Spoke

From Free net 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. Image:Wheel Iran.jpg 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.

1 Construction
2 Spoke Length
- 2.1 Derivation
3 See also
4 External links

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Construction

Spokes can be made of wood or metal. Some types of wheel 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.

The original type of spoked wheel with wooden spokes was used for horse drawn carriages. For use in bicycles, such wheels proved too heavy, so wheels with spokes made of tensioned, adjustable metal wires were introduced.

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.

The same thing happens in a pre-tensioned wire-spoked bicycle wheel. 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 "The Bicycle Wheel" by Jobst Brandt, http://www.astounding.org.uk/ian/wheel/index.html, 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 compressing (losing their pre-tension) as they roll under a loaded hub.

Wooden spokes are mounted radially while wire spokes are almost always mounted tangentially to the hub. Tangential spoking has several desireable effects:

The maximum load is being taken by two spokes at any time rather than by only one.
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 the hub.

Constructing a tension-spoked wheel from its constituent parts is called wheelbuilding and requires some experience for a strong and long-lasting end product.

In early motor cars (automobiles), wooden spoked wheels of the artillery type were normally used. With later development, the 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.

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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.

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 30mm,
r₁ = spoke hole circle radius of the hub, for example 35mm,
r₂ = nipple seat radius, equal to half the ERD of the rim, for example 301mm,
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^o 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^o/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

Image:Spoke-length.png

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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.

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