Week - 1 - Consistency of Units

AIM:-

The aim of this challenge is to convert different SI units/parameters into different Standard Unit Systems for making it easy to use the right units or unit systems in LS-Dyna & also to create a consistent table for easy reference in future.

OBJECTIVE:-

The main objective of this challenge is to convert all the given values of SI units into different system of units. As we all know LS-Dyna does not have any default system of units. So, we will convert all the given SI Units into system of units and create a table for reference and future use to ease the converting factors and save us our valuable time.

Note:- Also according to the challenge, we need to convert the SI Unit measurements for one only one unit system that is, gm mm ms. Rest all have to be tabulated.

PROCEDURE:-

Values of measurements which have to be converted are as follows:

• Mass = 1 Kg
• Length = 1 m
• Time = 1 s
• Force = 1 N
• Stress = 1 Pa
• Energy = 1 Nm
• Density = 1 Kg/`m^3`
• Young's Modulus = 210 GPa
• Velocity = 56.33 Kmph
• Grvaity = 9.8 m/`s^2`

Unit Systems in which all above SI Units have 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

Conversion Of SI Units into gm mm ms system of units.

• Mass = 1 kg

Ans) 1000 gm Conversion Factor = 1000

• Length = 1 m

Ans) 1000 mm Conversion Factor = 1000

• Time = 1 s

Ans) 1000 ms Conversion Factor = 1000

• Force = 1 N

Ans) Formula for calculating Force (F) is: F = Mass*Acceleration

Here, F = 1 Kg * `m/s^2`

Substituting Values from above, we get

F =`(1000gm*1000mm)/(1000ms)^2`

i.e. F = `1 (gm*mm)/(ms)^2`

Conversion Factor = 1

• Stress = 1 Pa

Ans) Formula for calculating Stress (Pa) is: Pa = `(1N)/m^2`

Here, Pa = `{1(gm*mm)/(ms)^2}/(1000mm)^2`

Because, N = `1 (gm*mm)/(ms)^2`from above equation.

Also, m = 1000 mm

i.e. Pa = `(10^-6gm)/(mm*ms^2)`

Conversion Factor = `10^-6`

• Energy = 1 Nm

Ans) Formula for calculating Energy (J) is: N*m

Here J = `1(gm*mm)/(ms)^2*1000mm`

Because, N = `1(gm*mm)/(ms)^2`

Also, m = 1000 mm

i.e. J = `(10^3 gm*mm^2)/(ms)^2`

Conversion Factor = `10^3`

• Density = `(1kg)/m^3`

Ans) Formula for calculating Density is: `(1kg)/m^3`

Here, Density = `(1000gm)/(1000mm)^3`

Density = `(1gm)/(1000000mm^3)`

i.e. Density = `(10^-6gm)/(mm^3)`

Conversion Factor = `10^-6`

• Young's Modulus = 210 GPa

Ans) Formula for calculating Young's Modulus is: 210 GPa

Here, 1 Pa =`(10^-6gm)/(mm*ms^2)` from above eqution.

Also, 1 GPa = `(10^9*10^-6gm)/(mm*ms^2)`

210 GPa = `(210*10^9*10^-6gm)/(mm*ms^2)`

i.e. Young's Modulus 210 GPa = `(210*10^3gm)/(mm*ms^2)`

Conversion Factor = `10^3`

• Velocity = 56.33 Kmph

Ans) Formula for calculating Velocity is: km/h

Here, 1 km = 1000000 mm = `10^6 mm`

Also, 1 h = `60min*60sec*1000` because, we are converting an Hour into Milli-Second.

So, 1 h = 3600000 ms = `36*10^5ms`

Velocity at 1 Kmph is:

1 km/h = `(10^6)/(36*10^5)`

i.e. 1 km/h = `(0.277mm)/(ms)`

Now, Velocity at 56.33 Kmph is:

56.33 km/h = `(56.33*0.277mm)/(ms)`

i.e. 56.33 km/h = `(15.60mm)/(ms)`

Conversion Factor = 0.277

• Gravity = `(9.88m)/s^2`

Ans) Formula for calculating Gravity is `(m)/s^2`

For Gravity at `(1m)/s^2` , we have

`(1m)/s^2`= `(1000mm)/(1000ms^2)`

`(1m)/s^2`= `(10^-3mm)/(ms^2)`

For Gravity at `(9.88m)/s^2`

`(9.88m)/s^2`= `(9.8*10^-3mm)/(ms^2)`

Conversion Factor = `10^-3`

`(4.368e9slug)/(ft*s^2)` `(32.144ft)/(s^2)` `(10^-9kg)/(mm*ms^2)` `(9.8*10^-3mm)/(ms^2)`

Unit Systems	Mass	Length	Time	Force	Stress	Energy	Density	Young's Modulus	Velocity	Gravity
Kg cm ms	1Kg	100cm	1000ms	`(10^-4kg*cm)/(ms^2)`	`(10^-8 kg)/(cm*ms^2)`	`(10^-2kg*cm^2)/(ms^2)`	`(10^-6kg)/(cm^3)`	`(2100 kg)/(cm*ms^2)`	`(1.5647cm)/(ms)`	`(9.8*10^-4cm)/(ms^2)`
Kg cm s	1Kg	100cm	1s	`(10^2kg*cm)/(s^2)`	`(10^-2kg)/(cm*s^2)`	`(10^4kg*cm^2)/(s^2)`	`(10^-6 kg)/(cm^3)`	`(210e+7kg)/(cm*s^2)`	`(1564.7cm)/s`	`(9.8*10^2cm)/(s^2)`
gm mm ms	1000gm	1000mm	1000ms	`(1 gm*mm)/(ms^2)`	`(10^-6 gm)/(mm*ms^2)`	`(10^3 gm*mm^2)/(ms^2)`	`(10^-6gm)/(mm^3`	`(210e3gm)/(mm*ms^2)`	`(15.647mm)/(ms)`	`(9.8*10^-3mm)/(ms^2)`
Kg m s	1Kg	1m	1s	`(1kgm)/(s^2)`	`(1kg)/(m*s^2)`	`(1kg*m^2)/(s^2)`	`(1kg)/(m^3)`	`(210e^9kg)/(m*s^2)`	`(15.647 m)/(s)`	`(9.8m)/(s^2)`
g cm s	1000gm	100cm	1s	`(10^5gm*cm)/(s^2)`	`(10gm)/(cm*s^2)`	`(10^7gm*cm^2)/(s^2)`	`(10^-3gm)/(cm^3)`	`(210e10gm)/(cm*s^2)`	`(1564.7cm)/(s)`	`(9.8*10^2cm)/(s^2)`
g cm us	1000gm	100cm	`10^6`us	`(10^-7gm*cm)/(us^2)`	`(10^-11gm)/(cm*us^2)`	`(10^-5gm*cm^2)/(us^2)`	`(10^-3gm)/(cm^3)`	`(2.10gm)/(cm*us^2)`	`(15.647*10^-4cm)/(us)`	`(9.8*10^-10cm)/(us^2`
g mm s	1000gm	1000mm	1s	`(10^6gm*mm)/(s^2)`	`(1gm)/(mm*s^2)`	`(10^9gm*mm^2)/(s^2)`	`(10^-6gm)/(mm^3)`	`(2.10e11gm)/(mm*s^2)`	`(15647mm)/s`	`(9.8*10^3mm)/(s^2)`
ton mm s	`10^-3`ton	1000mm	1s	`(1Ton*mm)/(s^2)`	`(10^-6Ton)/(mm*s^2)`	`(10^3Ton*mm)/(s^2)`	`(10^-12Ton)/(mm^3)`	`(210e3Ton)/(mm*s^2)`	`(15647mm)/s`	`(9.8*10^3mm)/(s^2)`
slug ft s	0.068 slug	3.28 ft	1s	`(0.2246slug*ft)/(s^2)`	`(0.0208slug)/(ft*s^2)`	`(0.7366slug*ft)/(s^2)`	`(1.93*10^-3slug)/(ft^3)`	`(51.322ft)/s`
Kg mm s	1Kg	1000mm	1s	`(10^3kg*mm)/(s^2)`	`(10^-3kg)/(mm*s^2)`	`(106kg*mm)/(s^2)`	`(10^-9kg)/(mm^3)`	`(210e6kg)/(mm*s^2)`	`(15647mm)/s`	`(9.8*10^3mm)/(s^2)`
g cm ms	1000gm	100cm	1000ms	`(10^-1gm*cm)/(ms^2)`	`(10^-5gm)/(cm*ms^2)`	`(10gm*cm)/(ms^2)`	`(10^-3gm)/(cm^3)`	`(210e4gm)/(cm*ms^2)`	`(1.5647cm)/(ms)`	`(9.8*10^-4cm)/(ms^2)`
Kg mm ms	1Kg	1000mm	1000ms	`(10^-3kg*mm)/(ms^2)`	`(1kg*mm)/(ms^2)`	`(10^-9kg)/(mm^3)`	`(210kg)/(mm*ms^2)`	`(15.647mm)/(ms)`

CONCLUSION:-

Hence, the given SI Units measurements are converted into the mentioned Unit Systems. Also now we have a well understanding of how units conversions work in LS-Dyna.

Also the talble for future references for units is made and can be used in LS-Dyna unit conversions.