Game Development Reference
In-Depth Information
Systems of Units
To describe the physical world, we need to measure things. We want to know how heavy some-
thing is or how fast it is traveling. In order to measure things, a system of units is required. It
would be nice if there were one universal system of units. Unfortunately, there are two widely
used systems of units, namely the International System of Units and the English System of
Units, and this is a situation that creates the potential for confusion and errors. Both systems
of units will be discussed in this section and conversion factors will be provided for moving
from one system to another.
The International System of Units, or
SI units
, includes three fundamental units of measure
for mass, length, and time. The unit of length in the SI system is the meter, the unit of mass is
the kilogram, and the unit of time is the second. The three quantities are usually abbreviated as
m
,
kg
, and
s
. Most other physical quantities, density, pressure, force, and so on, can be expressed
in terms of meters, kilograms, and seconds. There are also smaller SI units of measure that we
will use from time to time in this topic. A gram (
gm
) is 1/1000 or “one one-thousandths” of a
kilogram. A centimeter (
cm
) is 1/100 of a meter, and a millimeter (
mm
) is 1/1000 of a meter.
The unit of measure for temperature in the SI system is Kelvin (
K
).
An older of system of units known as the
English System
of Units is still widely used in
some countries. The unit of mass under the English system is the pound-mass (
lbm
) or the slug.
The unit of length is the foot (
ft
). One consistent element between the English and SI systems
is that time in both systems is measured in seconds. The English system is still widely used in
the United States and (as you might expect) England. Most of the rest of the world uses SI units.
Temperature in the English system is expressed in terms of degrees Fahrenheit (
o
F
) or Rankine (
R
).
The International System of Units is more logical in that different units of the same quantity
are related to each other by factors of ten. There are 100 centimeters in a meter and 1000 meters
in a kilometer (
km
). The English system involves more arbitrary conversion factors. There are
12 inches in a foot and 5280 feet in a mile.
This topic will tend to lean more to the SI system of units, but equivalent English unit
values for equations and constants will sometimes be provided. Table 2-1 shows the units of
measure for some common physical quantities, along with conversion factors for moving from
the English system to the SI system. If you multiply the value in English units by the conversion
factor, you will arrive at the value in SI units. For example, one mile is equal to 1.609
km
.
Table 2-1.
Units and Conversion Factors
Quantity
English Units
SI Units
Conversion Factor
Length
foot (
ft
)
mile
meter (
m
)
kilometer (
km
)
0.3048
1.609
Mass
pound-mass (
lbm
)
slug
kilogram (
kg
)
kilogram (
kg
)
0.4536
14.593
Force
pound (
lb
)
Newton (
N
)
4.448
Pressure
lb/in
2
N/m
2
6894.7
slug/ft
3
lbm/ft
3
kg/m
3
kg/m
3
Density
515.379
16.018
Fahrenheit (
o
F
)
Rankine (
R
)
Temperature
Kelvin (
K
)
Kelvin (
K
)
5/9(F + 459.67)
5/9
