# Velocity factor

The velocity factor (VF),[1] also called wave propagation speed or velocity of propagation (VoP or ${\displaystyle v_{\mathrm {P} }}$),[2] of a transmission medium is the ratio of the speed at which a wavefront (of an electromagnetic signal, a radio signal, a light pulse in an optical fibre or a change of the electrical voltage on a copper wire) passes through the medium, to the speed of light in a vacuum. For optical signals, the velocity factor is the reciprocal of the refractive index.

The speed of radio signals in a vacuum, for example, is the speed of light, and so the velocity factor of a radio wave in a vacuum is unity, or 100%. In electrical cables, the velocity factor mainly depends on the insulating material (see table below).

The use of the terms velocity of propagation and wave propagation speed to mean a ratio of speeds is confined to the computer networking and cable industries. In a general science and engineering context, these terms would be understood to mean a true speed or velocity in units of distance per time,[3] while velocity factor is used for the ratio.

## Typical velocity factors

Velocity factor is an important characteristic of communication media such as category 5 cables and radio transmission lines. Plenum data cable typically has a VF between 0.42 and 0.72 (42% to 72% of the speed of light in a vacuum) and riser cable around 0.70. A VF of 0.70 corresponds to a speed of approximately 210,000,000 m/s or 4.76 ns per metre.

Minimum velocity factors for network cables
VF (%)CableEthernet physical layer
74–79Cat-7 twisted pair
77RG-8/UMinimum for 10BASE5[4]
67Optical fiberMinimum for 10BASE-FL,[5] 100BASE-FX, ...
65RG-58A/UMinimum for 10BASE2[6]
65Cat-6A twisted pair10GBASE-T
64Cat-5e twisted pair100BASE-TX, 1000BASE-T
58.5Cat-3 twisted pairMinimum for 10BASE-T[7]

Some typical velocity factors for radio communications cables provided in handbooks and texts are given in the following table:[8][9]

VF (%)Transmission line
93HJ8-50B 3 inch Heliax coaxial cable (air dielectric)[10]
86RG-8 Belden 7810A coaxial cable (gas-injected foam high-density polyethylene)[11]
83RG-6 Belden 1189A coaxial cable, RG-11 Belden 1523A coaxial cable
82RG-8X Belden 9258 coaxial cable (foamed polyethylene dielectric)
77RG-8/U generic (foamed polyethylene)
66Belden 8723 twin shielded twisted pair stranded (polypropylene insulator)[12]
66RG-213 CXP213 (solid polyethylene dielectric)

## Calculating velocity factor

### Electric wave

VF equals the reciprocal of the square root of the dielectric constant (relative permittivity), ${\displaystyle \kappa }$ or ${\displaystyle \epsilon _{\mathrm {r} }}$, of the material through which the signal passes:

${\displaystyle \mathrm {VF} ={\frac {1}{\sqrt {\kappa }}}\ }$

in the usual case where the relative permeability, ${\displaystyle \mu _{\mathrm {r} }}$, is 1. In the most general case:

${\displaystyle \mathrm {VF} ={\frac {1}{\sqrt {\mu _{\mathrm {r} }\epsilon _{\mathrm {r} }}}}\ }$

which includes unusual magnetic conducting materials, such as ferrite.

The velocity factor for a lossless transmission line is given by:

${\displaystyle \mathrm {VF} ={\frac {1}{c_{\mathrm {0} }{\sqrt {L'C'}}}}\ }$

where ${\displaystyle L'}$ is the distributed inductance (in henries per unit length), ${\displaystyle C'}$ is the capacitance between the two conductors (in farads per unit length), and ${\displaystyle c_{\mathrm {0} }}$ is the speed of light in vacuum.

### Optical wave

VF equals the reciprocal of the refractive index ${\displaystyle {n}}$ of the medium, usually optical fiber.

${\displaystyle \mathrm {VF} ={\frac {1}{n}}\ }$

## References

1. Gottlieb, I.M., Practical RF power design techniques, TAB Books, 1993, ISBN 0-8306-4129-7, p.251 ('velocity factor')
2. Velocity of Propagation, General Cable Australia Pty Ltd, retrieved 2010-02-13
3. "velocity of propagation" in Walker, P.M.B., Chambers Science and Technology Dictionary, Edinburgh, 1991, ISBN 1-85296-150-3
4. IEEE 802.3 Clause 8.4.1.3
5. IEEE 802.3 Clause 15.3.1.3
6. IEEE 802.3 Clause 10.5.1.3
7. IEEE 802.3 Clause 14.4.2.4
8. H. Ward Silver, N0AX, ed. (2011). "Chapter 22: Component Data and References". The ARRL Handbook For Radio Communications (88th ed.). ARRL. p. 22.48. ISBN 978-0-87259-096-0.
9. Kaiser, Kenneth L. (2005). Transmission Lines, Matching, and Crosstalk. CRC Press. pp. 2–24. ISBN 9780849363627.
10. https://www.commscope.com/catalog/cables/pdf/part/1464/HJ8-50B.pdf
11. https://catalog.belden.com/techdata/EN/7810A_techdata.pd
12. "8723 Multi-Conductor - Shielded Twisted Pair Cable" (PDF). Belden.com. Retrieved 2017-07-06.