Week - 1 - Consistency of Units
Aim-To convert the Given measurement values to different Unit Systems
Value of the following measurements are given as follows:
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
Now, here are a few 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
Write the given measurements in the above different system of units. Also, mention the conversion factors.
Explanation-
As per the given data in the challenge, Ls Dyna does not follow any fixed or particular system of units.The user has to manuallly input the unit system he has to follow & it becomes very obvious that we need to keep consistency in our unit system. So in this challenge, our aim is to get familiar with different unit systems and use them efficiently to convert some measurements given here in the challenge in resp. systems.
Now, we will look at the provided measurements one by one and we'll convert them into the resp. unit system mentioned.
1.Mass 1 Kg-
Here we need to represent the kilogram value in different unit systems by converting it properly. After having a closer look at the unit systems provided, we can say that, the mass 1Kg will remain as it is in Kg cm ms, Kg cm s, kg m s, kg mm s, kg mm ms unit systems.
The conversion factors for the rest of the systems as follows
Grams to KG- 1000
Tons to KG- 0.001
Slugs to KG- 0.0685
2.Length 1M-
The measurement will remain as it is in kg m s unit system. The conversion factor for remaining units as follows
Cm to M- 100
MM to M- 1000
Ft to M- 0.3048
3.Time 1S-
The conversion factor for time in mili and micro seconds is as follows
S to ms- 1000
S to us- 1*10^6
Now, we will go for a detailed calculations of one of the unit systems
gm mm ms-
We will start with 1N force.
To start with, lets keep the basic unit system as KGS (SI) units
F= M * A
unit of mass - kg, unit of acceleration- m/s^2
so the unit of force becomes Kg.m/s^2.
Now, in order to convert the above KGS unit system into gm mm ms, we need to multiply the given system with a conversion factor.
Kg to gm- 1000
M to mm- 1000
S to ms- 1000
i.e.
1000gm*1000mm/ 1000^2 = 1.
Similarly we can calculate the rest of the measurements-
Stress 1Pa-
SI unit of pascal is N/m^2
we can represent above unit in KGS system
As 1N= 1Kg.m/s^2, we get the pascal in KGS system as Kg.m/s^2 * 1/m^2,
Here one m will get cancelled and the remaining term would be, Kg/ms^2. NOw we will convert this into gm mm ms,
1000/1000*1000^2 which will come down as 1*10^-6.
Energy 1Nm-
1Nm= 1Kg.m/s^2 * m
= 1Kg.m^2/ s^2
= 1000*1000^2/1000^2
=1000.
Density 1Kg/m^3-
= 1000/1000^3
=1*10^-6
Youngs modulus 210 GPa-
210Gpa= 210*10^9 Pa
=210*10^9 N/m^2
=210*10^9 Kg.m/s^2 * 1/m^2
=210*10^9 Kg/ms^2
=210*10^9 * 1000/1000*1000^2
=210*10^3
Velocity 56.33 KMPH-
=56.33*1000*1000mm/3600*1000ms
= 15.6472 mm/ms.
Gravity 9.8 m/s^2
=9.8*1000/1000^2
= 9.8*10^-3 mm/ms^2
The rest of the measurements have been calculated similarly and are tabulated below.
| 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 | |
| Kg cm ms | 1 | 100 | 1000 | 1*10^-4 | 1*10^-8 | 0.01 | 1*10^-6 | 2100 | 1.5647 | 9.8*10^-4 |
| Kg cm s | 1 | 100 | 1 | 100 | 0.01 | 10^4 | 1*10^-6 | 2100 | 1564.72 | 980 |
| gm mm ms | 1000 | 1000 | 1000 | 1 | 1*10^-6 | 1000 | 1*10^-6 | 210*10^3 | 15.6472 | 9.8*10^-3 |
| Kg m s | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 210*10^9 | 15.6472 | 9.8 |
| g cm s | 1000 | 100 | 1 | 1*10^5 | 10 | 1*10^7 | 1*10^-3 | 2.1*10^12 | 1564.72 | 980 |
| g cm us | 1000 | 100 | 1*10^6 | 0.1 | 1*10^-11 | 1*10^-5 | 1*10^-3 | 2.1 | 1.5647*10^-3 | 9.8*10^-10 |
| g mm s | 1000 | 1000 | 1 | 1*10^6 | 1 | 1*10^9 | 1*10^-6 | 2.1*10^11 | 15647.2222 | 9800 |
| ton mm s | 0.001 | 1000 | 1 | 1 | 1*10^-6 | 1000 | 1*10^-12 | 210*10^3 | 15647.2222 | 9800 |
| slug ft s | 0.0685 | 0.3048 | 1 | 0.0208 | 0.2247 | 6.3638*10^-3 | 2.419 | 4.7194*10^10 | 4.7692 | 2.987 |
| kg mm s | 1 | 1000 | 1 | 1000 | 1*10^-3 | 1*10^6 | 1*10^-9 | 210*10^6 | 15647.2222 | 9800 |
| g cm ms | 1000 | 100 | 1000 | 0.1 | 1*10^-5 | 10 | 1*10^-3 | 210*10^4 | 1.5647 | 9.8*10^-4 |
| kg mm ms | 1 | 1000 | 1000 | 1*10^-3 | 1*10^-9 | 1*10^-3 | 1*10^-9 | 210 | 15.6472 | 9.8*10^-3 |
Conclusion: The Values are Converted into respected Unit System. Since Ls Dyna doesn't have a specific unit system the above assignment will be useful in deploying the Units while performing Simulation.