Week - 1 - Consistency of Units
AIM :-
The aim of this challenge is to convert the given SI unit values of given quantities to all different parameters & also to prepare consistent unit system table for different unit system.
OBJECTIVE :-
The objective of this challenge is to convert the given values of the quantity to different system of units. And also prepare a table so that in near future while performing the various challenges of LS dyna it can be used frequently and without any issues. As LS Dyna don’t have any default system of units, so by preparing this table we can use it frequently to solve the challenges.
PROCEDURE :-
Each and every measurement given in the input parametres are converted into respective system of units. The input measurement values are displayed below,
1 Kg = 1000 gm = 0.001 ton = 0.068 slug
1 m = 1000 mm = 100 cm = 3.28 ft
1 s = 1000 ms = 106 us
The parameters to which different units to be assigned are:
- Mass = 1kg
- Length = 1m
- Time = 1s
- Force = 1N
- Stress = 1 Pa
- Energy = 1 Nm
- Density = 1 Kg/m3
- Young’s Modulus = 210 GPa
- Velocity = 56.33 kmph
- Gravity = 9.88 m/s2
The units in which the different parameters are to be converted are as follows:
- Kg cm ms
- Kg cm s
- gm mm ms
- kg m s
- g cm s
- g cm us
- g mm s
- ton mm s
- slug ft s
- kg mm s
- g cm ms
- kg mm ms
1.Conversion of SI unit to kg cm ms
- Mass = 1 kg
1 kg
- Length = 1m
100 cm
- Time = 1 sec
1000 ms
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s^2
=> (1 kg*100cm)/(1000ms)2
=> 10-4 (kg*cm)/ms2
Conversion factor = 10-4
- Stress = 1 Pa
1 Pa => 1N/m^2
As from the above derived 1N = 10-1 (kg cm)/ms2
=> {10-1 (kg cm/ms2)} / (100 cm2)
=> 10-3 kg/cm ms2
Conversion factor = 10-3
- Energy = 1 Nm
- 1N *1 m
- {10-4 kg cm/ms2} * 100 cm
- 10 kg cm2/ms2
- 10-2 kg cm2/ms2
Conversion factor = 10-2
- Density = 1Kg/m^3
- 1 kg / (100 cm)3
- 1 kg/1000000 cm3
- 10-6 kg/cm3
Conversion factor = 10-6
- Young’s Modulus = 210 GPa
1 Pa = 10-3 kg/cm*ms2
1 GPa = 109 * 10-3 kg/cm*ms2
210 GPa = 210 * 106 kg/cm*ms2
Conversion factor = 106
- Velocity = 56.33 Kmph
Km/h
1Km = 10000 cm = 104 cm
1 hr = 60min*60sec*1000 = 3600000= 36*105 ms
1 kmph
=> (104 )/(36*105)
=> 0.00277 cm/ms
56.33 kmph =
=> 56.33 * 0.00277 cm/ms
=> 0.1560 cm/ms
Conversion factor =0.00277
- Gravity = 9.88 m/s2
1 m/s2 = 100 cm/(1000ms)2 = 10 -4 cm/ms2
9.8 m/s2 = 9.8*10-4 cm/ms2
Conversion Factor = 10-4
2. Conversion of SI unit to kg cm s
- Mass = 1 kg
1 kg
- Length = 1m
100 cm
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s2
=> (1 kg*100cm)/(1s)2
=> 100 kg cm/s2
Conversion factor = 100
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 100 kg cm/s2
=> (100 kg cm/s2 )/ (100 cm)2
=> 10-2 kg/cm s2
Conversion factor = 10-2
- Energy = 1 Nm
- 1N *1 m
- 100 kg cm/s2 * 100 cm
- 104 kg cm2/s2
Conversion factor = 104
- Density = 1Kg/m^3
- 1 kg / (100 cm)3
- 1 kg/10000 cm3
- 10-4 kg/cm3
Conversion factor = 10-4
- Young’s Modulus = 210 GPa
1 Pa = 10-2 kg/cm s2
1 GPa = 109 * 10-2 kg/cm s2
210 GPa = 210 * 107 kg/cm*s2
Conversion factor = 107
- Velocity = 56.33 Kmph
Km/h
1Km = 10000 cm = 104 cm
1 hr = 60min*60sec
= 3600
= 3600 s
1 kmph
=> (104 )/(3600)
=> 2.77 cm/s
56.33 kmph =
=> 56.33 * 2.77 cm/s
=> 156.03 cm/s
Conversion factor =2.77
- Gravity = 9.88 m/s2
1 m/s2 = 100 cm/(1s)2
= 100 cm/s2
9.8 m/s2 = 9.8*100 cm/s2
Conversion Factor = 100
3. Conversion of SI unit to gm mm ms
- Mass = 1 kg
1000gm
- Length = 1m
1000 mm
- Time = 1 sec
1000 ms
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s^2
=> (1000gm*1000mm)/(1000ms)^2
=> 1 (gm*mm)/ms^2
Conversion factor = 1
- Stress = 1 Pa
1 Pa => 1N/m^2
As from the above derived 1N = 1(gm*mm/ms^2)
=> {1 (gm*mm/ms^2)} / (1000mm^2)
=> 1*10^-6 gm/mm*ms^2
Conversion factor = 10^-6
- Energy = 1 Nm
- 1N *1 m
- {1 gm*mm/ms^2} * 1000 mm
- 1000 gm*mm^2/ms^2
- 10^3 gm mm^2/ms^2
Conversion factor = 10^3
- Density = 1Kg/m^3
- 1000 gm / (1000 mm)^3
- 1 gm/1000000 mm^3
- 10^-6 gm/mm^3
Conversion factor = 10^-6
- Young’s Modulus = 210 GPa
1 Pa = 10^-6 gm/mm ms2
1 GPa = 109 * 10 -6 gm/mm ms2
210 GPa = 210 * 103 gm/mm ms2
Conversion factor = 103
- Velocity = 56.33 Kmph
Km/h
1Km = 1000000 mm = 106 mm
1 hr = 60min*60sec*1000
= 3600000
= 36*105 ms
1 kmph
=> (106 )/(36*105)
=> 0.277 mm/ms
56.33 kmph =
=> 56.33 * 0.277 mm/ms
=> 15.60 mm/ms
Conversion factor =0.277
- Gravity = 9.88 m/s^2
1 m/s2 = 1000mm/(1000ms2)
= 10 -3 mm/ms2
9.8 m/s2 = 9.8*10-3 mm/ms2
Conversion Factor = 10-3
4. Conversion of SI unit to kg m s
- Mass = 1 kg
1 kg
- Length = 1m
1 m
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s2
=> (1 kg*1m)/(1s)2
=> 1 kg m/s2
Conversion factor = 100
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 1 kg m/s2
=> (1 kg m/s2) / (1 m)2
=> 1 kg/m s2
Conversion factor = 1
- Energy = 1 Nm
- 1N *1 m
- 1 kg m/s2 * 1 m
- 1 kg m2/s2
Conversion factor = 1
- Density = 1Kg/m^3
- 1 kg / (1 m)3
- 1 kg/1 m3
- 10 kg/m3
Conversion factor = 10
- Young’s Modulus = 210 GPa
1 Pa = 1 kg/m s2
1 GPa = 109 * 1 kg/m s2
210 GPa = 210 * 109 kg/m s2
Conversion factor = 109
- Velocity = 56.33 Kmph
Km/h
1Km = 1000 m = 103 m
1 hr = 60min*60sec
= 3600 s
1 kmph
=> (103 )/(3600)
=> 0.277 m/s
56.33 kmph =
=> 56.33 * 0.277 m/s
=> 15.603 m/s
Conversion factor = 0.277
- Gravity = 9.88 m/s2
1 m/s2 = 1 m/(1s)2
= 1 m/s2
9.8 m/s2 = 9.8*1 m/s2
Conversion Factor = 1
5. Conversion of SI unit to g cm s
- Mass = 1 kg
1000gm
- Length = 1m
100 cm
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1000 g * 1m/s2
=> (1000 g*100cm)/(1s)2
=> 105 g cm/s2
Conversion factor = 105
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 105 g cm/s2
=> 105 g cm/s2/ (100 cm)2
=> 10 g/cm s2
Conversion factor = 10
- Energy = 1 Nm
- 1N *1 m
- 105 g cm/s2 * 100 cm
- 107 g cm2/s2
Conversion factor = 107
- Density = 1Kg/m^3
- 1000 g / (100 cm)3
- 1000 g/1000000 cm3
- 10-3 g/cm3
Conversion factor = 10-3
- Young’s Modulus = 210 GPa
1 Pa = 10 g/cm s2
1 GPa = 109 * 10 g/cm s2
210 GPa = 210 * 1010 g/cm s2
Conversion factor = 1010
- Velocity = 56.33 Kmph
Km/h
1Km = 10000 cm = 104 cm
1 hr = 60min*60sec
= 3600
= 3600 s
1 kmph
=> (104 )/(3600)
=> 2.77 cm/s
56.33 kmph =
=> 56.33 * 2.77 cm/s
=> 156.03 cm/s
Conversion factor =2.77
- Gravity = 9.88 m/s2
1 m/s2 = 100 cm/(1s)2
= 100 cm/s2
9.8 m/s2 = 9.8*100 cm/s2
Conversion Factor = 100
6. Conversion of SI unit to g cm us(micro-sec)
- Mass = 1 kg
1000 gm
- Length = 1m
100 cm
- Time = 1 sec
106 us
- Force = 1 N
F => mass* acceleration
=> 1000 g * 100 cm/(106 us)2
=> (1000 g*100 cm)/(106 us)2
=> 10-1 g cm/us2
Conversion factor = 10-1
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 10-1 g cm/us2
=> 10-1 g cm/us2/ (100 cm)2
=> 10-3 g/cm us2
Conversion factor = 10-3
- Energy = 1 Nm
- 1N *1 m
- 10-1 g cm/us2 * 100 cm
- 10 g cm2/us2
Conversion factor = 10
- Density = 1Kg/m^3
- 1000 g / (100 cm)3
- 1000 g/1000000 cm3
- 10-3 g/cm3
Conversion factor = 10-3
- Young’s Modulus = 210 GPa
1 Pa =10-3 g/cm us2
1 GPa = 109 * 10-3 g/cm us2
210 GPa = 210 * 106 g/cm us2
Conversion factor = 106
- Velocity = 56.33 Kmph
Km/h
1Km = 10000 cm = 104 cm
1 hr = 60min*60sec*106 us
= 36*108 us
= 36* 108 us
1 kmph
=> (104 )/(36*108)
=> 0.00000278 cm/ us
56.33 kmph =
=> 56.33 * 0.00000278 cm/us
=> 0.000156 cm/us
Conversion factor =0.00000278
- Gravity = 9.88 m/s2
1 m/s2 = 100 cm/(106 us)2
= 100 cm/ 1012 us2
9.8 m/s2 = 9.8*10-10 cm/us2
Conversion Factor = 10-10
7. Conversion of SI unit to g mm s
- Mass = 1 kg
1000 gm
- Length = 1m
1000 mm
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1000 g * 1m/s2
=> (1000 g*1000 mm)/(1s)2
=> 106 g mm/s2
Conversion factor = 106
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 106 g mm/s2
=> (106 g mm/s2 ) /(1000 mm)2
=> 1 g/mm s2
Conversion factor = 1
- Energy = 1 Nm
- 1N *1 m
- 106 g mm/s2 * 1000 mm
- 109 g mm2/s2
Conversion factor = 109
- Density = 1Kg/m^3
- 1000 g / (1000 mm)3
- 1000 g/1000000000 mm3
- 10-6 g/mm3
Conversion factor = 10-6
- Young’s Modulus = 210 GPa
1 Pa = 1 g/mm s2
1 GPa = 109 * 1 g/mm s2
210 GPa = 210 * 109 g/mm s2
Conversion factor = 109
- Velocity = 56.33 Kmph
Km/h
1Km = 1000000 mm = 106 mm
1 hr = 60min*60sec
= 3600
= 3600 s
1 kmph
=> (106 )/(3600)
=> 277.7 mm/s
56.33 kmph =
=> 56.33 * 277.7 mm/s
=> 15603 mm/s
Conversion factor =277.7
- Gravity = 9.88 m/s2
1 m/s2 = 1000 mm/(1s)2
= 1000 mm/s2
9.8 m/s2 = 9.8*1000 mm/s2
Conversion Factor = 103
8. Conversion of SI unit to ton mm ms
- Mass = 1 kg
0.001 ton
- Length = 1m
1000 mm
- Time = 1 sec
1000 ms
- Force = 1 N
F => mass* acceleration
=> 0.001 ton * 1m/s^2
=> (0.001 ton *1000 mm)/(1000ms)2
=> 10-6 ton mm/ms2
Conversion factor = 10-6
- Stress = 1 Pa
1 Pa => 1N/m^2
As from the above derived 1N = 10-6 (ton mm)/ms2
=> {10-6 (ton mm)/ms2} / (1000 mm)2
=> 10-12 ton/mm ms2
Conversion factor = 10-12
- Energy = 1 Nm
- 1N *1 m
- {10-6 (ton mm)/ms2} * 1000 mm
- 10-3 ton mm2/ms2
- 10-3 ton mm2/ms2
Conversion factor = 10-3
- Density = 1Kg/m^3
- 001 ton / (1000 mm)3
- 001 ton/1000000000 mm3
- 10-12 ton/mm3
Conversion factor = 10-12
- Young’s Modulus = 210 GPa
1 Pa = 10-12 ton/mm ms2
1 GPa = 109 * 10-12 ton/mm ms2
210 GPa = 210 * 10-3 ton/mm ms2
Conversion factor = 10-3
- Velocity = 56.33 Kmph
Km/h
1Km = 1000000 mm = 106 mm
1 hr = 60min*60sec*1000
= 3600000
= 36*105 ms
1 kmph
=> (106 )/(36*105)
=> 0.277 mm/ms
56.33 kmph =
=> 56.33 * 0.277 mm/ms
=> 15.60 mm/ms
Conversion factor =0.277
- Gravity = 9.88 m/s2
1 m/s2 = 1000 mm/(1000 ms)2
= 10 -3 mm/ms2
9.8 m/s2 = 9.8*10-3 mm/ms2
Conversion Factor = 10-3
9. Conversion of SI unit to slug ft s
- Mass = 1 kg
0.068 slug
- Length = 1m
3.28 ft
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s2
=> (0.068 slug*3.28 ft)/(1s)2
=> 0.22 slug ft/s2
Conversion factor = 0.22
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 0.22 slug ft/s2
=> 0.22 slug ft/s2 / (3.28 ft)2
=> 0.0205 slug/ft s2
Conversion factor = 0.0205
- Energy = 1 Nm
- 1N *1 m
- 22 slug ft/s2 * 3.28 ft
- 7216 slug ft2/s2
Conversion factor = 0.7216
- Density = 1Kg/m^3
- 1 kg / (1 m)3
- 068 slug/(3.28 ft)3
- 068 slug/ 35.29 ft3
- 0019 slug/ft3
Conversion factor = 0.0019
- Young’s Modulus = 210 GPa
1 Pa = 0.0205 slug/ft s2
1 GPa = 109 * 0.0205 slug/ft s2
210 GPa = 210 * 109 * 0.0205 slug/ft s2
210 GPa = 4.305*109 slug/ft s2
Conversion factor = 0.0205
- Velocity = 56.33 Kmph
Km/h
1Km = 1000 m = 103 m = 103 * 3.28 ft
1 hr = 60min*60sec
= 3600 s
1 kmph
=> (3.28*103 ft)/(3600 s)
=> 0.911 ft/s
56.33 kmph =
=> 56.33 * 0.911 ft/s
=> 51.316 ft/s
Conversion factor =0.911
- Gravity = 9.88 m/s2
1 m/s2 = 3.28 ft/(1s)2
= 3.28 ft/s2
9.8 m/s2 = 9.8*3.28 ft/s2 = 32.14 ft/s2
Conversion Factor = 3.28
10. Conversion of SI unit to kg mm s
- Mass = 1 kg
1 kg
- Length = 1m
1000 mm
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s2
=> (1 kg*1000 mm)/(1s)2
=> 1000 kg mm/s2
Conversion factor = 100
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 1000 kg mm/s2
=> (1000 kg mm/s2 )/ (1000 mm)2
=> 10-3 kg/mm s2
Conversion factor = 10-3
- Energy = 1 Nm
- 1N *1 m
- 1000 kg mm/s2 * 1000 mm
- 106 kg mm2/s2
Conversion factor = 106
- Density = 1Kg/m^3
- 1 kg / (1000 mm)3
- 1 kg/1000000000 mm3
- 10-9 kg/mm3
Conversion factor = 10-9
- Young’s Modulus = 210 GPa
1 Pa = 10-3 kg/mm s2
1 GPa = 109 * 10-3 kg/mm s2
210 GPa = 210 * 106 kg/mm s2
Conversion factor = 106
- Velocity = 56.33 Kmph
Km/h
1Km = 1000000 mm = 106 mm
1 hr = 60min*60sec
= 3600
= 3600 s
1 kmph
=> (106 )/(3600)
=> 277.78 mm/s
56.33 kmph =
=> 56.33 * 277.78 mm/s
=> 15603 mm/s
Conversion factor =277.78
- Gravity = 9.88 m/s2
1 m/s2 = 1000 mm/(1s)2
= 1000 mm/s2
9.8 m/s2 = 9.8*1000 mm/s2
Conversion Factor = 103
11. Conversion of SI unit to g cm ms
- Mass = 1 kg
1000gm
- Length = 1m
100 cm
- Time = 1 sec
1000 ms
- Force = 1 N
F => mass* acceleration
=> 1000 g * 1m/s2
=> (1000 g*100cm)/(1000 ms)2
=> 10-1 g cm/ms2
Conversion factor = 10-1
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 10-1 g cm/ms2
=> 10-1 g cm/ms2 / (100 cm)2
=> 10-3 g/cm ms2
Conversion factor = 10-3
- Energy = 1 Nm
- 1N *1 m
- 10-1 g cm/ms2 * 100 cm
- 10 g cm2/ms2
Conversion factor = 10
- Density = 1Kg/m^3
- 1000 g / (100 cm)3
- 1000 g/1000000 cm3
- 10-3 g/cm3
Conversion factor = 10-3
- Young’s Modulus = 210 GPa
1 Pa = 10-3 g/cm ms2
1 GPa = 109 * 10-3 g/cm ms2
210 GPa = 210 * 106 g/cm ms2
Conversion factor = 106
- Velocity = 56.33 Kmph
Km/h
1Km = 10000 cm = 104 cm
1 hr = 60min*60sec*1000
= 36*105 ms
= 36*105 ms
1 kmph
=> (105 cm)/( 36*105 ms)
=> 0.0277 cm/ms
56.33 kmph =
=> 56.33 * 0.0277 cm/ms
=> 1.5603 cm/ms
Conversion factor =0.0277
- Gravity = 9.88 m/s2
1 m/s2 = 100 cm/(1000 ms)2
= 10-4 cm/ms2
9.8 m/s2 = 9.8*10-4 cm/ms2
Conversion Factor = 10-4
12. Conversion of SI unit to kg mm ms
- Mass = 1 kg
1 kg
- Length = 1m
1000 mm
- Time = 1 sec
1000 ms
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s^2
=> (1 kg*1000 mm)/(1000ms)2
=> 10-3 (kg*mm)/ms2
Conversion factor = 10-1
- Stress = 1 Pa
1 Pa => 1N/m^2
As from the above derived 1N = 10-3 (kg*mm)/ms2
=> {10-3 (kg*mm)/ms2} / (1000 mm)2
=> 10-9 kg/mm ms2
Conversion factor = 10-9
- Energy = 1 Nm
- 1N *1 m
- {10-3 (kg mm)/ms2} * 1000 mm
- 1 kg mm2/ms2
- 1 kg mm2/ms2
Conversion factor = 1
- Density = 1Kg/m^3
- 1 kg / (1000 mm)3
- 1 kg/1000000000 mm3
- 10-9 kg/mm3
Conversion factor = 10-9
- Young’s Modulus = 210 GPa
1 Pa = 10-9 kg/mm ms2
1 GPa = 109 * 10-9 kg/mm ms2
210 GPa = 210 * 1 kg/mm ms2
Conversion factor = 1
- Velocity = 56.33 Kmph
Km/h
1Km = 1000000 mm = 106 mm
1 hr = 60min*60sec*1000
= 3600000
= 36*105 ms
1 kmph
=> (106 )/(36*105)
=> 0.277 mm/ms
56.33 kmph =
=> 56.33 * 0.277 mm/ms
=> 15.60 mm/ms
Conversion factor = 0.277
- Gravity = 9.88 m/s2
1 m/s2 = 1000 mm/(1000 ms)2
= 10 -3 mm/ms2
9.8 m/s2 = 9.8*10-3 mm/ms2
Conversion Factor = 10-3
CONCLUSION :-
Thus the given input measurements are converted into respective unit systmes and this is used in
LS-DYNA calculation.