I thought I’d share a cautionary tale and one of my deepest desires for Flex / Crunch. As you are probably aware, dimensions in Crunch are unitless. Thus it is 100% on the user to make sure they’re using a consistent unit system. In my experience, this is one of the most common sources of mistakes – especially in new hires who are unfamiliar with the unitless concept. I have made inconsistent unit system mistakes more times than I wish to admit, and especially in my tenderfoot days I used weight/volume enough times that I’m surprised I’m still gainfully employed.
This can be especially confusing as four of the common unit systems are
- CGS (metric)
- centimeter - gram - second
- length - mass - time
- MMTS (metric)
- milimeter - tonne (1000 kg) - second
- length - mass - time
- IPS (Imperial)
- inch - pound - second
- length - force - time
- FPS (Imperial)
- foot - pound - second
- length - force - time
Notice anything?
A big source of confusion is that you will almost always see densities given in mass/volume in metric systems and weight/volume in Imperial systems. For instance, MatWeb shows the following for SS-304L.
The metric value is already in CGS units and it’s straightforward to convert to MMTS or SI consistent unit systems. However, the English value is not in a consistent unit system. That value tells us how much a cubic inch of the material weighs on earth. You might recall that the slug is the unit mass in the Imperial system - the functional equivalent of the SI kg. However in the IPS system we actually need to use the slug-inch (aka slug or blob). Below I’ve attached a PDF I made for last fall’s “Intro to Linear Finite Elements” (CE En 507) course. Other than the first paragraph, it’s a verbatim copy of an appendix from Sandia’s Sierra User Manual (which can be found here).
Introduction_to_CAE____Consistent_Unit_Systems.pdf (116.9 KB)
You’ll note in the final paragraph that they state:
The weight per unit volume should be divided by the gravitational constant (386.4 in/s2 in this case) to obtain a mass per unit volume.
Of course, by “gravitational constant” they mean “gravitational acceleration on Earth” not the gravitational constant G. Also, you’ll find various values for this constant such as 386.0886 on Wikipedia.
This sort of leads into a feature I’d like to see in Flex / Crunch, which I’ve discussed with many of you. I’d like to see a built in unit system manager that allows entry of units (and their dimensionality) as received by the customer, as gathered from the web, or however else I wish to enter them. Then Crunch would convert them to a consistent unit system internally. Additionally, the user could request output to be in a certain unit and Crunch would embed the units in the outputs (to simplify post-processing for example).
In conclusion - be careful with units especially English units (I’m sure as a proud Frenchman, @florian would agree with this statement.)