# Unit Consistency

In Radioss, data for any unit system can be provided, but it is very important to keep the unit consistency. If your model did not keep unit consistency, this will lead to the incorrect results (unexpected behavior) or sometimes 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
- $\left[\text{J}\right]$
- Entpory
- $\left[\frac{\text{J}}{\text{K}}\right]$
- Strain rate
- $$\left[\frac{\text{1}}{\text{s}}\right]$$
- Permeability
- $$\left[\frac{\text{rad}}{\text{s}}\right]$$
- Time relaxation
- $\left[\text{s}\right]$
- Thermal expansion
- $$\left[\frac{\text{W}}{{\text{m}}^{2}\cdot \text{K}}\right]$$
- Thermal conductivity
- $\left[\frac{{}^{\text{o}}\text{K}}{\text{W}}\right]$
- 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 Unit

- 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 |