# Unit Consistency

In Radioss, data for any unit system can be provided, but it is very important to keep the unit consistency. If a model does not have unit consistency, it will lead to incorrect results (unexpected behavior) or may lead to an error in the calculation.

## Basic Units

SI     CGS Hydro US Japanese
Length m mm mm cm cm in mm
Mass kg Mg(Ton) kg g g lb kg
Time s s ms s µs s ms
Temperature K K K K K K K
Frequency Hz Hz Hz Hz Hz Hz Hz
Gravity 9.81 9.81E+03 9.81E-03 9.81E+02 9.81E-10 386 9.81E-03

## SI Unit Example

SI Unit Example
Length
$\left[\text{m}\right]$
Mass
$\left[\text{kg}\right]$
Time
$\left[\text{s}\right]$
Plane angle
$\left[\text{rad}\right]$
Temperature
$\left[\text{K}\right]$
Frequency
$\text{[Hz]}$
Rotational velocity
$\left[\frac{\text{rad}}{\text{s}}\right]$
Area
$\left[{\text{m}}^{2}\right]$
Volume
$\left[{\text{m}}^{3}\right]$
Moment of area (inertia)
$\left[{\text{m}}^{4}\right]$
Consumption
$\left[{\text{m}}^{2}\right]$
Speed
$\left[\frac{\text{m}}{\text{s}}\right]$
Acceleration
$\left[\frac{\text{m}}{{\text{s}}^{2}}\right]$
Tension
$\left[\frac{\text{m}}{{\text{s}}^{2}}\right]$
Lineic mass
$\left[\frac{\text{kg}}{\text{m}}\right]$
Surface mass
$\left[\frac{\text{kg}}{{\text{m}}^{2}}\right]$
Volume mass
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$
Mass flow
$\left[\frac{\text{kg}}{\text{s}}\right]$
Volume flow
$\left[\frac{{\text{m}}^{\text{3}}}{\text{s}}\right]$
Quantity of movement
$\left[\frac{kg\cdot m}{s}\right]$
Kinetic moment
$\left[\frac{kg\cdot m}{s}\right]$
Moment of inertial (l)
$\left[\text{kg}\cdot {\text{m}}^{\text{2}}\right]$
Moment of force
$\left[\mathrm{N}\cdot \mathrm{m}\right]$
Force
$\left[\text{N}\right]$
Linear force
$\left[\frac{\text{N}}{\text{m}}\right]$
Stiffness
$\left[\frac{\text{N}}{\text{m}}\right]$
Rotational stiffness
$\left[\frac{\text{N}•\text{m}}{\text{rad}}\right]$
Rotational damping
Torsion damping
$\left[\frac{kg\cdot {m}^{2}}{s\cdot rad}\right]$
Viscous damping
$\left[\frac{\text{kg}}{\text{s}}\right]$
Damping for bending
$\left[P{a}^{\lambda }\cdot s\right]$
Dynamic viscosity
$\left[\text{Pa}\cdot \text{s}\right]$
Kinematic viscosity
$\left[\frac{{\text{m}}^{\text{2}}}{\text{s}}\right]$
Density
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$
Power
$\left[\mathrm{W}\right]$
Energy
$\left[\text{J}\right]$
Enthalpy
$\left[\text{J}\right]$
Entropy
$\left[\frac{\text{J}}{\text{K}}\right]$
Strain rate
$\left[\frac{\text{1}}{\text{s}}\right]$
Time relaxation
$\left[\text{s}\right]$
Thermal expansion
$\left[\frac{1}{\text{K}}\right]$
Thermal conductivity
$\left[\frac{\text{W}}{\text{m}\cdot \text{K}}\right]$
Thermal resistance
$\left[\frac{\text{W}}{{\text{m}}^{2}\cdot \text{K}}\right]$
Specific heat (Cp, Cv)
$\left[\frac{kg}{{s}^{2}\cdot m\cdot K}\right]$
Specific heat capacity (Cp)
$\left[\frac{\text{J}}{{\text{m}}^{3}\cdot \text{K}}\right]$

## Verify Consistency

Use basic units Mass, Length, or Time so you can get all other units you need.

$Force=Mass\cdot Acceleration=\frac{Mass\cdot Length}{Tim{e}^{2}}$

$Pressure=\frac{Force}{Area}=\frac{Mass}{Length\cdot Tim{e}^{2}}$

$Energy=Force\cdot Length=\frac{Mass\cdot Lengt{h}^{2}}{Tim{e}^{2}}$

$Density=\frac{Mass}{Volume}=\frac{Mass}{Lengt{h}^{3}}$

$Acceleration=\frac{Length}{Tim{e}^{2}}$

$Volume=Lengt{h}^{3}$

For example, using base unit $\left[\text{kg}\right]$, $\left[\text{mm}\right]$, or $\left[\text{ms}\right]$, will provide the following units force, pressure or density.

$Force=\frac{Mass\cdot Length}{Tim{e}^{2}}=\frac{\left[kg\right]\cdot \left[mm\right]}{{\left[ms\right]}^{2}}=1{0}^{3}\frac{\left[kg\right]\cdot \left[m\right]}{{\left[s\right]}^{2}}=\left[kN\right]$

$Pressure=\frac{Mass}{Length\cdot Tim{e}^{2}}=\frac{\left[kg\right]}{\left[mm\right]\cdot {\left[ms\right]}^{2}}=1{0}^{9}\frac{\left[kg\right]}{\left[m\right]\cdot {\left[s\right]}^{2}}=\left[\mathrm{GPa}\right]$

$Energy=\frac{Mass\cdot Lengt{h}^{2}}{Tim{e}^{2}}=\frac{\left[kg\right]\cdot {\left[mm\right]}^{2}}{{\left[ms\right]}^{2}}=\frac{\left[kg\right]\cdot {\left[m\right]}^{2}}{{\left[s\right]}^{2}}=\left[J\right]$

$Density=\frac{Mass}{Lengt{h}^{3}}=\frac{\left[kg\right]}{{\left[mm\right]}^{2}}={10}^{6}\cdot \frac{\left[kg\right]}{{\left[m\right]}^{2}}$

## Check Units

Property Card
Check the thickness unit in property if it is shell
Material Card
Check density unit
Check E-modulus
Check stress unit if possible