A shaft's stiffness depends far more on its diameter than on its wall thickness

1 study

It is a consequence of the mechanics of materials, not the result of a comparison between shafts. A work on physics applied to archery derives from beam theory that in a thin-walled tube bending stiffness depends on the second moment of area of the cross-section, and that this grows with the cube of the radius but only in direct proportion to wall thickness. On the carbon shaft measured, radius 3.63 millimetres and wall 0.50, the moment is 6.10 times 10 to the minus 11 metres to the fourth, and from the measured stiffness the author derives an elastic modulus of about 85 gigapascals, in line with values for carbon. The formula describes an ideal tube, though, and the same author warns that the mechanical properties of carbon fibre composites are not well defined and even depend on direction: the modulus is not a fixed figure, so diameter alone is not enough to tell a shaft's spine. In the registry's bibliography nobody has measured the spine of shafts in which diameter and wall are changed one at a time.

Also phrased as: "shaft stiffness"; "diameter and spine"; "shaft wall thickness"; "why fat shafts are stiffer"; "arrow spine and diameter"

In practice

When choosing shafts it is taken for granted that, for the same material, a fatter shaft is stiffer, and that getting the same spine from a smaller diameter takes a different carbon or a thicker wall.

Evidence

2015
For Model Published later

From beam theory: for a tube whose wall is thin compared with its radius, the second moment of area of the cross-section, and therefore stiffness, is proportional to the cube of the radius and to wall thickness. For the carbon sample shaft, radius 3.63 ± 0.05 mm and wall 0.50 ± 0.07 mm, the moment is 6.10 × 10⁻¹¹ m⁴; from the measured stiffness the author derives an elastic modulus of 8.48 × 10¹⁰ N/m², in line with literature values for carbon fibre.

Applications of Physics to Archery · H. O. Meyer

Status history

2015 Transferred A work on physics applied to archery derives from beam theory that in a thin-walled tube the second moment of area of the cross-section, and therefore stiffness, grows with the cube of the radius and only linearly with thickness. On the carbon shaft measured, radius 3.63 millimetres and wall 0.50, the calculation gives a moment of 6.10 times 10 to the minus 11 metres to the fourth and an elastic modulus of about 85 gigapascals. It is a deduction from the mechanics of materials applied to a single shaft, with no comparison between shafts of different diameter, and a model on its own goes no further than transferred.

Research lines

Cite

APA

Campagna, M. (2026). A shaft's stiffness depends far more on its diameter than on its wall thickness (Version 1). In Evidence Registry. Retrieved 16 October 2026, from https://matteocampagna.com/en/registry/equipment/shaft-stiffness-diameter-wall

BibTeX

@misc{campagna2026_rigiditaastadiametroparete,
  author = {Campagna, Matteo},
  title = {A shaft's stiffness depends far more on its diameter than on its wall thickness},
  year = {2026},
  howpublished = {Evidence Registry, matteocampagna.com},
  url = {https://matteocampagna.com/en/registry/equipment/shaft-stiffness-diameter-wall},
  note = {Version 1; accessed 2026-10-16}
}

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