Editing Speed wobble

{{short description|Physics phenomenon affecting two wheeled vehicles}}
{{Technical|date=March 2020}}

'''Speed wobble''' (also known as '''shimmy''', '''tank-slapper''',<ref>{{Cite book |last=Hough |year=2000 |first=David L. |author-link=David L. Hough |title=Proficient Motorcycling: The Ultimate Guide to Riding Well |edition=2nd |publisher=BowTie Press|location=USA |url=https://books.google.com/books?id=yeAIAIxS-cgC |isbn=1-889540-53-6 |page=253 |chapter=Glossary |quote='''tank slapper:''' a speed wobble so severe that the handlebars bang alternately against the sides of the fuel tank}}</ref> or '''death wobble''') is a rapid side-to-side shaking of a vehicle's wheel(s) that occurs at high speeds and can lead to loss of control. It presents as a quick (4&ndash;10&nbsp;Hz) oscillation of primarily the steerable wheel(s), and is caused by a combination of factors, including initial disturbances and insufficient [[damping]], which can create a [[resonance]] effect. Initially, the rest of the vehicle remains mostly unaffected, until translated into a vehicle [[yaw (rotation)|yaw]] [[oscillation]] of increasing [[amplitude]], producing loss of control. 

Vehicles that can experience this oscillation include [[motorcycle]]s and [[bicycle]]s, [[skateboard]]s, and, in theory, any vehicle with a single steering pivot point and a sufficient amount of freedom of the steered wheel, including that which exists on some [[light aircraft]] with [[tricycle gear]] where instability can occur at speeds of less than {{Convert|80|km/h|mph|abbr=on}}; this does not include most [[automobile]]s. The initial instability occurs mostly at high speed and is similar to that experienced by shopping cart wheels and aircraft landing gear.<ref name="Wilson">{{cite book
| title = Bicycling Science
| url = https://archive.org/details/isbn_9780262731546
| url-access = registration
| edition = Third
| last = Wilson
| first = David Gordon
|author2=Jim Papadopoulos
| year = 2004
| publisher = The MIT Press
| isbn = 0-262-73154-1
| pages = [https://archive.org/details/isbn_9780262731546/page/263 263–390]}}</ref><ref name="Cossalter">{{cite book
| title = Motorcycle Dynamics
| edition = Second
| last = Cossalter
| first = Vittore
| year = 2006
| publisher = Lulu.com
| isbn = 978-1-4303-0861-4
| pages = 241–342}}</ref>

== Theory ==
Sustained oscillation has two necessary components: an [[underdamped]] [[order (differential equation)|second- or higher-order]] system and a [[positive feedback]] mechanism. An example of an underdamped second order system is a [[spring–mass system]], where the mass can bob up and down (oscillate) when hanging from a spring.

If shimmy cannot be designed out of the system, a device known as a [[steering damper]] may be used, which is essentially a [[notch filter]] designed to damp the shimmy at its known natural frequency.<ref>{{cite magazine
| title = Control of Motorcycle Steering Instabilities
| author = Simos Evangelou, David J.N. Limebeer, Robin S. Sharp, and Malcolm C. Smith
| date = October 2006
| magazine = IEEE Control Systems Magazine
| quote =  For machines with a stiff front frame, a steering damper is required to stabilize the wobble mode at high speeds, while older, more flexible machines may require a steering damper at intermediate speeds.
| citeseerx = 10.1.1.227.9657
}}</ref>

Shimmy is usually associated with the deformation of (rubber) tires. However, it can also be observed in nondeformable (e.g., steel) wheels. The phenomenon can be explained by introducing multicomponent dry friction forces,<ref>
{{cite journal
| last1 = Zhuravlev
| first1 = V.Ph.
| last2 = Klimov
| first2 = D.M.
| title = Theory of the shimmy phenomenon
| journal = Mechanics of Solids
| year = 2010
| volume =4
| issue = 3
| pages =324–330
| doi =  10.3103/S0025654410030039
| bibcode = 2010MeSol..45..324Z
| s2cid = 122904947
}}
</ref> apart from the usual forces considered in the literature.

Another explanation is that speed wobble is a [[Hopf bifurcation]], a mathematical phenomenon in which a stable fixed point of a dynamical system loses stability as a parameter changes, giving rise to a [[limit cycle]] (a path that a system follows repeatedly, looping back on itself in a predictable pattern, which other nearby behaviors tend to mimic over time). In the case of a speed wobble, the system changes from one state (a stable ride) to a second state, (constant amplitude oscillation), when one parameter (forward speed, or air speed) progresses through a critical point.
{{r |ST |p=1 |q=An alternative theory (or maybe these theories aren&apos;t mutually exclusive) is that speed wobble is an example of a "Hopf Bifurcation" (no, Hopf is not a typo). Simply put, a system that is stable, operating normally, and as it should, can cease operating normally when one parameter changes, the parameter in the case of speed wobble being velocity. At that point the system becomes unstable, and a "periodic orbit" comes into existence, such orbit, as I understand it, expressed as the oscillation in your bike during a speed wobble. The aeroelastic flutter described above is a kind of Hopf Bifurcation.}}
{{r |VN_LZ |p=1 |q=A linear analysis leading to resonance is appropriate for any system where there is an oscillator that is being forced at a special frequency — the resonance frequency — and when this happens, the amplitude can simply build to infinity. This is not what happens in bicycle instability for two reasons: first, there is no periodic forcing that causes the high-speed wobble (in fact, it can happen on a smooth road); and second, there is not a phenomenon that shows a characteristic building of amplitude. Instead, the high-speed wobble is a critical phenomena, which is typical of bifurcations and bifurcation theory in general. Below the critical parameter value, you see one thing, in this case a stable equilibrium characteristic of a smooth ride, and slightly above the critical parameter, the smooth ride is no longer stable (but it still exists as an equilibrium, but an unstable equilibrium, just as standing a stick upright is an equilibrium but unstable because if it tips even slightly away from the exact equilibrium, it quickly drifts away), but the now unstable equilibrium gives way to a stable periodic orbit, which is the wobble. And as the parameter increases, the amplitude of the wobble can increase to some larger but fixed amplitude. —Erik M. Bollt, W. Jon Harrington Professor of Mathematics, Clarkson University}}

== In two-wheeled vehicles ==
Wobble or shimmy begins when some otherwise minor irregularity accelerates the wheel to one side. The irregularity may be a wheel which is [[roundness (object)|out-of-round]], out-of-true, or [[tire balance#Dynamic balance|out-of-balance]].{{r |ST}} As the wheel rotates, it will exert a [[oscillation|cyclic]] load to the vehicle frame, which if matched with the system's (vehicle and attached accessories) [[resonance|resonant frequency]], can produce a speed wobble.{{r |ST}} During the wheel rotation, a restoring force is applied in phase with the progress of the irregularity, and the wheel turns to the other side where the process is repeated. If there is insufficient [[steering damper|damping]] in the steering the oscillation will increase until system failure. The oscillation frequency can be changed by changing the forward speed, making the bike stiffer or lighter, or increasing the stiffness of the steering, of which the rider is a main component.<ref name="Wilson" /> While wobble or shimmy can be easily remedied by adjusting speed, position, or grip on the handlebar, it can be fatal if left uncontrolled.<ref>{{cite news
| title = Crash kills cyclist
| last = Kettler
| first = Bill
|date=2004-09-15
| work = Mail Tribune
| url = http://www.mailtribune.com/article/20040915/BIZ/309159999
| accessdate = 2016-07-10
}}</ref>

Other things being equal, speed wobble is generally less likely to occur in a mountain bike compared to a road bike, because a mountain bike's frame generally has more damping from the [[bicycle suspension|suspension system]], and the tire knobs also produce some damping between the vehicle and road interface.{{r |ST |p=1 |q=I&apos;ve seen experts say that increased tire pressure can add stiffness to road tires, but the knobbies on MTB tires don&apos;t subtract stiffness, rather they add damping.}}

Since shimmy frequency is independent of bike speed, gyroscopic effects "are clearly not essential to the phenomenon."<ref name="Wilson" /> The top five influences on wobble have been found to be lateral stiffness of the front tire, steering damper, height of bike center of mass, distance of bike center of mass from rear wheel, and [[cornering force|cornering stiffness]] of the front tire.<ref name="Cossalter"/><ref>{{cite journal
 | author = Manfred Plöchl
 |author2=Johannes Edelmann |author3=Bernhard Angrosch |author4=Christoph Ott
 | title = On the wobble mode of a bicycle
 | journal = Vehicle System Dynamics 
 | volume = 50
 | issue = 3
 | pages = 415–429
 | publisher = Taylor & Francis
 | date = 7 Jul 2011
 | issn = 0042-3114
 | doi=10.1080/00423114.2011.594164|bibcode=2012VSD....50..415P |s2cid=110507657 }}</ref>

An academic paper that investigated wobble through physical experimentation and computer modeling concludes: "the influence on wobble mode of front tire characteristics, front frame inertia and chassis stiffness were shown. In particular, it shows that [by] increasing front tire inflation, chassis stiffness, and front frame inertia about steering axis and decreasing sideslip stiffness of front tire, wobble mode damping is improved, promoting vehicle stability."<ref>{{cite conference |first=Salvador |last=Mauro |author2=Fabris, Davide |title=Study of stability of a two wheeled vehicle through experiments on the road and in laboratory |date=May 27–28, 2004 |location=Modena, Italy |url=http://www.dinamoto.it/dinamoto/7_MDRG_papers/_MDRG%20Papers%20in%20PDF%20format/2004_04%20Study%20of%20stability%20of%20a%20two%20wheeled%20vehicle%20MODENA.pdf |accessdate=2008-08-31}}</ref>

== In single-wheeled mobility devices ==
Speed wobbles occur on electric unicycles ([[Electric unicycle|EUC]]) and single-wheeled skateboards (such as a [[Onewheel]]). "To fix Onewheel wobbles, both feet need to be repositioned by inching them to a position that properly provides a center of gravity. The Onewheel’s controller is designed to only balance the board from front-to-back having no control of the side-to-side movement."<ref>{{Cite web |title=Onewheel Wobbles & Feels Unstable [How-to Fix the Wobbling] |url=https://trailwheel.com/onewheel-wobbles-feels-unstable-how-to-fix-it/ |website=Trailwheel|date=7 October 2022 }}</ref>

==See also==
* [[Bicycle and motorcycle dynamics]]
* [[Caster flutter]]
* [[Fishtailing]]
* [[Hunting oscillation]]
* [[Pilot-induced oscillation]]
* [[Self-oscillation]]
* [[Tire balance]]
* [[Trailer (vehicle)]]
* [[Vehicle dynamics]]

==References==
{{Reflist|refs=

<ref name=ST>{{cite web |url=https://www.slowtwitch.com/Tech/Speed_Wobble_5033.html |title=Speed Wobble |last=Empfield |first=Dan |work=slowtwitch.com |date=2015-04-24 |access-date=2019-08-23 |url-status=live |archive-url=https://web.archive.org/web/20150607171541/https://www.slowtwitch.com/Tech/Speed_Wobble_5033.html |archive-date=2015-06-07}}</ref>

<ref name=VN_LZ>{{cite web |url=https://www.velonews.com/gear/technical-faq-bifurcation-and-high-speed-shimmy/ |title=Technical FAQ: Bifurcation and high-speed shimmy |last=Zinn |first=Lennard |work=[[VeloNews]] |date=2013-11-19 |access-date=2019-08-23 |url-status=live |archive-url=https://web.archive.org/web/20190824043356/https://www.velonews.com/2013/11/technical-faq/technical-faq-bifurcation-and-high-speed-shimmy_309601 |archive-date=2019-08-24}}</ref>

}}

== External links ==
*[https://www.sheldonbrown.com/brandt/shimmy.html Bicycle speed wobbles]
*[http://www.flyingsnail.com/Sprung/tankslapper.html &#91;Flash&#93; video of motorcycle+rider crashing due to a death wobble]
*[http://www2.ee.ic.ac.uk/cap/cappp/projects/2/files/wobble_0_65.avi Animation of shimmy]
*[http://www2.ee.ic.ac.uk/cap/cappp/projects/2/files/weave_0_65.avi Animation of death wobble]
*[https://www.youtube.com/watch?v=i5Dapy1xUq0 Video of a high-speed streamlined bicycle crash showing death wobble]
*[https://www.youtube.com/watch?v=wj9PNNChVm4 Video of a truck with death wobble]

[[Category:Automotive suspension technologies]]
[[Category:Cycling]]
[[Category:Dynamics (mechanics)]]
[[Category:Motorcycle dynamics]]