Game Development Reference
In-Depth Information
Earth's rotation requires that gravity provide a centripetal acceleration of
0.03369 m s −2 . Thus a small part of the force of gravity that makes objects
feel heavy is being counteracted by the spinning of Earth, which makes
them feel lighter.
Subtracting this apparent centrifugal force from the force of gravity
gives us 9.83 − 0.03369 ≈ 9.796, but now the value is too small, not the
9.81 we were looking for. The reason is that gravity exhibits variations in
magnitude over Earth's surface. The biggest source of this variation is the
centripetal acceleration we have just calculated; it varies with latitude. We
computed its magnitude assuming r was Earth's radius; the resulting value
for gravity of 9.796 is actually the correct strength of gravity at the equator.
As the latitude increases and we move towards the poles, the radius r of
the circular path (which has constant latitude) decreases. At the poles,
the radius shrinks to zero, and objects rotate but do not move in a circular
path. Thus there is no apparent centrifugal force at the poles, and the force
of gravity is equal to the 9.83 value we computed above. The value 9.81 is
known as the “standard value,” and is the average force of gravity at sea
level at a latitude of about 45 o .
Now that we've discussed at some length the strength of gravity in the
real world, let's talk about how this number is often completely irrelevant in
video games. In certain genres, such as racing or flight simulators, realism
is important. However, in most other video games, the first law of video
game physics applies. (Hey, Newton made up some laws, so why can't we?)
First Law of Video Game Physics
Reality is overrated.
For example, first-person shooters are notorious for poor jumping me-
chanics. The most important reason is probably the fundamental fact that
you cannot see your feet, yet some first-person games have for some reason
added jumping puzzles. But even many third-person shooters that adopt an
over-the-shoulder camera also have jumping mechanics that just don't feel
right. Why? In most first-person shooters, when you jump, you are given
an initial burst of upward velocity, and then your position is simulated just
like every other airborne object in the world, using gravity, which causes
your motion to be parabolic. Compare this to the jump mechanic in most
third-person action games. Most of these games do not simulate jumps us-
ing a constant acceleration. Instead, your character will spring up almost
instantaneously after you hit the button, and reach a maximum height very
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