Spoke
Encyclopedia
A spoke is one of some number of rods radiating from the center of a wheel
(the hub where the axle
connects), connecting the hub with the round traction surface.
The term originally referred to portions of a log which had been 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
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 he used.
was invented to allow the construction of lighter and swifter vehicles. The earliest known examples are in the context of the Andronovo culture
, dating to ca. 2000 BCE. Soon after this, horse cultures of the Caucasus
region used horse-drawn spoked-wheel war chariots 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
and Athens
. Celt
ic chariots introduced an iron
rim around the wheel in the 1st millennium BCE. The spoked wheel was in continued use without major modification until the 1870s, when wire wheels and rubber tire
s were invented.
or compression
.
drawn carriage
s and wagon
s. In early motor cars, wooden spoked wheels of the artillery
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.
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
s, motorcycle
s, and automobile
s.
, 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.
A spoke is one of some number of rods radiating from the center of a wheel
(the hub where the axle
connects), connecting the hub with the round traction surface.
The term originally referred to portions of a log which had been 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
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 he used.
was invented to allow the construction of lighter and swifter vehicles. The earliest known examples are in the context of the Andronovo culture
, dating to ca. 2000 BCE. Soon after this, horse cultures of the Caucasus
region used horse-drawn spoked-wheel war chariots 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
and Athens
. Celt
ic chariots introduced an iron
rim around the wheel in the 1st millennium BCE. The spoked wheel was in continued use without major modification until the 1870s, when wire wheels and rubber tire
s were invented.
or compression
.
drawn carriage
s and wagon
s. In early motor cars, wooden spoked wheels of the artillery
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.
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
s, motorcycle
s, and automobile
s.
, 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.
A spoke is one of some number of rods radiating from the center of a wheel
(the hub where the axle
connects), connecting the hub with the round traction surface.
The term originally referred to portions of a log which had been 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
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 he used.
was invented to allow the construction of lighter and swifter vehicles. The earliest known examples are in the context of the Andronovo culture
, dating to ca. 2000 BCE. Soon after this, horse cultures of the Caucasus
region used horse-drawn spoked-wheel war chariots 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
and Athens
. Celt
ic chariots introduced an iron
rim around the wheel in the 1st millennium BCE. The spoked wheel was in continued use without major modification until the 1870s, when wire wheels and rubber tire
s were invented.
or compression
.
drawn carriage
s and wagon
s. In early motor cars, wooden spoked wheels of the artillery
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.
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
s, motorcycle
s, and automobile
s.
, 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) 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.
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 disk brakes, which have torque transferred from the rim to the disk - in the opposite direction - (via the hub) when braking.
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
s up to the 1960s. Spoked wheels are still popular on motorcycles.
, 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.
For wheels with crossed spokes (which are the norm), the desired spoke length is
where
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
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 r3: 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
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 r2-r1cos(α) and a width of r1sin(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
.
Wheel
A wheel is a device that allows heavy objects to be moved easily through rotating on an axle through its center, facilitating movement or transportation while supporting a load, or performing labor in machines. Common examples found in transport applications. A wheel, together with an axle,...
(the hub where the axle
Axle
An axle 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 its surroundings, with the wheels rotating around the axle. In the former case, bearings or bushings are provided at the mounting points where the axle...
connects), connecting the hub with the round traction surface.
Spokeshave
A spokeshave is a tool used to shape and smooth wooden rods and shafts - often for use as wheel spokes, chair legs ,, self bows,and arrows. It can also be used to carve canoe paddles.-Modern:...
is a tool
Tool
A tool is a device that can be used to produce an item or achieve a task, but that is not consumed in the process. Informally the word is also used to describe a procedure or process with a specific purpose. Tools that are used in particular fields or activities may have different designations such...
originally developed for this purpose. Eventually, the term spoke was more commonly applied to the finished product of the wheelwright
Wheelwright
A wheelwright is a person who builds or repairs wheels. The word is the combination of "wheel" and the archaic word "wright", which comes from the Old English word "wryhta", meaning a worker or maker...
's work, than to the materials he used.
History
The spoked wheelWheel
A wheel is a device that allows heavy objects to be moved easily through rotating on an axle through its center, facilitating movement or transportation while supporting a load, or performing labor in machines. Common examples found in transport applications. A wheel, together with an axle,...
was invented to allow the construction of lighter and swifter vehicles. The earliest known examples are in the context of the Andronovo culture
Andronovo culture
The Andronovo culture, is a collection of similar local Bronze Age cultures that flourished ca. 21200–1400 BCE in western Siberia and the west Asiatic steppe. It is probably better termed an archaeological complex or archaeological horizon...
, dating to ca. 2000 BCE. Soon after this, horse cultures of the Caucasus
Caucasus
The Caucasus, also Caucas or Caucasia , is a geopolitical region at the border of Europe and Asia, and situated between the Black and the Caspian sea...
region used horse-drawn spoked-wheel war chariots 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
Minoan civilization
The Minoan civilization was a Bronze Age civilization that arose on the island of Crete and flourished from approximately the 27th century BC to the 15th century BC. It was rediscovered at the beginning of the 20th century through the work of the British archaeologist Arthur Evans...
dominance and consolidations led by pre-classical Sparta
Sparta
Sparta or Lacedaemon, was a prominent city-state in ancient Greece, situated on the banks of the River Eurotas in Laconia, in south-eastern Peloponnese. It emerged as a political entity around the 10th century BC, when the invading Dorians subjugated the local, non-Dorian population. From c...
and Athens
Athens
Athens , is the capital and largest city of Greece. Athens dominates the Attica region and is one of the world's oldest cities, as its recorded history spans around 3,400 years. Classical Athens was a powerful city-state...
. Celt
Celt
The Celts were a diverse group of tribal societies in Iron Age and Roman-era Europe who spoke Celtic languages.The earliest archaeological culture commonly accepted as Celtic, or rather Proto-Celtic, was the central European Hallstatt culture , named for the rich grave finds in Hallstatt, Austria....
ic chariots introduced an iron
Iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...
rim around the wheel in the 1st millennium BCE. The spoked wheel was in continued use without major modification until the 1870s, when wire wheels and rubber tire
Tire
A tire or tyre is a ring-shaped covering that fits around a wheel rim to protect it and enable better vehicle performance by providing a flexible cushion that absorbs shock while keeping the wheel in close contact with the ground...
s were invented.
Construction
Spokes can be made of wood, metal, or synthetic fiber depending on whether they will be in tensionTension (mechanics)
In physics, tension is the magnitude of the pulling force exerted by a string, cable, chain, or similar object on another object. It is the opposite of compression. As tension is the magnitude of a force, it is measured in newtons and is always measured parallel to the string on which it applies...
or compression
Physical compression
Physical compression is the result of the subjection of a material to compressive stress, which results in reduction of volume as compared to an uncompressed but otherwise identical state. The opposite of compression in a solid is tension. In any medium transmitting waves, the opposite of...
.
Compression spokes
The original type of spoked wheel with wooden spokes was used for horseHorse
The horse is one of two extant subspecies of Equus ferus, or the wild horse. It is a single-hooved mammal belonging to the taxonomic family Equidae. The horse has evolved over the past 45 to 55 million years from a small multi-toed creature into the large, single-toed animal of today...
drawn carriage
Carriage
A carriage is a wheeled vehicle for people, usually horse-drawn; litters and sedan chairs are excluded, since they are wheelless vehicles. The carriage is especially designed for private passenger use and for comfort or elegance, though some are also used to transport goods. It may be light,...
s and wagon
Wagon
A wagon is a heavy four-wheeled vehicle pulled by draught animals; it was formerly often called a wain, and if low and sideless may be called a dray, trolley or float....
s. In early motor cars, wooden spoked wheels of the artillery
Artillery wheel
The artillery wheel was developed for use on gun carriages when it was found that the lateral forces involved in horse artillery manoeuvres caused normally-constructed cart wheels to collapse. Rather than having its spokes mortised into a wooden nave , it has them fitted together then bolted into...
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
Radius
In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...
. 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 bicycleBicycle
A bicycle, also known as a bike, pushbike or cycle, is a human-powered, pedal-driven, single-track vehicle, having two wheels attached to a frame, one behind the other. A person who rides a bicycle is called a cyclist, or bicyclist....
s, heavy wooden-spoked wheels were replaced by lighter wheels with spokes made of tensioned, adjustable metal wires, called wire wheels
Wire wheels
The rims of wire wheels are connected to their hubs by wire spokes. Although these wires are generally stiffer than a typical wire rope, they function mechanically the same as tensioned flexible wires, keeping the rim true while supporting applied loads.Wire wheels are used on most bicycles and...
. These are also used in wheelchair
Wheelchair
A wheelchair is a chair with wheels, designed to be a replacement for walking. The device comes in variations where it is propelled by motors or by the seated occupant turning the rear wheels by hand. Often there are handles behind the seat for someone else to do the pushing...
s, motorcycle
Motorcycle
A motorcycle is a single-track, two-wheeled motor vehicle. Motorcycles vary considerably depending on the task for which they are designed, such as long distance travel, navigating congested urban traffic, cruising, sport and racing, or off-road conditions.Motorcycles are one of the most...
s, and automobile
Automobile
An automobile, autocar, motor car or car is a wheeled motor vehicle used for transporting passengers, which also carries its own engine or motor...
s.
Types
Some types of wheels have removable spokes which 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 steelStainless steel
In metallurgy, stainless steel, also known as inox steel or inox from French "inoxydable", is defined as a steel alloy with a minimum of 10.5 or 11% chromium content by mass....
, 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
KGF
KGF may refer to:*Keratinocyte Growth Factor*King George's Fields A UK set of 471 memorial playing fields and recreation grounds*Kolar Gold Fields*The IATA code for Sary-Arka Airport, Karaganda, Kazakhstan...
(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.
A spoke is one of some number of rods radiating from the center of a wheel
Wheel
A wheel is a device that allows heavy objects to be moved easily through rotating on an axle through its center, facilitating movement or transportation while supporting a load, or performing labor in machines. Common examples found in transport applications. A wheel, together with an axle,...
(the hub where the axle
Axle
An axle 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 its surroundings, with the wheels rotating around the axle. In the former case, bearings or bushings are provided at the mounting points where the axle...
connects), connecting the hub with the round traction surface.
Spokeshave
A spokeshave is a tool used to shape and smooth wooden rods and shafts - often for use as wheel spokes, chair legs ,, self bows,and arrows. It can also be used to carve canoe paddles.-Modern:...
is a tool
Tool
A tool is a device that can be used to produce an item or achieve a task, but that is not consumed in the process. Informally the word is also used to describe a procedure or process with a specific purpose. Tools that are used in particular fields or activities may have different designations such...
originally developed for this purpose. Eventually, the term spoke was more commonly applied to the finished product of the wheelwright
Wheelwright
A wheelwright is a person who builds or repairs wheels. The word is the combination of "wheel" and the archaic word "wright", which comes from the Old English word "wryhta", meaning a worker or maker...
's work, than to the materials he used.
History
The spoked wheelWheel
A wheel is a device that allows heavy objects to be moved easily through rotating on an axle through its center, facilitating movement or transportation while supporting a load, or performing labor in machines. Common examples found in transport applications. A wheel, together with an axle,...
was invented to allow the construction of lighter and swifter vehicles. The earliest known examples are in the context of the Andronovo culture
Andronovo culture
The Andronovo culture, is a collection of similar local Bronze Age cultures that flourished ca. 21200–1400 BCE in western Siberia and the west Asiatic steppe. It is probably better termed an archaeological complex or archaeological horizon...
, dating to ca. 2000 BCE. Soon after this, horse cultures of the Caucasus
Caucasus
The Caucasus, also Caucas or Caucasia , is a geopolitical region at the border of Europe and Asia, and situated between the Black and the Caspian sea...
region used horse-drawn spoked-wheel war chariots 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
Minoan civilization
The Minoan civilization was a Bronze Age civilization that arose on the island of Crete and flourished from approximately the 27th century BC to the 15th century BC. It was rediscovered at the beginning of the 20th century through the work of the British archaeologist Arthur Evans...
dominance and consolidations led by pre-classical Sparta
Sparta
Sparta or Lacedaemon, was a prominent city-state in ancient Greece, situated on the banks of the River Eurotas in Laconia, in south-eastern Peloponnese. It emerged as a political entity around the 10th century BC, when the invading Dorians subjugated the local, non-Dorian population. From c...
and Athens
Athens
Athens , is the capital and largest city of Greece. Athens dominates the Attica region and is one of the world's oldest cities, as its recorded history spans around 3,400 years. Classical Athens was a powerful city-state...
. Celt
Celt
The Celts were a diverse group of tribal societies in Iron Age and Roman-era Europe who spoke Celtic languages.The earliest archaeological culture commonly accepted as Celtic, or rather Proto-Celtic, was the central European Hallstatt culture , named for the rich grave finds in Hallstatt, Austria....
ic chariots introduced an iron
Iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...
rim around the wheel in the 1st millennium BCE. The spoked wheel was in continued use without major modification until the 1870s, when wire wheels and rubber tire
Tire
A tire or tyre is a ring-shaped covering that fits around a wheel rim to protect it and enable better vehicle performance by providing a flexible cushion that absorbs shock while keeping the wheel in close contact with the ground...
s were invented.
Construction
Spokes can be made of wood, metal, or synthetic fiber depending on whether they will be in tensionTension (mechanics)
In physics, tension is the magnitude of the pulling force exerted by a string, cable, chain, or similar object on another object. It is the opposite of compression. As tension is the magnitude of a force, it is measured in newtons and is always measured parallel to the string on which it applies...
or compression
Physical compression
Physical compression is the result of the subjection of a material to compressive stress, which results in reduction of volume as compared to an uncompressed but otherwise identical state. The opposite of compression in a solid is tension. In any medium transmitting waves, the opposite of...
.
Compression spokes
The original type of spoked wheel with wooden spokes was used for horseHorse
The horse is one of two extant subspecies of Equus ferus, or the wild horse. It is a single-hooved mammal belonging to the taxonomic family Equidae. The horse has evolved over the past 45 to 55 million years from a small multi-toed creature into the large, single-toed animal of today...
drawn carriage
Carriage
A carriage is a wheeled vehicle for people, usually horse-drawn; litters and sedan chairs are excluded, since they are wheelless vehicles. The carriage is especially designed for private passenger use and for comfort or elegance, though some are also used to transport goods. It may be light,...
s and wagon
Wagon
A wagon is a heavy four-wheeled vehicle pulled by draught animals; it was formerly often called a wain, and if low and sideless may be called a dray, trolley or float....
s. In early motor cars, wooden spoked wheels of the artillery
Artillery wheel
The artillery wheel was developed for use on gun carriages when it was found that the lateral forces involved in horse artillery manoeuvres caused normally-constructed cart wheels to collapse. Rather than having its spokes mortised into a wooden nave , it has them fitted together then bolted into...
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
Radius
In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...
. 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 bicycleBicycle
A bicycle, also known as a bike, pushbike or cycle, is a human-powered, pedal-driven, single-track vehicle, having two wheels attached to a frame, one behind the other. A person who rides a bicycle is called a cyclist, or bicyclist....
s, heavy wooden-spoked wheels were replaced by lighter wheels with spokes made of tensioned, adjustable metal wires, called wire wheels
Wire wheels
The rims of wire wheels are connected to their hubs by wire spokes. Although these wires are generally stiffer than a typical wire rope, they function mechanically the same as tensioned flexible wires, keeping the rim true while supporting applied loads.Wire wheels are used on most bicycles and...
. These are also used in wheelchair
Wheelchair
A wheelchair is a chair with wheels, designed to be a replacement for walking. The device comes in variations where it is propelled by motors or by the seated occupant turning the rear wheels by hand. Often there are handles behind the seat for someone else to do the pushing...
s, motorcycle
Motorcycle
A motorcycle is a single-track, two-wheeled motor vehicle. Motorcycles vary considerably depending on the task for which they are designed, such as long distance travel, navigating congested urban traffic, cruising, sport and racing, or off-road conditions.Motorcycles are one of the most...
s, and automobile
Automobile
An automobile, autocar, motor car or car is a wheeled motor vehicle used for transporting passengers, which also carries its own engine or motor...
s.
Types
Some types of wheels have removable spokes which 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 steelStainless steel
In metallurgy, stainless steel, also known as inox steel or inox from French "inoxydable", is defined as a steel alloy with a minimum of 10.5 or 11% chromium content by mass....
, 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
KGF
KGF may refer to:*Keratinocyte Growth Factor*King George's Fields A UK set of 471 memorial playing fields and recreation grounds*Kolar Gold Fields*The IATA code for Sary-Arka Airport, Karaganda, Kazakhstan...
(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.
A spoke is one of some number of rods radiating from the center of a wheel
Wheel
A wheel is a device that allows heavy objects to be moved easily through rotating on an axle through its center, facilitating movement or transportation while supporting a load, or performing labor in machines. Common examples found in transport applications. A wheel, together with an axle,...
(the hub where the axle
Axle
An axle 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 its surroundings, with the wheels rotating around the axle. In the former case, bearings or bushings are provided at the mounting points where the axle...
connects), connecting the hub with the round traction surface.
Spokeshave
A spokeshave is a tool used to shape and smooth wooden rods and shafts - often for use as wheel spokes, chair legs ,, self bows,and arrows. It can also be used to carve canoe paddles.-Modern:...
is a tool
Tool
A tool is a device that can be used to produce an item or achieve a task, but that is not consumed in the process. Informally the word is also used to describe a procedure or process with a specific purpose. Tools that are used in particular fields or activities may have different designations such...
originally developed for this purpose. Eventually, the term spoke was more commonly applied to the finished product of the wheelwright
Wheelwright
A wheelwright is a person who builds or repairs wheels. The word is the combination of "wheel" and the archaic word "wright", which comes from the Old English word "wryhta", meaning a worker or maker...
's work, than to the materials he used.
History
The spoked wheelWheel
A wheel is a device that allows heavy objects to be moved easily through rotating on an axle through its center, facilitating movement or transportation while supporting a load, or performing labor in machines. Common examples found in transport applications. A wheel, together with an axle,...
was invented to allow the construction of lighter and swifter vehicles. The earliest known examples are in the context of the Andronovo culture
Andronovo culture
The Andronovo culture, is a collection of similar local Bronze Age cultures that flourished ca. 21200–1400 BCE in western Siberia and the west Asiatic steppe. It is probably better termed an archaeological complex or archaeological horizon...
, dating to ca. 2000 BCE. Soon after this, horse cultures of the Caucasus
Caucasus
The Caucasus, also Caucas or Caucasia , is a geopolitical region at the border of Europe and Asia, and situated between the Black and the Caspian sea...
region used horse-drawn spoked-wheel war chariots 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
Minoan civilization
The Minoan civilization was a Bronze Age civilization that arose on the island of Crete and flourished from approximately the 27th century BC to the 15th century BC. It was rediscovered at the beginning of the 20th century through the work of the British archaeologist Arthur Evans...
dominance and consolidations led by pre-classical Sparta
Sparta
Sparta or Lacedaemon, was a prominent city-state in ancient Greece, situated on the banks of the River Eurotas in Laconia, in south-eastern Peloponnese. It emerged as a political entity around the 10th century BC, when the invading Dorians subjugated the local, non-Dorian population. From c...
and Athens
Athens
Athens , is the capital and largest city of Greece. Athens dominates the Attica region and is one of the world's oldest cities, as its recorded history spans around 3,400 years. Classical Athens was a powerful city-state...
. Celt
Celt
The Celts were a diverse group of tribal societies in Iron Age and Roman-era Europe who spoke Celtic languages.The earliest archaeological culture commonly accepted as Celtic, or rather Proto-Celtic, was the central European Hallstatt culture , named for the rich grave finds in Hallstatt, Austria....
ic chariots introduced an iron
Iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...
rim around the wheel in the 1st millennium BCE. The spoked wheel was in continued use without major modification until the 1870s, when wire wheels and rubber tire
Tire
A tire or tyre is a ring-shaped covering that fits around a wheel rim to protect it and enable better vehicle performance by providing a flexible cushion that absorbs shock while keeping the wheel in close contact with the ground...
s were invented.
Construction
Spokes can be made of wood, metal, or synthetic fiber depending on whether they will be in tensionTension (mechanics)
In physics, tension is the magnitude of the pulling force exerted by a string, cable, chain, or similar object on another object. It is the opposite of compression. As tension is the magnitude of a force, it is measured in newtons and is always measured parallel to the string on which it applies...
or compression
Physical compression
Physical compression is the result of the subjection of a material to compressive stress, which results in reduction of volume as compared to an uncompressed but otherwise identical state. The opposite of compression in a solid is tension. In any medium transmitting waves, the opposite of...
.
Compression spokes
The original type of spoked wheel with wooden spokes was used for horseHorse
The horse is one of two extant subspecies of Equus ferus, or the wild horse. It is a single-hooved mammal belonging to the taxonomic family Equidae. The horse has evolved over the past 45 to 55 million years from a small multi-toed creature into the large, single-toed animal of today...
drawn carriage
Carriage
A carriage is a wheeled vehicle for people, usually horse-drawn; litters and sedan chairs are excluded, since they are wheelless vehicles. The carriage is especially designed for private passenger use and for comfort or elegance, though some are also used to transport goods. It may be light,...
s and wagon
Wagon
A wagon is a heavy four-wheeled vehicle pulled by draught animals; it was formerly often called a wain, and if low and sideless may be called a dray, trolley or float....
s. In early motor cars, wooden spoked wheels of the artillery
Artillery wheel
The artillery wheel was developed for use on gun carriages when it was found that the lateral forces involved in horse artillery manoeuvres caused normally-constructed cart wheels to collapse. Rather than having its spokes mortised into a wooden nave , it has them fitted together then bolted into...
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
Radius
In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...
. 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 bicycleBicycle
A bicycle, also known as a bike, pushbike or cycle, is a human-powered, pedal-driven, single-track vehicle, having two wheels attached to a frame, one behind the other. A person who rides a bicycle is called a cyclist, or bicyclist....
s, heavy wooden-spoked wheels were replaced by lighter wheels with spokes made of tensioned, adjustable metal wires, called wire wheels
Wire wheels
The rims of wire wheels are connected to their hubs by wire spokes. Although these wires are generally stiffer than a typical wire rope, they function mechanically the same as tensioned flexible wires, keeping the rim true while supporting applied loads.Wire wheels are used on most bicycles and...
. These are also used in wheelchair
Wheelchair
A wheelchair is a chair with wheels, designed to be a replacement for walking. The device comes in variations where it is propelled by motors or by the seated occupant turning the rear wheels by hand. Often there are handles behind the seat for someone else to do the pushing...
s, motorcycle
Motorcycle
A motorcycle is a single-track, two-wheeled motor vehicle. Motorcycles vary considerably depending on the task for which they are designed, such as long distance travel, navigating congested urban traffic, cruising, sport and racing, or off-road conditions.Motorcycles are one of the most...
s, and automobile
Automobile
An automobile, autocar, motor car or car is a wheeled motor vehicle used for transporting passengers, which also carries its own engine or motor...
s.
Types
Some types of wheels have removable spokes which 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 steelStainless steel
In metallurgy, stainless steel, also known as inox steel or inox from French "inoxydable", is defined as a steel alloy with a minimum of 10.5 or 11% chromium content by mass....
, 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
KGF
KGF may refer to:*Keratinocyte Growth Factor*King George's Fields A UK set of 471 memorial playing fields and recreation grounds*Kolar Gold Fields*The IATA code for Sary-Arka Airport, Karaganda, Kazakhstan...
(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
Tioga
-Communities:In the United States:*Tioga, California, former name of Bennettville, California*Tioga, Louisiana*Tioga, New York, a town in Tioga County*Tioga County, New York, a county at the Pennsylvania border*Tioga, North Dakota, a city in Williams County...
'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) 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 tangentTangent
In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. More precisely, a straight line is said to be a tangent of a curve at a point on the curve if the line passes through the point on the curve and has slope where f...
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 disk brakes, which have torque transferred from the rim to the disk - in the opposite direction - (via the hub) when braking.
Wheelbuilding
Constructing a tension-spoked wheel from its constituent parts is called wheelbuildingWheelbuilding
Wheelbuilding is the art and science of assembling a wheel from its component rim, spokes, nipples and hub.-Goals:...
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
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 . The nipples will fit in holes in the rim, so that the head of the nipple is on the outermost part of the rim, while the other end of the 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
Sports car
A sports car is a small, usually two seat, two door automobile designed for high speed driving and maneuverability....
s up to the 1960s. Spoked wheels are still popular on motorcycles.
Spoke length
When building a bicycle wheelWheelbuilding
Wheelbuilding is the art and science of assembling a wheel from its component rim, spokes, nipples and hub.-Goals:...
, 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
where
- d = distance from the center of hub to flangeFlangeA flange is an external or internal ridge, or rim , for strength, as the flange of an iron beam such as an I-beam or a T-beam; or for attachment to another object, as the flange on the end of a pipe, steam cylinder, etc., or on the lens mount of a camera; or for a flange of a rail car or tram wheel...
, for example 30 mm, - r1 = spoke hole circle radius of the hub, for example 35 mm,
- r2 = nipple seat radius, equal to half the ERD (Effective Rim Diameter, 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,
- r3 = 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
Disc brake
The disc brake or disk brake is a device for slowing or stopping the rotation of a wheel while it is in motion.A brake disc is usually made of cast iron, but may in some cases be made of composites such as reinforced carbon–carbon or ceramic matrix composites. This is connected to the wheel and/or...
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 r3: 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
Wheelbuilding
Wheelbuilding is the art and science of assembling a wheel from its component rim, spokes, nipples and hub.-Goals:...
spoked wheels (zero crossings), the formula simplifies to
Derivation
The spoke length formula computes the length of the space diagonalSpace diagonal
In a rectangular box or a magic cube, the four space diagonals are the lines that go from a corner of the box or cube, through the center of the box or cube, to the opposite corner...
of an imaginary rectangular box
Cuboid
In geometry, a cuboid is a solid figure bounded by six faces, forming a convex polyhedron. There are two competing definitions of a cuboid in mathematical literature...
. 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 r2-r1cos(α) and a width of r1sin(a).
Equivalently, the law of cosines
Law of cosines
In trigonometry, the law of cosines relates the lengths of the sides of a plane triangle to the cosine of one of its angles. Using notation as in Fig...
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
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...
.
See also
- Bicycle wheelBicycle wheelA bicycle wheel is a wheel, most commonly a wire wheel, designed for bicycle. A pair is often called a wheelset, especially in the context of ready built "off the shelf" performance-oriented wheels....
- Spoke nippleSpoke nippleA 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 . The nipples will fit in holes in the rim, so that the head of the nipple is on the outermost part of the rim, while the other end of the nipple...
- Spoke wrenchSpoke wrenchA spoke wrench or spoke key is a small wrench or tool used to adjust the tension in the spokes of a bicycle wheel, sulky wheel, wheelchair wheel, or similar...
- SpokeshaveSpokeshaveA spokeshave is a tool used to shape and smooth wooden rods and shafts - often for use as wheel spokes, chair legs ,, self bows,and arrows. It can also be used to carve canoe paddles.-Modern:...
- WheelbuildingWheelbuildingWheelbuilding is the art and science of assembling a wheel from its component rim, spokes, nipples and hub.-Goals:...