Week - 1 - Consistency of Units

Aim : Convert given measurements into different system of units and finding their corresponding conversion factors.

Purpose :LS-DYNA doesn't have a default system of units. User needs to input material properties and physical dimensions according to a consistent system of units as per their choice. This warrants that to use LS-DYNA in different circumstances, users has to be conversant with converting quantities from one system of units to another.

SI UNIT

Mass : Kg (Kilogram)

Length : M ( meter)

Time : s ( second)

Force : N ( newton)
1 N = Kg X m / s^2

stress : Pa ( pascal)

1 Pa = 1 N / m^2
=( 1 Kg X m / s^2 ) / m^2 .... ( put N = Kg X m / s^2)
= Kg /m s^2

Energy = J ( jule)
J = Nm
= (Kg X m / s^2 )/ m .... (put N = Kg X m / s^2)
= Kg . m^2 / s^2

Density : Rh ( Rho)
Rh = 1Kg/m3

YOUNG'S Modulus = Pa
1 Pa = 1 Kg /m s^2

Velocity= KMPH ( 10X3 / 3600 ) m/s
= 0.2777 m/s

GRAVITY = 9.8 m/s2

Also we know that below conversion factor

K = 1X10^3 g
M = 1X10^6 g
G = 1 x 10^9 g

now we will convert kg-m-s unit system to kg-cm-ms

Mass : 1 Kg

length : 1 meter = 10^2 cm

Time : 1 s = 1X10^3 ms

force = 1 N = 1 Kg X m / s^2
= 1 Kg x 10^2 cm / 10^3 x 10^3 ms^2
= 1 x 10^-4 kg*cm / ms^2

stress : 1 pa = 1 Kg /m s^2
= 1 kg / 10^2 cm x 10^3 x 10^3 ms^2
= 1 x 10 ^-8 kg/cm*ms^2

Energy = 1 J = Kg . m^2 / s^2
= 1 kg * 10^2 x 10^2 cm^2 / 10^3 X 10^3 ms^2
= 10^-2 Kg .cm^2 / ms^2

Density = 1 Rh = 1Kg/m3
= 1 Kg / 10^2 x 10^2 x 10^2 cm^3
=10^-6 Kg / cm^3
Density ( steel) = 7800 kg /m^3
= 7800 x 10^-6 kg /cm^3
=7.8E-3 kg/cm^3

YOUNG'S Modulus = 1 Pa = 1 Kg /m s^2
=1 x 10^-4 kg*cm / ms^2
Young's modulus (steel) = 210 GPa = 210 X 10^ 9 Pa
= 210 X10^9 x10^-4 kg*cm /ms^2
= 210E+5 kg*cm /ms^2

Velocity = KMPH ( 10^3 / 3600 ) m/s
= 10^3 X 10^2 / 3600 x10^3 cm/ms
= 10^2/3600 cm/ms
= 0.027777 cm/ms
Velocity(56.33 KMPH) = 56.33 X 0.027777 cm/ms
= 1.560341 cm/ms

GRAVITY = 1 m /s^2
= 1 X10^2 cm / 10^3 *10^3 ms^3
= 10-4 cm/ ms^3
Gravity (steel) = 9.8 m/s^2
= 9.8E-4 cm/ms^2

simillarly . for Kg-cm-s

Mass = 1 Kg

Lenth = 10^2 cm

Time = 1 s

Force = 1 N = 1 Kg X m / s^2 = 1 Kg x 10^2 cm / s^2
= 10^2 kg cm/s^2

stress : 1 Pa = Kg /m s^2
=1 Kg / 10^2 cm s^2
= 10^-2 kg /cm s^2

Energy : 1 J = Kg . m^2 / s^2
= 1 kg X 10^2 x 10^2 cm^2 / s^2
= 10^4 kg cm^2 / s^2

Density (steel) : 7800 Kg /m^3
=7800 Kg / 10^2*10^2*10^2 cm^3
= 7800 X 10-6 kg / cm^3
= 7.8 E-3 Kg /cm^3

Young Modulus ( steel) : 210 GPa = 210 X10^9 Pa = 210 X10^9 Kg /m s^2
= 210 X 10^9 Kg / 10^2 cm * s^2
2.10 X 10^9 kg /cm s^2 = 2.10E+9 Kg/cm*s^2

Velocity ( 56.33 KMPH) : 56.33 X 10^5 cm / 3600 s
= 1.56E+3 cm/s

Gravity : 9.8m/s2 = 9.8 X 10^2 cm / s^2

now, gm mm ms

Mass : 1 kg = 10^3 ramm

length : 1 m = 10^3 mm

time : 1 s =10^3 ms

Force : 1 N = 1 Kg X m / s^2 = 10^3 g x 10^3 mm / 10^3*10^3 ms^2
= 1 g*mm /ms^2

Stress : 1 Pa = 1 Kg /m s^2 = 10^3 g / 10^3 mm x 10^6 ms^2
=10^-6 g/mm*ms^2

Energy : 1 J = 1 Kg . m^2 / s^2= 10^3 g x 10^6 mm^2/ 10^6 ms^2
= 10^3 g.mm^2 /ms^2

Density (steel) : 7800 kg/m^3 = 7800 * 10^3 g / 10^9 mm^3
=7.8 E-3 g/mm^3

Young modulus (steel) : 210 GPa = 210 X 10^9 Pa = 210X10^9 x 10^-6 g/mm*ms^2
=210 X 10^3 g/ mm*ms^2

Velocity ( 56.33KMPH ): 56.33 x 10^6 mm / 3600x 10^3 ms
=15.64 mm/ms

Gravity : 9.8m/s2 = 9.8 X10^3 mm/ 10^6 ms^2
= 9.8 X 10^-3 mm/ms^2

kg m s ( SI unit )

Mass : 1kg

Length : 1 m

Time : 1 s

Force : N ( newton)
1 N = 1 Kg X m / s^2

stress : Pa ( pascal)

1 Pa = 1 N / m^2
=( 1 Kg X m / s^2 ) / m^2 .... ( put N = Kg X m / s^2)
= Kg /m s^2

Energy = J ( jule)
J = Nm
= (Kg X m / s^2 )/ m .... (put N = Kg X m / s^2)
= Kg . m^2 / s^2

Density : Rh ( Rho)
Rh = 1Kg/m3

YOUNG'S Modulus = Pa
1 Pa = 1 Kg /m s^2

Velocity= KMPH ( 10X3 / 3600 ) m/s
= 0.2777 m/s

GRAVITY = 9.8 m/s2

g cm s

Mass : 1 Kg = 10^3 g

Length : 1 m = 10^2 cm

Time : 1 s

Force : 1 N = 1 Kg X m / s^2 = 10^3 g x 10^2 cm / s^2
= 10^5 g.cm/s^2

Stress : 1 Pa = 1 N / m^2 = 10^5 g.cm/s^2 / 10^4 cm^2
= 10 g/cm. s^2

Energy : 1 J = 1 Kg . m^2 / s^2 = 10^3 g x 10^4 cm^2/ s^2
= 10^7 g.cm^2/ s^2

Density (steel) : 7800 Kg/m^3 = 7800 x 10^3 g/ 10^6 cm^3
=7.8 g/cm^3

Young Modulus (steel) : 210 GPa = 210 x 10^9 Pa = 210x10^9 x 10 g/cm. s^2
=210E10 g/cm.s^2

Velocity (56.33KMPH) = 56.33 X 10^5 cm / 3600 s
= 1.56E+3 cm/s

Gravity (9.8m/s^2) = 9.8X10^2 cm /s^2
= 9.8E+2 cm/s^2

g cm us

um= 10E+6 second

Mass : 10^3 g = 1 kg

Time : 10^6 us = 1 s

length : 10^2 cm = 1 m

force : 1 N = 1 Kg X m / s^2 = 10^3 g x 10^2 cm / 10^6^2 us^2
= 10^-7 g.cm/us^2

stress : 1 Pa = 1 N / m^2 = 1x 10^-7 g.cm/us^2 / 10^4 cm^2
=10^-11 g/cm.us^2

Energy : 1 J = 1 Kg . m^2 / s^2 = 10^3 g x 10^4 cm^2 / 10^12 us^2
= 10^-5 g.cm^2/us^2

Density (steel) : 7800 Kg/m^3 = 7800 x 10^3 g / 10^6 cm^3
= 7.8 g/cm^3

Youngs modulus (steel) : 210 GPa : 210 X10^9 Pa = 210x 10^9 x10-11 g/cm.us^2
=210E-2 g/ cm.us^2

Velocity (56.33KMPH) : 56.33 X 10^5 cm / 3600X 10^6 us
= 1.56E-3 cm/us

Gravity : 9.81 m/s^2 = 9.81 X 10^2 cm / 10^12 us ^2
=9.81E-10 cm/us^2

g mm s
Mass : 10^3 g

Length = 10^3 mm

Time = 1 s

Force : 1 N = 1 Kg X m / s^2 = 10^3 g x 10^3 mm / s^2
= 10^6 g.mm/s^2

Stress : 1 Pa = 1 N / m^2 = 10^6 g.mm/s^2 / 10^6 mm^2
1 g / mm.s^2

Energy : 1 J = 1 Kg . m^2 / s^2 = 10^3 g x 10^6 mm^2/s^2
= 10^9 g.mm^2/ s^2

Density (steel) : 7800 kg/m^3
=7800 x 10^3 g / 10^9 mm^3
= 7.8 E-3 g/mm^3

Young's modulus : 210 Gpa = 210X10^9 Pa = 210X10^9 g / mm.s^2

Velocity : 56.33KMPH : 56.33 X 10^6 mm / 3600 s =1.56E+4 mm/s

Gravity : 9.81 m/s^2 = 9.81 X 10^3 mm / s^2

ton mm s

Tonn = 10E+3 kg

Mass : 1 kg = 10^-3 tonn

Lenth : 1 m = 10^3 mm

time : 1 s

force :1N =1 Kg X m / s^2 = 10^-3 tonn x 10^3 mm / s^2
= 1 tonn. mm / s^2

Stress : 1 Pa = 1 N / m^2 = 1 tonn. mm / s^2 / 10^6 mm^2
= 10^-6 tonn/ mm.s^2

Energy : 1 J = 1 Kg . m^2 / s^2 = 10^-3 tonn x 10^6 mm^2 / s^2
=10^3 tonn*mm^2 / s^2

Density (steel) ;7800 kg /m^3 = 7800 X 10^-3 tonn / 10^-9 mm
= 7.8E+9 tonn /mm^3

Young's Modulus (steel) : 210 Gpa = 210 X 10^ 9 Pa = 210 x10^9 x 10^-6 tonn/ mm.s^2
= 210X10^3 tonn / mm.s^2

Velocity (56.33KMPH ) = 56.33 X 10^6 mm / 3600 s
=1.56E+4 mm/s

Gravity : 9.81 m /s^2 = 9.81 X 10^3 mm / s^2

slug ft s

Mass = 1 kg : 0.0685218 slug = 68.52X10^-3 Slug

Length = 1 m = 3.28084 ft

time = 1 s

Force : 1 N = 1 Kg X m / s^2 = 68.52 X 10^-3 slug * 3.28084 ft / s^2
= 0.2248 slug*ft/s^2

Stress : 1 Pa = 1 N / m^2 = 0.2248 slug*ft/s^2 / (3.28084)^2 ft^2
= 10.7639 slug/ ft* s^2

energy : 1 J = 1 Kg . m^2 / s^2 = 68.52X10^-3 Slug * (3.28084 ft )^2 / s^2
=0.7375 slug *ft^2 / s^2

Density (7800 kg/m^3) = 7800 x 68.52X10^-3 Slug / (3.28084 ft )^3
= 14.4717 slug /ft^3

Young's modulus (steel) : 210 GPa = 210X10^9 Pa = 210E+9 x 10.7639 slug/ ft* s^2
= 2.26E+12 slug/ ft* s^2

Velocity : 56.33KMPH = 56.33 X10^3 x 3.28084 ft / 3600 s
= 51.336 Ft /s

Gravity : 9.81 m/s^2 = 9.81x 3.28084 ft / s^2
= 32.185 ft /s^2

kg mm s

Mass : 1 kg

Length = 1 m = 10^3 mm

time = 1 s

Force = 1 N = 1 Kg X m / s^2 = 1 Kg * 10^3 mm / s^2
= 10^3 kg*mm/ s^2

Stress: 1 pa = 1 N / m^2 = 10^3 kg*mm/ s^2 / 10^6 mm^2
10^-3 kg / mm*s^2

Energy : 1 J = 1 Kg . m^2 / s^2 = 1 Kg x 10^6 mm^2 / s^2
= 10^6 kg.mm^2/s^2

Density (steel) = 7800 kg/m^3 = 7800 kg / 10^9 mm^3
=7.8 x 10^-6 kg / mm^2

Young's modulus (steel) : 210 GPa = 210 X 10^9 Pa = 210X10^9 x 10^-3 kg / mm*s^2
= 210x10^6 kg /mm.s^2

Velocity ( 56.33KMPH) = 56.33 X 10^6 mm / 3600 s
=1.56E+4 mm/s

Gravity : 9.81 m/s^2 = 9.81 X10^3 mm /s^2

g cm ms

Mass = 1 kg = 10^3 g

length = 1 m = 10^2 cm

time = 1 s = 10^3 ms

Force = 1 N =1 Kg X m / s^2 = 10^3 g x 10^2 cm / 10^6 ms^2
= 10^-1 g.cm/ms^2

Stress : 1 Pa = 1 N / m^2 = (10^-1 g.cm/ms^2 ) / 10^4 cm^2
= 10^-5 g/ cm*ms^2

energy : 1 J = 1 Kg . m^2 / s^2 = 10^3 g * 10^4 cm^2 / 10^6 ms^2
=10 g.cm/ms^2

Density (steel) : 7800 Kg/m^3 = 7800x 10^3 / 10^6 cm^3
=7.8 g/cm^3

Young's Modulus (steel)= 210X 10^9 Pa = 210X10^9 x10^-5 g/ cm*ms^2
=210x 10^4 g/ cm*ms^2

Velocity 56.33KMPH = 56.33 X10^5 cm / 3600 x10^3 ms
= 1.56 cm/ms

Gravity : 9.81 m/s^2 = 9.81x10^2 cm / 10^6 ms^2
= 9.81x10^-4 cm/ms^2

kg mm ms

Mass : 1 Kg

Length = 1 m = 10^3 mm

Time =1 s =10^3 ms

Force = 1 N = 1 Kg X m / s^2 = 1Kg x 10^3 mm / 10^6 ms^2
= 10^-3 kg.mm/ms^2

Stress : 1Pa = 1 N / m^2 = 10^-3 kg.mm/ms^2 / 10^6 mm^2
=10^-9 kg / mm.ms^2

Energy : 1 J =1 Kg . m^2 / s^2 = 1Kg x 10^6 mm ^2 / 10^6 ms ^2
1 Kg mm^2/ms^2

Density (steel) = 7800 Kg/m^3 = 7800 kg / 10^9 mm^3
=7.8E-6 kg/mm^3

Young's Modulus( steel) ; 210X10^9 Pa = 210x 10^9 x 10^-9 kg / mm.ms^2
= 210 Kg /mm.ms^2

Velocity 56.33KMPH = 56.33X10^6 / 3600X10^3 mm/ms
= 15.65 mm/ms

gravity 9.81 m/s^2 = 9.81 X10^3 mm / 10^6 ms^2
= 9.81 X 10^-3 mm/ms^2

The details charts is shared below

Sr No	Unit system	Mass	length	Time	Force	Stress	Energy	DENSITY	YOUNG'S Modulus	Velocity	GRAVITY
1	Kg-m-s	1 Kg	1 m	1 s	1 N = 1 Kg * m / s^2	1 Pa = 1 Kg /m s^2	1 J = 1 Kg . m^2 / s^2	7800 Kg/m3	210 Gpa = 210*E+9 Pa	56.33KMPH	9.8m/s2
2	Kg cm ms	1 Kg	10^2 cm	10^3 ms	1 x 10^-4 kg*cm / ms^2	1 x 10 ^-8 kg/cm*ms^2	10^-2 Kg .cm^2 / ms^2	7.8E-3 kg/cm^3	210E+5 kg*cm /ms^2	1.560341 cm/ms	9.8E-4 cm/ms^2
3	Kg cm s	1 Kg	10^2 cm	1 s	10^2 kg cm/s^2	10^-2 kg /cm s^2	10^4 kg cm^2 / s^2	7.8 E-3 Kg /cm^3	2.10 kg /cm s^2	1.56E+3 cm/s	9.8 X 10^2 cm / s^2
4	gm mm ms	10^3 g	10^3 mm	10^3 ms	1 g*mm /ms^2	10^-6 g/mm*ms^2	10^3 g.mm^2 /ms^2	7.8 E-3 g/mm^3	210 X 10^3 g/ mm*ms^2	15.64 mm/ms	9.8 X 10^-3 mm/ms^2
5	Kg m s	1 Kg	1 m	1 s	1 N = 1 Kg * m / s^2	1 Pa = 1 Kg /m s^2	1 J = 1 Kg . m^2 / s^2	7800 Kg/m3	210E+9 Pa	56.33KMPH	9.8m/s2
6	g cm s	10^3 g	10^2 cm	1 s	10^5 g.cm/s^2	10 g/cm. s^2	10^7 g.cm^2/ s^2	7.8 g/cm^3	210E+10 g/cm.s^2	1.56E+3 cm/s	9.8E+2 cm/s^2
7	g cm us	10^3 g	10^2 cm	10^6 us	10^-7 g.cm/us^2	10-11 g/cm.us^2	10^-5 g.cm^2/us^2	7.8 g/cm^3	210E-2 g/ cm.us^2	1.56E-3 cm/us	9.81E-10 cm/us^2
8	g mm s	10^3 g	10^3 mm	1 s	10^6 g.mm/s^2	1 g / mm.s^2	10^9 g.mm^2/ s^2	7.8 E-3 g/mm^3	210X10^9 g / mm.s^2	1.56E+4 mm/s	9.81 X 10^3 mm / s^2
9	ton mm s	10^-3 tonn	10^3 mm	1 s	1 tonn. mm / s^2	10^-6 tonn/ mm.s^2	10^3 tonn*mm^2 / s^2	7.8E+9 tonn /mm^3	210X10^3 tonn / mm.s^2	1.56E+4 mm/s	9.81 X 10^3 mm / s^2
10	slug ft s	68.52X10^-3 Slug	3.28084 ft	1 s	0.2248 slug*ft/s^2	10.7639 slug/ ft* s^2	0.7375 slug *ft^2 / s^2	14.4717 slug /ft^3	2.26E+12 slug/ ft* s^2	51.336 Ft /s	32.185 ft /s^2
11	kg mm s	1 Kg	10^3 mm	1 s	10^3 kg*mm/ s^2	10^-3 kg / mm*s^2	10^6 kg.mm^2/s^2	7.8 x 10^-6 kg / mm^2	210x10^6 kg /mm.s^2	1.56E+4 mm/s	9.81 X10^3 mm /s^2
12	g cm ms	10^3 g	10^2 cm	10^3 ms	10^-1 g.cm/ms^2	10^-5 g/ cm*ms^2	10 g.cm/ms^2	7.8 g/cm^3	210x 10^4 g/ cm*ms^2	1.56 cm/ms	9.81x10^-4 cm/ms^2
13	kg mm ms	1Kg	10^3 mm	10^3 ms	10^-3 kg.mm/ms^2	10^-9 kg / mm.ms^2	1 Kg mm^2/ms^2	7.8E-6 kg/mm^3	210 Kg /mm.ms^2	15.65 mm/ms	9.81 X 10^-3 mm/ms^2