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I've been studying mechanical simulation with nastran/patran, nowadays.

I knew weight density is used in imperial unit system, instead of mass density.

I feel using weight density is tedious, because I have to put a conversion factor to change weight density into mass density, when I perform dynamic simulation, always.

I just had used SI unit in my whole life, so that I don't know which advantage there is in using weight density, compared to using mass density.

Could anyone explain why weight density is used in imperial unit, instead of mass density?

And then, what is the advantage of weight density, compared to mass density?

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    $\begingroup$ I think the more common term for this quantity is specific weight. It is not an "imperial unit system" quantity, but an engineering quantity. It can be expressed as force per unit volume, which can be expressed in any unit system, including the metric system. You should read the wikipedia page on its uses: en.m.wikipedia.org/wiki/Specific_weight $\endgroup$
    – Paul
    Commented Aug 26, 2016 at 4:28

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There isn't a profound reason for this. It is just that in US customary units (don't call them "Imperial" any more - first, Britain no longer has an empire, and second, the UK no longer uses them in any serious engineering work) force, pressure, and stress are measured in weight units, but mass and density are measured in mass units.

There is a "weight unit of mass", the slug, but it is based on lengths measured in feet, not in inches, so it still needs another conversion factor of 12 applied to it for most engineering work.

It is generally less error-prone to include the conversion factor in the input to software as "the acceleration due to gravity" (or in Nastran the reciprocal of that number, for some perverse reason) rather than do all the conversions by hand. Unless you are working in the space industry (e.g. your are modelling a the deployment of a lunar lander) the value of the "magic conversion factor" is always the same.

The average engineer in the USA knows the density of mild steel is about 0.28lb/in^3, but probably wouldn't recognize 7.25e-4 as the density of anything!

Of course there is an analogous situation in SI units. If you want to include the weight of an object as a force in your model, the weight of a mass $m$ kilograms is $mg$ Newtons. But there are many engineering situations where the weight of an object is negligible compared with the other forces acting on it, and can be ignored.

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  • $\begingroup$ After reading your answer, I thought units using weight is convenient in force related calculation, and units using mass is convenient in mass related calculation. $\endgroup$
    – KKS
    Commented Aug 26, 2016 at 7:03
  • $\begingroup$ "imperial" is still the unit of certain measures in the UK, and is not the same as US units. E.g. gallon vs. imperial gallon. $\endgroup$
    – Carl Witthoft
    Commented Aug 26, 2016 at 11:23

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