Unit Conversion Tables
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Unit Conversion Tables This document contains information on using units in Mechanica and on converting values between different systems of units. This document includes the following sections: Topic Introduction Basic Equalities System of Units Basic Units Examples of Values for Gravitational Acceleration and Selected Properties of Steel Correspondence Between Mass and Force Correspondence Between Mass and Pounds-mass Conversion of Basic Units Correspondence Between Degrees Celsius and Degrees Fahrenheit Note: Throughout this document, scientific notation is written as you would type it in Mechanica. For example, 2.07 x 1011 is written as 2.07e11.
Introduction Mechanica does not store information concerning the physical dimensions (units) of the numerical data that you enter. Therefore, whenever you enter numerical data into Mechanica, you must ensure that you are using a consistent set of units. For example, if you enter distance in terms of inches and force in terms of pounds-force, then you must enter Young's modulus in terms of pounds-force per square inch. In this system of units, Mechanica reports stress in terms of pounds-force per square inch. If you do not use a consistent set of units when entering data, the values computed by Mechanica will be meaningless. This document provides an overview of the physical dimensions of many of the quantities in Mechanica. The following abbreviations are used throughout this document: L = length M = mass T = time F = force E = energy (heat) P = power D = temperature (such as F, C, K) R = angle radian When choosing a consistent set of units, you must decide which quantities will form the basic physical dimensions and which quantities will be derived from the basic dimensions. Usually, you will choose either mass, length, and time (MLT) or force, length, and time (FLT) as the basic dimensions. The connection between these two systems is given by Newton's second law of
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motion: force = mass x acceleration the dimensions of which are: F = ML/T2 Some quantities in Thermal are usually expressed in terms of energy and power, the dimensions of which are determined from their definitions: energy (work, heat) = force x distance E = FL power = energy รท time P = E/T
Basic Equalities Following is a list of many of the quantities in Mechanica and the physical dimensions of each expressed in terms of common physical dimensions and also in terms of MLT and FLT.
Quantity
Common
MLT
FLT
length
L
L
L
time
T
T
T
mass
M
M
FT2/L
force
F
ML/T2
F
temperature
D
D
D
area
L2
L2
L2
volume
L3
L3
L3
velocity
L/T
L/T
L/T
acceleration
L/T2
L/T2
L/T2
angle, rotation
R
R
R
rotational velocity
R/T
R/T
R/T
rotational acceleration
R/T2
R/T2
R/T2
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density
M/L3
M/L3
FT2/L4
moment, torque
FL
ML2/T2
FL
distributed force along a curve
F/L
M/T2
F/L
distributed moment along a curve
F
ML/T2
F
distributed force over a surface, pressure, stress, Young's modulus
F/L2
M/LT2
F/L2
distributed moment over a surface
F/L
M/T2
F/L
translational stiffness
F/L
M/T2
F/L
rotational stiffness
FL/R
ML2/T2R
FL/R
coefficient of thermal expansion
/D
/D
/D
moment of inertia of beam crosssectional area
L4
L4
L4
mass moment of inertia
ML2
ML2
FLT2
energy, work, heat (E)
FL
ML2/T2
FL
power, heat transfer rate (P)
E/T
ML2/T3
FL/T
temperature gradient
D/L
D/L
D/L
heat flux
P/L2
M/T3
F/TL
thermal conductivity
P/LD
ML/T3D
F/TD
convection coefficient
P/L2D
M/T3D
F/LTD
specific heat (Cp)
E/MD
L2/T2D
FL/MD
System of Units To define a system of units, you assign a unit of measure to each of the physical dimensions. This section provides the units of the above quantities in four different systems of units, two
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different metric systems, MKS and mmNs, and two different English systems, FPS and IPS. The MKS system of units uses MLT as the basic dimensions. The mmNs, FPS, and IPS systems of units use FLT as the basic dimensions.
MKS Following are the basic and some of the derived units of the MKS system:
Basic Units
Some Derived Units
M: kilogram (kg)
F: kg-m/sec2 = Newton (N)
L: meter (m)
E: N-m = Joule (J)
T: second (sec)
P: J/sec = Watt (W)
D: degree Celsius ( C)
mmNS Following are the basic and some of the derived units of the mmNS system:
Basic Units
Some Derived Units
F: Newton (N)
M: (N-sec2/mm) (kg-m/N-sec2) (1000mm/m) = 1000 kg = tonne(t)
L: millimeter (mm)
E: (N-mm) (J/N-m) (m/1000mm) = J/1000 = mJ
T: second (sec)
P: (mJ/sec) (J/1000mJ) (W-sec/J) = W/1000 = mW
D: degree Celsius ( C)
mmKS Following are the basic and some of the derived units of the mmKS system:
Basic Units
Some Derived Units
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M: kilogram (kg)
2 F: kg-mm/sec = mN
L: millimeter (mm)
E: mN-mm =
T: second (sec)
P:
J
J/sec = W
D: degree Celsius ( C)
FPS Following are the basic and some of the derived units of the FPS system:
Basic Units
Some Derived Units
F: pound-force (lbf)
M: lbf-sec2/ft = slug
L: foot (ft)
E: ft-lbf
T: second (sec)
P: ft-lbf/sec
D: degree Fahrenheit ( F)
IPS Following are the basic and some of the derived units of the IPS system:
Basic Units
Some Derived Units
F: pound-force (lbf)
M: lbf-sec2/in
L: inch (in)
E: lbf-in
T: second (sec)
P: lbf-in/sec
D: degree Fahrenheit ( F)
CGS Following are the basic and some of the derived units of the CGS system:
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Basic Units
Some Derived Units
M: gram (g)
F: g-cm/sec
2
= 10
-5
N = dyne
L: centimeter (cm)
2 2 -7 E: g-cm /sec = 10 J = erg
T: second (sec)
2 3 -7 P: g-cm /sec = 10 W
D: degree Celsius ( C)
Pro/E Default Following are the basic and some of the derived units of the Pro/E Default system:
Basic Units
Some Derived Units
M: pounds-mass (lbm)
2 F: in-lbm/sec
L: inch (in)
2 2 E: in -lbm/sec
T: second (sec)
2 3 P: in -lbm/sec
D: degree Fahrenheit ( F)
Basic Units Using the definitions from the previous section, the units of the quantities in these four systems are as follows:
Units
Metric (MKS)
Metric (mmNS)
English (FPS)
English (IPS)
length
m
mm
ft
in
time
sec
sec
sec
sec
mass
kg
tonne
slug
lbfsec2/in
force
N
N
lbf
lbf
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temperature
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C
C
F
F
area
m2
mm2
ft2
in2
volume
m3
mm3
ft3 (cuft)
in3 (cuin)
velocity
m/sec
mm/sec
ft/sec
in/sec
acceleration
m/sec2
mm/sec2
ft/sec2
in/sec2
angle, rotation
rad
rad
rad
rad
rotational velocity
rad/sec
rad/sec
rad/sec
rad/sec
rotational acceleration
rad/sec2
rad/sec2
rad/sec2
rad/sec2
density
kg/m3
tonne/mm3
slug/ft3
lbfsec2/in4
moment, torque
N-m
N-mm
ft-lbf
in-lbf
distributed force along a curve
N/m
N/mm
lbf/ft
lbf/in
distributed moment along a curve
N
N
lbf
lbf
distributed force over a surface, pressure, stress, Young's modulus
N/m2 (Pa)
N/mm2 (MPa)
lbf/ft2
lbf/in2 (psi)
translational stiffness
N/m
N/mm
lbf/ft
lbf/in
rotational stiffness
N-m/rad
N-mm/rad
lbfft/rad
lbfin/rad
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coefficient of thermal expansion
/ C
/ C
/ F
/ F
moment of inertia of beam cross-sectional area
m4
mm4
ft4
in4
mass moment of inertia
kg-m2
tonne-mm2
slug-ft2
lbf-insec2
energy, work, heat (E)
J
mJ
ft-lbf
in-lbf
power, heat transfer rate (P)
W
mW
ftlbf/sec
inlbf/sec
temperature gradient
C/m
C/mm
F/ft
F/in
heat flux
W/m2
mW/mm2
lbf/ftsec
lbf/insec
thermal conductivity
W/mC
mW/mmC
lbf/secF
lbf/secF
convection film coefficient
W/m2C
mW/mm2C
lbf/ftsec- F
lbf/insec- F
specific heat (Cp)
J/kgC
mJ/tonneC
ftlbf/slugF
in2/sec2F
Note: 1W = 1N-m/sec, 1mJ = 1N-mm, 1mW = 1N-mm/sec, N/m2 = Pascal (Pa)
The numerical values of conductivity are the same in the MKS and mmNS systems and in the FPS and IPS systems. In Structure, units of modal frequency results are always cycles per unit time or Hz. The units of time are affected by the force/length/time units you used to define the model. Structure never reports modal frequency in terms of radians per unit time.
Examples of Values for Gravitational Acceleration and Selected Properties of Steel
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The following table shows examples of approximate values for acceleration, density, Young's modulus, thermal coefficient of expansion, and thermal conductivity:
Metric (MKS)
Metric (mmNS)
English (FPS)
English (IPS)
g (gravitational acceleration)
9.81 m/sec2
9810 mm/sec2
32.2 ft/sec2
386 in/sec2
density (steel)
7830.0 kg/m3
7.83e-9 tonne/mm3
15.2 slug/ft3
7.33e-4 lbsec2/in4
Young's modulus (steel)
2.07e11 N/m2
2.07e5 N/mm2
4.32e9 lb/ft2
3.0e7 lb/in2
coefficient of thermal expansion (steel)
12e-6/ C
12e-6/ C
6.5e-6/ F
6.5e-6/ F
thermal conductivity (steel)
43.37 W/mC
43.37 mW/mmC
5.4 lbf/secF (25 Btu/hrft- F)
5.41bf/secF (2.083 Btu/hr-inF)
Units
Correspondence Between Mass and Force The following list describes the correspondence between mass and force at sea level for four common unit systems: 1 kg weighs 9.81 Newtons 1 tonne weighs 9810 Newtons 1 slug weighs 32.2 lbs 1 (lb-sec2/in) weighs 386 lbs
Correspondence Between Mass and Pounds-mass In some English systems of units, mass is sometimes given in pounds-mass (lbm). The relationship between pounds-mass and mass in the FPS and IPS systems of units is determined by the fact that one pound-mass weighs one pound-force in the gravitational field of the earth at sea level: lbf = lbm x g
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where g = 32.2 ft/sec2 = 386 in/sec2 Therefore: lbm = 1/386 lbf-sec2/in lbm = 1/32.2 lbf-sec2/ft = 1/32.2 slug
Conversion of Basic Units The following tables show conversion factors for various quantities:
Length Conversion Factors m
mm
ft
in
1m =
1
1000
3.281
39.37
1 mm =
1.0e-3
1
3.281e3
3.937e-2
1 ft =
0.3048
304.8
1
12
1 in =
2.54e2
25.4
8.333e2
1
Mass Conversion Factors
kg
tonne (Nsec2/mm)
slug (lbsec2/ft)
1 kg =
1
1.0e-3
6.852e2
5.71e-3
1 tonne =
1000
1
68.52
5.71
1 slug =
14.59
14.59e-
1
8.333e-
lbsec2/in
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3 1 lbsec2/in =
175.1
2
0.1751
12
1
kg m2
tonne mm2
slug ft2
lbf-sec2 -in
1 kg m2 =
1
1000
.738
8.85
1 tonne mm2 =
1e-3
1
7.375e4
8.85e-3
1.356
1.356e3
1
12
0.113
113
1/12
1
Moments of Inertia
1 slug ft =
2
1 lbf-sec2in =
Force Conversion Factors N
Kg-force
lb
1 N =
1
0.101972
0.2248
1 lb =
4.448
0.453594
1
Moment Conversion Factors
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N-m
N-mm
lb-ft
lb-in
1 N-m =
1
1000
0.7376
8.851
1 Nmm =
1.0e3
1
7.376e4
8.851e3
1 lb-ft =
1.356
1356
1
12
1 lb-in =
0.113
113
8.33e-2
1
Density Conversion Factors
slug/ft3
lbsec2/ in4
1e-12
1.94e3
9.36e8
1e12
1
1.94e9
9.36e4
1 slug/ft3 =
515
5.15e10
1
4.82e5
1 lbsec2/in4 =
1.07e7
1.07e5
20700
1
kg/m3
tonne/ mm3
1 kg/m3 =
1
1 tonne/mm3 =
Stress Conversion Factors N/m2
N/mm2
lb/ft2
lb/in2
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1 N/m2 =
1
1e-6
2.09e2
1.45e4
1 N/mm2 =
1e6
1
20900
145
1 lb/ft2 =
47.9
47.9e -5
1
6.94e3
1 lb/in2 =
6890
6.89e -3
144
1
Translational Stiffness Conversion Factors N/m
N/mm
lb/ft
lb/in
1 N/m =
1
1.0e-3
6.8525e2
5.7104e3
1 N/mm =
1000
1
68.525
5.710
1 lb/ft =
14.593
1.4593e2
1
8.33e-2
1 lb/in =
175.118
1.7512e5
12
1
Rotational Stiffness Conversion Factors
1 N-m/rad =
Nm/rad
Nmm/rad
lb-ft/rad
lb-in/rad
1
1000
0.7376
8.851
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1 Nmm/rad =
1.0e-3
1
7.376e-4
8.851e-3
1 lb-ft/rad =
1.356
1356
1
12
1 lb-in/rad =
0.113
113
8.33e-2
1
Thermal Conductivity Conversion Factors
W/mC
mW/ mmC
Btu/ hr-ftF
Btu/ hr-inF
1 W/mC=
1
1
0.5777
4.817e -2
0.1249
1 mW/mmC=
1
1
0.5777
4.817e -2
0.1249
1 Btu/hrft- F =
1.731
1.731
1
8.333e -2
0.2162
1 Btu/hrin- F =
20.76
20.76
12
1
2.594
1 lbf/secF=
8.007
8.007
4.626
0.3854
1
lbf/ sec- F
Correspondence Between Degrees Celsius and Degrees Fahrenheit The following two formulas describe the correspondence between the Celsius and Fahrenheit degree scales: C = ( F 32)/1.8 F = 1.8 C + 32 Thus, a temperature difference of 1 C is equal to a difference of 1.8 F.
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