Week - 1 - Consistency of Units
PROJECT : CONVERSION OF UNITS
AIM / OBJECTIVE : To convert and write the given measurements of SI units with different system of units. Also, mention the conversion factors.
***LS-dyna uses different input system of units as user defined and is not set to default thus it varies with respect to application and depends upon industry.
In this project we will convert the SI unit system for the given measurements to other different system of units along with mentioning their conversion factor.
Units in automotive industry : kg,mm,ms as standard,
Units in construction industry : tonne,m,s as standard.
CONVERSION FACTOR : is the multiplication factor use to convert units from one system of units to another.
Ex : To convert 1 kg to grams : 1 kg * 1000 g/kg = 1000 g ...........CONVERSION FACTOR IS : 1000 g/kg,
Ex : To convert 1 m to mm : 1 m * 1000 mm/m = 1000 mm ..... CONVERSION FACTOR IS : 1000 mm/m.
To perform a detailed calculation of conversion of SI units to g,mm,ms and for the rest of the units a table is to be created with corresponding units as per measurements.
GIVEN MEASUREMENTS : ,
MASS 1kg
LENGTH 1m
TIME 1s
FORCE 1N
STRESS 1Pa
ENERGY 1Nm
DENSITY 1 Kg/m3
YOUNG'S Modulus 210 GPa
Velocity 56.33 KMPH
GRAVITY 9.8m/s2
UNITS OF SI TO BE CONVERTED TO THE BELOW SYSTEM OF UNITS :
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
DETAILED CALCULATION OF CONVERSION OF SI UNITS TO g,mm,ms along with conversion factor :
MASS 1 kg = 103 g
LENGTH 1 m = 103 mm
TIME 1 s = 103 ms
FORCE 1 N = 1 kg.m/s2 = 103 g * 103 mm / 106 ms2 = 1 g.mm / ms2
STRESS 1 Pa = 1 N/m2 = 1 g.mm / ms2 /106 mm2 = 10-6 g/mm.ms2
ENERGY 1 N.m = (1 g.mm/ms2) × (103 mm) = 103 g.mm2/ms2
DENSITY 1 kg/m3 = 103 g/109 mm3 = 10-6 g/mm3
YOUNG'S MODULUS 210 GPa = 210*103 N/mm2 = 210×103 g/mm.ms2
VELOCITY 56.33 Km/h = 56.33*(103 mm / 3.6*103 ms ) = 15.647 mm/ms
GRAVITY 9.8 m/s2 = 9.8*(103 mm / 106 ms2) = 9.8*10-3 mm.ms2
TABLE FOR CONVERSION OF SI UNITS TO OTHER SYSTEM OF UNITS :
| Unit System | Mass | Length | Time | Force | Stress | Energy | Density | Young's Modulus | Velocity | Gravity |
|---|---|---|---|---|---|---|---|---|---|---|
| Kg cm ms | 1 kg | 100 cm | 1 ms | 104 kg.cm/ms2 | 104 kg/cm.ms2 | 106 kg.cm2/ms2 | 10-3 kg/cm3 | 210×106 kg/cm.ms2 | 1.5647 cm/ms | 9.8 cm/ms2 |
| Kg cm s | 1 kg | 100 cm | 1 s | 104 kg.cm/s2 | 104 kg/cm.s2 | 106 kg.cm2/s2 | 10-3 kg/cm3 | 210×106 kg/cm.s2 | 156.47 cm/s | 980 cm/s2 |
| gm mm ms | 103 g | 103 mm | 1 ms | 1 g.mm/ms2 | 10-6 g/mm.ms2 | 103 g.mm²/ms2 | 10-6 g/mm3 | 210×103 g/mm.ms2 | 15.647 mm/ms | 9.8×10-3 mm/ms2 |
| Kg m s | 1 kg | 1 m | 1 s | 1 N | 1 Pa | 1 Nm | 1 kg/m3 | 210 GPa | 56.33 km/h | 9.8 m/s2 |
| g cm s | 103 g | 100 cm | 1 s | 103 g.cm/s2 | 103 g/cm.s2 | 1 g.cm2/s2 | 10-3 g/cm3 | 210×106 g/cm.s2 | 1564.7 cm/s | 980 cm/s2 |
| g cm us | 103 g | 100 cm | 106 µs | 103 g.cm/µs2 | 10-3 g/cm.µs2 | 103 g.cm2/µs2 | 10-9 g/cm3 | 210×103 g/cm.µs2 | 1.5647 cm/µs | 9.8 cm/µs2 |
| g mm s | 103 g | 103 mm | 1 s | 1 g.mm/s2 | 10-6 g/mm.s2 | 103 g.mm2/s2 | 10-6 g/mm3 | 210×103 g/mm.s2 | 15.647 mm/s | 9.8×10-3 mm/s2 |
| tonne mm s | 10-3 ton | 103 mm | 1 s | 10-3 ton.mm/s2 | 10-6 ton/mm.s2 | 1 ton.mm2/s2 | 10-6 ton/mm3 | 210 ton/mm.s2 | 15.647 mm/s | 9.8×10-3 mm/s2 |
CONCLUSION : The system of units has been converted from SI units to other system of units and a detailed calculation of SI units to g,mm,ms has been derived with conversion factor.