> <span class="cs1-format">(PDF)</span>. <i><a href="Society_of_Automotive_Engineers" class="mw-redirect" title="Society of Automotive Engineers">Society of Automotive Engineers</a></i>.</cite> A new way of representing tyre data obtained from measurements in pure cornering and pure braking conditions.</li>

<li><cite id="CITEREFGillespie1992" class="citation book cs1">Gillespie, Thomas D. (1992). <i>Fundamentals of vehicle dynamics</i> (2nd printing. ed.). Warrendale, PA: Society of Automotive Engineers. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-56091-199-9</bdi>.</cite> Mathematically oriented derivation of standard vehicle dynamics equations, and definitions of standard terms.</li>

<li><cite id="CITEREFMilliken2002" class="citation journal cs1"><a href="William_F._Milliken%2C_Jr." class="mw-redirect" title="William F. Milliken, Jr.">Milliken, William F.</a> (2002). "Chassis Design – Principles and Analysis". <i><a href="Society_of_Automotive_Engineers" class="mw-redirect" title="Society of Automotive Engineers">Society of Automotive Engineers</a></i>.</cite> Vehicle dynamics as developed by Maurice Olley from the 1930s onwards. First comprehensive analytical synthesis of vehicle dynamics.</li>

<li><cite id="CITEREFMillikenDouglas_L.1995" class="citation book cs1"><a href="William_F._Milliken%2C_Jr." class="mw-redirect" title="William F. Milliken, Jr.">Milliken, William F.</a>; Douglas L. (1995). <i>Race car vehicle dynamics</i> (4. printing. ed.). Warrendale, Pa.: Society of Automotive Engineers. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-56091-526-3</bdi>.</cite> Latest and greatest, also the standard reference for automotive suspension engineers.</li>

<li><cite id="CITEREFLimitedHelmut_StollJürgen_W._Betzler2001" class="citation book cs1">Limited, Jörnsen Reimpell; Helmut Stoll; Jürgen W. Betzler (2001). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20121102023811/http://www.scribd.com/doc/15362943/The-Automotive-Chassis-Engineering-Principles-by-Reimpell-Stoll-Betzler"><i>The automotive chassis : engineering principles</i></a>. Translated from the German by AGET (2nd ed.). Warrendale, Pa.: Society of Automotive Engineers. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-7680-0657-5</bdi>. Archived from <a rel="nofollow" class="external text" href="https://www.scribd.com/doc/15362943/The-Automotive-Chassis-Engineering-Principles-by-Reimpell-Stoll-Betzler">the original</a> on 2012-11-02<span class="reference-accessdate">. Retrieved <span class="nowrap">2017-09-17</span></span>.</cite> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{cite book}}</code>: </span><span class="cs1-visible-error citation-comment"><code class="cs1-code">|last=</code> has generic name (help)</span> Vehicle dynamics and chassis design from a race car perspective.</li>

<li><cite id="CITEREFGuiggiani2014" class="citation book cs1"><a href="Massimo_Guiggiani" title="Massimo Guiggiani">Guiggiani, Massimo</a> (2014). <a rel="nofollow" class="external text" href="http://www.dimnp.unipi.it/guiggiani-m/interactive.html"><i>The Science of Vehicle Dynamics</i></a> (1st. ed.). Dordrecht: Springer. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-94-017-8532-7</bdi>.</cite> Handling, Braking, and Ride of Road and Race Cars.</li>

<li><cite id="CITEREFMeywerk2015" class="citation book cs1">Meywerk, Martin (2015). <i>Vehicle Dynamics</i> (1st. ed.). West Sussex: John Wiley & Sons. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-118-97135-2</bdi>.</cite> Lecture Notes to the MOOC Vehicle Dynamics of iversity</li></ul>

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</style><div id="Automotive_handling97" style="font-size:114%;margin:0 4em">Automotive handling</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Main topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Automobile_handling" title="Automobile handling">Car handling</a></li>

<li><a href="Center_of_mass" title="Center of mass">Center of mass</a></li>

<li><a href="Downforce" title="Downforce">Downforce</a></li>

<li><a href="Drifting_(motorsport)" title="Drifting (motorsport)">Drifting</a></li>

<li><a href="Electronic_stability_control" title="Electronic stability control">Electronic Stability Control</a></li>

<li><a href="Fishtailing" title="Fishtailing">Fishtailing</a></li>

<li><a href="Inboard_brake" title="Inboard brake">Inboard brake</a></li>

<li><a href="Understeer_and_oversteer" title="Understeer and oversteer">Oversteer</a></li>

<li><a href="Steering" title="Steering">Steering</a></li>

<li><a href="Suspension_(vehicle)" class="mw-redirect" title="Suspension (vehicle)">Suspension</a></li>

<li><a href="Transaxle" title="Transaxle">Transaxle</a></li>

<li><a href="Understeer_and_oversteer" title="Understeer and oversteer">Understeer</a></li>

<li><a href="Unsprung_mass" title="Unsprung mass">Unsprung mass</a></li>

<li><a href="Weight_transfer" title="Weight transfer">Weight transfer</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Spring_(device)" title="Spring (device)">Spring</a> types</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Air_suspension" title="Air suspension">Pneumatic</a></li>

<li><a href="Torsion_spring" title="Torsion spring">Torsion</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Car_suspension" title="Car suspension">Suspension</a> types</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Dependent</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Semi-independent</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Twist-beam_rear_suspension" title="Twist-beam rear suspension">Twist beam</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Independent_suspension" title="Independent suspension">Independent</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Double_wishbone_suspension" title="Double wishbone suspension">Double wishbone</a> <small>(<a href="Jaguar_independent_rear_suspension" title="Jaguar independent rear suspension">Jaguar IRS</a>)</small></li>

<li><a href="Dubonnet_suspension" title="Dubonnet suspension">Dubonnet</a></li>

<li><a href="MacPherson_strut" title="MacPherson strut">MacPherson strut</a> <small>(<a href="Chapman_strut" title="Chapman strut">Chapman strut</a>)</small></li>

<li><a href="Multi-link_suspension" title="Multi-link suspension">Multi-link</a></li>

<li><a href="Sliding_pillar_suspension" title="Sliding pillar suspension">Sliding pillar</a></li>

<li><a href="Swing_axle" title="Swing axle">Swing axle</a></li>

<li><a href="Trailing_arm" class="mw-redirect" title="Trailing arm">Trailing arm</a> <small>(<a href="Semi-trailing_arm" class="mw-redirect" title="Semi-trailing arm">Semi-trailing arm</a>)</small></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-07-28" href="https://en.wikipedia.org/wiki/?title=Vehicle_dynamics&oldid=1303003822">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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