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Wedge height from angle and width

How high should the wedge be at the edge?

Answer: A correction wedge or shim is prescribed in degrees, eg 4° varus in the heel, but on the workbench it's ground and built up in millimetres. The height on the high side is the width the wedge spans times the tangent of the angle. The calculator converts the angle to mm, so you can build up, grind and check the wedge with callipers. It's used for heel and forefoot corrections in insoles and for wedges in the sole of orthopaedic footwear.

Formula

Kilehøjde = bredde × tan(vinkel)

tan is calculated here with series expansion x + x³/3 + 2x⁵/15 + 17x⁷/315 where x is angle in radians (accurate to 0.01 mm up to 20°)

Thumb rule: at 1° the height is approximately 1.75% of the width

Symbols and units in the formula
SymbolMeaningUnit
vinkel_graderOrdered wedge angle°
bredde_mmWidth the wedge spans (e.g. heel width on the insole)mm
=Wedge height at high edgemm
=Height per degree at this widthmm/°
=Height in the middle of the wedgemm

Validity and source

Source
Trigonometri: højde = bredde × tan(vinkel)

Does not apply when

  • Width is the width the wedge actually lies over on the insole, not the width of the foot as a whole. Check the finished wedge with a protractor on a flat surface. The angle is ordered by the practitioner.

Worked example

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

Substituted

  • Ordered wedge angle4 °
  • Width the wedge spans (e.g. heel width on the insole)65 mm

Giver

  • Wedge height at high edge4.5 mm
  • Height per degree at this width1.13 mm/°
  • Height in the middle of the wedge2.3 mm

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Sådan bruger du den

Du bruger den, når en kile eller postering er ordineret i grader, og du skal opbygge eller slibe den i mm på værkstedet.

Step by step

  1. Find den ordinerede vinkel.
  2. Mål den bredde, kilen ligger over på indlægget.
  3. Højde = bredde × tan(vinkel).
  4. Opbyg kilen, og kontrollér med skydelære i den høje kant.

Typical errors

  • At bruge fodens bredde i stedet for kilens.
  • At regne vinklen af hele indlæggets længde.
  • At glemme at kilen trykkes sammen under belastning, hvis materialet er blødt.

Examples from everyday life

Hælpostering på 4°

Posteringen er 4°, og hælens bredde på indlægget er 65 mm.

Ordered wedge angle
4 °
Width the wedge spans (e.g. heel width on the insole)
65 mm

It means: Kilen skal være 4.5 mm i den høje kant og 2.3 mm midt på.

Udvendig kile i sålen

En sko skal have en udvendig kile på 3° over en sålbredde på 90 mm.

Ordered wedge angle
3 °
Width the wedge spans (e.g. heel width on the insole)
90 mm

It means: Kilen skal være 4.7 mm i kanten. Hver grad giver 1.57 mm/° ved denne bredde.

Rule of thumb

1° giver ca. 1,75 mm pr. 100 mm bredde.

How to check the answer

Læg indlægget på en plan flade, og mål vinklen med en vinkelmåler.