Special Considerations for Density

Specifying material density properly with IPS units.

Density is defined as mass/volume. In SI units, mass is given in kilograms and volume in cubic-meters so density is in kg/m3 – easy. But in IPS units, mass is given in something called a Slug. What the heck is a Slug?

It turns out that the Slug is the unit of mass in the US common system of units, where the pound is the unit of force (lbf). The pound is therefore the unit of weight since weight is defined as the force of gravity on an object. Weight is related to mass by the well-known equation w=m*g where w is weight, m is mass and g is the acceleration of gravity. So, something with a mass of 1 slug at the earth’s surface (where g=32.174 ft/s2) weighs 32.174 lbf. If you invert this equation, m=w/g, so 1 slug = 1 lbf*s2/ft.

However, density is often specified in many references in units of lbs/ft3 when it should be in slugs/ft3. SimSolid Cloud uses the proper mass/volume definition. In the IPS (inch-pound-second) system of units, this inch equivalent density is given as Snails/in3 where a Snail is 12 slugs. Since 1 snail =lbf*s2/in, SimSolid Cloud specifies density in IPS in units of lbf*s2/in4. Wow, confusing isn’t it?

To make it easy, the recommendation is to enter material properties in SI units. SimSolid Cloud converts them on-the-fly for those that use IPS.

If you insist on entering material properties in IPS, be sure to enter density in lbf*s2/in4. To convert density given as lb/in3 (weight/volume) to lbf*s2/in4 (mass/volume) just divide by the acceleration of gravity (which is 386.0886 in/s2).
Note: For those that really want to appear smart, a “snail” is also referred to as a “slinch” (combination of slug and inch).

In a few references density is given with respect to specific gravity. Specific gravity is the density of a substance divided by the density of water. At standard temperature and pressure, water has a density of 1000 kg/cm3. As an example, since the density of steel is 7820 kg/m3, its Specific Gravity would be given as 7.82. So, when encountering a reference for density in Specific Gravity, multiply the value by 1000 and enter it as kg/m3.