Week - 1 - Consistency of Units

Aim:

The Aim of this Challenge is to be familiar with different Unit Conversion methods, as LS-DYNA doesn't have  default System of Units. 

Calculation for SI Units to gm/mm/ms:

Force: By Emprical Newtons laws of motion, the Force is defined as F = mass * acceleration, The SI Unit of Mass is Kg. Acceleration is the rate of Change of Velocity and has the unit of m/s^2.  Hence in SI Unit the Force has the Unit of Kg-m/s^2, which is collectively called as "Newton(N)". 

1 kg = 1000 grams

1 m = 1000 mm

1 s = 1000 milli seconds.

If i want to Convert Force from SI System to gg/mm/ms seconds, we need to find out the Conversion Factor. The Conversion Factor can be found out just by simply substitute the Values in grams, millimeter and Milliseconds.

1 N = 1kg-m/s^2 = 1000(g)*1000(mm)/(1000ms)^2 = 1, In this Case the Conversion Factor Comes out to be 1. Hence if we have Force of 100 N in SI- System,  In gg/mm/ms system the Force value is still 100 N as Conversion Factor Comes out to be 1.

Stress & Pressure: The SI- Unit of the Pressure is Pa which is N/m2, In SI-Units the Force has the Unit of Kg-m/s^2, which is Collectively Called as N. The Unit of Pressure interms of Fundamental Quantities of Measure in SI- Units is given by "kg/ms^2" so if we substitute for kg, m & s in g, mm and ms, We get,

kg/ms^2 = (1000g)/(1000mm * 1000ms^2) = 10^-6. Hence if we want to Convert the Value of Pressure or Stress from SI-System to gg/mm/ms system, we need to multiply the value in SI- units  by 10^-6. In short if the Pressure/stress Value is 50000000 pa in SI-units, then in gg/mm/ms system the Value Pressure/stress value is 50Mpa.

Energy: The Unit of Energy in SI-units is Joules (J), it can be also expressed as N-m. If we express the Energy interms of Fundamental Quantities of Measure in SI- Units, then we get, kg-m^2/s^2,if we substitute for kg, m & s in g, mm and ms, We get,

kg-m^2/s^2 = (1000 * (1000)^2)/(1000^2) = 1000. Hence if we want to Convert the Value of Energy from SI-units to gg/mm/ms system, then we need to multiply the Value in SI- Units by 1000. In short if we have the Energy Value of 5J in SI-units, then it corrosponds to 5000mJ (milli Joules) in gg/mm/ss system. 

Density: The Unit of Density in SI-units is kg/m^3. if we substitute for kg, m & s in g, mm and ms, We get,

kg/m^3 = (1000)/(1000)^3 = (1000)^-2. Hence if we want to Convert the Value of Density from SI-Units to gg/mm/ms system, then we need to multiply the Value in SI- Units by 10^-6. For Example if we have the Value of Density of steel as 7800kg/m^3, if we want to express interms of gg/mm/ms, then the Density is Expressed as 7.8 * 10^-3 g/mm^3.

Young's Modulus: The Unit of Young's Modulus in SI- Units is in Pascals, Hence we need to multiply by 10^-6 to convert it to gg/mm/ms units. For Example the Young's Modulus of Steel is 2.1e11 in SI unit of Systems, if we use it in gg/mm/ms system then we need to multiply 2.1e11 by 10e-6 which will give 2.1e5.

Velocity:
The Unit of Velocity in SI-Unit is m/s. if we substitute for kg, m & s in g, mm and ms, We get

m/s = 1000mm/(1000ms) =1 . So if we have Velocity in m/s in SI-units, then the same Value represents  the Velocity in mm/ms as the Conversion factor becomes"1". Given Value of Velocity in assignment is 56.33 Kmph,

1 Km = 1000m ; 1 hour = 3600 seconds. so if we want to conver Kmph to m/s we need to multiply the value in kmph by (1000/3600), therefore 56.33kmph = (56.33*1000)/3600 = 15.64m/s. 

If we want to convert m/s to mm/ms we need to multiply the value in m/s by 1 which means 56.33Kmph is 15.64mm/ms.

Acceleration due to Gravity:

The Value of Acceleration due to gravity is 9.8 m/s2. if we substitute for kg, m & s in g, mm and ms, We get,

m/s^2 = 1000mm/(1000mm)^2 = 10^-3. So if we have Acceleration due to gravity in SI-Units, then we need to multiply 10^-3 with m/s^2 to change to mm/ms^2. Hence the Value of Acceleration due to gravity is 9.8*10^-3 mm/ms^2.

Similarly different Units Conversions are Practised and the Results are tabulated in the Table Below.

System	Mass	Length	Time	Force(N)	Stress(N/m2)	Energy(N-m)	Young's Modulus(Gpa)	Density of Steel(kg/m3)	Velocity(m/s)	Acceleration due to Gravity(m/s2)
SI	Kg	m	s	1	1	1	2.10E+11	7.83E+03	15.65	9.8
Kg/cm/s	Kg	cm	s	1.00E-02	1.00E+02	1.00E-04	2.10E+09	7.83E-03	1.56E+03	9.81E+02
Kg/cm/ms	kg	cm	ms	1.00E+04	1.00E+08	1.00E+02	2.10E+03	7.83E-03	1.56E+00	9.81E-04
g/cm/s	g	cm	s	1.00E-05	1.00E-01	1.00E-07	2.10E+12	7.83E+00	1560	981
g/cm/us	g	cm	us	1.00E+07	1.00E+11	1.00E+05	2.1	7.83	1.57E-03	9.81E-10
g/mm/s	g	mm	s	1.00E-06	1	1.00E-09	2.10E+11	7.83E-02	1.57E+04	9.81E+03
ton/mm/s	ton	mm	s	1	1.00E+06	1.00E-03	2.10E+05	7.83E-09	1.56E+04	9.81E+03
slug/ft/s	slug	ft	s	4.483	48.235	1.366	1.01E+13	15.1902	51.332	32.1768
kg/mm/s	kg	mm	s	1.00E-02	1.00E+03	1.00E-06	2.10E+08	7.83E-06	15650	9810
g/cm/ms	g	cm	ms	10	1.00E+05	0.1	2.10E+06	7.83	1.56	9.81E-04
kg/mm/ms	kg	mm	ms	1000	1.00E+09	1	2.10E+02	7.83E-06	15.65	9.81E-03

Conclusion:
The Conversion of Units are Practised and Learned during this week.