SPOKE LENGTH FORMULA BASED ON HUB AND RIM MEASUREMENTS, AND OTHER WHEEL LACING INFORMATION |
This Web site covers the formula for calculating spoke length based on the measurements of the hub and rim. While primarily for experienced wheel builders that are interested in the formula for calculating spoke length, I have put information and a link page on this site that should be able to assist all interested in wheel building and cycling in general.At the bottom of this page are the links to the related pages of this site. Included is a WHEEL BUILDING page that has links to the two best wheel building sites I found on the Internet that could help out an inexperienced builder, and a LINKS page that has links to other Web sites that are cycling related and can provide anyone with information about bicycles and cycling.
In order to be able to use the spoke length formula, you will need to be able to take measurements in mm, preferably with a metric tape measure, and you will need a calculator that can at least do square roots. If you only have an English tape measure, the numbers can be converted to millimeters. If you do this you need to be real careful, or the numbers could be too far off to work well. A scientific calculator that can handle the cosine (COS) function would also be handy, but if you do not have one with the COS function I have included a page that has the COS figures for the most common hubs, labeled COSINE. A page explaining the measurements that are needed is included, it is very important that the measurements are done properly for the formula to be accurate, this page is labeled MEASURE. It is recommended that you look over this page before playing around with the formula to see what the measurements entail and what things to check for before starting. This page also tells how to compensate for rear rims that have offset and how to check for rims that have a large amount of spoke hole stagger from the center line that can affect the spoke length values. Some wide mountain bike rims I built into wheels had spoke hole stagger that affected the spoke length.
This site was designed around bicycle wheels, but the information applies to any laced wheel. Tricycle, wheelchair, and motorcycle wheels all can use this formula to determine spoke length, mathematically there is no difference. It can also be used to determine spoke length for wheels for bike trailers, motorcycle sidecars and baby joggers. Any wheel built with spokes can have the spoke length calculated with this formula.
This site was initially constructed to help someone who is building a wheel using vintage or unusual components that aren't listed in spoke length tables. It can also help someone that wishes to calculate the length needed for building non typical wheels, for instance bicycle wheels laced with the Crow's Foot pattern that isn't listed in most spoke length calculators, or wheels for a wheelchair that have the rims off center. Or it can help someone who just wants to calculate spoke length so they don't have to ask down at a bike shop and rely on someone else every time they want to build a new wheel.
I have included a page on lacing techniques that will cover rim off center lacing, radial lacing, Crow's Foot lacing, and a new strong rear wheel lacing that I have recently tried and really like. This page also has other lacing and spoke length information that should help someone who wishes to design their own lacing pattern, or try something out that they have heard about but don't know how to figure out the spoke lengths. Spoke length tolerance and corrections for some problems are also covered. This is a good page for anyone interested in building spoked wheels and I suggest you check it out for information and ideas. This page is labeled LACING.
The formula works off of trigonometry and the law that for a right triangle, the length of the longest side squared equals the sum of the squares of the two shorter sides. It also uses the cosine factor for right triangles, which relates to the number of spokes in the wheel and the lacing patern. I have included a page that explains all of this in more detail, labeled TRIG. In addition to explaining how trigonometry applies to the formula, this page explains the basic physics of a spoked wheel. That is how the major weight bearing and road shock forces affect and act on a spoked wheel.
For spokes laced radially from the hub, the formula is simple because all you need to know is the radius at the rim, the radius at the hub and the hub flange's offset from the hubs center. For cross laced patterns, the formula is more complex because in addition to the above, you also need to figure in the distances of both the horizontal and vertical displacement of the spoke at the hub, which is related to where the spoke would go if it was laced radially. Here are the two formulas:
CROSS LACED SPOKE FORMULA |
RADIAL SPOKE FORMULA |
What the abbreviations stand for is:
SL = Spoke Length
RRSP = Rim Radius plus Spoke Penetration
HSR = Hub Spoke Radius
SAA = Spoke Anchor Angle
HFO = Hub Flange Offset
What they mean is:The SL is the calculated value of the spoke length you are looking for.
The RRSP is the radius of the inside of the rim plus the penetration of the spoke into the rim.
The HSR is the radius of the spoke holes on the hub. The radius needed is not of the centers of the holes but of their outer most edge.
The SAA is the angle of the spoke hole in the hub that the spoke will connect to, in relation to the spoke hole in the hub that is directly in line with the spoke hole in the rim where the spoke connects. It is dependent upon the lacing pattern. Radial wheels don't have any crosses so the anchor spoke hole of the hub is directly in line with this hole in the rim and the SAA is 0.
The HFO is the distance from the hubs flanges to the hubs center. On most front, or other non dished wheels, this is simply the distance between the flanges divided by two. For wheels with dish like most rear wheels, or for a wheel you would like to build off center, this is different for each side of the hub.
The information on how to take these measurements, and any related calculations, are on the MEASURE page. It is important that the measurements used to calculate these values are taken off the hub and rim properly for the formula to work.
I have used five non-standard fonts in creation of this site. If you do not have these fonts, these pages will not look exactly like the way I created them (they will still be readable, just in the wrong font). While this is just a minor detail, I have these five font's available to you. Most Windows, 98 or better, should have these fonts. I am not sure if they work on an Apple, I don't have access to an Apple computer to test them out. If the following examples don't look different than the "STANDARD" font at the top, you don't have that font. If you select "DOWNLOAD" below the fonts, you will download a Zip file. If you don't have PKZip, I included a link access to PKWare below the DOWNLOAD select. After you get the font's extracted, place them in the "Fonts" directory. Here are the five fonts:STANDARD: The Quick Lazy FoxSelect here to download the fonts.
ALGERIAN: The Quick Lazy Fox
ARIAL: The Quick Lazy Fox
BOOKMAN: The Quick Lazy Fox
COMIC: The Quick Lazy Fox
VERDANA: The Quick Lazy Fox
This site was created and is maintained by Robert Torre. The Bicycle was the apex of mans development of individual transportation. Cars rely on many components and concepts originally designed for bicycles, like rubber tires, and metal chains (all timing chains are a development of the bike chain). The first cars were essentially large motorized tricycles, and used drive chains. Drive shafts were also developed for bikes in the 1800's, before they were used in cars. Bikes outsell cars 3 to 1 around the world, and move far more people every day.If you have any problems, comments, questions or suggestions, you can e-mail me at rtower@internetcds.com.
Thanks to the few trillion electrons
that donated their time and energy.
Last updated 7-1-2001.