查看“︁汉斯·B·帕塞卡”︁的源代码

{{infobox person/Wikidata|fetchwikidata=ALL}}
'''汉斯·巴斯蒂安·帕塞卡'''（{{lang-en|Hans Bastiaan Pacejka}}，{{bd|1934年||2017年|9月}}<ref>{{cite news|title=Tribute: Hans Pacejka 1934-2017|url=https://www.tiretechnologyinternational.com/news/people-news/tribute-hans-pacejka-1934-2017.html|accessdate=1 October 2017|publisher=Tire Technology International|date=September 19, 2017|archive-date=2020-12-01|archive-url=https://web.archive.org/web/20201201120202/https://www.tiretechnologyinternational.com/news/people-news/tribute-hans-pacejka-1934-2017.html|dead-url=no}}</ref>）是一名车辆动力学专家，尤其是在轮胎动力学领域，他的理论已经成为行业标准。<ref>{{cite web
| url = http://www.racer.nl/reference/pacejka.htm
| title = Pacejka's Magic Formula
| author = Ruud van Gaal
| publisher = Racer
| date = December 23, 2010
| accessdate = 2011-03-19
| archive-date = 2011-05-18
| archive-url = https://web.archive.org/web/20110518052631/http://www.racer.nl/reference/pacejka.htm
| dead-url = no
}}</ref><ref name="Cossalter">{{cite book
| title = Motorcycle Dynamics
| url=https://books.google.com/books?id=rJTQxITnkbgC&printsec=frontcover&dq=motorcycle+dynamics#PPA47,M1
| edition = 2nd
| last = Cossalter
| first = Vittore
| year = 2006
| publisher = Lulu.com
| isbn = 978-1-4303-0861-4
| pages = 39}}</ref> 他是荷兰[[代尔夫特理工大学]]的名誉教授。<ref name="Pacejka">{{cite book
| title = Tyre and vehicle dynamics
| url = https://books.google.com/books?id=ddQeAQAAIAAJ&dq=Tire%20dynamics
| last = Pacejka
| first = Hans B.
| year = 2006
| edition = 2nd
| pages = back cover
| publisher = [[国际汽车工程师学会]]
| isbn = 978-0-7680-1702-1}}</ref>

==帕塞卡“魔术公式”轮胎模型==
[[File:Magic Formula Curve.png|thumb|right|魔术公式曲线]]
帕塞卡在过去的20多年中提出了一系列 [[轮胎]] 模拟模型。它们被称为“魔术公式”，因为这些公式的构造并无具体的物理学依据，但却能在很大范围内准确拟合轮胎结构和操控性能的关系，像魔术一样神奇。对于每个轮胎接地面中产生的力或力矩，魔术公式使用10-20个[[系数]]进行描述，形成对实验数据的精确拟合，特别是对横向力，纵向力和回正力矩。在给定的垂直载荷，[[外倾角]]和[[侧偏角]]下，这些参数将生成一系列公式，预测接地面中产生的力和力矩的大小。<ref>{{cite web
| url = http://phors.locost7.info/phors21.htm
| title = The Physics of Racing, Part 21: The Magic Formula: Longitudinal Version
| author = Brian Beckman
| year = 2001
| accessdate = 2011-03-26
| archive-url = https://web.archive.org/web/20110226113608/http://phors.locost7.info/phors21.htm
| archive-date = 2011-02-26
| dead-url = yes
}}</ref>
帕塞卡轮胎模型广泛应用与专业车辆动力学仿真和赛车游戏中，因为它们足够精确，易于编程，并且易于求解。<ref>http://www.tut.fi/plastics/tyreschool/moduulit/moduuli_10/hypertext/index.html {{Wayback|url=http://www.tut.fi/plastics/tyreschool/moduulit/moduuli_10/hypertext/index.html |date=20110927223346 }} MF is "easy to handle, accurate, low effort"</ref> 帕塞卡模型的一个缺陷是当它嵌入计算程序时，它无法解决低速问题，因为分母中的一个速度项导致公式发散。<ref>Beckman, Brian (2007) [http://channel9.msdn.com/Blogs/Charles/Brian-Beckman-The-Physics-in-Games-Real-Time-Simulation-Explained ''Brian Beckman: The Physics in Games - Real-Time Simulation Explained''] {{Wayback|url=http://channel9.msdn.com/Blogs/Charles/Brian-Beckman-The-Physics-in-Games-Real-Time-Simulation-Explained |date=20110517083654 }}, at ''channel9.msdn.com'', Jun 08, 2007, [http://mschnlnine.vo.llnwd.net/d1/ch9/4/7/8/4/1/3/Beckman_GamePhysics.wmv min. 29:53-33:45] {{Wayback|url=http://mschnlnine.vo.llnwd.net/d1/ch9/4/7/8/4/1/3/Beckman_GamePhysics.wmv |date=20120324222403 }} quotation:</ref>帕塞卡模型的一个替代模型是刷子模型，这是一个可以通过解析方法推导而出的模型，但是要获得好的拟合效果，仍然需要经验曲线，<ref>Jacob Svendenius, Björn Wittenmark (2003) [http://www.nt.ntnu.no/users/skoge/prost/proceedings/ecc03/pdfs/317.pdf ''Brush Tire Model with increased Flexibility''] {{Wayback|url=http://www.nt.ntnu.no/users/skoge/prost/proceedings/ecc03/pdfs/317.pdf |date=20150206175210 }}, In ''European Control Conference'', September 2003.</ref><ref>{{cite web|url=http://www.tut.fi/plastics/tyreschool/moduulit/moduuli_10/hypertext/index.html|title=''Modelling of tyres''|publisher=|access-date=2019-09-25|archive-date=2011-09-27|archive-url=https://web.archive.org/web/20110927223346/http://www.tut.fi/plastics/tyreschool/moduulit/moduuli_10/hypertext/index.html|dead-url=no}}</ref>并且它也没有魔术公式精确。<ref>http://www.tut.fi/plastics/tyreschool/moduulit/moduuli_10/hypertext/index.html {{Wayback|url=http://www.tut.fi/plastics/tyreschool/moduulit/moduuli_10/hypertext/index.html |date=20110927223346 }} "These models are not expected to give a very accurate correspondence with measurement but should predict the qualitative trends."</ref>
求解一个基于高频魔术公式曲线的模型也是一个问题，这取决与曲线的参数是如何计算的。<ref>https://www.edy.es/dev/2011/12/facts-and-myths-on-the-pacejka-curves/ {{Wayback|url=https://www.edy.es/dev/2011/12/facts-and-myths-on-the-pacejka-curves/ |date=20200916174335 }} {{quotation|A typical video game runs its physics engine at 50 Hz (50 calculation cycles per second). The slip formulas require a very high calculation rate (~500 – 700 Hz) in order to provide acceptable results. One of the causes is that calculating ω involves the wheel’s inertia and the torque from the vehicle’s engine. This generates rapidly changing values which cause huge slip ratios at low calculation rates.}}</ref> 滑移速度（车辆速度和轮胎接地面速度的差）会发生快速变化，导致模型变成一个[[刚性方程]]，这个能会需要特殊的求解器。

魔术公式的一般形式是：
:<math>R(k) = d \cdot \sin \left\{ c \cdot \arctan \left[ b\left(1 - e\right)k + e \cdot \arctan\left(bk\right)\right]\right\} \,</math>

其中''b'', ''c'', ''d'' ,''e'' 是拟合常数，''R''是侧偏量''k''产生的力或力矩。

==参见==
*[[车辆动力学]]
*[[郭孔辉]]

==参考文献==
{{reflist}}

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[[Category:汽車工程師]]
[[Category:代尔夫特理工大学教师]]