# Atkinson friction factor

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**Atkinson friction factor** is a measure of the resistance to airflow of a duct. It is widely used in the [mine ventilation](/source/Underground_mine_ventilation) industry but is rarely referred to outside of it.

Atkinson friction factor is represented by the symbol k and has the same units as air density (kilograms per cubic metre in [SI units](/source/SI), lbfmin^2/ft^4 in [Imperial units](/source/Imperial_unit)). It is related to the more widespread [Fanning friction factor](/source/Fanning_friction_factor) by

k = \frac{1}{2}\rho f,

in which \rho is the [density of air](/source/Density_of_air) in the shaft or roadway under consideration and f is Fanning friction factor (dimensionless). It is related to the [Darcy friction factor](/source/Darcy_friction_factor) by

k = \frac{1}{2}\rho \frac{\lambda}{4},

in which \lambda is the Darcy friction factor (dimensionless).

It was introduced by John J Atkinson in an early mathematical treatment of mine ventilation (1862) and has been known under his name ever since.

## See also

- [Atkinson resistance](/source/Atkinson_resistance)

## References

- NCB Mining Dept., *Ventilation in coal mines: a handbook for colliery ventilation officers,* National Coal Board 1979.

## Further reading

- [1999 paper giving the derivation of k](https://www.mvsengineering.com/files/Publications/08th_US-1.pdf)
- Atkinson, J J, *Gases met with in Coal Mines, and the general principles of Ventilation* Transactions of the Manchester Geological Society, Vol. III, p.218, 1862

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