Game Development Reference
In other words, the resulting planar force is the total force with the component
in the direction of the contact normal removed. In the equation this component is
removed by adding the reaction force, which is equal and opposite to the force in the
direction of the contact and therefore cancels it out.
The dependence of static friction on the normal reaction force is an important
result. It allows rock climbers to walk up a (more than) vertical slope by pushing
against another wall at their back—the increase in reaction force means increased
friction. Push hard enough and there'll be enough friction to overcome your weight
and keep you from falling.
Another important feature of the previous equations is that friction doesn't de-
pend on the area that is in contact with the ground. A rock climber with bigger feet
doesn't stick better. Despite being slightly counterintuitive (for me at least), this is
fortunate because nowhere in our engine have we considered the size of the contact
area. Contact area does become important in some cases where the objects can de-
form at the point of contact (tire models spring immediately to mind), but they are
very complex and well beyond the scope of this topic, so we'll stick with the basic
Returning to our block on the ground: as we exert more force, friction pushes
back until we reach μ static |
, the limit of static friction. If we increase the force input
by a fraction, the friction force drops suddenly and we enter the world of dynamic
Dynamic friction, also called “kinetic friction,” behaves in a similar way to static fric-
tion but has a different coefficient of friction.
When objects at the contact are moving relative to one another, they are typically
leaving contact at the microscopic level. Figure 15.4 shows static and dynamic friction
magnified many times. Once the object is in motion, the roughness on each object
isn't meshing as closely, so dynamic friction is a less powerful force.
Dynamic friction always obeys the equation
f dynamic =−ˆ
v planar μ dynamic
where μ dynamic is the coefficient of dynamic friction. Notice that the direction of fric-
tion has changed. Rather than acting in the opposite direction to the planar force (as
it did for static friction), it now acts in the opposite direction to the velocity of the
object. This is significant: if you stop exerting a force on a stationary object, then the
friction force will instantly stop too. If you stop exerting a force on a moving object,
friction will not stop: the object will be slowed to a halt by dynamic friction.
Just like static friction, dynamic friction coefficients can be found in some physics
reference books for different combinations of materials.
It is rare in game physics engines to distinguish in practice between static and dy-
namic friction. They tend to be rolled together into a generic friction value. When the
object is stationary, the friction acts as static friction, acting against any force exerted.