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A spoke is one of some number of rods radiating from the center of a
wheel A wheel is a circular component that is intended to rotate on an axle Bearing (mechanical), bearing. The wheel is one of the key components of the wheel and axle which is one of the Simple machine, six simple machines. Wheels, in conjunction wi ...
(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, bearing ...
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 Adventure game#Puzzle adventure, puzzle adventure video game. It is the sequel to ''Myst'' and second in the Myst (series), ''Myst'' series of games. Developed by Cyan Worlds, it was initially published by Red Orb Entertainment, a ...
(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 A spokeshave is a hand tool used to shape and smooth woods in woodworking jobs such as making cart wheel spokes, chair legs, paddles, bows, and arrows. The tool consists of a blade fixed into the body of the tool, which has a handle for each han ...
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 ba ...
originally developed for this purpose. Eventually, the term spoke was more commonly applied to the finished product of the
wheelwright A wheelwright is a craftsman who builds or repairs wooden wheels. The word is the combination of "wheel" and the word "wright", (which comes from the Old English word "''wryhta''", meaning a worker or shaper of wood) as in shipwright and arkw ...
's work, than to the materials they used.


History

The spoked
wheel A wheel is a circular component that is intended to rotate on an axle Bearing (mechanical), bearing. The wheel is one of the key components of the wheel and axle which is one of the Simple machine, six simple machines. Wheels, in conjunction wi ...
was invented to allow the construction of lighter and swifter vehicles. Earliest physical evidence for spoked wheels were found in
Sintashta culture The Sintashta culture (russian: Синташтинская культура, Sintashtinskaya kul'tura), around 2050–1900 BCE, is the first phase of the Sintashta–Petrovka culture. or Sintashta–Arkaim culture,. and is a late Middle Bronze Ag ...
, 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 historically ...
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  ...
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 The Minoan civilization was a Bronze Age Aegean civilization on the island of Crete and other Aegean Islands, whose earliest beginnings were from 3500BC, with the complex urban civilization beginning around 2000BC, and then declining from 1450B ...
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 referre ...
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 ...
. Neo-
Chalcolithic The Copper Age, also called the Chalcolithic (; from grc-gre, χαλκός ''khalkós'', "copper" and  ''líthos'', "stone") or (A)eneolithic (from Latin '' aeneus'' "of copper"), is an archaeological period characterized by regular ...
/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 f ...
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 Tension may refer to: Science * Psychological stress * Tension (physics), a force related to the stretching of an object (the opposite of compression) * Tension (geology), a stress which stretches rocks in two opposite directions * Voltage or el ...
or
compression Compression may refer to: Physical science *Compression (physics), size reduction due to forces *Compression member, a structural element such as a column *Compressibility, susceptibility to compression * Gas compression *Compression ratio, of a ...
.


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 y ...
-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 an ...
s and
wagon A wagon or waggon is a heavy four-wheeled vehicle pulled by draught animals or on occasion by humans, used for transporting goods, commodities, agricultural materials, supplies and sometimes people. Wagons are immediately distinguished from ...
s. 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 siege ...
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. Bic ...
s, heavy wooden-spoked wheels were replaced by lighter wheels with spokes made of tensioned, adjustable metal wires, called
wire wheels 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 ...
. 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), cerebr ...
s,
motorcycle A motorcycle (motorbike, bike, or trike (if three-wheeled)) is a two or three-wheeled motor vehicle steered by a handlebar. Motorcycle design varies greatly to suit a range of different purposes: long-distance travel, commuting, cruising ...
s,
automobile A car or automobile is a motor vehicle with Wheel, wheels. Most definitions of ''cars'' say that they run primarily on roads, Car seat, seat one to eight people, have four wheels, and mainly transport private transport#Personal transport, pe ...
s, and early
aircraft An aircraft is a vehicle that is able to fly by gaining support from the air. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines ...
.


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 corros ...
, while cheaper bicycles may use
galvanized Galvanization or galvanizing ( also spelled galvanisation or galvanising) is the process of applying a protective zinc coating to steel or iron, to prevent rusting. The most common method is hot-dip galvanizing, in which the parts are submerged ...
(also called "rustless") or chrome plated spokes. While a good quality spoke is capable of supporting about 225
kgf KGF or ''kgf'' may refer to: *Keratinocyte growth factor *King George's Fields, UK, recreation grounds *Kolar Gold Fields *The IATA code for Sary-Arka Airport, Karaganda, Kazakhstan * ''K.G.F'' (film series), Indian Kannada-language film series * ...
(c. 500
pounds-force The pound of force or pound-force (symbol: lbf, sometimes lbf,) is a unit of force used in some systems of measurement, including English Engineering units and the foot–pound–second system. Pound-force should not be confused with pound-ma ...
or 2,200
newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * ''Newton'' (film), a 2017 Indian film * Newton ( ...
s) 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, ma ...
) 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. More ...
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 ...
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 A spoke nipple holds a bicycle wheel's rim to each spoke. The spoke nipple is a headed cylinder with threading on the inside through part of its length (there is an unthreaded lead-in nearest the "flats"). Traditionally, the nipples fit in hol ...
. 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 steered by a handlebar. Motorcycle design varies greatly to suit a range of different purposes: long-distance travel, commuting, cruising ...
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. Bic ...
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 hol ...
or a rear wheel with chain
derailleur Shimano 600 front derailleur (1980) A derailleur is a variable-ratio bicycle gearing system consisting of a chain, multiple sprockets of different sizes, and a mechanism to move the chain from one sprocket to another. Modern front and rear d ...
, 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 In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite t ...
, 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 In geometry, a space diagonal (also interior diagonal or body diagonal) of a polyhedron is a line connecting two vertices that are not on the same face. Space diagonals contrast with '' face diagonals'', which connect vertices on the same face (bu ...
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 In trigonometry, the law of cosines (also known as the cosine formula, cosine rule, or al-Kashi's theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles. Using notation as in Fig. 1, the law of cosines states ...
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 In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite t ...
.


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 designed ...
*
Spoke nipple A spoke nipple holds a bicycle wheel's rim to each spoke. The spoke nipple is a headed cylinder with threading on the inside through part of its length (there is an unthreaded lead-in nearest the "flats"). Traditionally, the nipples fit in hol ...
*
Spoke wrench A spoke wrench or spoke key is a small wrench or tool used to adjust the tension in the spokes of a tension-spoked wheel. A spoke wrench is sometimes called a nipple wrench, as it is the spoke nipple – not the spoke – that is turned in the pr ...
*
Spokeshave A spokeshave is a hand tool used to shape and smooth woods in woodworking jobs such as making cart wheel spokes, chair legs, paddles, bows, and arrows. The tool consists of a blade fixed into the body of the tool, which has a handle for each han ...
*
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 ...
*
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 sam ...


Notes


References


External links


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