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

Verify Consistency

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

$F o r c e = M a s s \cdot A c c e l e r a t i o n = \frac{M a s s \cdot L e n g t h}{T i m e^{2}}$ $F o r c e = M a s s \cdot A c c e l e r a t i o n = \frac{M a s s \cdot L e n g t h}{T i m e^{2}}$

$P r e s s u r e = \frac{F o r c e}{A r e a} = \frac{M a s s}{L e n g t h \cdot T i m e^{2}}$ $P r e s s u r e = \frac{F o r c e}{A r e a} = \frac{M a s s}{L e n g t h \cdot T i m e^{2}}$

$E n e r g y = F o r c e \cdot L e n g t h = \frac{M a s s \cdot L e n g t h^{2}}{T i m e^{2}}$ $E n e r g y = F o r c e \cdot L e n g t h = \frac{M a s s \cdot L e n g t h^{2}}{T i m e^{2}}$

$D e n s i t y = \frac{M a s s}{V o l u m e} = \frac{M a s s}{L e n g t h^{3}}$ $D e n s i t y = \frac{M a s s}{V o l u m e} = \frac{M a s s}{L e n g t h^{3}}$

$A c c e l e r a t i o n = \frac{L e n g t h}{T i m e^{2}}$ $A c c e l e r a t i o n = \frac{L e n g t h}{T i m e^{2}}$

$V o l u m e = L e n g t h^{3}$ $V o l u m e = L e n g t h^{3}$

For example, using base unit $[kg]$ $[kg]$ , $[mm]$ $[mm]$ , or $[ms]$ $[ms]$ , will provide the following units force, pressure or density.

$F o r c e = \frac{M a s s \cdot L e n g t h}{T i m e^{2}} = \frac{[k g] \cdot [m m]}{{[m s]}^{2}} = 1 0^{3} \frac{[k g] \cdot [m]}{{[s]}^{2}} = [k N]$ $F o r c e = \frac{M a s s \cdot L e n g t h}{T i m e^{2}} = \frac{[k g] \cdot [m m]}{{[m s]}^{2}} = 1 0^{3} \frac{[k g] \cdot [m]}{{[s]}^{2}} = [k N]$

$P r e s s u r e = \frac{M a s s}{L e n g t h \cdot T i m e^{2}} = \frac{[k g]}{[m m] \cdot {[m s]}^{2}} = 1 0^{9} \frac{[k g]}{[m] \cdot {[s]}^{2}} = [GPa]$ $P r e s s u r e = \frac{M a s s}{L e n g t h \cdot T i m e^{2}} = \frac{[k g]}{[m m] \cdot {[m s]}^{2}} = 1 0^{9} \frac{[k g]}{[m] \cdot {[s]}^{2}} = [GPa]$

$E n e r g y = \frac{M a s s \cdot L e n g t h^{2}}{T i m e^{2}} = \frac{[k g] \cdot {[m m]}^{2}}{{[m s]}^{2}} = \frac{[k g] \cdot {[m]}^{2}}{{[s]}^{2}} = [J]$ $E n e r g y = \frac{M a s s \cdot L e n g t h^{2}}{T i m e^{2}} = \frac{[k g] \cdot {[m m]}^{2}}{{[m s]}^{2}} = \frac{[k g] \cdot {[m]}^{2}}{{[s]}^{2}} = [J]$

$D e n s i t y = \frac{M a s s}{L e n g t h^{3}} = \frac{[k g]}{{[m m]}^{2}} = 10^{6} \cdot \frac{[k g]}{{[m]}^{2}}$ $D e n s i t y = \frac{M a s s}{L e n g t h^{3}} = \frac{[k g]}{{[m m]}^{2}} = 10^{6} \cdot \frac{[k g]}{{[m]}^{2}}$

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
Load: Check force unit; Check gravity unit, if using /GRAV
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	10⁷N	10⁵J	Mbar	7.8e+00	2.1e+00	9.81e-10	2.06e-06