Week - 1 - Consistency of Units

OBJECTIVE:

The objective of this challenge is to understand how to convert given parameters from SI unit system to different unit systems and to calculate conversion factors.

LS-DYNA does not have a unit system option. And the user must input all the values of different parameters consistetly in a fixed unit system. So a good understanding of conversions from one system to another is required.

Given measurements of different parameters are-

MASS                       1kg
LENGTH                    1m
TIME                        1s
FORCE                      1N
STRESS                    1Pa
ENERGY                    1Nm
DENSITY                   1Kg/m3
YOUNG'S Modulus      210GPa
Velocity                     56.33KMPH
GRAVITY                   9.8m/s2

CONVERSION CALCULATIONS AND TABLES:

Conversion factors for fundamental quantities(mass, length and time) are

Mass      1kg =1000 gm =0.01 tonne =0.068 slug

Length   0.001km =1m =100 cm =1000 mm =3.28 ft

Time     1s =1000 ms =1e+6 us

 Calculation of all parameters for conversion from SI unit to g/mm/ms unit system:

(Conversion factors mentioned are for SI unit to (g mm ms) system)

                             SI units(kg m s)               Conversion to (g mm ms)

Mass                      1kg                                 1000 g

Length                    1m                                 1000 mm

Time                       1s                                  1000 ms

Force                      1N=1 kg*m/s2             =(1000g*1000mm)/(1000ms*1000ms)

                                                                   =1 g*mm/ms2

                              conversion factor          =1

Stress                    1Pa=1 kg/(m*s2)           =1000g/(1000mm*1000ms*1000ms)

                                                                  =1e-6 g/(mm*ms2)

                              conversion factor         =1e-6

Energy                   1Nm=1 kg*m2/s2          =(1000g*1000mm*1000mm)/(1000ms*1000ms)

                                                                  =1000 g*mm2/ms2

                             conversion factor         =1e+3

Density                  1kg/m3                         =1000g/(1e+9 mm3)

                                                                  =1e-6 g/mm3

                              conversion factor         =1e-6

Young's Modulus     210Gpa =210e+9 Pa     =210e+9(kg/m*s2) =210e+9*(1e-6) g/(mm*ms2)

                                                                  =210e+3 g/(mm*ms2)

                                                                  =2.1e+5 g/(mm*ms2)

                             conversion factor          =1e-6

Velocity                 56.33 km/h

                            =56.33*1000m/3600s

                            =15.647 m/s                 =15.647*1000mm/1000ms

                                                                  =15.647 mm/ms

                             conversion factor          =1

Gravity                 9.8 m/s2                         =9.8*1000mm/(1e+6 ms2)

                                                                    =9.8e-3 mm/ms2

                            conversion factor           =1e-3        

Table with the parameters in different unit systems

Unit system	Mass 1kg	Length 1m	Time 1s	Force 1N	Stress 1Pa	Energy 1Nm	Density 1Kg/m3	Young's Modulus 210Gpa	Velocity 56.33 Kmph	Gravity 9.8m/s2
kg m s	1 kg	1 m	1 s	1 kg*m/s2	1 kg/(m*s2)	1 kg*m2/s2	1 kg/m3	2.1e+11 kg/(m*s2)	15.647 m/s	9.8 m/s2
kg cm ms	1 kg	100 cm	1000 ms	1e-4 kg*cm/ms2	1e-8 kg/(cm*ms2)	1e-2 kg*cm2/ms2	1e-6 kg/cm3	2.1e+3 kg/(cm*ms2)	1.5647 cm/ms	9.8e-4 cm/ms2
kg cm s	1 kg	100 cm	1 s	100 kg*cm/s2	1e-2 kg/(cm*s2)	1e+4 kg*cm2/s2	1e-6 kg/cm3	2.1e+9 kg/(cm*s2)	1564.7 cm/s	9.8e+2 cm/s2
g mm ms	1000 g	1000 mm	1000 ms	1 g*mm/ms2	1e-6 g/(mm*ms2)	1000 g*mm2/ms2	1e-6 g/mm3	2.1e+5 g/(mm*ms2)	15.647 mm/ms	9.8e-3 mm/ms2
g cm s	1000 g	100 cm	1 s	1e+5 g*cm/s2	10 g/(cm*s2)	1e+7 g*cm2/s2	1e-3 g/cm3	2.1e+12 g/(cm*s2)	1564.7 cm/s	9.8e+2 cm/s2
g cm us	1000 g	100 cm	1e+6 us	1e-7 g*cm/us2	1e-11 g/(cm*us2)	1e-5 g*cm2/us2	1e-3 g/cm3	2.1 g/(cm*us2)	15.647e-4 cm/us	9.8e-10 cm/us2
g mm s	1000 g	1000 mm	1 s	1e+6 g*mm/s2	1 g/(mm*s2)	1e+9 g*mm2/s2	1e-6 g/mm3	2.1e+11 g/(mm*s2)	15647 mm/s	9.8e+3 mm/s2
ton mm s	0.001 ton	1000 mm	1 s	1 ton*mm/s2	1e-6 ton/(mm*s2)	1000 ton*mm2/s2	1e-12 ton/mm3	2.1e+5 ton/(mm*s2)	15647 mm/s	9.8e+3 mm/2
slug ft s	0.068 slug	3.28 ft	1 s	0.2246 slug*ft/s2	0.0208 slug/(ft*s2)	0.7366 slug*ft2/s2	1.93e-3 slug/ft3	4.36e+9 slug/(ft*s2)	51.322 ft/s	32.144 ft/s2
kg mm s	1 kg	1000 mm	1 s	1000 kg*mm/s2	1e-3 kg/(mm*s2)	1e+6 kg*mm2/s2	1e-9 kg/mm3	2.1e+8 kg/(mm*s2)	15647 mm/s	9.8e+3 mm/s2
g cm ms	1000 g	100 cm	1000 ms	0.1 g*cm/ms2	1e-5 g/(cm*ms2)	10 g*cm2/ms2	1e-3 g/cm3	2.1e+6 g/(cm*ms2)	1.5647 cm/ms	9.8e-4 cm/ms2
kg mm ms	1 kg	1000 mm	1000 ms	1e-3 kg*mm/ms2	1e-9 kg/(mm*ms2)	1 kg*mm2/ms2	1e-9 kg/mm3	210 kg/(mm*ms2)	15.647 mm/ms	9.8e-3 mm/ms2

Conversion factors for given parameters from SI unit system to different systems-

Unit system - kg cm ms

Parameter	Units	Conversion factor
Force	kg*cm/ms2	1e-4
Stress	kg/(cm*ms2)	1e-8
Energy	kg*cm2/ms2	1e-2
Density	kg/cm3	1e-6
Young's Modulus	kg/(cm*ms2)	1e-8
Velocity	cm/ms	0.1
Gravity	cm/ms2	1e-4

Unit system - kg cm s

Parameter	Units	Conversion factor
Force	kg*cm/s2	1e+2
Stress	kg/(cm*s2)	1e-2
Energy	kg*cm2/s2	1e+4
Density	kg/cm3	1e-6
Young's Modulus	kg/(cm*s2)	1e-2
Velocity	cm/s	1e+2
Gravity	cm/s2	1e+2

Unit system - g mm ms

Parameter	Units	Conversion factor
Force	g*mm/ms2	1
Stress	g/(mm*ms2)	1e-6
Energy	g*mm2/ms2	1e+3
Density	g/mm3	1e-6
Young's Modulus	g/(mm*ms2)	1e-6
Velocity	mm/ms	1
Gravity	mm/ms2	1e-3

Unit system - g cm s

Parameter	Units	Conversion factor
Force	g*cm/s2	1e+5
Stress	g/(cm*s2)	10
Energy	g*cm2/s2	1e+7
Density	g/cm3	1e-3
Young's Modulus	g/(cm*ms2)	10
Velocity	cm/s	100
Gravity	cm/s2	100

Unit system - g cm us

Parameter	Units	Conversion factor
Force	g*cm/us2	1e-7
Stress	g/(cm*us2)	1e-11
Energy	g*cm2/us2	1e-5
Density	g/cm3	1e-3
Young's Modulus	g/(cm*us2)	1e-11
Velocity	cm/us	1e-4
Gravity	cm/us2	1e-10

Unit system - g mm s

Parameter	Units	Conversion factor
Force	g*mm/s2	1e+6
Stress	g/(mm*s2)	1
Energy	g*mm2/s2	1e+9
Density	g/mm3	1e-6
Young's Modulus	g/(mm*s2)	1
Velocity	mm/s	1000
Gravity	mm/s2	1000

Unit system - ton mm s

Parameter	Units	Conversion factor
Force	ton*mm/s2	1
Stress	ton/(mm*s2)	1e-6
Energy	ton*mm2/s2	1000
Density	ton/mm3	1e-12
Young's Modulus	ton/(mm*s2)	1e-6
Velocity	mm/s	1000
Gravity	mm/s2	1000

Unit system -slug ft s

Parameter	Units	Conversion factor
Mass	Slug	0.068
Length	ft	3.28
Time	s	1
Force	slug*ft/s2	0.2246
Stress	slug/(ft*s2)	0.0208
Energy	slug*ft2/s2	0.7366
Density	slug/ft3	1.93e-3
Young's Modulus	slug/(ft*s2)	0.0208
Velocity	ft/s	3.28
Gravity	ft/s2	3.28

Unit system -kg mm s

Parameter	Units	Conversion factor
Force	kg*mm/s2	1000
Stress	kg/(mm*s2)	1e-3
Energy	kg*mm2/s2	1e+6
Density	kg/mm3	1e-9
Young's Modulus	kg/(mm*s2)	1e-3
Velocity	mm/s	1000
Gravity	mm/s2	1000

Unit system - g cm ms

Parameter	Units	Conversion factor
Force	g*cm/ms2	0.1
Stress	g/(cm*ms2)	1e-5
Energy	g*cm2/ms2	10
Density	g/cm3	1e-3
Young's Modulus	g/(cm*ms2)	1e-5
Velocity	cm/ms	0.1
Gravity	cm/ms2	1e-4

Unit system - kg mm ms

Parameter	Units	Conversion factor
Force	kg*mm/ms2	1e-3
Stress	kg/(mm*ms2)	1e-9
Energy	kg*mm2/ms2	1
Density	kg/mm3	1e-9
Young's Modulus	kg/(mm*ms2)	1e-9
Velocity	mm/ms	1
Gravity	mm/ms2	1e-3

LEARNING OUTCOME:

• A good understanding of different unit systems and conversion from one unit system to another.
• Conversion factors and it's calculation.