# Talk:Spoke

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## Other uses of spokes

Incidentally... old bent bicycle spokes are sometimes kept in toolkits

• They are useful for unblocking plugs etc.
• They may be used as lockpicks.
• A cardboard splash guard inserted in pletcher rack can be prevented from sagging by sticking in a couple of spokes, which shouldn't be too bent. The cardboard must extend to the end of the rear wheel to keep the seat of your pants dry and the mud stripe off your back. Metarhyme 23:47, 30 December 2006 (UTC)

## How to compute the spoke length formula using a calculator

The spoke length formula is only as accurate as your fingers are at data input and manipulation. Switch the calculator to scientific mode: View -> Scientific. Use a pencil with an eraser to write down the hub's spoke hole diameter and the ERD (effective rim diameter, or the circle made by the ends of the spokes in a built wheel). Write down the flange from center distance (a) as well. Half of the hub diameter is radius one and half of the ERD is radius two, write these down, too. Input the degrees according to the cross number and the number of spokes, then get the cosine. Multiply that by 2, by radius one and by radius two. Put that in memory and clear the display. Input radius one -> square -> plus -> input radius two -> square -> plus -> input a -> square -> equals; then subtract -> memory recall -> equals. Then to get that figure's square root, put a tick in the [ ] Inv box and x^2 should give you a non-ridiculous spoke length. Run it several times to be sure that you did not make a mistake.

Great directions! Indeed, it took me two or three tries with the calculator to get the right, non-ridiculous result. Erm, why do you need an eraser on the pencil? --RainerBlome 22:53, 23 December 2005 (UTC)

• The eraser is to impeach and convict offensive pencilings prior to replacing them with pencilings that better reflect truth. Metarhyme 21:42, 25 December 2005 (UTC)

This statement: "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."

appears to contradict this statement: "Tangential spoking has several desirable effects: The maximum load is being taken by two spokes at any time rather than by only one."

Is there a reference for either one? The Bicycle wheel#Reaction to load seems to confirm the first statement. Without a reference, the second one, the 'desirable effect' one should go. -AndrewDressel 02:08, 22 August 2006 (UTC)

Okay. Out it comes. -AndrewDressel 01:49, 23 August 2006 (UTC)

## history of spokes

Can we get a section (or at least something) on the development/history of spokes? When did people stop using solid wheels and convert over to spokes and why? That sort of thing. Reinventing the wheel and such. Ornen (talk) 03:26, 1 September 2008 (UTC)

## Tioga

It was actually Sugino who made the disc and sold them under the Sugino brand, Tioga just resold them under their Tioga brand name with mass marketing. Here is the patent http://www.google.com/patents?id=TkEhAAAAEBAJ&pg=PA3&dq=United+States+Patent+5064250#v=onepage&q=United%20States%20Patent%205064250&f=false

--Bensimmo (talk) 09:47, 30 October 2009 (UTC)

## Calculation

Does anyone have any first hand experience with this equation (the one now on the spoke article page, used to determine length of a bicycle wheel.):

${\displaystyle l={\sqrt {a^{2}+{r_{1}}^{2}+{r_{2}}^{2}-2\,r_{1}r_{2}\cos(\alpha )}}}$

I mean has anyone built a bicycle wheel after choosing spokes based on it's output. I've been messing around with it for a while now, and it has been consistently giving me 10.7mm longer lengths than my usual method (an excel file from sheldonbrown.com) when I changed the ERD but leaving the other variables the same. I did it for 6 different ERDs and all of them came out 10.7mm longer. Some random googleing brought me this, that does produce the same results as the equation we've got posted here. Could very well be that I'm overlooking something obvious, but thought I'd look for input. --Keithonearth (talk) 07:19, 13 December 2009 (UTC)

Well, I have to admit that I did make a stupid mistake, and that's the main reason that the numbers were coming out different. I had the calculator set to radians. oops. So now the numbers are very close to the excel file's output, but still a mm or two off. I'd be happier if they were the same, or I understood the reason for the difference, but I guess the numbers the equation is giving us could be right. I'll have to build a wheel or two from the math. --Keithonearth (talk) 21:39, 16 January 2010 (UTC)
If a wheel is well tensioned, there will be both elastic and inelastic strain - the formula doesn't provide for this stretching, which is slight. At the moment, Sapin is willing to point, under their Calculate by hand heading, to the formula on the article page - a quality endorsement. Having the end of the spoke stop exactly where you thought it would in the nipple can be accomplished, but nudging the formula needs figuring Kilograms of force exerted over effective length of diameter of spoke. Straight guage 2 mm spokes have a radius of one, which simplifies exponentiation in the modulus of elasticity of steel formula. Skipping that, you can guess that the length will be shorter than the ideal mathematical distance, but by exactly how much depends. - 173.24.245.10 (talk) 07:55, 8 April 2012 (UTC) (Sapin replaced their spoke calculator page, removing the calculate by hand reference.) - 173.24.245.10 (talk) 20:00, 12 August 2012 (UTC)

It is essential to get correct dimensions of rim and hub to get a good estimate of spoke length. Here is an aid to trusting your own measurements: measure rim and hub A 2 mm diameter spoke will stretch very little but stretch is a factor with strained skinny spokes. The modulus of elasticity of steel is 21,000 Kilograms per square millimeter; strain equals tension divided by elasticity. You want to divide the stress (kgf) to be applied to the spoke by the elasticity of the spoke. The elasticity is π × spoke radius mm^2 × 21,000 ÷ effective length in mm. - 173.24.113.190 (talk) 08:01, 30 November 2018 (UTC)

## Do hubs hang from the wheel?

wire wheel

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The physics is a bit too complex to me, but it seems that it's all a matter of point of view. It's the reduction of tention on the lower spokes that allows the (almost unchanged) tention on the upper spokes to bear the load. I imagine I am over simplifying this. In any case the article seems to be very unclear on the matter, and I would love to see it improved, but I am unsure if my understanding is accurate.--Keithonearth (talk) 03:30, 28 December 2008 (UTC)

Bicycle wheel has a couple of concise sentences with plenty of references. -AndrewDressel (talk) 17:58, 28 December 2008 (UTC)
I don't think the two articles should be merged, but I would like to see just one copy of this topic with all the best references. Arguably, it belongs here, in the more general article, but all the sources are specific to bicycle wheels. I'm tempted to suggest that both these aritlce link to a new, specific article, but I don't think there is enough material to warrent a stand-alone article on the subject. Anyone have a preference or an even better idea? -AndrewDressel (talk) 14:27, 29 December 2008 (UTC)
The current consensus among sources seems to be that under load, the few spokes at the bottom reduce tension and the rest only slightly increase tension. Jobst Brandt and Ian somebody interprets this to mean that the hub stands on the few spokes directly below it. Tom Fine interprets this to mean that the hub hangs from the rim. It seems to me that we should state something like the first sentence as fact with multiple references, and then quote specific authors semantic interpretations as exactly that. -AndrewDressel (talk) 14:49, 29 December 2008 (UTC)
I'm not sure where the best place to put the references/discution would be either, I kind of think not that many people would be reading the Wire wheels page, and way more will be reading the bicycle wheel page. Would it be possible to keep the discusion brief enough (Like two Sentences) that redundancy wouldn't be too tragic? Putting that aside for now, the way you phrase it above, seems to me to be by far the best I've heard so far, and is way better than on the article page.--Keithonearth (talk) 19:44, 29 December 2008 (UTC)
Having seen some flame wars on the the subject, I'd suggest stating something like the first sentence as the classic or conventional view, then that some using FEA argue the contrary, and finally that the argument hinges (buckles?) on whether a reduction in tension implies structural support. Nice work on the subheadings, btw. NebY (talk) 09:00, 30 December 2008 (UTC)
To say the tension changes as a fact, then the two interpretation (as you say Andrew) should avoid an edit war, no? How about: "Under load, the few spokes at the bottom reduce tension and the rest only slightly increase tension. This has been interprated as either meaning that the hub is supported by the spokes under it, (ref,ref) or that the hub "hangs" from the rim (ref). I think that fits with NebY's suggestion too. The main thing as far as I'm concerned it to remove the unattributed quote. --Keithonearth (talk) 20:10, 30 December 2008 (UTC)
Done. Thanks for your help. -AndrewDressel (talk) 12:48, 31 December 2008 (UTC)
Thank you. (didn't see the change till just now) Great job!--Keithonearth (talk) 04:21, 4 January 2009 (UTC)
I do not want to start an edit war, but there is less controversy about this than you seem to imply by your attempt at even-handedness. You might consider the following thought experiment when deciding which viewpoint to prefer. If the hub hangs from the upper spokes, then you might expect that decreasing the tension in the bottom spokes to zero would not matter much. --AJim (talk) 00:53, 9 September 2010 (UTC)
Someone might expect that, but they would be incorrect. -AndrewDressel (talk) 15:08, 24 June 2012 (UTC)
This also suggests that you ought to be able to set the spoke tension really low. --AJim (talk) 00:53, 9 September 2010 (UTC)
It might suggest that to someone, but they would also incorrect. -AndrewDressel (talk) 15:08, 24 June 2012 (UTC)
From the hanging point of view, you should need only enough combined tension in the upper spokes to support the load. --AJim (talk) 00:53, 9 September 2010 (UTC)
I see nothing in the "hanging point of view" that limits spoke tension in this way. -AndrewDressel (talk) 15:08, 24 June 2012 (UTC)
I believe there is good evidence in the references that the bottom spokes must stay in tension or the wheel will fail. Brandt devotes the first part of his book to explaining the idea that the bottom spokes support the load; see pages 6-32. Consider this quote from p 28: "Wheel Collapse ... a bicycle landing from a sufficiently high jump, could untension its bottom spokes on impact and leave its rim laterally unsupported. At this moment the wheel is unstable and will collapse to the side." He also says earlier, on p 10, "Of course the wheel is not supported by the bottom spokes only. Without the rest of the spokes, the bottom ones would have no tension. Standing, in this case, means that the spokes at the bottom are the ones that change stress; they are being shortened and respond structurally as rigid columns. They are rigid as long as they remain tensioned (my emphasis)." --AJim (talk) 00:53, 9 September 2010 (UTC)
The issue is exactly his assertion that the bottom spokes "respond structurally as rigid columns". They simply do not, by any definition of "rigid column" that I can find. They are not in compression unless the wheel fails, and the way that most spoke nipples simply press towards the hub against a hole in the rim, or Euler's buckling criteria, depending on how one prefers to look at it, prevents them from ever being in more than a tiny fraction of the compressive force that would be required to support the loads that most wire wheels support. -AndrewDressel (talk) 15:08, 24 June 2012 (UTC)
Most people would agree, based on their own experience, that a wire will not behave as a rigid column when in compression. --AJim (talk) 00:53, 9 September 2010 (UTC)
I don't believe I follow your point here. In the previous sentence, you appear to be supporting Brandt's position, but you seem to be opposing it in this sentence. -AndrewDressel (talk) 15:08, 24 June 2012 (UTC)
I really think you could have a more enlightening discussion of this subject in the article. --AJim (talk) 00:53, 9 September 2010 (UTC)
I believe that citing sources on both sides of the argument and trying to explain their positions is about enlightened as this is going to get. I don't believe there is any controversy about what actually happens as wire wheels support a load. Instead, the controversy lies simply in what words we use to describe it. -AndrewDressel (talk) 15:08, 24 June 2012 (UTC)

## Forester

I've taken out the addition, provided below, with the edit comment that "the reference is fine, but we don't need the details."

Forester demonstrated this by direct measurement of change in spoke length as the wheel rotated under load. Spoke length decreased between the 5 o'clock and 7 o'clock positions with a maximum decrease of about 0.004 inch at 6 o'clock. The reduction in downward pull on the hub, calculated from the dimensions of the spokes, closely equaled the load carried.

What I mean is that the testing methodologies of none of the other sources are discusses. Readers looking for such details can check the sources directly. Also, details such as the investigator's name and the measured displacement without the total spoke length or other details necessary to interpret the number seem out of place. -AndrewDressel (talk) 03:10, 5 July 2010 (UTC)

From the Analysis for design of spoked bicycle wheels article, I think that the maximum load is around 490N (=?kg) (more load is possible by increasing the spokes. Also, from what I read at wikipedia, the load can be increased by reducing the wheel size. Having some formula's for this would be useful to integrate to the article.

Generally, the maximum load for the tyre is far less, around 145kg per tyre (or 290 kg for a person sitting on a bicycle since it has 2 wheels, see http://www.bikeforums.net/archive/index.php/t-320799.html ) 91.182.215.56 (talk) 09:37, 30 August 2010 (UTC)

That would be a little hard to come by. The maximum load will be a function of the rim material and cross section; the spoke material, size, and number; and the wheel size. Good luck finding a formula for that. -AndrewDressel (talk) 14:18, 30 August 2010 (UTC)

## Number of spokes

The number of spokes in a wheel (or the size of the angle between one spoke and another) affects the deformation of the wheel, and is a trade-off between wheel size, total weight, construction complexity and rigidity of the materials used.

Is this only about compression spokes, the section into which the sentence was inserted, or all spokes. -AndrewDressel (talk) 16:18, 13 September 2010 (UTC)

Kick scooter wheels with fewer spokes will give a "bumpier" ride than ones with many spokes.

Is this true of all spoke-wheeled vehicles, or just kick scooters. If the latter, why? Either way, why is it so, and can we find a source? -AndrewDressel (talk) 16:18, 13 September 2010 (UTC)

The calculation for the length of radial spokes:

${\displaystyle l={\sqrt {a^{2}+(r_{2}-r_{1})^{2}}}}$

seemed to be incorrect, as a, the angle between the flange hole and the rim hole, is by definition 0 for radial spokes; this equation is not dimensionally consistent anyway. Based on trigonometry and comparison to the equation for crossed spokes, it should be:

${\displaystyle l={\sqrt {d^{2}+(r_{2}-r_{1})^{2}}}}$

where d is the center-to-flange distance. I changed it, but forgot to leave an edit comment (and not logged in!), so here's my explanation.

Also, based on definition of spoke length, r3 should be in the radial wheel version also.

${\displaystyle l={\sqrt {d^{2}+(r_{2}-r_{1})^{2}}}-r_{3}}$

Withlyn (talk) 21:46, 8 June 2011 (UTC)

Both correct and taken care of. --RainerBlome (talk) 22:34, 15 October 2018 (UTC)

## usual spoke diameters table error?

I don't believe the "section areas" are correct.

The formula for the area of a circle is pi * (radius^2). The table has the "section area" as the square of the diameter.

For example, a diameter of 2mm is listed as having a "section area" of 4mm^2. The radius of 2mm diameter is 1mm. pi*(1^2) is 3.14mm^2 and some change.

Perhaps a spoke pro who knows math can verify that "section area" actually means the "area of the cross section" of the spoke instead of being an industry idiom. Shiropinkus (talk) 07:45, 7 June 2015 (UTC)

## Spoked wheel?

Typing "spoked wheel" into Wikipedia only brings you to a page about some Indian author, and the only way to find this page is by searching for "spoke". That seems problematic to me. Even if you assume "spoke" and "spoked wheel" are parts of each other, there should at least be a redirect to this page or something. AnnaGoFast (talk) 07:44, 19 January 2018 (UTC)

Done: spoked wheel. -AndrewDressel (talk) 12:12, 20 January 2018 (UTC)