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Bicycle tire

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A bicycle tire mounted on a wheel
A cross section of a clincher tire with a puncture preventing layer (in blue) between the casing and the tread
An inner tube rolled up for storage or to be carried as a spare

A bicycle tire is a tire that fits on the wheel of a bicycle, unicycle, tricycle, quadracycle, bicycle trailer, or trailer bike. They may also be used on wheelchairs and handcycles, especially for racing. Bicycle tires provide an important source of suspension, generate the lateral forces necessary for balancing and turning, and generate the longitudinal forces necessary for propulsion and braking. They are the second largest source, after air drag, of power consumption on a level road.[1] The modern detachable pneumatic bicycle tire contributed to the popularity and eventual dominance of the safety bicycle.[2]

Modern bicycle tires can be classified by several different criteria:

  • how they attach to the rim: clincher or tubular,
  • if and how they hold air: tubed, tubeless, or solid,
  • what type of tread they have: slick or knobby.

History

New Mail Ladies Safety bicycle, circa 1891, with solid rubber tires
A tubed, clincher tire showing the inner tube protruding between the tire and the rim
Tubular tire rolled from rim to show glue between them
Clincher cross section schematic with 1: rim, 2: rim strip, 3: rim braking surface, 4: bead core, 5: inner tube, 6: casing, 7: tread

The first bicycle "tires" were iron bands on the wooden wheels of velocipedes.[3] These were followed by solid rubber tires on penny-farthings.[4] The first patent for "rubberized wheels" was granted to Clément Ader in 1868.[5] In an attempt to soften the ride, rubber tires with a hollow core were also tried.[6]

The first practical pneumatic tire was made by John Boyd Dunlop in 1887 for his son's bicycle, in an effort to prevent the headaches his son had while riding on rough roads. (Dunlop's patent was later declared invalid because of prior art by fellow Scot Robert William Thomson.) Dunlop is credited with "realizing rubber could withstand the wear and tear of being a tire while retaining its resilience".[7] This led to the founding of Dunlop Pneumatic Tyre Co. Ltd in 1889. By 1890, it began adding a tough canvas layer to the rubber to reduce punctures. Racers quickly adopted the pneumatic tire for the increase in speed it enabled.

Finally, the detachable tire was introduced in 1891 by Édouard Michelin. It was held on the rim with clamps, instead of glue, and could be removed to replace or patch the separate inner tube.[2]

Attaching to the rim

Three main techniques for attaching a bicycle tire to a rim have been developed: clincher, wired and tubular.[8] Clinchers originally did not have wire in the beads and the shape of the bead interlocked with a flange on the rim, relying on air pressure to hold the tire bead in place. However, this type of tire is no longer in general use and the term clincher has transferred to the modern wired-on tire. For the remainder of this article, the modern use of the word clincher will be assumed.

In an attempt to provide the best attributes of both wired and tubular methods, tubular clinchers have also been offered.[9]

Clincher

Most bicycle tires are clincher for use with "clincher" rims. These tires have a steel wire or Kevlar fiber bead that interlocks with flanges in the rim. A separate airtight inner tube enclosed by the rim supports the tire carcass and maintains the bead lock. An advantage of this system is that the inner tube can be easily accessed in the case of a leak to be patched or replaced.

The ISO 5775-2 standard defines designations for bicycle rims. It distinguishes between

  1. Straight-side (SS) rims
  2. Crochet-type (C) rims
  3. Hooked-bead (HB) rims

Traditional wired-on rims were straight-sided. Various "hook" (also called "crochet") designs re-emerged in the 1970s to hold the bead of the tire in place,[10][11] resulting in the modern clincher design. This allows higher (80–150 psi or 6–10 bar) air pressures than older wired-on tires. In these designs, it is the interlocking of the bead with the rim, not the tight fit or resistance to stretching of the bead, that keeps the tire on the rim and contains the air pressure.[12]

Tubular or sew-up

Main article: Tubular tires

Some tires are torus-shaped and attached to tubular rims with adhesive. The rim provides a shallow circular outer cross-section in which the tire lies instead of flanges on which tire beads seat.

Holding air

Bicycle tires may hold air or not. The ones that hold air do so either with a separate, relatively impermeable inner tube, or between the tire and rim, in a tubeless system. The ones that do not hold air use some kind of elastomer instead.

Tubed

A tubed tire has a separate inner tube, made of butyl rubber or latex, that provides a relatively airtight barrier inside the tire.[13] A vast majority of the tire systems in use are clinchers, due to the relative simplicity of repairs and wide availability of replacement inner tubes.

Tubeless

Tubeless tires are primarily used on mountain bikes due to their ability to use low air pressure for better traction without getting pinch flats.[14] Tubeless tires work similarly to clinchers in that the bead of the tire is specifically designed to interlock into a corresponding tubeless rim, but without an inner tube. Air is inflated directly into the tire, and once "locked" into the rim, the system is airtight. Liquid sealants are often injected into tubeless tires to prevent punctures. Pinch flats are impossible in a tubeless setup because there is no tube to pinch; however, air can escape if the bead lock is compromised from too much lateral force on the tire or deformation of the rim/tire due to hard impact with an object. Tubeless technology has progressed significantly over the last few years, and road-specific tubeless technologies for narrow tires are now gaining popularity.

Road tubeless

In 2006, Shimano and Hutchinson introduced a tubeless system for road bicycles.[15] Tubeless tires have not yet gained popular acceptance in road racing due to lack of sponsorship, the tradition of using tubular tires and the fact that, even without the innertube, the combined weight of tubeless rims and tires is more than top-of-the-line tubular tire wheelsets.[16] Road tubeless is gaining popularity among riders for whom the benefits are worth the costs.[17]

Solid

Besides solid rubber tires before the pneumatic tire was invented, solid tires, made of polyurethane[18][19] or microcellular foam[20] are also offered for 100% flat prevention. Much of the desirable suspension quality of the pneumatic tire is lost, and ride quality suffers.[21]

Airless

An example of an airless tire for bicycles is the high-priced Energy return wheel. Other more commercial products are available from Greentyre[22] Puncture Proof Tyres Ltd[23] KIK-Reifen [24] Trendwizzard[25] and Hutchinson.[26]

Construction

Bicycle tires consist of a cloth casing covered by a rubber tread. In the case of clinchers, the casing wraps around two beads, one on each edge.

Casing

Bicycle tire casing is made of cloth, usually nylon, though cotton and silk have also been used. The casing provides the resistance against stretching necessary to contain the internal air pressure while remaining flexible enough to conform to the ground surface. The thread count of the cloth affects the weight and performance of the tire, and high thread counts are generally preferred.

The fibers of the cloth in most bicycle tires are not woven together, but kept in separate plies so that they can move more freely to reduce wear and rolling resistance. They are also usually oriented diagonally, forming bias plies. Radial ply has been attempted, but found to provide undesirable handling characteristics.[27]

Tread

Different treads on knobby mountain bike tires
A slick tire with squared-off tread profile

The tread is the part of the tire that contacts the ground.

Compound

The tread is made of butyl rubber that often includes additives such as carbon black, which gives it its characteristic color, and silicon. These additives improve wear resistance usually at the expense of traction. Some tires have a dual-compound tread that is tougher in the middle and grippier on the edges.[28] Many modern tires are available with treads in a variety or combination of colors.[29][30] Road racing tires with different tread compounds for the front and rear have been developed, attempting to provide more traction in front and less rolling resistance in the rear.[31]

Pattern

Treads fall somewhere along the spectrum from smooth or slick to knobby. Smooth treads are intended for on-road use, where a tread pattern offers no improvement in traction.[32] However, many otherwise slick tires have a light tread pattern, due to the common belief that a slick tire will be slippery in wet conditions. Knobby treads are intended for off-road use, where the tread texture can help improve traction on soft surfaces. Many treads are omnidirectional—the tire can be installed in either orientation—but some are unidirectional and designed to be oriented a certain way. Some tires, especially for mountain bikes have a tread which is intended either for the front wheel or the rear wheel.[33] A special tread pattern, with small dimples, has been developed to reduce air drag.[34]

Profile

The profile of the tread is usually circular, matching the shape of the casing inside it and allowing the tire to roll to the side as the bicycle leans for turning or balancing. More-squared profiles are sometimes used on mountain bike tires and novelty tires designed to look like automotive racing slicks,[35] as on wheelie bikes.

Bead

The bead of clincher tires must be made of a material that will stretch very little to prevent the tire from expanding off of the rim under internal air pressure.

Wire

Wire beads are used on inexpensive tires. Though they cannot be folded, they can at least be twisted into three smaller hoops.

Kevlar
A foldable mountain and road bicycle tire

Kevlar beads are used on expensive tires, and these are also called "foldable".

Sidewall

The sidewall of the casing, the part not intended to contact the ground, may receive one of several treatments.

Gum wall

Tires with sidewalls made of natural rubber are called "gum wall". The tan colored, natural rubber lacks additives to help protect it from ozone.[36]

Skin wall

Tires with very little rubber, if any, covering the sidewall are called "skin wall". This reduces rolling resistance at the cost of less damage protection.[37]

Variations

A punctured tire.

Puncture resistance

Some tires include an extra layer between the tread and the casing (as shown in the cross section pictured above) to help prevent punctures either by being tough or simply by being thick. These extra layers are usually associated with higher rolling resistance.[38]

Studs

A studded, knobby tire

Metal studs may be embedded in the tread of knobby tires to improve traction on ice.[39]

Reflective

Some tires have a reflective strip on their sidewalls to improve visibility at night. Others have reflective material embedded in the tread.[30]

Aerodynamics

In addition to the dimple tread pattern mentioned above, at least one tire has an extra "wing" to cover the gap between the tire sidewall and the wheel rim and reduce drag.[40]

Indoor use

At least one modern bicycle tire has been designed specifically for indoor use on rollers or trainers. It minimizes the heat build up and excessive wear that traditional tires experience in this environment and is not suitable for use on pavement.[41]

Different front and rear

Besides the different tread patterns available on some mountain bike tires mentioned above, front and rear tire sets are available for road bikes with different tread patterns, tread compounds, and sizes for the front and rear wheels.[42] Other scenarios involve replacing a damaged tire, and leaving the other one unchanged.

Self inflating

Bicycle tires have been developed that pump themselves up as they roll forward.[43][44]

Parameters

Sizes

The modern tire-size designations (e.g. "37-622", also known as ETRTO) are defined by international standard ISO 5775, along with corresponding rim size designations (e.g., "622×19C"). Older English (inch, e.g. "28×1-5/8×1-3/8") and French (metric, e.g. "700x35C") designations are also still used, but can be ambiguous. The diameter of the tire must match the diameter of the rim, but the width of the tire only has to be in the range of widths appropriate for the width of the rim,[45] while also not exceeding the clearances allowed by the frame, brakes, and any accessories such as fenders. Diameters vary from a large 910 mm, for touring unicycles, to a small 125 mm, for roller skiing.[46] Widths vary from a narrow 18 mm to a wide 119 mm for the Surly Big Fat Larry.[47]

Further information: Bicycle wheel#Sizes

Balloon

62x 203 Michelin balloon tire on front wheel of 1960s Bootie Folding Cycle

A balloon tire (or fat tire) is a type of wide, low-pressure tire that first appeared on cruiser bicycles in the USA in the 1930s. They are typically 2 inches (51 mm) to 4.7 inches (120 mm) wide and are often used on mountain bikes and for riding in snow.[48][49]

In the 1960s Raleigh made its small-wheeled RSW 16 with balloon tires so it would have a soft ride like the fully suspended Moulton Bicycle. Other manufacturers then used the same idea for their own small wheelers. Examples include the Co-operative Wholesale Society (CWS) Commuter, the Trusty Spacemaster and the Stanningley (UK)-made Bootie Folding Bicycle.

Inflation pressure

The inflation pressure of bicycle tires ranges from below 2 bar (200 kPa; 29 psi) for tubeless mountain bike tires[14] to 15 bar (1,500 kPa; 218 psi) for tubular track racing tires.[50] The pressure rating of tires is usually stamped somewhere on the sidewall. It may be indicated as "Maximum Pressure", or "Inflate to ..." and is usually expressed as a range (for example, "6–8 bar or 600–800 kPa or 87–116 psi". Inflating to the lower number in the pressure range will tend to increase traction and make the ride more comfortable. Inflating to the higher number will tend to make the ride more efficient and will decrease the chances of getting a flat tire.[51]

One published guideline for clincher inflation pressure is to pick the value for each wheel that produces a 15% reduction in the distance between the wheel rim and the ground when loaded (i.e. with the rider and cargo) compared to when unloaded. Pressures below this lead to increased rolling resistance and likelihood of pinch-flats. Pressures above this lead to less rolling resistance in the tire itself, but to larger energy losses in the frame and rider.[52] Bicycle tires are essentially thin-walled pressure vessels and so the circumferential force in the casing is directly proportional to the internal pressure and to the tire diameter, and the force in the longitudinal direction is half of this.

Inner tubes are not completely impermeable to air and slowly lose pressure over time. Butyl inner tubes hold pressure better than latex.[53] Tires inflated from carbon dioxide canisters (often used for roadside repairs) or helium (occasionally used for elite track racing) lose pressure more quickly, because the first gas, despite being a large molecule, is slightly soluble in rubber,[54] and the second is a very small atom which passes quickly through any porous material. At least one public bicycle sharing system, Bixi, is inflating tires with nitrogen, instead of simple air, which is already 78% nitrogen, in an attempt to keep the tires at the proper inflation pressure longer,[55] though the effectiveness of this is debatable.[56][57][58]

Effect of temperature

Since the volume of gas and the gas itself inside a tire is not altered significantly by a change of temperature, the ideal gas law states that the pressure of the gas should be directly proportional to the absolute temperature. Thus, if a tire is inflated to 4 bar (400 kPa; 58 psi) at room temperature, 20 °C (68 °F), the pressure will increase to 4.4 bar (440 kPa; 64 psi) (+6%) at 40 °C (104 °F) and decrease to 3.6 bar (360 kPa; 52 psi) (-13%) at −20 °C (−4 °F).

Effect of atmospheric pressure

The net air pressure on the tire is the difference between the internal inflation pressure and the external atmospheric pressure, 1 bar (100 kPa; 15 psi), and most tire pressure gauges report this difference. If a tire is inflated to 4 bar (400 kPa; 58 psi) at sea level, the absolute internal pressure would be 5.15 bar (515 kPa; 74.7 psi) (+24%), and this is the pressure that the tire would need to contain if it were moved to a location with no atmospheric pressure, such as the vacuum of free space. At the highest elevation of commercial air travel, 12,000 metres (39,000 ft), the atmospheric pressure is reduced to 0.2 bar (20 kPa; 2.9 psi), and that same tire would have to contain 4.95 bar (495 kPa; 71.8 psi) (+20%).

Rim width

While not strictly a tire parameter, the width of the rim on which any given tire is mounted has an influence on the size and shape of the contact patch, and possibly the rolling resistance and handling characteristics.[59] The European Tyre and Rim Technical Organisation (ETRTO) publishes a guideline of recommended rim widths for different tire widths:[60]

ETRTO approved rim width (mm)
tire width straight rim width crotchet rim width
18 - 13C
20 - 13C
23 16 13C-15C
25 16-18 13C-17C
28 16-20 15C-19C
32 16-20 15C-19C
35 18-22 17C-21C
37 18-22 17C-21C
40 20-24 19C-23C
44 20-27 19C-25C
47 20-27 19C-25C
50 22-30.5 21C-25C
54 27-30.5 25C-29C
57 27-30.5 25C-29C
62 30.5 29C

In 2006, it was expanded for allowing wide tires up to 50mm on 17C rims and 62mm on 19C rims.[61] Ideally, the tire width should be 1.8 to 2 times the rim width, but a ratio from 1.4 to 2.2 should fit, and even 3 for hooked rims.[62]

Furthermore, Mavic recommends maximum pressures in addition to rim width,[63] and Schwalbe recommends specific pressures:[64]

Schwalbe and Mavic pressure recommendations
tire width Schwalbe rec. Mavic max. rim
18 mm (0.71 in) 10.0 bars (145 psi) 13C
20 mm (0.79 in) 9.0 bars (131 psi) 9.5 bars (138 psi) 13C
23 mm (0.91 in) 8.0 bars (116 psi) 9.5 bars (138 psi) 13C-15C
25 mm (0.98 in) 7.0 bars (102 psi) 9.0 bars (131 psi) 13C-17C
28 mm (1.1 in) 6.0 bars (87 psi) 8.0 bars (116 psi) 15C-19C
32 mm (1.3 in) 5.0 bars (73 psi) 6.7 bars (97 psi) 15C-19C
35 mm (1.4 in) 4.5 bars (65 psi) 6.3 bars (91 psi) 17C-21C
37 mm (1.5 in) 4.5 bars (65 psi) 6.0 bars (87 psi) 17C-23C
40 mm (1.6 in) 4.0 bars (58 psi) 5.7 bars (83 psi) 17C-23C
44 mm (1.7 in) 3.5 bars (51 psi) 5.2 bars (75 psi) 17C-25C
47 mm (1.9 in) 3.5 bars (51 psi) 4.8 bars (70 psi) 17C-27C
50 mm (2.0 in) 3.0 bars (44 psi) 4.5 bars (65 psi) 17C-27C
54 mm (2.1 in) 2.5 bars (36 psi) 4.0 bars (58 psi) 19C-29C
56 mm (2.2 in) 2.2 bars (32 psi) 3.7 bars (54 psi) 19C-29C
60 mm (2.4 in) 2.0 bars (29 psi) 3.4 bars (49 psi) 19C-29C
63 mm (2.5 in) 3.0 bars (44 psi) 21C-29C
66 mm (2.6 in) 2.8 bars (41 psi) 21C-29C
71 mm (2.8 in) 2.5 bars (36 psi) 23C-29C
76 mm (3.0 in) 2.1 bars (30 psi) 23C-29C

Fatbikes tires of 100 to 130 mm (4 to 5 inches) width are typically mounted on 65 to 100 mm rims.[65]

Forces and moments generated

Bicycle tires generate forces and moments between the wheel rim and the pavement that can affect bicycle performance, stability, and handling.

Vertical force

The vertical force generated by a bicycle tire is approximately equal to the product of inflation pressure and contact patch area.[66] In reality, is it usually slightly more than this because of the small but finite rigidity of the sidewalls.

The vertical stiffness, or spring rate, of a bicycle tire, as with motorcycle and automobile tires, increases with inflation pressure.[67]

Rolling resistance

Rolling resistance is a complex function of the materials and construction methods used and the inflation pressure, with higher pressure (up to a limit), thinner casing layers, wider tires (compared to narrower tires at the same pressure and of the same material and construction),[68] larger-diameter wheels,[69] and more-elastic tread material all tending to have less rolling resistance. Rolling resistance coefficients may vary from 0.002 to 0.010,[1][50][70][71] and have been found to decrease with inflation pressure and increase with vertical load.[72] A study at the University of Oldenburg found that Schwalbe Standard GW HS 159 tires have a Crr of 0.00455 for the ISO size 47-406 (20 in x 1.5 in) and, for the same model tire, a Crr of 0.00336 for the ISO size 37-622 (700c): a size to resistance ratio of about −1.8.[73]

Cornering force and camber thrust

As with other pneumatic tires, bicycle tires generate cornering force that varies with slip angle and camber thrust that varies with camber angle. These forces have been measured by several researchers since the 1970s,[74][75] and have been shown to influence bicycle stability.[76][77]

Brands and manufacturing companies

Notable bicycle tire brands and manufacturers include:

See also

References

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  2. ^ a b Herlihy, David V. (2004). Bicycle, The History. Yale University Press. p. 252. ISBN 0-300-10418-9. As the pneumatic-tire safety gained popularity, the sport generated unprecedented popular interest.
  3. ^ Herlihy, David V. (2004). Bicycle, The History. Yale University Press. p. 76. ISBN 0-300-10418-9.
  4. ^ Herlihy, David V. (2004). Bicycle, The History. Yale University Press. p. 159. ISBN 0-300-10418-9.
  5. ^ Tony Hadland and Hans-Erhard Lessing (2014). Bicycle Design, An Illustrated History. MIT Press. p. 59. ISBN 978-0-262-02675-8.
  6. ^ Herlihy, David V. (2004). Bicycle, The History. Yale University Press. p. 246. ISBN 0-300-10418-9.
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  24. ^ https://www.ssl-id.net/kik-reifen.de/shop/shop/freizeit/freizeit-fahrradreifen/pu-reifen/index.php
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  26. ^ "Serenity".
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  35. ^ "1967 Schwinn Sting-Ray". SchwinnStingRay.net. Retrieved 22 June 2010.
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  49. ^ "Pugsley". Retrieved 20 September 2011.
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  51. ^ Frank Berto (2006). "All About Tire Inflation" (PDF). Beach Cities Cycling Club. Retrieved 6 August 2012.
  52. ^ Jan Heine (2006). "Optimizing Your Tire Pressure for Your Weight" (PDF). Bicycle Quarterly. Retrieved 28 June 2010.
  53. ^ Brown, Sheldon. "Tube (inner)". Sheldon Brown. Retrieved 29 June 2010.
  54. ^ Lennard Zinn (3 February 2009). "Technical Q&A with Lennard Zinn – Large molecules and short frames". VeloNews.com. Retrieved 20 January 2013. It turns out however that the leakage rate of CO2 is huge, and the reason is that it is actually soluble in butyl rubber and is thus not constrained to normal permeation loss, it can transfer straight through the bulk rubber resulting in severe tire pressure loss on the order of a single day.
  55. ^ Ross Lydall (21 May 2010). "Taking a ride on Boris's hot wheels hire bikes". London Evening Standard. Archived from the original on 29 June 2010. Retrieved 29 June 2010. {{cite web}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help)
  56. ^ "Do Nitrogen-Filled Tires Enhance Fuel-Efficiency?". Scientific American. 30 September 2008. Retrieved 29 June 2010.
  57. ^ Tom and Ray Magliozzi (February 2005). "Dear Tom and Ray". CarTalk.com. Retrieved 29 June 2010.
  58. ^ Gene Petersen (4 October 2007). "Tires – Nitrogen air loss study". Consumer Reports. Retrieved 10 December 2011. Bottom line: Overall, consumers can use nitrogen and might enjoy the slight improvement in air retention provided, but it's not a substitute for regular inflation checks.
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  63. ^ "Manuel Technique 2012" (PDF) (in French). Mavic. p. 23.
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  65. ^ "Tire geometries" (PDF). Surly Bikes.
  66. ^ Lennard Zinn (27 March 2012). "Tech FAQ: More on fast-rolling tires". VeloNews. Retrieved 29 April 2013. If you were to pump your rear tire up to 100 psi, then your contact patch would be exactly one square inch in area. (This is because the tire would push down on the ground with 100 pounds of force while the ground would push up against the tire with the equal and opposite 100 pounds of force, and since there is a pressure of 100 pounds per square inch in your tire, then the area of contact is one square inch.
  67. ^ Foale, Tony (2006). Motorcycle Handling and Chassis Design (Second ed.). Tony Foale Designs. ISBN 978-84-933286-3-4.
  68. ^ Lennard Zinn (13 March 2012). "Tech FAQ: Seriously, wider tires have lower rolling resistance than their narrower brethren". VeloNews. Retrieved 6 August 2012.
  69. ^ James Huang (12 February 2011). "Bicycle tires – puncturing the myths". BikeRadar. Retrieved 21 March 2011.
  70. ^ Jobst Brandt (8 August 1996). "Rolling resistance of Tires". Retrieved 20 February 2011.
  71. ^ "Tire Rolling Resistance". Roues Artisanales. 1 January 2006. Archived from the original on 6 January 2011. Retrieved 20 February 2011. {{cite web}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help)
  72. ^ "Influence of tyre pressure and vertical load on coefficient of rolling resistance and simulated cycling performance" (PDF). Ergonomics. 10: 1361–1371. 1999. doi:10.1080/001401399185009. Retrieved 3 July 2011. {{cite journal}}: Unknown parameter |authors= ignored (help)
  73. ^ "Rolling resistance of bicycle tires". Archived from the original on 4 July 2006. Retrieved 22 August 2006. {{cite web}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help)
  74. ^ "Measuring sideslip and camber characteristics of bicycle tyres". Vehicle System Dynamics. 2011. doi:10.1080/00423114.2011.615408.
  75. ^ Alberto Doria, Mauro Tognazzo, Gianmaria Cusimano, Vera Bulsink, Adrian Cooke, and Bart Koopman (2012). "Identification of the mechanical properties of bicycle tyres for modelling of bicycle dynamics". Vehicle System Dynamics. doi:10.1080/00423114.2012.754048.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  76. ^ Sharp, Robin S. (November 2008). "On the Stability and Control of the Bicycle". Applied Mechanics Reviews. 61 (6). ASME: 060803-01–060803-24. doi:10.1115/1.2983014. ISSN 0003-6900.
  77. ^ Manfred Plochl, Johannes Edelmann, Bernhard Angrosch, and Christoph Ott (July 2011). "On the wobble mode of a bicycle". Vehicle System Dynamics. 50 (3): 415–429. doi:10.1080/00423114.2011.594164.{{cite journal}}: CS1 maint: multiple names: authors list (link)
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