Spoke (wheel)

Spoked wheel of a carriage

Wagon wheel from Choga Zanbil , Iran. Mid to end of the 2nd millennium BC Chr.
Tehran National Museum

Model of an old spoked wheel, wooden spokes only partially radial

Spokes connect the near-axis hub -positively to the circular rim of a wheel . A functionally complete wheel still contains the wheel bearing in the hub and the tire on the outside of the rim .

The spoked wheel type is a form of lightweight construction - in contrast to this is the solid wheel , for example on railways.

A distinction is made between constructions that primarily use compressive forces or tensile forces . A - rarely occurring - single-spoke wheel has only one spoke, which also has to absorb bending moment .

The spokes of a wheel typically span one or two conical surfaces or just one plane. Spokes in the wheel can carry additional attachments, fulfill functions and transmit forces. They can stand isolated from one another, lie crossed against one another, be connected with wire and soldered at crossing points or - mainly for decoration - run twisted together.

history

Spokes on a water wheel in the old salt works in Bad Reichenhall

Spoked wheels appeared around 2000 BC. BC in the Eastern European Sintaschta culture and are still in use today in a similar construction. With their thick cross-sections, the spokes transfer the compressive forces from the rim to the hub. In the ancient Orient , the first spoked wheels appeared in the late Bronze Age with the use of the two-wheeled chariot . In some cases, they replaced the heavy disc wheels that had been customary up to that time , which, for example, were still in use in Anatolia until the last century. The oldest surviving example of a bronze wheel with four spokes in Europe comes from the Swiss settlement of Cortaillod . It has a diameter of 47 cm, a hub length of 37 cm and weighs around 10 kg. In contrast, only wheels with six or more spokes, such as those shown on some Egyptian frescoes , were really resilient . With the improvement of wood processing techniques, spokes made of wood appeared. Eg for team - carts are in use today. Assyrian chariots first had six, since Tiglat-Pileser III. eight spokes.

bicycle

Spoked wheel of a bicycle with crossed spokes

The front and rear wheels of bicycles are called wheels .

material

Most of the spokes on bicycles are made of stainless steel, which guarantees high strength. Cheaper wheels are sometimes made with spokes made of chrome-plated or galvanized non-rustproof steel. Titanium and carbon spokes are also made, although the latter material has proven to be too prone to breakage.

Construction principle

The spokes on bicycles or motorcycles and "oldtimers" are comparatively thin and numerous (usually 36 per wheel) and are only subjected to tension. The spokes put the rim under high tension and transmit tensile forces between the rim and the hub. When driving, the forces are continuously diverted from the load point below via the rim to the spokes currently on top, which are then subjected to greater tensile loads. Since bicycle spokes can only be subjected to insignificant pressure when driving, the spoked wheel is minimally compressed at the lower point, an effect that cannot be seen with the naked eye due to the use of rubber tires on spoked wheels, but can only be detected with precision extensometers .

The spokes can be arranged radially or tangentially . In the case of radial lacing , the necessary pretensioning of the entire spoke construction is released extremely quickly when a single spoke is relaxed by loosening the spoke attachment or when the spoke breaks, as the spokes are relaxed in a chain reaction. The wheel becomes unstable and the entire structure is destroyed very quickly. A certain advantage of the radial lacing is the weight savings through shorter spokes and the even more compact design of the impeller.

Spoked wheels in which the spokes are arranged more or less tangentially to the bolt circle of the hub flange are significantly more stable and fail-safe . With most wheels, the spokes on one side of the hub, pointing in or against the direction of rotation, usually cross one to three times. If a spoke is damaged, loosened or broken, the necessary pre-tensioning of the overall construction is not released and the tensile forces are distributed to other spokes. If the spoke defect persists, however, the other spokes will gradually loosen due to the higher load.

Spoke types

Spokes usually have a 2 mm thread (FG 2.3 according to DIN 79012), rolled to avoid breaking notches , onto which the spoke nipple is screwed in order to fasten this spoke end in the rim . At the other end, bicycle spokes have an arc of around 95 °, at the end of which the spoke head is in the form of a lens. This head holds the spoke in a countersunk transverse hole in the flange of the hub .

By far the most common spokes have a circular cross-section with a diameter of 2.0 mm . Spokes with a smaller cross-section in the straight part and / or with a larger cross-section in the arch are widespread for higher-quality wheels and those with particularly heavy loads. Due to the smaller cross-section in the straight part, the spokes can stretch slightly in the event of impact, so that the spoke arch is not so heavily stressed. Diameters of 1.5 and 1.8 mm in the straight part and 2.18 and 2.34 mm in the arch are common. A wheel with thinner spokes is also less stiff, so that the combination of a few and thin spokes is only acceptable for wheels that are very lightly loaded.

Spokes with a reinforced arch and a diameter that remains constant over the rest of the length are also called thickening spokes (ED). If the middle part is thinner, one speaks of double-thick spokes (DD), provided that both ends have the same diameter, and of 3D spokes , if the spoke material, apart from the head, has three different diameters.

To reduce the air resistance, spokes are used that do not have a circular cross-section in the straight middle section, but are flat. One also speaks of knife, saber or aero spokes. However, measurements from cycling magazines, among others, showed that the air resistance of knife spokes that are not exactly aligned in the direction of movement increases drastically and can even be slightly above the round spokes. A similar effect occurs in strong cross winds . The lower air resistance is only significant at a speed of around 40 km / h. There are also different cross-sections for flat spokes.

Straight, not angled spokes are less common. They require hubs with slots instead of spoke holes. The advantage of straight spokes is that there is no arch as a potential weak point. The disadvantage is the significantly higher price. Instead of the head, Z-spokes have a Z-shaped bent end that can be hooked into the hub flange bore without the spoke having to be threaded in from the threaded part. This is an advantage in the event of a breakdown on the way, especially on a rear wheel with a large sprocket.

Repair options for broken spokes

For repairs while traveling, some types of bicycles (such as those from Koga-Miyata ) had perforated straps on the top of the chainstay to clamp 2 spare spokes, which also protected the strut from chain slap. Some spare spokes of suitable lengths can simply be attached to the outside of a strut with adhesive strips or ropes or, more elaborately, housed in the seat tube. Repair spokes made from steel cable with a central part are expensive, they can be rolled up and because of the thick joints (pressing in of the cable) always have Z-heads.

In order for spokes to be gripped by enough threads of the nipple, to have adjustment play and not stick into the hose, they each need a length of about 2 mm. A total of six different spoke lengths per bike are required as a reserve for the front and rear wheels. By kinking sharply by around 100 °, hooking two spokes and securing the hook connection with a steel tube with an inner diameter of 4 mm, any length can be temporarily bridged.

Technical details

Another design are corrugated spokes, the slightly undulating middle part of which is intended to produce a resilient effect.

Spokes are made of stainless steel - rustproof (predominantly today), steel , aluminum , titanium and carbon fiber. Steel spokes are galvanized , nickel-plated or chrome-plated . The tensile strength of high-quality steel spokes is 1200 N / mm² and more.

There are different methods of installing spokes in a wheel. A distinction is made in particular between the tangential and radial lacing. For details, see impeller .

Textile spokes have recently been developed at the TU Chemnitz.

Tensile load on the spokes

In today's bicycles, wire spokes are only subjected to tension. This is the only way to hold the nipple positively in the rim . Well-measured pretensioning of the spokes during wheel manufacture and a certain tightening over time to compensate for settling and elongation keep the loaded spokes under tension when the wheel rolls.

The load on the axle presses on the wheel hub. Since the spokes can practically only transmit tensile forces, the force is not transmitted from the wheel hub directly downwards, but upwards to the rim and only over this downwards and over the tire to the ground. Under the load, the tire squeezes a little wide over a certain length. In this area - the tire contact patch - the tire transfers the pressure to a segment of the rim in which perhaps 1, 2 or 3 spokes are located.

The vertically acting weight force introduced into the rim in the upper part is absorbed by the currently horizontal spokes. In addition, the rim has a certain inherent rigidity , so that it hardly deforms under the action of force. Ideally considered without any rim deformation, and the mostly 36 spokes divided into 4 sectors of 9 pieces each, the spokes currently below are unloaded, the front and rear spoke sectors stabilize the rim and the upper spoke sector carries the axle load . The top 9 by increasing the pulling force by 1/36 of the axle load.

A spoke works well in the system when it appropriately decreases its tensile force along the small path of displacement and deformation of the rim (below).

A 1.8 mm thin spoke has a good 2.5 mm² cross-sectional area. Times 1200 N / mm² tensile strength results in a maximum tensile force of 3000 N. If 1000 N of this is used as a pretensioning force, the wheel below carries 1000 N for each relaxed spoke, i.e. around 100 kg of weight. If the spokes are completely relaxed at the base due to insufficient pre-tensioning force, when the spoke nipple unrolls a little lifts out of its seat in the rim for a moment, causing crackling and often further loosening of the nipple.

For every revolution of the wheel, there is a rather short, stronger relaxation (below) and a less strong but longer lasting additional tension (above) in every well-tensioned spoke. These waves in the course of the spoke tension over time increase with the axle load and are superimposed by impacts from an uneven road surface. The centrifugal force has a comparatively small effect : 1 kg of rotating outer wheel mass at a diameter of 630 mm, a speed of 72 km / h and a wheel circumference of 2 m results in a centrifugal force of 138 N per spoke (of 36).

Axial moments introduced by the hub through acceleration or braking, inclined contact force when kicking or cornering a tricycle with vertical wheels put additional stress on the spokes. Vibrations in the frame are also transmitted as spoke forces. "Bike stands" that only hold a small part of the wheel circumference look particularly rough - even when tilting an "unpacked" bike, jumping with your legs on a lying bike, to be observed when unicycling, or grippy approaching with lateral movement to the bike after jumping, Fall or slip.

A piece of the rim only 10 cm long, which is pushed upwards by the tire in the area of the 2 lowest spokes, is dented by less than 1 mm under a load of 90 kg, corresponding to the ground pressure force of approx. 900 N, as the length of the carrier is only 1/6 of the rim diameter.

Pure tensile loading of the spokes makes flexible so-called emergency spokes possible, which consist of a solid cord or (in the middle part) of steel cable and can therefore be rolled up and packed without risk of kinking and inserted into the bike more easily on the go.

Spoke length

The length of the spoke is defined as the length from the inside of the bend of the crank (exactly on the inside edge of the spoke head) to the straight end including the thread. This is measured by hooking into the beginning of a thin ruler or a spoke gauge.

Before building a wheel, the necessary spoke length must be determined using the following formula:

${\ displaystyle L = {\ sqrt [{2}] {a ^ {2} + {\ frac {D _ {\ mathrm {w}} ^ {2} + d ^ {2} -2 \ cdot D _ {\ mathrm {w}} \ cdot d \ cdot \ cos (\ alpha)} {4}}}} - {\ frac {d _ {\ mathrm {s}}} {2}}}$

It is

${\ displaystyle \ alpha = 2 \ pi \, {\ frac {n _ {\ mathrm {k}}} {n _ {\ mathrm {s}}}}}$ in radians or

${\ displaystyle \ alpha = 360 ^ {\ circ} \, {\ frac {n _ {\ mathrm {k}}} {n _ {\ mathrm {s}}}}}$ in degrees.

The parameters are as follows:

${\ displaystyle L}$ → spoke length

${\ displaystyle D _ {\ mathrm {w}}}$ → effective rim diameter; 'effective rim diameter' ERD (distance between the spoke nipple head contact surfaces at two opposite rim holes - is also specified by the rim manufacturer)

${\ displaystyle d}$ → Bolt circle diameter of the spoke holes in the flange

${\ displaystyle a}$ → Distance spoke flange to hub center

${\ displaystyle n _ {\ mathrm {k}}}$ → Number of spoke crossings

${\ displaystyle n _ {\ mathrm {s}}}$ → Number of spokes per flange

${\ displaystyle d _ {\ mathrm {s}}}$ → spoke hole diameter

If the ERD is not known, it can also be measured using two spokes. The spokes are inserted with spoke nipples through opposite spoke holes and fixed with a rubber band between the heads with a slight pull. Then the distance between the spoke heads is measured. The spokes are then pulled out of the rim again without twisting the nipples. The ERD is then the sum of the effective spoke lengths (distance between the lower edge of the nipple head and the end of the spoke head) and the previously measured spoke head distance. The measurement should be carried out twice, over two rim diameters rotated by 90 ° against each other, and the mean value should be taken to compensate for errors from possible rim ovality.

Motorcycle

In technical terms, all of the above also applies to wire-spoke wheels on motorcycles and automobiles. In the national standard DIN 74371-1 until July 2006, angled spokes for motorcycles with the threads M 5, M 4, M 3.5 and M 3 were standardized as a smooth spoke and as a thickening spoke (ED), earlier also as a double-thick spoke. Spoke and in recommended standard lengths. The standard recommended an angle of 95 ° in the bend. The standard edition of December 1957 recommends steel as a material with a tensile strength of 1000 to 1400 N / mm². Non-angled wire spokes have also been used in motorcycle designs.

automobile

Artillery wheels

Artillery wheel with wooden spokes and removable rim. This bike has pneumatic tires. (approx. 1910)

Early automobiles were often equipped like carriages with steel-reinforced wooden spoke wheels , so-called artillery wheels, with usually eight to twelve spokes per wheel. The spokes were initially firmly attached to the hub. That was impractical because the tire had to be changed directly on the vehicle and a broken wheel could only be repaired on site with great effort. They made do with removable rims and carried one or more of them with mounted tires as replacements. Wheels that could be removed from the hub flange began to gain acceptance from around 1910.

In the 1920s, some manufacturers used cast iron artillery wheels. Both forms were replaced by steel disc wheels in the early 1930s , after they had appeared as accessories a few years earlier.

Wire spoke wheels

Spoked wheel of an English roadster from the 1960s

Wire spoke wheels have also been used for predominantly light and sporty automobiles since the end of the 19th century. Rudge invented the removable spoked wheel with central locking in 1907 , which was a feature of many sporty vehicles until the 1960s. In the 1920s and 1930s, it was fashionable to hide the spoke wheels under a metal cover that was secured with the same latch that held the wheel.

Bend angles other than 95 ° occur on automobiles , and in some designs the spokes are arranged in more than 2 levels per wheel.

railroad

Replica of a running axle of the Adler steam locomotive with spoked wheels
(original from 1835, replica from 1935)

Steel spokes of the operational replica of the eagle in the Nuremberg Transport Museum

The first railway wheels were often designed as wooden spoked wheels, which was originally influenced by the tradition of coach building. The large drive wheels of modern steam locomotives were later made entirely of steel, but were still designed as spoked wheels to save weight. The first full-line electric locomotives also had spoked wheels.

literature

Michael Gressmann, Franz Beck, Rüdiger Bellersheim: specialist knowledge of bicycle technology. 1st edition, Verlag Europa-Lehrmittel, Haan-Gruiten, 2006, ISBN 3-8085-2291-7
Fritz Winkler, Siegfried Rauch: Bicycle technology repair, construction, production. 10th edition, BVA Bielefelder Verlagsanstalt GmbH & Co. KG, Bielefeld, 1999, ISBN 3-87073-131-1
Rob van der Plas: The bicycle workshop - repair and maintenance step by step. 1st edition, BVA Bielefelder Verlaganstalt, Bielefeld, 1995, ISBN 3-87073-147-8
Christian Smolik, Stefan Etzel: The new bicycle repair book. 9th edition, BVA Bielefelder Verlaganstalt, Bielefeld, 2010, ISBN 978-3-87073-055-0

Web links

Comfortable spoke length calculator on Speichenrechner.de
Spoke length calculator on fahrradmonteur.de
Section through a car artillery wheel (Packard 1911 ) (accessed October 17, 2012)

Individual evidence

↑ Manfred Russo: Tupperware & Pinstripe. Böhlau Verlag Wien, 2000, ISBN 978-3-205-99163-2 ( limited preview in the Google book search).

^ Di Cosmo: The Northern Frontier in Pre-Imperial China. In: Cambridge History of Ancient China. 1999, pp. 885–966, here p. 903, refers to finds from the Andronowo culture around 2026 BC. Chr.

^ PF Kuznetsov: The emergence of Bronze Age chariots in eastern Europe. In: Antiquity. Vol. 80, No. 309, 2006, ISSN 0003-598X , pp. 638–645, online ( memento of the original of July 7, 2012 in the web archive archive.today ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2
↑ wheel building. Retrieved April 16, 2018 .
↑ Better than steel spokes: This wheel has spokes made of textile fibers ingenieur.de, September 2, 2016, accessed June 17, 2020.

[books-S3pvueRo4HIC-PP46-1] Manfred Russo: Tupperware & Pinstripe. Böhlau Verlag Wien, 2000, ISBN 978-3-205-99163-2 ( limited preview in the Google book search).

[2] Di Cosmo: The Northern Frontier in Pre-Imperial China. In: Cambridge History of Ancient China. 1999, pp. 885–966, here p. 903, refers to finds from the Andronowo culture around 2026 BC. Chr.