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 does not have any default system of units, so by preparing this table we can use it frequently to solve the challenges.
Procedure:-
Detailed calculation for conversion from SI unit to gm/mm/ms unit system:
Mass: 1Kg=1000gm, Conversation Factor = 1*1000 = 103;
Length: 1m=1000mm, Conversation Factor = 1*1000 = 103;
Time: 1s=1000ms, Conversation Factor = 1*1000 = 103;
Force: 1N = 1(kg*m)/S2
= 1(1000gm*1000mm)/ (1000ms)2
= 1(gm*mm)/ms2, Conversation Factor = 1
Stress: 1Pa = 1 N/m2 = ((1Kg*m)/S2))/ m2
= ((1000gm*1000mm)/1000000 ms2)/1000000mm2
= ((1gm*mm)/ms2)/106 mm2
= 10-6 gm/mm*ms2, Conversation Factor = 10-6
Energy: 1Nm = (1 Kg*m/S2)*m
= ((1000gm*1000mm)/1000000 ms2) * 1000mm
= 103 (gm*mm2) / ms2, Conversation Factor = 103
Density: 1Kg/m3 = 1000gm / 109 mm3
= 10-6 gm/mm3, Conversation Factor = 10-6
Young’s Modulus: 210GPa = 210 * 109 N/m2
= 210*109 ((Kg*m)/S2) / m2
= 210*109 ((1000gm*1000mm)/1000000 ms2)/1000000mm2
= 210*109 ((gm*mm)/ms2)/106 mm2
= 210*103 gm/mm*ms2, Conversation Factor = 103
Velocity: 56.33KMPH = (56.33 * 1000m) / H
= (56.33 * 106mm) / 3600 * 1000 ms
= (56.33 * 106mm) / 36 * 105 ms
= 15.6472 mm/ms, Conversation Factor = 5/18
Gravity: 9.8 m/S2 = 9.8 (1000mm)/ (1000000ms)
= 9.8 (103mm) / 106ms2
= 9.8 * 10-3 mm/ms2, Conversation Factor = 10-3
Systems of Units:
|
Units |
Mass |
Length |
Time |
Force |
Stress |
Energy |
|
Kg cm ms |
1kg |
102cm |
103ms |
10-4kg*cm/ms2 |
10-8kg/cm*ms2 |
10-2kg*cm2/ms2 |
|
Kg cm s |
1kg |
102cm |
1s |
102kg*cm/s2 |
10-2kg/cm*s2 |
104kg*cm2/s2 |
|
gm mm ms |
103gm |
103mm |
103ms |
1gm*mm/ms2 |
10-6gm/mm*ms2 |
103gm*mm2/ms2 |
|
Kg m s |
1kg |
1m |
1s |
1 kg*m/S2 |
1 kg/m*s2 |
1 kg*m2/s2 |
|
gm cm s |
103gm |
102cm |
1s |
105gm*cm/S2 |
10 gm/cm*ms2 |
107gm*cm2/s2 |
|
gm cm µs |
103gm |
102cm |
106µs |
10-7gm*cm/µs2 |
10-11gm/cm*µs2 |
10-5gm*cm2/µs2 |
|
gm mm s |
103gm |
103mm |
1s |
106gm*mm/s2 |
1 gm/mm*s2 |
109gm*mm2/s2 |
|
Ton mm s |
10-3gm |
103mm |
1s |
1 ton*mm/s2 |
10-6 ton/mm*s2 |
103 ton*mm2/s2 |
|
Slug ft s |
0.068slug |
3.28 ft |
1s |
0.224 slug*ft/s2 |
0.0208slug/ft*s2 |
0.7366slug*ft2/s2 |
|
Kg mm s |
1kg |
103mm |
1s |
103kg*mm/s2 |
10-3kg/mm*s2 |
106 kg*mm2/s2 |
|
gm cm ms |
103gm |
102cm |
103ms |
10-1gm*cm/ms2 |
10-5gm/cm*ms2 |
10 gm*cm2/ms2 |
|
Kg mm ms |
1kg |
103mm |
103ms |
10-3kg*mm/ms2 |
10-9kg/mm*ms2 |
1 kg*mm2/ms2 |
|
Units |
Density |
Young’s Modulus |
Velocity |
Gravity |
|
Kg cm ms |
10-6kg/cm3 |
2100kg/cm*ms2 |
1.56472 cm/ms |
9.8*10-4 cm/ms2 |
|
Kg cm s |
10-6kg/cm3 |
210*107kg/cm*s2 |
1564.72 cm/s |
9.8*102 cm/s2 |
|
gm mm ms |
10-6gm/mm3 |
210*103gm/mm*ms2 |
15.6472 mm/ms |
9.8*10-3 mm/ms2 |
|
Kg m s |
1 kg/m3 |
210*109 N/m2 |
15.6472 m/s |
9.8 m/s2 |
|
gm cm s |
10-3gm/cm3 |
210*1010gm/cm*s2 |
1564.72 cm/s |
9.8*102 cm/s2 |
|
gm cm µs |
10-3gm/cm3 |
2.1gm/cm*µs2 |
15.64*10-4 cm/µs |
9.8*10-10 cm/µs2 |
|
gm mm s |
10-6gm/mm3 |
210*1011gm/mm*s2 |
156472 mm/s |
9.8*103 mm/s2 |
|
Ton mm s |
10-12 ton/mm3 |
210*103 ton/mm*s2 |
156472 mm/s |
9.8*103 mm/s2 |
|
Slug ft s |
1.93*10-3slug/ft3 |
4.368 slug/ft*s2 |
51.322 ft/s |
32.144 ft/s2 |
|
Kg mm s |
10-9 kg/mm3 |
210*106kg/mm*s2 |
156472 mm/s |
9.8*103 mm/s2 |
|
gm cm ms |
10-3gm/cm3 |
210*104gm/cm*ms2 |
1.56472 cm/ms |
9.8*10-4 cm/ms2 |
|
Kg mm ms |
10-9kg/mm3 |
210 kg/mm*ms2 |
15.6472 mm/ms |
9.8*10-3 mm/s2 |
As LS-DYNA has no unit system,so we have to convert each units as per requirements.