Spoke
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2008-07-06T17:45:11Z
BOT-Superzerocool
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robot Adding: [[es:Radio (rueda)]]
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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.
[[Image:Wheel Iran.jpg|thumb|right|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]].]]
[[Image:Cartwheel and axle assembly.jpg|thumb|right|The remains of a pair of [[cartwheel]]s with metal axle assembly.]]
[[Image:Ox wagon at Aliwal North.jpg|thumb|right|An [[Ox-wagon]] in [[Aliwal North]], [[Eastern Cape]]. Note the three missing spokes and the metal tyre.]]
[[Image:Wooden Spokes.JPG|right|thumb|Wooden spoke wheel with metal rim from antique truck on display in [[Underground Atlanta]].]]
[[Image:Bicycle wheel.jpg|right|thumb|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.
== Construction ==
Spokes can be made of wood, metal, or synthetic fiber depending on whether they will be in [[Tension (mechanics)|tension]] or [[Physical compression|compression]].
===Compression spokes===
The original type of spoked wheel with wooden spokes was used for [[horse]] drawn [[carriage]]s and [[wagon]]s. In early motor cars, wooden spoked wheels of the [[Artillery wheel|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 [[Radius|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.<ref name="Hansen">{{cite web
| url = http://www.hansenwheel.com/Wagon%20Wheels.htm
| accessdate = 2006-08-22
| title = Hansen Wheel and Wagon Shop
| year = 2006
}}</ref>
===Tension spokes===
For use in [[bicycle]]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.
====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 [[kgf]] (c. 500 [[pounds-force]] or 2,200 [[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.<ref name="hand<ref name="spinergy">{{cite web
| title = PBO Spoke Technology
| year = 2006
| url = http://www.spinergy.com/Bicycle/tech_specialFeature_PBO.html
| accessdate = 2006-08-21
}}</ref> 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.
====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 [http://www.astounding.org.uk/ian/wheel/index.html 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 [[tangent]]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 (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 (bicycle part)|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 car]]s up to the 1960s. Spoked wheels are still popular on motorcycles.
== Spoke length ==
When [[Wheelbuilding|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
:<math>l = \sqrt{ a^2 + {r_1}^2 + {r_2}^2 - 2 \, r_1 r_2 \cos(\alpha)} </math>
where
* ''a'' = distance from the central point to the [[flange]], for example 30 mm,
* ''r''<sub>1</sub> = spoke hole circle radius of the hub, for example 35 mm,
* ''r''<sub>2</sub> = nipple seat radius, equal to half the [[ISO_5775#ERD_-_European_Rim_Dimensions|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 [[Wheelbuilding|radially]] spoked wheels, the formula simplifies to
:<math>l = \sqrt{a^2 + (r_2 - r_1)^2} .</math>
[[Image:spoke-length.png|thumb|300px|right|A flat view of a crossed wheel with one spoke visible]]
=== Derivation ===
The spoke length formula computes the length of the [[space diagonal]] [http://mathworld.wolfram.com/SpaceDiagonal.html] of an imaginary [[cuboid|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''<sub>2</sub>-''r''<sub>1</sub>cos(''α'') and a width of ''r''<sub>1</sub>sin(''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 ==
<div class="references-small">
<references/>
</div>
==External links==
{{Wiktionary}}
These pages are in German:
*[http://www.nabendynamo.de/mont28.htm Hub dynamo assembly instructions with spoke length formula and a nice diagram]
*[http://www.rst.mp-all.de/splaenge.htm Online spoke length calculator, uses slightly different measures than the above formula]
[[Category:Bicycle parts]]
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[[es:Radio (rueda)]]
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