Game Development Reference
In-Depth Information
There are two forms of friction: static and dynamic. They behave in slightly dif-
ferent ways.
15.3.1
S TATIC AND D YNAMIC F RICTION
Static friction is a force that stops an object from moving when it is stationary. Con-
sider a block that is resting on the ground. If the block is given some force, friction
between the block and the ground will resist this force. This is a kind of reaction
force: the more you push, the more friction pushes back. At some point, however, the
pushing force is too much for friction, and the object begins to move.
Because static friction keeps objects from moving, it is sometimes called “stic-
tion.” The static friction force depends on the materials at the point of contact and
the reaction force:
|
f static |
μ static |
r
|
,
where r is the reaction force in the direction of the contact normal, f static is the friction
force generated, and μ static is the coefficient of static friction.
The coefficient of friction encapsulates all the material properties at the contact
in a single number. The value depends on both objects; it cannot be generated simply
by adding a coefficient for one object to one for another. In fact it is an empirical
quantity: it is discovered by experiment and cannot be reliably calculated.
In physics reference books you will often find tables of the coefficient of friction
for different pairs of materials. In a game development setting the coefficient for a
particular contact is more often the result of guesswork or trial and error. I have in-
cluded a table of friction coefficients that I find useful in appendix B.
Notice that the preceding formula is an inequality: it uses the
symbol. This
means that the magnitude of the friction force can be anything up to and including
μ
. In fact, up to this limit it will be exactly the same as the force exerted on the
object. So the overall expression for the static friction force is
|
r
|
f planar
f planar
f static =
whichever is smaller in magnitude ,
μ static |
r
|
where f planar is the total force on the object in the plane of the contact only, because
the resulting force in the direction of the contact normal is generating the reaction
force. The reaction force and the planar force can be calculated from the total force
applied:
· d
where d is the contact normal and f is the total force exerted, and
r
=−
f
f planar =
f
+
r