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The '''poundal''' (symbol: '''pdl''') is a [[Units of measurement|unit]] of [[force]] that is part of the [[foot–pound–second system]] of units, in [[Imperial units]] introduced in 1877, and is from the specialized subsystem of  English absolute (a coherent system).
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


:<math>1\,\text{pdl} = 1\,\tfrac{\text{lb}_m \cdot \text{ft}}{\text{s}^2} </math>
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
The poundal is defined as the force necessary to accelerate 1 [[pound-mass]] to 1 foot per second per second.
* Only registered users will be able to execute this rendering mode.
1 pdl = {{val|0.138254954376|ul=N}} exactly.<!-- 1 pound-mass expressed in kilograms, times 1 foot expressed in meters, equals 1 poundal expressed in newtons -->
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


== Background ==
Registered users will be able to choose between the following three rendering modes:
English units require re-scaling of either force or mass to eliminate a numerical proportionality constant in the equation ''F = ma''. The poundal represents one choice, which is to rescale units of force. Since a pound of ''force'' ([[pound force]]) accelerates a pound of ''mass'' ([[Pound (mass)|pound mass]]) at 32.174&nbsp;049&nbsp;ft/s<sup>2</sup> (9.80665&nbsp;m/s<sup>2</sup>; the [[Standard gravity|acceleration of gravity]], ''g''), we can scale down the unit of force to compensate, giving us one that accelerates 1 pound mass at 1&nbsp;ft/s<sup>2</sup> rather than at 32.174&nbsp;049&nbsp;ft/s<sup>2</sup>; and that is the poundal, which is approximately {{Frac|1|32}} of a pound force.


For example, a force of 1200 poundals is required to accelerate a person of 150 pounds mass at 8 feet per second squared:
'''MathML'''
:<math>150\,\text{lb}_m \cdot 8\,\tfrac{\text{ft}}{\text{s}^2} = 1200\,\text{pdl}</math>
:<math forcemathmode="mathml">E=mc^2</math>


{{GravEngAbs}}
<!--'''PNG''' (currently default in production)
The poundal-as-force, pound-as-mass system is contrasted with an alternative system in which pounds are used as ''force'' (pounds-force), and instead, the ''mass'' unit is rescaled by a factor of roughly 32. That is, one pound-force will accelerate one pound-mass at 32 feet per second squared; we can scale ''up'' the unit of ''mass'' to compensate, which will be accelerated by 1&nbsp;ft/s<sup>2</sup> (rather than 32&nbsp;ft/s<sup>2</sup>) given the application of one pound force; this gives us a unit of mass called the [[Slug (mass)|slug]], which is about 32 pounds mass. Using this system (slugs and pounds-force), the above expression could be expressed as:
:<math forcemathmode="png">E=mc^2</math>
:<math>4.66\,\text{slug} \cdot 8\,\tfrac{\text{ft}}{\text{s}^2} = 37.3\,\text{lb}_F</math>


Note: Slugs (32.174&nbsp;049&nbsp;{{lbm}}) and poundals (1/32.174&nbsp;049&nbsp;{{lbf}}) are never used in the same system, since they are opposite solutions of the same problem.
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


Rather than changing either force or mass units, one may choose to express acceleration in units of the [[standard gravity|acceleration due to Earth's gravity]] (called ''g''). In this case, we can keep both pounds-mass and pounds-force, such that applying one pound force to one pound mass accelerates it at one unit of acceleration (''g''):
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].
:<math>150\,\text{lb}_m \cdot 0.249\,g = 37.3\,\text{lb}_F</math>


Expressions derived using poundals for force and {{lbm}} for mass (or {{lbf}} for force and slugs for mass) have the advantage of not being tied to conditions on the surface of the earth. Specifically, computing ''F'' = ''ma'' on the moon or in deep space as poundals, {{lbm}}·ft/s<sup>2</sup> or {{lbf}} = slug·ft/s<sup>2</sup>, avoids the constant tied to acceleration of gravity on earth.
==Demos==


== Conversion ==
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:
{{Units of force}}


== See also ==
[[Slug (mass)]]


==References==
* accessibility:
* Obert, Edward  F., “Thermodynamics”, McGraw-Hill Book Company Inc., New York 1948; Chapter I, Survey of Dimensions and Units, pages 1–24.
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
{{reflist}}
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


<!--Categories-->
==Test pages ==
[[Category:Units of force]]
 
[[Category:Imperial units]]
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
[[Category:Customary units of measurement in the United States]]
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]
 
*[[Inputtypes|Inputtypes (private Wikis only)]]
*[[Url2Image|Url2Image (private Wikis only)]]
==Bug reporting==
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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