Editing Velocity factor

{{Short description|Ratio of the speed at which a wavefront passes through the medium to the speed of light in vacuum}}
The '''velocity factor''' ('''VF'''),<ref>Gottlieb, I.M., ''Practical RF power design techniques'', TAB Books, 1993, {{ISBN|0-8306-4129-7}}, p.251 ('velocity factor')</ref> also called '''wave propagation (relative) speed''' or '''(relative) velocity of propagation''' ('''VoP''' or {{nobreak|'''<math>v_\mathrm{P}</math>'''),}}<ref>''[https://web.archive.org/web/20240712045911/www.generalcable.co.nz/getattachment/f81f14ee-7bec-4841-82d5-84b2df58b4f5/Velocity-of-Propagation.aspx Velocity of Propagation]'', General Cable Australia Pty Ltd, retrieved 2010-02-13</ref> 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 vacuum. For optical signals, the velocity factor is the reciprocal of the [[refractive index]].

The speed of radio signals in [[vacuum]], for example, is the [[speed of light]], and so the velocity factor of a radio wave in vacuum is 1.0 (unity). In air, the velocity factor is [[List of refractive indices|~0.9997]]. 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,<ref>"velocity of propagation" in Walker, P.M.B., ''Chambers Science and Technology Dictionary, Edinburgh, 1991, {{ISBN|1-85296-150-3}}</ref> while ''velocity factor'' is used for the ratio.

== Typical velocity factors ==
Velocity factor is an important characteristic of communication media such as [[category 5 cable]]s and radio [[transmission line]]s. [[Plenum cable|Plenum data cable]] typically has a VF between 0.42 and 0.72 (42% to 72% of the speed of light in vacuum) and riser cable around 0.70 (approximately 210,000,000&nbsp;[[metres per second|m/s]] or 4.76&nbsp;[[nanosecond|ns]] per metre).

:{| class="wikitable"
|+ Minimum velocity factors allowed for network cable standards
|-
!style="width:5em;"| VF<br/>(%) !! Cable type !! [[Ethernet physical layer]]
|-
| {{center|74~79%}}        || [[Category 7 cable|Cat-7]] [[twisted pair]] || 
|-
| {{center|77%&emsp;}}     || RG-8/U || Minimum for [[10BASE5]]<ref>IEEE 802.3 Clause 8.4.1.3 ''The minimum required velocity of propagation is 0.77 c.''</ref>
|-
| {{center|67%&emsp;}}     || [[Fiber-optic communication|Optical fiber]] (silica glass) || Minimum for [[10BASE-FL]],<ref>IEEE 802.3 clause 15.3.1.3 ''The propagation delay shall be ≤5 μs/km. (This is equivalent to a velocity of propagation of 0.67c.)''</ref><br/>[[100BASE-FX]], ...
|-
| {{center|67%&emsp;}}     || [[Plastic optical fiber]] || [[Gigabit Ethernet#1000BASE-RHx|1000BASE-RH''x'']]<br/>[[Poly(methyl methacrylate)|PMMA]] 
|-
| {{center|63%&emsp;}}     || Plastic optical fiber || [[polystyrene]] 
|-
| {{center|65%&emsp;}}     || RG-58A/U || Minimum for [[10BASE2]]<ref>IEEE 802.3 Clause 10.5.1.3 ''The minimum required velocity of propagation is 0.65 c.''</ref>
|-
| {{center|65%&emsp;}}     || [[Category 6A cable|Cat-6A]] [[twisted pair]] || [[10GBASE-T]]
|-
| {{center|64%&emsp;}}     || [[Category 5 cable|Cat-5e]] [[twisted pair]] || [[100BASE-TX]], [[1000BASE-T]]
|-
| {{center|58.5%}}   || [[Category 3 cable|Cat-3]] [[twisted pair]] || Minimum for [[10BASE-T]]<ref>IEEE 802.3 Clause 14.4.2.4 ''The maximum propagation delay of twisted pair shall be 5.7 ns/m (minimum velocity of 0.585 × c).''</ref>
|}

Some typical velocity factors for radio communications cables provided in handbooks and texts are given in the following table:<ref>{{cite book |editor-first = H. Ward |editor-last= Silver |year= 2011 |title= The ARRL Handbook for Radio Communications |edition= 88th |publisher = [[ARRL]] |place= Newington, CT |isbn= 978-0-87259-096-0 |chapter= Chapter 22: Component Data and References |page= 22.48}}</ref><ref>{{cite book |first=Kenneth L. |last=Kaiser |year=2005 |title=Transmission Lines, Matching, and Crosstalk |publisher=[[CRC Press]] |place=Boca Raton, FL |isbn=978-0-8493-6362-7 |pages=2–24 |url=https://books.google.com/books?id=QWFd-33xXvgC&pg=SA2-PA24 }}</ref>

:{| class="wikitable"
|-
!style="width:5em;"| VF<br/>(%) !! Transmission line !! Center insulation
|-
| {{center|95~99%}}  || [[Ladder line|open-wire line ("ladder line")]] || air insulated
|-
| {{center|93%}}     || HJ8-50B 3 inch Heliax [[coaxial cable]] || air dielectric<ref>{{cite web |title=HJ8-50B |website=commscope.com |url=https://www.commscope.com/globalassets/digizuite/112335-p360-hj8-50b-external.pdf?r=1 |access-date=22 March 2022 }}</ref>
|-
| {{center|86%}}     || RG-8 [[Belden (electronics company)|Belden]] 7810A [[coaxial cable]] || gas-injected foamed<br/>high-density polyethylene<ref>{{cite report |title = Belden Global Catalog |id=7810A |lang=EN |via=belden.com |url=https://catalog.belden.com/techdata/EN/7810A_techdata.pdf }}</ref>
|-
| {{center|83%}}     || RG-6 Belden 1189A coaxial cable,<br/>RG-11 Belden 1523A coaxial cable || 
|-
| {{center|82%}}     || RG-8X Belden 9258 coaxial cable || foamed polyethylene dielectric 
|-
| {{center|80%}}     || Belden 9085 [[twin-lead]] || 
|-
| {{center|77%}}     || RG-8/U generic || foamed polyethylene 
|-
| {{center|66%}}     || Belden 8723 twin shielded<br/> stranded [[twisted pair]] || polypropylene insulator<ref>{{cite web |title=8723 multi-conductor, shielded twisted pair cable |website=Belden.com |url=http://www.belden.com/techdatas/english/8723.pdf |archive-url=https://web.archive.org/web/20180119120036/https://catalog.belden.com/techdata/EN/8723_techdata.pdf |archive-date=2018-01-19 |access-date=2017-07-06 }}</ref>
|-
| {{center|66%}}     || RG-213 CXP213 || solid polyethylene dielectric 
|}

== Calculating velocity factor ==
===Electric wave===
VF equals the [[reciprocal (mathematics)|reciprocal]] of the [[square root]] of the [[dielectric constant]] ([[relative permittivity]]), <math>\kappa</math> or <math>\epsilon_\mathrm{r}</math>, of the material through which the signal passes:

:<math>\mathrm{VF} = { \frac{1}{\sqrt{\kappa}} } \ </math>

in the usual case where the [[Permeability (electromagnetism)#relative permeability|relative permeability]], <math>\mu_\mathrm{r}</math>, is 1. In the most general case:

:<math>\mathrm{VF} = { \frac{1}{\sqrt{\mu_\mathrm{r}\epsilon_\mathrm{r}}} } \ </math>

which includes unusual magnetic conducting materials, such as [[Ferrite (magnet)|ferrite]].

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

:<math>\mathrm{VF} = { \frac{1}{c_\mathrm{0}\sqrt{L'C'}} } \ </math>

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

===Optical wave===
VF equals the reciprocal of the [[refractive index]] <math>{n}</math> of the medium, usually [[optical fiber]].

:<math>\mathrm{VF} = { \frac{1}{n} } \ </math>

==See also==
{{div col|colwidth=22em}}
* [[Coaxial cable]]
* [[Propagation delay]]
* [[Signal velocity]]
* [[Speed of electricity]]
* [[Speed of sound]]
* [[Telegrapher's equations]]
{{div col end}}

==References==
{{Reflist}}

[[Category:Electromagnetic radiation]]
[[Category:Velocity]]