77:
89:
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343:) 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. Metal spokes can also be ovalized or bladed to reduce aerodynamic drag, and butted (double or even triple) to reduce weight while maintaining strength.
1231:, in Antiquity, Vol 94, Issue 374, April 2020, p. 367: "...The 12 calibrated radiocarbon dates belonging to the Sintashta horizon range between 2050 and 1760 cal BC (at 95.4% confidence; Epimakhov & Krause 2013: 137). These dates correlate well with the seven AMS-sampled Sintashta graves in the associated KA-5cemetery, which date to 2040–1730 cal BC (95.4% confidence...)".
121:
109:
1086:
801:
is the angle between (1) the radius to a nipple hole in the rim to which a spoke is attached, and, (2) the radius to the flange hole holding the spoke. The spoke crosses either 1, 2, or 3 oppositely pointing spokes depending on the lacing design. On the flange, the angle between the radii of adjacent
449:
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 hub-mounted brakes such as disk or band brakes, which transfer torque from the rim
1228:
346:
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
837:: The size of the spoke holes in the flange does not matter for the needed spoke length. This term removes the effect of the hole size. Since the holes are usually small (just over 2 mm in diameter), the effect is small and in practice matters little.
466:. The other end is commonly peened into a disk or uncommonly 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
57:
650:
473:
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
264:
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.
1106:. 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
318:
Some types of wheels have removable spokes that can be replaced individually if they break or bend. These include bicycle and wheelchair wheels. High quality bicycles with conventional wheels use spokes of
806:(for equally spaced holes). For each spoke crossed, the hub is rotated with reference to the rim one "angle between adjacent flange holes". Thus, multiplying the "angle between adjacent flange holes" by
272:. 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.
1080:
690:= half of effective Rim Diameter (ERD), or the diameter the ends of the spokes make in a built wheel (see 'Discussion' attached to this article for explanation) of the rim, for example 301 mm,
986:
498:, the spokes must have the correct length, otherwise there may not be enough threads engaged, producing a weaker wheel, or they may protrude through the rim and possibly puncture the inner tube.
351:) 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.
203:/proto-historic period (1800-1200 BCE) paintings in various regions of India such as Chibbar Nulla, Chhatur Bhoj Nath Nulla, Kathotia, etc. depict the usage of chariots with spoked wheels.
816:. For example, a 32 spoke wheel has 16 spokes per side, 360° divided by 16 equals 22.5°. Multiply 22.5° ("angle between adjacent flange holes") by the number of crossings to get the angle
779:: 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
462:
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
1146:
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
519:
136:(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. A
1796:
1465:
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For bicycle spokes, the spoke length is defined from the flange seat to the thread tip. For spokes with bent ends, the nominal spoke length does
160:
was invented to allow the construction of lighter and swifter vehicles. The earliest physical evidence for spoked wheels were found in the
1310:
1242:
1393:
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rim around the wheel in the 1st millennium BCE. The spoked wheel was in continued use without major modification until the 1870s, when
1811:
1293:
1346:
1229:"Chariots in the Eurasian Steppe: a Bayesian approach to the emergence of horse-drawn transport in the earlysecond millennium BC"
993:
1368:
893:
290:, heavy wooden-spoked wheels were replaced by lighter wheels with spokes made of tensioned, adjustable metal wires, called
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originally developed for this purpose. Eventually, the term spoke was more commonly applied to the finished product of the
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Online spoke length calculator (German), uses slightly different measures than the above formula
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Spokes can be made of wood, metal, or synthetic fiber depending on whether they will be in
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645:{\displaystyle l={\sqrt {d^{2}+{r_{1}}^{2}+{r_{2}}^{2}-2\,r_{1}r_{2}\cos(a)}}-r_{3}}
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For wheels with crossed spokes (which are the norm), the desired spoke length is
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1203:
Neumayer 1800-1200 BCE; Celeste Paxton 2300-1000 BCE). See
Bradshaw Foundation,
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Constructing a tension-spoked wheel from its constituent parts is called
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173:
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93:
68:. The wheel is dated to the late 2nd millennium BCE and was excavated at
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1272:
Voices from the past: Researcher explores a mystery across 40 centuries
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spokes. While a good quality spoke is capable of supporting about 225
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713:= number of spokes to be used for one side of the wheel, for example
665:
467:
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269:
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133:
65:
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to the brake in the opposite direction—(via the hub) when braking.
112:
Wooden spoke wheel with metal rim from antique truck on display in
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The original type of spoked wheel with wooden spokes was used for
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for the greater part of three centuries. They moved deep into the
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679:= spoke hole circle radius of the hub, for example 19.5 mm,
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Wire spokes can be radial to the hub but are more often mounted
218:
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141:
132:
The term originally referred to portions of a log that had been
81:
50:
1447:
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connects), connecting the hub with the round traction surface.
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spoked wheels (zero crossings), the formula simplifies to the
332:
41:
is one of some number of rods radiating from the center of a
1075:{\displaystyle l={\sqrt {d^{2}+(r_{2}-r_{1})^{2}}}-r_{3}.}
27:
Part of a wheel extending radially from the hub to the rim
664:= distance from the center of hub (along the axis) to
1089:
A flat view of a crossed wheel with one spoke visible
996:
981:{\displaystyle (l+r_{3})^{2}=(r_{2}-r_{1})^{2}+d^{2}}
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522:
1098:
The spoke length formula computes the length of the
478:
up to the 1960s. Spoked wheels are still popular on
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257:. In early motor cars, wooden spoked wheels of the
104:. Note the three missing spokes and the metal tire.
1074:
980:
737:= number of crossings per spoke, for example 3 and
644:
188:dominance and consolidations led by pre-classical
1243:"Chariots in the Chalcolithic Rock Art of Indian"
168:2000 BCE. Soon after this, horse cultures of the
1205:The Prehistoric Paintings of the Pachmarhi Hills
510:include the width of the spoke at the bent end.
822:—if 3-crosses, the 32 spoke wheel has an angle
1260:Chariots in the Chalcolithic Rock Art of India
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793:is different for the left and right sides.
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148:'s work than to the materials they used.
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1207:, for proto-historic/chalocolithic.
25:
1337:. Yale University Press. p.
1284:Neumayer, Erwin (28 March 2013).
323:, while cheaper bicycles may use
60:A spoked wheel on display at the
1544:
1311:"The Chariot in Indian Rock Art"
84:wheels with metal axle assembly.
1797:2nd-millennium BC introductions
701:= radius of spoke holes in the
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1:
1369:"Hansen Wheel and Wagon Shop"
1286:Prehistoric Rock Art of India
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327:(also called "rustless") or
988:; or solving for the length
783:or a rear wheel with chain
1833:
1270:Celeste Paxton (2016), in
1227:Lindner, Stephan, (2020).
705:, for example 1.1 mm,
279:
268:Wooden spokes are mounted
29:
1812:Horse-drawn vehicle parts
1542:
668:, for example 30 mm,
294:. These are also used in
261:type were normally used.
80:The remains of a pair of
496:building a bicycle wheel
1331:Herlihy, David (2004).
209:chariots introduced an
62:National Museum of Iran
1396:. 2006. Archived from
1394:"PBO Spoke Technology"
1371:. 2006. Archived from
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355:usual spoke diameters
184:after the breaking of
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32:Spoke (disambiguation)
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1588:Quick release skewer
1334:Bicycle: the History
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881:being the base, and
848:, with spoke length
828:of 67.5°. Regarding
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126:tension-spoked wheel
30:For other uses, see
1148:Pythagorean theorem
846:Pythagorean theorem
356:
114:Underground Atlanta
1142:Equivalently, the
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241:Compression spokes
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1817:Sintashta culture
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1309:Neumayer, Erwin.
1241:Neumayer, Erwin.
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460:wheelbuilding
454:Wheelbuilding
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368:section area
367:
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329:chrome plated
326:
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48:
44:
40:
33:
19:
1670:Bowden cable
1573:Spoke nipple
1567:
1421:. Sapim N.V.
1413:
1402:. Retrieved
1398:the original
1388:
1377:. Retrieved
1373:the original
1363:
1352:. Retrieved
1333:
1326:
1317:
1304:
1285:
1279:
1266:
1254:
1236:
1223:
1199:
1170:Spoke wrench
1165:Spoke nipple
1141:
1136:
1129:
1125:
1118:
1111:
1107:
1097:
883:
882:
874:
873:
865:
864:
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811:
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797:
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789:
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750:
746:
741:
740:
733:
732:
709:
708:
702:
694:
693:
683:
682:
672:
671:
660:
659:
654:
512:
507:
505:
493:
490:Spoke length
472:
464:spoke nipple
457:
447:tangentially
444:
345:
337:pounds-force
317:
306:, and early
285:
267:
263:
244:
228:
225:Construction
205:
201:Chalcolithic
198:
164:, dating to
155:
131:
102:South Africa
98:Aliwal North
70:Choqa Zanbil
38:
36:
18:Spoked wheel
1766:Skirt guard
1711:Bottle cage
1694:Peripherals
1675:Cable guide
1625:Master link
1439:(in German)
1318:Harrapa.com
502:Calculation
480:motorcycles
476:sports cars
431:3.2 mm
420:2.9 mm
409:2.6 mm
398:2.3 mm
387:2.0 mm
376:1.8 mm
304:automobiles
300:motorcycles
296:wheelchairs
292:wire wheels
286:For use in
235:compression
217:and rubber
215:wire wheels
156:The spoked
146:wheelwright
1791:Categories
1761:Reflectors
1756:Spoke card
1635:Derailleur
1598:Drivetrain
1578:Valve stem
1536:Suspension
1491:Handlebars
1404:2011-10-21
1379:2006-08-22
1354:2009-09-29
1215:References
1185:Wire wheel
1175:Spokeshave
1094:Derivation
785:derailleur
781:disc brake
773:Regarding
468:rear gears
361:wire gauge
325:galvanized
282:Wire wheel
138:spokeshave
49:where the
1751:Saddlebag
1741:Mudguards
1726:Kickstand
1644:Gear case
1639:Hub gears
1501:Head tube
1057:−
1032:−
943:−
630:−
616:
586:−
434:10.24 mm
339:or 2,200
259:artillery
251:carriages
1746:Panniers
1731:Lighting
1649:Sprocket
1611:Crankset
1531:Fork end
1516:Seatpost
1154:See also
842:radially
758:360° ⋅ 3
484:bicycles
423:8.41 mm
412:6.76 mm
401:5.29 mm
379:3.24 mm
365:diameter
335:(c. 500
308:aircraft
288:bicycles
270:radially
174:chariots
170:Caucasus
94:ox-wagon
1716:Fairing
1685:Ferrule
1665:Shifter
1658:Cabling
1583:Dustcap
1506:Headset
767:
755:
745:= 360°
727:
715:
341:newtons
249:-drawn
231:tension
152:History
1807:Wheels
1771:Fender
1701:Basket
1630:Cogset
1555:Wheels
1521:Saddle
1345:
1292:
872:minus
769:= 60°.
703:flange
666:flange
655:where
349:aramid
255:wagons
207:Celtic
194:Athens
190:Sparta
186:Minoan
124:Metal
66:Tehran
1680:Brake
1616:Chain
1606:Pedal
1568:Spoke
1483:Frame
1314:(PDF)
1246:(PDF)
1191:Notes
854:plus
494:When
390:4 mm
314:Types
247:horse
219:tires
158:wheel
140:is a
134:riven
64:, in
45:(the
43:wheel
39:spoke
1706:Bell
1620:Belt
1563:Tire
1511:Fork
1496:Stem
1343:ISBN
1290:ISBN
1135:sin(
1124:cos(
840:For
729:=18,
482:and
253:and
211:iron
199:Neo-
192:and
142:tool
82:cart
51:axle
1339:141
1139:).
613:cos
508:not
428:10G
417:11G
406:12G
395:13G
384:14G
373:15G
333:kgf
233:or
196:.
96:in
92:An
47:hub
1793::
1341:.
1316:.
1288:.
1150:.
764:18
718:36
486:.
470:.
310:.
302:,
298:,
237:.
166:c.
100:,
37:A
1637:/
1618:/
1467:e
1460:t
1453:v
1407:.
1382:.
1357:.
1320:.
1298:.
1274:.
1248:.
1137:a
1133:1
1130:r
1126:α
1122:1
1119:r
1117:-
1115:2
1112:r
1108:d
1070:.
1065:3
1061:r
1050:2
1046:)
1040:1
1036:r
1027:2
1023:r
1019:(
1016:+
1011:2
1007:d
1001:=
998:l
974:2
970:d
966:+
961:2
957:)
951:1
947:r
938:2
934:r
930:(
927:=
922:2
918:)
912:3
908:r
904:+
901:l
898:(
884:d
879:1
875:r
870:2
866:r
861:3
857:r
851:l
835:3
831:r
825:a
819:a
813:a
808:k
804:m
798:a
790:d
776:d
761:/
751:m
749:/
747:k
742:a
734:k
724:2
721:/
710:m
699:3
695:r
688:2
684:r
677:1
673:r
661:d
638:3
634:r
625:)
622:a
619:(
608:2
604:r
598:1
594:r
589:2
581:2
574:2
570:r
564:+
559:2
552:1
548:r
542:+
537:2
533:d
527:=
524:l
347:(
116:.
72:.
34:.
20:)
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