# Spoke

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
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 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 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.<ref name="Hansen">Template:Cite web</ref>

### Tension spokes

For use in bicycles, wooden-spoked wheels proved too heavy, so wheels with spokes made of tensioned, adjustable metal wires were introduced. 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. Since bicycle and wheelchair wheel spokes are only in tension, flexible and strong materials, such as synthetic fibers, are also used.<ref name="hand<ref name="spinergy">Template:Cite web</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.

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 by losing some of its pre-tension. Despite the common misconception that a bicycle wheel "hangs" from its upper spokes, the upper spokes show no significant change in tension.

For explanations, computer models, and tests confirming this odd behavior, see <A HREF="http://www.astounding.org.uk/ian/wheel/index.html">The Bicycle Wheel</A> 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 but are more often mounted tangentially to the hub. Tangential spoking has several desirable effects:

• It counteracts the tendency of a driven hub to turn in relation to the rim, which can damage the spokes.
• The pull of the spokes at the hub is tangential rather than radial. This permits a lighter design of hub, because the spoke heads cannot easily shear out of the flange at this angle.

#### Wheelbuilding

Constructing a tension-spoked wheel from its constituent parts is called wheelbuilding and requires some experience 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

$l = \sqrt{ a^2 + {r_1}^2 + {r_2}^2 - 2 \, r_1 r_2 \cos(\alpha)}$

where

• a = distance from the central point to the flange, 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 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

$l = \sqrt{a^2 + (r_2 - r_1)^2} .$
Image:Spoke-length.png
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 r2-r1cos(α) and a width of r1sin(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.

<references/>