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==Analysis and simulation== The dynamic behavior of vehicles can be analysed in several different ways.<ref>{{cite journal|last=Elkady|first=Mustafa|author2=Elmarakbi, Ahmed |title=Modelling and analysis of vehicle crash system integrated with different VDCS under high speed impacts|journal=Central European Journal of Engineering|date=26 September 2012|volume=2|issue=4|pages=585β602|doi=10.2478/s13531-012-0035-z|bibcode=2012CEJE....2..585E|s2cid=109017056|url=http://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}}</ref> This can be as straightforward as a simple [[Tuned mass damper|spring mass]] system, through a three-[[Degrees of freedom (mechanics)|degree of freedom]] (DoF) bicycle model, to a large degree of complexity using a [[Multibody system|multibody system simulation]] package such as [[MSC Software|MSC ADAMS]] or [[Modelica]]. As computers have gotten faster, and software user interfaces have improved, commercial packages such as [[Applied Intuition|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 [[Electronic stability control|advanced controller]] designs provided as [[Software-in-the-loop simulation|software in the loop]] (SIL) with controller design software such as [[Simulink]], 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.<ref>Rachel Evans ''[https://www.vi-grade.com/dynatc/attachments-0542-361e/Automotive%20Testing%20Technology%20oct2015.pdf Quantum leaps]'', Automotive Testing Technology International, September 2015, p.43 quote from [[MTS Systems Corporation|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''"</ref> 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. [[Sim racing|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]]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: * [[Bundorf analysis|Linear range constant radius understeer]] * Fishhook * [[Frequency response]] * [[Lane change]] * [[Moose test]] * Sinusoidal steering * [[Skidpad]] * [[Swept path analysis]] {{Further|Performance driving techniques}}
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