Principles of slow braking:
(a) if the cyclist is decelerating
then there must be a net force pointing backwards.
This force will come from friction between
wheel and ground, which may or may not be slipping
relative to each other.
(b) don't forget angular momentum conservation.
What is angular momentum? You can choose ANY point
you want, and the rate of change of angular momentum
is the sum of the couples acting about
that point. Angular momentum isn't only
possessed by things that go round. A moving
roller-skater has got angular momentum about
a point on the ground, for example.
So, consider the angular momentum about a point
just under the front wheel. The friction forces
acting on the front and back wheels both have
no couple about this point, but
if the cyclist slows down, her angular
momentum
about this point has reduced. Where is the couple
coming from to give this reduction in AM?
Answer: the vertical reaction forces on
the front and back wheels will adjust to provide
the appropriate couple, in combination with the
weight of the cyclist. The force acting
upwards on the front wheel will get bigger during braking
(regardless of which wheel is doing the braking).
The force upwards on the back wheel will be reduced
during braking.
Now, the maximum frictional force you can get is
widely assumed to be proportional to the
perpendicular reaction force, so
we can immediately conclude that, while braking is happening,
the maximum slowing force you can get from the back wheel
is smaller than the maximum slowing force you can
get from the front wheel.
If you apply back brakes alone, hard,
what will happen is that the wheel will skid:
there will be a rather useless slow deceleration
associated with an equilibrium condition where a little
bit of vertical force is coming up the back wheel,
just enough to provide the appropriate (proportional)
friction for the deceleration that is happening.
If you jam on the back brakes hard, you WILL skid (no matter how
sticky the tires are).
In contrast, you can get much more effective braking from the
front wheel. As the brakes are put on harder, more and more of the
(mg) total reaction force is delivered by the front wheel
and the maximum frictional slowing force that can be delivered by the
front wheel also increases. If you want to stop fast,
the front brake is definitely the brake you should be
using. If it is applied hard, there is a possibility of the bike
being so well slowed that the cyclist goes over the front wheel.
This can happen in two ways:
(i) the cyclist brakes hard and does not hold on to the bike with firm
arms; the cyclist allows herself to continue forwards (with arms bending)
so that her body is above the front wheel; I'll talk
no more about this sort of accident, which is avoidable by
holding one's arms in a fixed posture.
(ii) the cyclist maintains a fixed posture, and the braking is so severe
that the necessary allocation of the (mg) reaction
between the two wheels from the above angular momentum story
requires a negative force on the back wheel; this cannot be provided,
and the back wheel leaves the ground. The bike is now
rotating about the axle of the front wheel.
In some retarded countries of the world, the fact that
it is possible to go over the front wheel
when using the front brake has been used to promote the
idea that the front brake is dangerous and should not be used.
In Florida when I rented a bike, all the available bikes
had back brakes only. Another myth about brakes is
that it is safer to apply the front brake a fraction
of a second after the rear brake. The correct advice for stopping fast
is that you should always squeeze the front brake harder
than the back one (to maximize the deceleration
without the back wheel skidding), and that you should practice
using the front brake because it is `dangerous'.