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§ 16

Spindle length

How long should the spokes be for a 29" rear wheel with 32 spokes, 3-cross?

Answer: When you build or rebuild a wheel, the spokes must be the right length, or the nipple won't reach the thread, or the spoke sticks through the rim tape. Spoke length is the distance from the hole in the hub flange to the rim's ERD circle in space, and it depends on the cross pattern. The calculator works one side at a time, because flange distance differs on the drive side and opposite side on a rear wheel and with disc brakes. All measurements come from the rim and hub's datasheet or you measure yourself.

Formula

L = √( (ERD/2)² + (hulkreds/2)² + flange² − 2 × (ERD/2) × (hulkreds/2) × cos α ) − egerhul/2

α = antal kryds × 720° ÷ egetal (fx 3-kryds med 32 eger: 3 × 720 ÷ 32 = 67,5°). Listen giver cos α direkte

Flange distance is measured from the hub's centre plane not from the lock nut. On a rear wheel the drive side is shorter so the spokes are shorter there

ERD is the diameter where the spoke end sits in the nipple. It's in the rim's datasheet or measured with two spokes and a ruler

Symbols and units in the formula
SymbolMeaningUnit
erd_mmRim's ERD (effective spoke diameter datasheet or measured)mm
hulkreds_mmHub flange's bolt circle diametermm
flange_mmDistance from hub centre to flange (this side)mm
moensterEgetal og kryds-mønster (α = kryds × 720° ÷ egetal)—
egerhul_mmDrill hole diameter in the flangemm
=Spindle length (this side)mm
=Rounded to nearest whole mmmm
=Distance before correction for drill holemm

Validity and source

Source
Geometry (cosine law same formula as DT Swiss and Sheldon Brown spoke calculators)

Does not apply when

  • The formula gives the geometrical length. Round to the nearest length you can get and always test-assemble one spoke before you order the whole set. Thin spokes stretch a bit under the tension.

Worked example

The calculator's own default values inserted. The figures are calculated with exactly the formula the tool uses.

Substituted

  • Rim's ERD (effective spoke diameter datasheet or measured)600 mm
  • Hub flange's bolt circle diameter58 mm
  • Distance from hub centre to flange (this side)33 mm
  • Egetal og kryds-mønster (α = kryds × 720° ÷ egetal)0.38
  • Drill hole diameter in the flange2.60 mm

Giver

  • Spindle length (this side)290.7 mm
  • Rounded to nearest whole mm291 mm
  • Distance before correction for drill hole292.0 mm

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Sådan bruger du den

Når du bygger et nyt hjul eller skifter fælg eller nav, skal egerne have den rigtige længde, ellers når nippelen ikke gevindet, eller egeren stikker op i fælgbåndet. Beregneren giver længden for én side ad gangen ud fra fælgens ERD, navets mål og kryds-mønsteret. Baghjul og hjul med skivebremse har forskellig længde på de to sider.

Step by step

  1. Find fælgens ERD i databladet, eller mål den med to eger og en lineal.
  2. Mål navflangens hulkredsdiameter og afstanden fra navets midte til flangen på den side, du regner.
  3. Vælg egetal og kryds-mønster.
  4. Læs egerlængden, og regn den anden side bagefter.

Typical errors

  • At måle flangeafstanden fra låsemøtrikken i stedet for fra navets midte.
  • At bruge fælgens diameter i stedet for ERD.
  • At regne begge sider ens på et baghjul.

Examples from everyday life

29"-baghjul, drevsiden

Du bygger et baghjul med 32 eger, 3-kryds. Fælgen har ERD 600 mm, navflangen 58 mm hulkreds og 20,5 mm fra navets midte på drevsiden.

Rim's ERD (effective spoke diameter datasheet or measured)
600 mm
Hub flange's bolt circle diameter
58 mm
Distance from hub centre to flange (this side)
20.5 mm
Egetal og kryds-mønster (α = kryds × 720° ÷ egetal)
32 eger, 3-kryds (α = 67,5°)
Drill hole diameter in the flange
2.6 mm

It means: Egerne på drevsiden skal være 289.6 mm, rundet til 290 mm.

Samme hjul, modsatte side

På den modsatte side (skivebremsesiden) sidder flangen 33,5 mm fra navets midte.

Rim's ERD (effective spoke diameter datasheet or measured)
600 mm
Hub flange's bolt circle diameter
58 mm
Distance from hub centre to flange (this side)
33.5 mm
Egetal og kryds-mønster (α = kryds × 720° ÷ egetal)
32 eger, 3-kryds (α = 67,5°)
Drill hole diameter in the flange
2.6 mm

It means: Her skal egerne være 290.8 mm, rundet til 291 mm. De er længere, fordi flangen sidder længere ude.

Forhjul med 36 eger, 3-kryds

Et forhjul til en bycykel med dynamonav: ERD 605 mm, hulkreds 38 mm, flangen 35 mm fra midten på begge sider.

Rim's ERD (effective spoke diameter datasheet or measured)
605 mm
Hub flange's bolt circle diameter
38 mm
Distance from hub centre to flange (this side)
35 mm
Egetal og kryds-mønster (α = kryds × 720° ÷ egetal)
36 eger 3-kryds eller 24 eger 2-kryds (α = 60°)
Drill hole diameter in the flange
2.6 mm

It means: Egerne skal være 294.2 mm, rundet til 294 mm, på begge sider.

Rule of thumb

En mm længere ERD giver ca. ½ mm længere eger. Et kryds mere giver markant længere eger: på et 29"-hjul med 32 eger er der ca. 10 mm mellem 2- og 3-kryds.

How to check the answer

Egerlængden skal være lidt mindre end halvdelen af ERD. Radial egring giver de korteste eger.