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A spoke is one of some number of rods radiating from the center of a wheel (the hub where the
axle An axle or axletree is a central shaft for a rotating wheel or gear. On wheeled vehicles, the axle may be fixed to the wheels, rotating with them, or fixed to the vehicle, with the wheels rotating around the axle. In the former case, beari ...
connects), connecting the hub with the round traction surface. The term originally referred to portions of a log that had been
riven ''Riven'' is a puzzle adventure video game. It is the sequel to '' Myst'' and second in the ''Myst'' series of games. Developed by Cyan Worlds, it was initially published by Red Orb Entertainment, a division of Broderbund. ''Riven'' was distri ...
(split lengthwise) into four or six sections. The radial members of a wagon wheel were made by carving a spoke (from a log) into their finished shape. A spokeshave is a
tool A tool is an object that can extend an individual's ability to modify features of the surrounding environment or help them accomplish a particular task. Although many animals use simple tools, only human beings, whose use of stone tools dates b ...
originally developed for this purpose. Eventually, the term spoke was more commonly applied to the finished product of the wheelwright's work, than to the materials they used.


History

The spoked wheel was invented to allow the construction of lighter and swifter vehicles. Earliest physical evidence for spoked wheels were found in Sintashta culture, dating to 2000 BC. Soon after this, horse cultures of the
Caucasus The Caucasus () or Caucasia (), is a region between the Black Sea and the Caspian Sea, mainly comprising Armenia, Azerbaijan, Georgia, and parts of Southern Russia. The Caucasus Mountains, including the Greater Caucasus range, have historica ...
region used horse-drawn spoked-wheel war
chariots A chariot is a type of cart driven by a charioteer, usually using horses to provide rapid motive power. The oldest known chariots have been found in burials of the Sintashta culture in modern-day Chelyabinsk Oblast, Russia, dated to c. 2000&nbs ...
for the greater part of three centuries. They moved deep into the Greek peninsula where they joined with the existing Mediterranean peoples to give rise, eventually, to classical Greece after the breaking of Minoan dominance and consolidations led by pre-classical
Sparta Sparta ( Doric Greek: Σπάρτα, ''Spártā''; Attic Greek: Σπάρτη, ''Spártē'') was a prominent city-state in Laconia, in ancient Greece. In antiquity, the city-state was known as Lacedaemon (, ), while the name Sparta referr ...
and
Athens Athens ( ; el, Αθήνα, Athína ; grc, Ἀθῆναι, Athênai (pl.) ) is both the capital and largest city of Greece. With a population close to four million, it is also the seventh largest city in the European Union. Athens dominates a ...
. Neo-
Chalcolithic The Copper Age, also called the Chalcolithic (; from grc-gre, χαλκός ''khalkós'', "copper" and  ''líthos'', "Rock (geology), stone") or (A)eneolithic (from Latin ''wikt:aeneus, aeneus'' "of copper"), is an list of archaeologi ...
/proto-historic period (1800-1200 BCE) paintings in various regions of India such as Chibbar Nulla, Chhatur Bhoj Nath Nulla, Kathotia, etc. depict the usage of chariots with spoked wheels.
Celt The Celts (, see pronunciation for different usages) or Celtic peoples () are. "CELTS location: Greater Europe time period: Second millennium B.C.E. to present ancestry: Celtic a collection of Indo-European peoples. "The Celts, an ancient ...
ic chariots introduced an
iron Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in ...
rim around the wheel in the 1st millennium BC. The spoked wheel was in continued use without major modification until the 1870s, when wire wheels and rubber
tire A tire (American English) or tyre (British English) is a ring-shaped component that surrounds a Rim (wheel), wheel's rim to transfer a vehicle's load from the axle through the wheel to the ground and to provide Traction (engineering), t ...
s were invented.


Construction

Spokes can be made of wood, metal, or synthetic fiber depending on whether they will be in tension or compression.


Compression spokes

The original type of spoked wheel with wooden spokes was used for
horse The horse (''Equus ferus caballus'') is a domesticated, one-toed, hoofed mammal. It belongs to the taxonomic family Equidae and is one of two extant subspecies of ''Equus ferus''. The horse has evolved over the past 45 to 55 million yea ...
-drawn
carriage A carriage is a private four-wheeled vehicle for people and is most commonly horse-drawn. Second-hand private carriages were common public transport, the equivalent of modern cars used as taxis. Carriage suspensions are by leather strapping ...
s and wagons. In early motor cars, wooden spoked wheels of the
artillery Artillery is a class of heavy military ranged weapons that launch munitions far beyond the range and power of infantry firearms. Early artillery development focused on the ability to breach defensive walls and fortifications during si ...
type were normally used. In a simple wooden wheel, a load on the hub causes the wheel rim to flatten slightly against the ground as the lowermost wooden spoke shortens and compresses. The other wooden spokes show no significant change. Wooden spokes are mounted radially. They are also dished, usually to the outside of the vehicle, to prevent wobbling. Also, the dishing allows the wheel to compensate for expansion of the spokes due to absorbed moisture by dishing more.


Tension spokes

For use in
bicycle A bicycle, also called a pedal cycle, bike or cycle, is a human-powered or motor-powered assisted, pedal-driven, single-track vehicle, having two wheels attached to a frame, one behind the other. A is called a cyclist, or bicyclist. B ...
s, heavy wooden-spoked wheels were replaced by lighter wheels with spokes made of tensioned, adjustable metal wires, called wire wheels. These are also used in
wheelchair A wheelchair is a chair with wheels, used when walking is difficult or impossible due to illness, injury, problems related to old age, or disability. These can include spinal cord injuries ( paraplegia, hemiplegia, and quadriplegia), ce ...
s,
motorcycle A motorcycle (motorbike, bike, or trike (if three-wheeled)) is a two or three-wheeled motor vehicle Steering, steered by a Motorcycle handlebar, handlebar. Motorcycle design varies greatly to suit a range of different purposes: Long-distance ...
s,
automobile A car or automobile is a motor vehicle with wheels. Most definitions of ''cars'' say that they run primarily on roads, seat one to eight people, have four wheels, and mainly transport people instead of goods. The year 1886 is regarded ...
s, and early
aircraft An aircraft is a vehicle that is able to flight, fly by gaining support from the Atmosphere of Earth, air. It counters the force of gravity by using either Buoyancy, static lift or by using the Lift (force), dynamic lift of an airfoil, or in ...
.


Types

Some types of wheels have removable spokes that can be replaced individually if they break or bend. These include bicycle and wheelchair wheels. High quality bicycles with conventional wheels use spokes of
stainless steel Stainless steel is an alloy of iron that is resistant to rusting and corrosion. It contains at least 11% chromium and may contain elements such as carbon, other nonmetals and metals to obtain other desired properties. Stainless steel's r ...
, while cheaper bicycles may use galvanized (also called "rustless") or chrome plated spokes. While a good quality spoke is capable of supporting about 225 kgf (c. 500 pounds-force or 2,200 newtons) of tension, they are used at a fraction of this load to avoid suffering fatigue failures. Since bicycle and wheelchair wheel spokes are only in tension, flexible and strong materials such as synthetic fibers, are also occasionally used. Metal spokes can also be ovalized or bladed to reduce aerodynamic drag, and butted (double or even triple) to reduce weight while maintaining strength. A variation on the wire-spoked wheel was Tioga's "Tension Disk", which appeared superficially to be a solid disk but was in fact constructed using the same principles as a normal tension-spoked wheel. Instead of individual wire spokes, a continuous thread of Kevlar (
aramid Aramid fibers, short for aromatic polyamide, are a class of heat-resistant and strong synthetic fibers. They are used in aerospace and military applications, for ballistic-rated body armor fabric and ballistic composites, in marine cordage, mar ...
) was used to lace the hub to the rim under high tension. The threads were encased in a translucent disk for protection and some aerodynamic benefit, but this was not a structural component.


Tangential lacing

Wire spokes can be radial to the hub but are more often mounted
tangent In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. Mo ...
ially to the hub. Tangential spoking allows for the transfer of torque between the rim and the hub. Tangential spokes are thus necessary for the drive wheel, which has torque at the hub from pedalling, and any wheels using hub-mounted brakes such as disk or band brakes, which transfer torque from the rim to the brake in the opposite direction—(via the hub) when braking.


Wheelbuilding

Constructing a tension-spoked wheel from its constituent parts is called
wheelbuilding Wheelbuilding is the process of assembling wire wheels (generally a bicycle wheel, but including wheelchairs, and some cars). The components of a wire wheel are the rim, spokes, nipples, and hub. Goals The wheelwright must ensure that the wh ...
and requires the correct building procedure for a strong and long-lasting end product. Tensioned spokes are usually attached to the rim or sometimes the hub with a spoke nipple. The other end is commonly peened into a disk or uncommonly bent into a "Z" to keep it from pulling through its hole in the hub. The bent version has the advantage of replacing a broken spoke in a rear bicycle wheel without having to remove the rear gears. Wire wheels, with their excellent weight-to-strength ratio, soon became popular for light vehicles. For everyday cars, wire wheels were soon replaced by the less expensive metal disc wheel, but wire wheels remained popular for
sports car A sports car is a car designed with an emphasis on dynamic performance, such as handling, acceleration, top speed, the thrill of driving and racing capability. Sports cars originated in Europe in the early 1900s and are currently produced by ...
s up to the 1960s. Spoked wheels are still popular on
motorcycle A motorcycle (motorbike, bike, or trike (if three-wheeled)) is a two or three-wheeled motor vehicle Steering, steered by a Motorcycle handlebar, handlebar. Motorcycle design varies greatly to suit a range of different purposes: Long-distance ...
s and
bicycle A bicycle, also called a pedal cycle, bike or cycle, is a human-powered or motor-powered assisted, pedal-driven, single-track vehicle, having two wheels attached to a frame, one behind the other. A is called a cyclist, or bicyclist. B ...
s.


Spoke length

When building a bicycle wheel, the spokes must have the correct length, otherwise there may not be enough threads engaged, producing a weaker wheel, or they may protrude through the rim and possibly puncture the inner tube.


Calculation

For bicycle spokes, the spoke length is defined from the flange seat to the thread tip. For spokes with bent ends, the nominal spoke length does ''not'' include the width of the spoke at the bent end. For wheels with crossed spokes (which are the norm), the desired spoke length is :l = \sqrt - r_3 where * ''d'' = distance from the center of hub (along the axis) to
flange A flange is a protruded ridge, lip or rim (wheel), rim, either external or internal, that serves to increase shear strength, strength (as the flange of an iron beam (structure), beam such as an I-beam or a T-beam); for easy attachment/transfer of ...
, for example 30 mm, * ''r''1 = spoke hole circle radius of the hub, for example 19.5 mm, * ''r''2 = half of effective Rim Diameter (ERD), or the diameter the ends of the spokes make in a built wheel (see 'Discussion' attached to this article for explanation) of the rim, for example 301 mm, * ''r''3 = radius of spoke holes in the ''flange'', for example 1.1 mm, * ''m'' = number of spokes to be used for one side of the wheel, for example 36/2=18, * ''k'' = number of crossings per spoke, for example 3 and * ''a'' = 360° ''k''/''m'', for example 360°*3/18 = 60°. Regarding ''d'': For a symmetric wheel such as a front wheel with no disc brake, this is half the distance between the flanges. For an asymmetric wheel such as a front wheel with
disc brake A disc brake is a type of brake that uses the calipers to squeeze pairs of pads against a disc or a "rotor" to create friction. This action slows the rotation of a shaft, such as a vehicle axle, either to reduce its rotational speed or to h ...
or a rear wheel with chain derailleur, the value of ''d'' is different for the left and right sides. ''a'' is the angle between (1) the radius to a nipple hole in the rim to which a spoke is attached, and, (2) the radius to the flange hole holding the spoke. The spoke crosses either 1, 2, or 3 oppositely pointing spokes depending on the lacing design. On the flange, the angle between the radii of adjacent holes is 360°/''m'' (for equally spaced holes). For each spoke crossed, the hub is rotated with reference to the rim one "angle between adjacent flange holes". Thus, multiplying the "angle between adjacent flange holes" by ''k'' gives the angle ''a''. For example, a 32 spoke wheel has 16 spokes per side, 360° divided by 16 equals 22.5°. Multiply 22.5° ("angle between adjacent flange holes") by the number of crossings to get the angle ''a''—if 3-crosses, the 32 spoke wheel has an angle ''a'' of 67.5°. Regarding ''r''3: The size of the spoke holes in the flange does not matter for the needed spoke length. This term removes the effect of the hole size. Since the holes are usually small (just over 2 mm in diameter), the effect is small and in practice matters little. For radially spoked wheels (zero crossings), the formula simplifies to the Pythagorean theorem, with spoke length ''l'' plus ''r''3 being the slope, ''r''2 minus ''r''1 being the base, and ''d'' being the rise: :(l + r_3)^2 = (r_2 - r_1)^2 + d^2; or solving for the length :l = \sqrt - r_3.


Derivation

The spoke length formula computes the length of the space diagonal of an imaginary rectangular box. Imagine holding a wheel in front of you such that a nipple is at the top. Look at the wheel from along the axis. The spoke through the top hole is now a diagonal of the imaginary box. The box has a depth of ''d'', a height of ''r''2-''r''1cos(''α'') and a width of ''r''1sin(''a''). Equivalently, the law of cosines may be used to first compute the length of the spoke as projected on the wheel's plane (as illustrated in the diagram), followed by an application of the Pythagorean theorem.


See also

*
Bicycle wheel A bicycle wheel is a wheel, most commonly a wire wheel, designed for a bicycle. A pair is often called a wheelset, especially in the context of ready built "off the shelf" performance-oriented wheels. Bicycle wheels are typically designe ...
* Spoke nipple * Spoke wrench * Spokeshave *
Wheelbuilding Wheelbuilding is the process of assembling wire wheels (generally a bicycle wheel, but including wheelchairs, and some cars). The components of a wire wheel are the rim, spokes, nipples, and hub. Goals The wheelwright must ensure that the wh ...
*
Wire wheel Wire wheels, wire-spoked wheels, tension-spoked wheels, or "suspension" wheels are wheels whose rims connect to their hubs by wire spokes. Although these wires are generally stiffer than a typical wire rope, they function mechanically the same ...


Notes


References


External links


Online spoke length calculator (German), uses slightly different measures than the above formula
{{Bike equipment Bicycle parts Wheels Chariots