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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 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. Eventually, the term spoke was more commonly applied to the finished product of the wheelwright's work, than to the materials he used.
Spokes can be made of wood, metal, or synthetic fiber depending on whether they will be in tension or compression.
The original type of spoked wheel with wooden spokes was used for horse drawn carriages and wagons. 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.[1]
For use in bicycles, 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 wheelchairs, motorcycles, and automobiles.
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 steel, while cheaper bicycles may use galvanized (also called "rustless") or chrome plated spokes. While a good quality spoke is capable of supporting about 225 kg (c. 500 pounds) 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.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.
Pre-tensioned wire-spoked wheel react similarly to a load. The load on the hub causes the wheel rim to flatten slightly against the ground as the lowermost pre-tensioned spoke shortens and compresses, losing some of its pre-tension. Perhaps surprisingly, the upper spokes show no significant change in tension.
For explanations, computer models, and tests confirming this odd behavior, see The Bicycle Wheel by Jobst Brandt, and Figure 10 in http://www.duke.edu/~hpgavin/papers/HPGavin-Wheel-Paper.pdf, which all show the lower spokes of pre-tensioned bicycle wheels losing their pre-tension as they roll under a loaded hub.
Wire spokes can be radial to the hub but are more often mounted tangentially 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 (via the hub) when braking.
Constructing a tension-spoked wheel from its constituent parts is called wheelbuilding 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 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 drive gears: freewheel or cassette.
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 cars up to the 1960s. Spoked wheels are still popular on motorcycles.
When building a bicycle wheel, the spokes must have the right length. If the spokes are too short, they can not be tightened. If they are too long they will touch the rim tape, possibly puncturing the tire.
For wheels with crossed spokes (which are the norm), the desired spoke length is
:
where
★ ''a'' = distance from the central point to the flange, for example 30 mm,
★ ''r''1 = spoke hole circle radius of the hub, for example 35 mm,
★ ''r''2 = nipple seat radius, equal to half the ERD of the rim, for example 301 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
★ ''α'' = 360° ''k''/''m''.
Regarding ''a'': 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 ''a'' is different for the left and right sides.
''α'' is the angle between the radius through the hub hole and the radius through the corresponding spoke hole. The angle between hub hole radii is 360°/''m'' (for evenly spaced holes). For each crossing, one spoke hole further down the hub is used, multiplying the angle by the number of crossings ''k''. For example, a 32 spoke wheel has 16 spokes per side, 360° divided by 16 equals 22.5°. Multiply 22.5° (one cross) by the number of crossings to get the angle - if 3-cross, the 32 spoke wheel has an angle ''α'' of 67.5 degrees.
For radially spoked wheels, the formula simplifies to
:
The spoke length formula computes the length of the space diagonal [1] 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 ''a'', a height of ''r''2-''r''1cos(''α'') and a width of ''r''1sin(''α'').
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.
★ Bicycle wheel
★ Spoke nipple
★ Spoke wrench
★ Spokeshave
★ Wheelbuilding
1. Hansen Wheel and Wagon Shop
2. PBO Spoke Technology
These pages are in German:
★ Hub dynamo assembly instructions with spoke length formula and a nice diagram
★ Online spoke length calculator, uses slightly different measures than the above formula
A spoked wheel on display at The National Museum of Iran, in Tehran. The wheel is dated to the late 2nd millennium BC and was excavated at Choqa Zanbil.
The remains of a pair of cartwheels with metal axle assembly.
Wooden spoke wheel with metal rim from antique truck on display in Underground Atlanta.
Metal spoke wheel from a bicycle.
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. Eventually, the term spoke was more commonly applied to the finished product of the wheelwright's work, than to the materials he used.
| Contents |
| Construction |
| Compression spokes |
| Tension spokes |
| Types |
| Reaction to load |
| Tangential lacing |
| Wheelbuilding |
| Spoke length |
| Calculation |
| Derivation |
| See also |
| References |
| External links |
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 drawn carriages and wagons. 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.[1]
Tension spokes
For use in bicycles, 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 wheelchairs, motorcycles, and automobiles.
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 steel, while cheaper bicycles may use galvanized (also called "rustless") or chrome plated spokes. While a good quality spoke is capable of supporting about 225 kg (c. 500 pounds) 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.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.
Reaction to load
Pre-tensioned wire-spoked wheel react similarly to a load. The load on the hub causes the wheel rim to flatten slightly against the ground as the lowermost pre-tensioned spoke shortens and compresses, losing some of its pre-tension. Perhaps surprisingly, the upper spokes show no significant change in tension.
For explanations, computer models, and tests confirming this odd behavior, see The Bicycle Wheel by Jobst Brandt, and Figure 10 in http://www.duke.edu/~hpgavin/papers/HPGavin-Wheel-Paper.pdf, which all show the lower spokes of pre-tensioned bicycle wheels losing their pre-tension as they roll under a loaded hub.
Tangential lacing
Wire spokes can be radial to the hub but are more often mounted tangentially 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 (via the hub) when braking.
Wheelbuilding
Constructing a tension-spoked wheel from its constituent parts is called wheelbuilding 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 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 drive gears: freewheel or cassette.
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 cars up to the 1960s. Spoked wheels are still popular on motorcycles.
Spoke length
When building a bicycle wheel, the spokes must have the right length. If the spokes are too short, they can not be tightened. If they are too long they will touch the rim tape, possibly puncturing the tire.
Calculation
For wheels with crossed spokes (which are the norm), the desired spoke length is
:
where
★ ''a'' = distance from the central point to the flange, for example 30 mm,
★ ''r''1 = spoke hole circle radius of the hub, for example 35 mm,
★ ''r''2 = nipple seat radius, equal to half the ERD of the rim, for example 301 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
★ ''α'' = 360° ''k''/''m''.
Regarding ''a'': 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 ''a'' is different for the left and right sides.
''α'' is the angle between the radius through the hub hole and the radius through the corresponding spoke hole. The angle between hub hole radii is 360°/''m'' (for evenly spaced holes). For each crossing, one spoke hole further down the hub is used, multiplying the angle by the number of crossings ''k''. For example, a 32 spoke wheel has 16 spokes per side, 360° divided by 16 equals 22.5°. Multiply 22.5° (one cross) by the number of crossings to get the angle - if 3-cross, the 32 spoke wheel has an angle ''α'' of 67.5 degrees.
For radially spoked wheels, the formula simplifies to
:
A flat view of a crossed wheel with one spoke visible
Derivation
The spoke length formula computes the length of the space diagonal [1] 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 ''a'', a height of ''r''2-''r''1cos(''α'') and a width of ''r''1sin(''α'').
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
★ Spoke nipple
★ Spoke wrench
★ Spokeshave
★ Wheelbuilding
References
1. Hansen Wheel and Wagon Shop
2. PBO Spoke Technology
External links
These pages are in German:
★ Hub dynamo assembly instructions with spoke length formula and a nice diagram
★ Online spoke length calculator, uses slightly different measures than the above formula
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