# Velocity factor

The velocity factor (VF), also called wave propagation speed or velocity of propagation (VoP or $v_{\mathrm {P} }$ ), 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, 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 (%) Cable Ethernet physical layer
74–79 Cat-7 twisted pair
77 RG-8/U Minimum for 10BASE5
67 Optical fiber Minimum for 10BASE-FL, 100BASE-FX, ...
65 RG-58A/U Minimum for 10BASE2
65 Cat-6A twisted pair 10GBASE-T
64 Cat-5e twisted pair 100BASE-TX, 1000BASE-T
58.5 Cat-3 twisted pair Minimum for 10BASE-T

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

VF (%) Transmission line
95–99 Open-wire "Ladder" Line
93 HJ8-50B 3 inch Heliax coaxial cable (air dielectric)
86 RG-8 Belden 7810A coaxial cable (gas-injected foam high-density polyethylene)
83 RG-6 Belden 1189A coaxial cable, RG-11 Belden 1523A coaxial cable
82 RG-8X Belden 9258 coaxial cable (foamed polyethylene dielectric)
80 Belden 9085 twin-lead
77 RG-8/U generic (foamed polyethylene)
66 Belden 8723 twin shielded twisted pair stranded (polypropylene insulator)
66 RG-213 CXP213 (solid polyethylene dielectric)

## Calculating velocity factor

### Electric wave

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

$\mathrm {VF} ={\frac {1}{\sqrt {\kappa }}}\$ in the usual case where the relative permeability, $\mu _{\mathrm {r} }$ , is 1. In the most general case:

$\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:

$\mathrm {VF} ={\frac {1}{c_{\mathrm {0} }{\sqrt {L'C'}}}}\$ where $L'$ is the distributed inductance (in henries per unit length), $C'$ is the capacitance between the two conductors (in farads per unit length), and $c_{\mathrm {0} }$ is the speed of light in vacuum.

### Optical wave

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

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