# 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 |

Plane angle | rad | rad | rad | rad | rad | rad | rad |

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
- $\left[\frac{\text{N}\u2022\text{m}}{\text{rad}}\right]$
- Rotational damping
- $\left[\frac{\text{N\u2022m\u2022s}}{\text{rad}}\right]$
- Torsion damping
- $\left[\frac{kg\cdot {m}^{2}}{s\cdot rad}\right]$
- Viscous damping
- $\left[\frac{\text{kg}}{\text{s}}\right]$
- Damping for bending
- $\left[\frac{\text{N\u2022s}}{\text{m}}\right]$
- Quadratic bulk viscosity
- $$\left[P{a}^{\lambda}\cdot s\right]$$
- 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
- Load
- Check force unit
- Length
- Measure the geometry length unit with HyperCrash or HyperMesh

All units must be consistent.

## Most Popular Units (with steel examples)

Mass | Length | Time | Force | Energy | Stress | Density | Young's module | Gravity | Yield stress |
---|---|---|---|---|---|---|---|---|---|

kg | m | s | N | J | Pa | 7.8e+03 | 2.1e+11 | 9.81e+00 | 2.06e+05 |

g | mm | ms | N | mJ | MPa | 7.8e-03 | 2.1e+05 | 9.81e-03 | 2.06e+02 |

kg | mm | ms | KN | J | GPa | 7.8e-06 | 2.1e+02 | 9.81e-03 | 2.06e-01 |

Mg (ton) | mm | s | N | mJ | MPa | 7.8e-09 | 2.1e+05 | 9.81e+03 | 2.06e+02 |

g | cm | micros | 10^{7}N |
10^{5}J |
Mbar | 7.8e+00 | 2.1e+00 | 9.81e-10 | 2.06e-06 |