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Challenge

Week - 1 - Consistency of Units

BBasini Bibek Rao23 Feb 2022

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

We have to convert these to respective systems.

Kg cm ms

Kg cm s

g 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

Solution

Units:

  • Units are standards for expressing and comparing the measurements of physical quantities.
  • SI units are a standard of units described for different physical quantities to express their magnitude.
  • Ex- kg for mass, seconds for time, meter for length, kelvin for temperature, newton for force, etc.

In the case of LS-Dyna:

  • While using LS-Dyna solver for simulation we often fall into a trap of inconsistent unit selection because inherently this solver doesn't have any units predefined and that makes a reason for unwanted simulation results.
  • In order to get away with this problem, we have to be very conscious while choosing the units.
  • Also, a very important thing is to choose a proper unit for a certain use case, like for larger simulations using meter can be obvious but for the case of deflection of the beam using the meter is obsolete.
  • So this challenge focuses on this complexities of LS Dyna.

For the kg cm ms

  1. Mass, 1kg= 1kg, multiplying factor = 1
  2. Length, 1m= 100 cm, multiplying factor = 100
  3. Time, 1s = 1000 ms, multiplying factor = 1000
  4. Force, 1N = 1 `(kg.m)/s^2` = `1 * ((1kg)* (100 cm))/(10^6 ms^2)`= `10^-4 (kg*cm)/(ms^2)`, multiplying factor = `10^-4`
  5. Stress, 1Pa = 1 `N/m^2`= `1* 10^-4/(10^4 cm^2)` = `10^-8 (kg)/(ms^2*cm`, multiplying factor = `10^-8`
  6. Energy, 1Nm = `1* 10^-4 (kg*cm)/(ms^2)*100 cm`= `10^-2 (kg*cm^2)/(ms^2)`, multiplying factor = `10^-2`
  7. Density, 1 `(kg)/m^3`= `1* (kg)/(10^6 *cm^3`= `10^-6 (kg)/(cm^3)`, multiplying factor = `10^-6`
  8. Young's modulus = 210 GPa = `210*10^9*Pa`= `210 *10^9* 10^-8* (kg)/(ms^2*cm)=210*10* (kg)/(ms^2*cm)`, multiplying factor = 10
  9. Velocity, 56.33 KMPH = `56.33* (10^5 cm)/(3600*1000*ms)=56.33*1/36*(cm)/(ms)`, multiplying factor = `1/36`
  10. Gravity, 9.8 `m/s^2=9.8*(100cm)/(10^6*ms^2)=9.8*10^-4*(cm)/(ms^2)`, multiplying factor = `10^-4`

For kg cm s

  1. Mass, 1kg= 1kg, multiplying factor = 1
  2. Length, 1m= 100 cm, multiplying factor = 100
  3. Time, 1s = 1 s, multiplying factor = 1
  4. Force, 1N = 1 `(kg.m)/s^2` = `1 * ((1kg)* (100 cm))/( s^2)= 10^2 (kg*cm)/(s^2)`, multiplying factor = `10^2`
  5. Stress, 1Pa = 1 `N/m^2`= `1* 10^2/(10^4 cm^2)` = `10^-2 (kg)/(s^2*cm`, multiplying factor = `10^-2`
  6. Energy, 1Nm = `1* 10^2 (kg*cm)/(s^2)*100 cm = 10^4 (kg*cm^2)/(s^2)`, multiplying factor = `10^4`
  7. Density, 1 `(kg)/m^3`= `1* (kg)/(10^6 *cm^3`= `10^-6 (kg)/(cm^3)`, multiplying factor = `10^-6`
  8. Young's modulus = 210 GPa = `210*10^9*Pa= 210 *10^9* 10^-2* (kg)/(s^2*cm)=210*10^7* (kg)/(s^2*cm)`, multiplying factor = `10^7`
  9. Velocity, 56.33 KMPH = `56.33* (10^5 cm)/(3600*s)=56.33*250/9*(cm)/(s)`, multiplying factor = `250/9`
  10. Gravity, `9.8 m/s^2=9.8*(100cm)/(s^2)=9.8*10^2*(cm)/(s^2)`, multiplying factor = `10^2`

For g mm ms

  1. Mass, 1kg= 1000g, multiplying factor = 1000
  2. Length, 1m= 1000 mm, multiplying factor = 1000
  3. Time, 1s = 1000 ms, multiplying factor = 1000
  4. Force, 1N =`1 (kg.m)/s^2 = 1 * ((1000g)* (1000 mm))/(10^6 ms^2)= 1 (g*mm)/(ms^2)` , multiplying factor = 1
  5. Stress,`1Pa = 1 N/m^2= 1* 1(g*mm)/(ms^2)*1/(10^6 mm^2) = 10^-6 (g)/(ms^2*mm` , multiplying factor = `10^-6`
  6. Energy, 1Nm =`1* 1(g*mm)/(ms^2)*1000 mm= 10^3 (g*mm^2)/(ms^2)` , multiplying factor = `10^3`
  7. Density, 1 = `(kg)/m^3= 1* (1000* g)/(10^9 *mm^3) = 10^-6 (g)/(mm^3)`, multiplying factor = `10^-6`
  8. Young's modulus = 210 GPa = `210*10^9*Pa= 210 *10^9* 10^-6* (g)/(ms^2*mm)=210*10^3* (g)/(ms^2*mm)` , multiplying factor = `10^3`
  9. Velocity, 56.33 KMPH = `56.33* (10^6 mm)/(3600*1000*ms)=56.33*10/36*(mm)/(ms)` , multiplying factor = `10/36`
  10. Gravity, 9.8 `m/s^2=9.8*(1000mm)/(10^6*ms^2)=9.8*10^-3*(mm)/(ms^2)` , multiplying factor = `10^-3`

For kg m s

  1. Mass, 1kg= 1kg, multiplying factor = 1
  2. Length, 1m= 1 m, multiplying factor = 1
  3. Time, 1s = 1 s, multiplying factor = 1
  4. Force, 1N = 1`(kg.m)/s^2 = 1 * ((1kg)* (1 m))/( s^2)= 1 (kg*m)/(s^2)` , multiplying factor = 1
  5. Stress, 1Pa = 1 `N/m^2= 1*N/m^2` , multiplying factor =1
  6. Energy, 1Nm = 1Nm , multiplying factor =1
  7. Density, 1 `(kg)/m^3`= `1 (kg)/m^3` , multiplying factor = 1
  8. Young's modulus = 210 GPa = `210*10^9*Pa` , multiplying factor = `10^9`
  9. Velocity, 56.33 KMPH = `56.33* (10^3 m)/(3600*s)=56.33*5/18*(m)/(s)` , multiplying factor = `5/18`
  10. Gravity, `9.8 m/s^2=9.8(m)/(s^2)` , multiplying factor = 1

For g cm s

  1. Mass, 1kg= 1000g, multiplying factor = 1000
  2. Length, 1m= 1 m, multiplying factor = 1
  3. Time, 1s = 1 s, multiplying factor = 1
  4. Force, 1N = 1 `(kg.m)/s^2 = 1 * ((1000g)* (100 cm))/( s^2)= 10^5 (g*cm)/(s^2)`, multiplying factor = `10^5`
  5. Stress, 1Pa = 1`N/m^2= 1* 10^5/(10^4 cm^2) = 10 (g)/(s^2*cm` , multiplying factor = 10
  6. Energy, 1Nm =`1* 10^5 (g*cm)/(s^2)*100 cm = 10^7 (g*cm^2)/(s^2)` , multiplying factor = `10^7`
  7. Density, 1 `(kg)/m^3`= `1* (1000*g)/(10^6 *cm^3)= 10^-3 (g)/(cm^3)` , multiplying factor = `10^-3`
  8. Young's modulus = 210 GPa = `210*10^9*Pa= 210 *10^9* 10* (g)/(s^2*cm)=210*10^10* (g)/(s^2*cm)` , multiplying factor = `10^10`
  9. Velocity, 56.33 KMPH = `56.33* (10^5 cm)/(3600*s)=56.33*250/9*(cm)/(s)`, multiplying factor = `250/9`
  10. Gravity, `9.8 m/s^2=9.8*(100cm)/(s^2)=9.8*10^2*(cm)/(s^2)`, multiplying factor = `10^2`

For g cm us

  1. Mass, 1kg= 1000g, multiplying factor = 1000
  2. Length, 1m= 1 m, multiplying factor = 1
  3. Time, 1s = `10^6 mus` , multiplying factor = `10^6`
  4. Force, 1N = 1 `(kg.m)/s^2 = 1 * ((1000g)* (100 cm))/(10^12* mus^2)= 10^-7 (g*cm)/(mus^2)`, multiplying factor = `10^-7`
  5. Stress, 1Pa = 1`N/m^2= 1* 10^-7/(10^4 cm^2) = 10^-11* (g)/(mus^2*cm` , multiplying factor = `10^-11`
  6. Energy, 1Nm = `1* 10^-7 (g*cm)/(mus^2)*100 cm = 10^-5 (g*cm^2)/(mus^2)` , multiplying factor = `10^-5`
  7. Density, 1 `(kg)/m^3`= `1* (1000*g)/(10^6 *cm^3)= 10^-3 (g)/(cm^3)` , multiplying factor = `10^-3`
  8. Young's modulus = 210 GPa = `210*10^9*Pa= 210 *10^9* 10^-11* (g)/(mus^2*cm)=210*10^-2* (g)/(mus^2*cm)` , multiplying factor = `10^-2`
  9. Velocity, 56.33 KMPH = `56.33* (10^5 cm)/(3600*10^6*mus)=56.33*1/36000*(cm)/(mus)` , multiplying factor = `1/36000`
  10. Gravity, `9.8 m/s^2=9.8*(100cm)/(10^12*mus^2)=9.8*10^-10*(cm)/(mus^2)` , multiplying factor = `10^-10`

For g mm s

  1. Mass, 1kg= 1000g, multiplying factor = 1000
  2. Length, 1m= 1000 mm, multiplying factor = 1000
  3. Time, 1s = 1 s, multiplying factor = 1
  4. Force, 1N =`1 (kg.m)/s^2 = 1 * ((1000g)* (1000 mm))/( s^2)= 10^6 (g*mm)/(s^2)` , multiplying factor = `10^6`
  5. Stress, `1Pa = 1 N/m^2= 1* 10^6*(g*mm)/(s^2)*1/(10^6 mm^2) = 1* (g)/(s^2*mm` , multiplying factor = 1
  6. Energy, 1Nm = `1* 10^6*(g*mm)/(s^2)*1000 mm= 10^9* (g*mm^2)/(s^2)` , multiplying factor = `10^9`
  7. Density, 1 = `(kg)/m^3= 1* (1000* g)/(10^9 *mm^3) = 10^-6 (g)/(mm^3)`, multiplying factor = `10^-6`
  8. Young's modulus = 210 GPa = `210*10^9*Pa= 210 *10^9*1* (g)/(s^2*mm)=210*10^9* (g)/(s^2*mm)` , multiplying factor = `10^9`
  9. Velocity, 56.33 KMPH = `56.33* (10^6 mm)/(3600*s)=56.33*277.78*(mm)/(s)` , multiplying factor = `277.78`
  10. Gravity, 9.8 `m/s^2=9.8*(1000mm)/(s^2)=9.8*10^3*(mm)/(s^2)` , multiplying factor = `10^3`

For ton mm s

  1. Mass, 1kg= `10^-3`ton, multiplying factor = `10^-3`
  2. Length, 1m= 1000 mm, multiplying factor = 1000
  3. Time, 1s = 1 s, multiplying factor = 1
  4. Force, 1N = 1`(kg.m)/s^2 = 1 * ((10^-3 *Ton)* (1000 mm))/( s^2)= 1 *(Ton*mm)/(s^2)` , multiplying factor = 1
  5. Stress, 1Pa = 1`N/m^2= 1* 1/(10^6 mm^2) = 10^-6* (Ton)/(s^2*mm)` , multiplying factor = `10^-6`
  6. Energy, 1Nm =`1* 1 *(Ton*mm)/(s^2)*1000* mm = 10^3* (Ton*mm^2)/(s^2)` , multiplying factor = `10^3`
  7. Density, 1`(kg)/m^3= 1* (10^-3* Ton)/(10^9 *mm^3)= 10^-12*(Ton)/(mm^3)` , multiplying factor = `10^-12`
  8. Young's modulus = 210 GPa =`210*10^9*Pa= 210 *10^9* 10^-6* (Ton)/(s^2*mm)=210*10^3* (Ton)/(s^2*mm)` , multiplying factor = `10^3`
  9. Velocity, 56.33 KMPH = `56.33* (10^6 mm)/(3600*s)=56.33*277.78*(mm)/(s)` , multiplying factor = `277.78`
  10. Gravity, `9.8 m/s^2=9.8*(1000mm)/(s^2)=9.8*10^3*(mm)/(s^2)`, multiplying factor = `10^3`

For slug ft s

  1. Mass, 1kg= 0.068 slug, multiplying factor = 0.068
  2. Length, 1m= 3.280 ft, multiplying factor = 3.280
  3. Time, 1s = 1 s, multiplying factor = 1
  4. Force, 1N = 1`(kg.m)/s^2 = 1 * ((0.068*slug)* (3.280*ft))/( s^2)= 0.223(slug*ft)/(s^2)` , multiplying factor = 0.223
  5. Stress, 1Pa = 1 `N/m^2= 0.223*(slug*ft)/(s^2)*1/(10.76*ft^2)=0.02*(slug)/(s^2*ft)` , multiplying factor =0.02
  6. Energy, 1Nm = `1*0.023*(slug*ft)/(s^2)*3.280*ft=0.075*(slug*ft^2)/(s^2)` , multiplying factor =0.075
  7. Density, 1 `(kg)/m^3= (0.068*slug)/(35.28*ft^3)=1.93*10^-3*(slug)/(ft^3)` , multiplying factor = `1.93*10^-3`
  8. Young's modulus = 210 GPa =`210*10^9*0.02*(slug)/(s^2*ft)=210*2*10^7*(slug)/(s^2*ft)` , multiplying factor = `2*10^7`
  9. Velocity, 56.33 KMPH = `56.33* (10^3*3.280 *ft)/(3600*s)=56.33*41/45*(ft)/(s)` , multiplying factor = `41/45`
  10. Gravity, `9.8 m/s^2=9.8*(3.280*ft)/(s^2)` , multiplying factor = 3.280

For kg mm s

  1. Mass, 1kg= 1kg, multiplying factor = 1
  2. Length, 1m= 1000 mm, multiplying factor = 1000
  3. Time, 1s = 1 s, multiplying factor = 1
  4. Force, 1N = 1`(kg.m)/s^2 = 1 * ((1kg)* (1000 mm))/( s^2)= 10^3 (kg*mm)/(s^2)` , multiplying factor = `10^3`
  5. Stress, 1Pa = 1`N/m^2= 1* 10^2/(10^6 mm^2) = 10^-4 (kg)/(s^2*mm)` , multiplying factor = `10^-4`
  6. Energy, 1Nm = `1* 10^3 *(kg*mm)/(s^2)*1000* mm = 10^6 (kg*mm^2)/(s^2)`, multiplying factor = `10^6`
  7. Density, 1`(kg)/m^3= 1* (kg)/(10^9 *mm^3)= 10^-9*(kg)/(mm^3)` , multiplying factor = `10^-9`
  8. Young's modulus = 210 GPa =`210*10^9*Pa= 210 *10^9* 10^-4* (kg)/(s^2*mm)=210*10^5* (kg)/(s^2*mm)` , multiplying factor = `10^5`
  9. Velocity, 56.33 KMPH = `56.33* (10^6 mm)/(3600*s)=56.33*277.78*(mm)/(s)` , multiplying factor = `277.78`
  10. Gravity, `9.8 m/s^2=9.8*(1000mm)/(s^2)=9.8*10^3*(mm)/(s^2)`, multiplying factor = `10^3`

For g cm ms

  1. Mass, 1kg= 1000g, multiplying factor = 1000
  2. Length, 1m= 1 m, multiplying factor = 1
  3. Time, 1s = 1000 ms, multiplying factor = 1000
  4. Force, 1N = 1 `(kg.m)/s^2 = 1 * ((1000g)* (100 cm))/( 10^6*ms^2)= 10^-1 (g*cm)/(ms^2)` , multiplying factor = `10^-1`
  5. Stress, 1Pa = 1`N/m^2= 1* 10^-1(g*cm)/(10^4* cm^2*ms^2) = 10^-5* (g)/(ms^2*cm)` , multiplying factor = `10^-5`
  6. Energy, 1Nm = `1* 10^-1 *(g*cm)/(ms^2)*100 cm = 10* (g*cm^2)/(ms^2)` , multiplying factor = 10
  7. Density, 1 `(kg)/m^3`= `1* (1000*g)/(10^6 *cm^3)= 10^-3 (g)/(cm^3)` , multiplying factor = `10^-3`
  8. Young's modulus = 210 GPa = `210*10^9*Pa= 210 *10^9* 10^-5* (g)/(ms^2*cm)=210*10^4* (g)/(ms^2*cm)` , multiplying factor = `10^4`
  9. Velocity, 56.33 KMPH = `56.33* (10^5 cm)/(3600*1000*ms)=56.33*1/36*(cm)/(ms)` , multiplying factor = `1/36`
  10. Gravity, `9.8 m/s^2=9.8*(100cm)/(10^6*ms^2)=9.8*10^-4*(cm)/(ms^2)`, multiplying factor = `10^-4`

For kg mm ms

  1. Mass, 1kg= 1kg, multiplying factor = 1
  2. Length, 1m= 1000 mm, multiplying factor = 1000
  3. Time, 1s = 1000 ms, multiplying factor = 1000
  4. Force, 1N = 1 `(kg.m)/s^2` = `1 * ((1kg)* (1000 mm))/(10^6 ms^2)`= `10^-3 (kg*mm)/(ms^2)` , multiplying factor = `10^-3`
  5. Stress, 1Pa = 1 `N/m^2`= `1* 10^-3/(10^6 mm^2)` = `10^-9 (kg)/(ms^2*mm)` , multiplying factor = `10^-9`
  6. Energy, 1Nm = `1* 10^-3*(kg*mm)/(ms^2)*1000 *mm= 1* (kg*mm^2)/(ms^2)` , multiplying factor = 1
  7. Density, 1 `(kg)/m^3= 1* (kg)/(10^9 *mm^3)= 10^-9 (kg)/(mm^3)` , multiplying factor = `10^-9`
  8. Young's modulus = 210 GPa = `210*10^9*Pa`= `210 *10^9* 10^-9* (kg)/(ms^2*mm)=210*1* (kg)/(ms^2*mm)` , multiplying factor = 1
  9. Velocity, 56.33 KMPH =`56.33* (10^6 mm)/(3600*1000*ms)=56.33*5/18*(mm)/(ms)` , multiplying factor = `5/18`
  10. Gravity, 9.8 `m/s^2=9.8*(1000mm)/(10^6*ms^2)=9.8*10^-3*(mm)/(ms^2)`, multiplying factor = `10^-3`
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