Slip Angles - Beyond Counter-steering
In the
discussion on countersteering
you learned a great deal about camber thrust and how it helps convert
the lean of a wheel into a turn of that wheel. We will now look at the
tires more closely and see that though camber thrust helps change the
direction of travel of the wheel, the fact that the tires are flexible
results in phenomena that tends to fight changing direction.
Specifically, we will look at one kind of tire deformation (torsional)
that accounts for under- and oversteering.
Tires
can deform in four ways:
Tortionally - this is a difference in axial deflection from the
front to the back of the contact patch. Think of a turn to the
right. If the rim of the wheel towards the front leads the contact
patch and the rim of the wheel towards the back trails the contact
patch then it is clear that the rim has twisted to the right more
than has the contact patch. (See the second diagram below.)
To
the right you see a representation of a tire as seen from the top. The
green area is what the contact patch would look like if you had x-ray
vision. This representation is of a tire that is moving in the
direction it is pointed.
The
lower the air pressure within the tire is, the greater will be the radial
deformity of the tire. That is, the larger the bulging will be
around the contact patch and the larger the contact patch itself will
be.
The
bulging demonstrates that the sidewalls of a tire have great
flexibility. Because the flexing of rubber generates heat, but is a
poor conductor of that heat, if your tire pressure is too low you can
damage the sidewalls by riding on under-inflated tires - a
catastrophic failure can result.
Te get
a feeling for what torsional deformity is, sit on your
motorcycle at a dead stop and turn the handlebars 20 degrees in either
direction. When you let go of the handlebars the front wheel will be
pointed something between 15 and 18 degrees from where it was before
you turned it - not 20 degrees. Indeed, if you paid attention you
noticed the handlebars 'spring' back part way when you let go of them.
How can you account for this phenomena?
Obviously,
the contact patch did not turn as far as you thought it would when you
turned the handlebars. Why? Because the contact patch has traction
with the road surface and the tire's sidewalls flexed (torsionally
deformed). The fact that there was a springing back of part of the
movement of the handlebars is merely the result of the torsional
deformity 'unwinding' when force was removed.

Torsional
deformity happens whenever you are moving in other than a straight
line. The diagram to the right shows a tire (from the top - ignoring
lean angle) on a bike that is making a right turn. You will note that
the direction the wheel actually travels is determined by which way
the contact patch is pointed, NOT the wheel itself. Further, the
diagram is illustrative of what happens to BOTH the front and rear
tires. Indeed, because of the greater camber thrust of the front tire,
the discussion so far is more apt of what happens with the rear tire
than of the front one.
The
angular difference between the direction the contact is pointing and
that of the wheel itself is called its slip angle. It
should be apparent that if the slip angles for the front and rear
tires are the same, the bike will steer essentially as if there was no
slip angle at all. But, at least for a motorcycle, you will find that
the tire in the rear generates a larger slip angle than does the tire
in the front.
If the
rear slip angle is larger than the front one you have a condition
known as oversteer while if the front slip angle is
larger, the condition known as understeer
results.
You
will recall that a slip angle results from a combination of the facts
that the tire's sidewalls are flexible AND that the tire has traction.
Note that if there is no traction (riding on ice, for example) then
the slip angle will become essentially zero. On the other hand, if a
wheel travels in a direction other than the one its contact patch is
pointing, then you have a SLIDE angle rather than a slip angle. Slide
angles and slip angles are VERY DIFFERENT.
Let me
make this very clear. Inertia determines the direction a bike will
travel if it slides. If you lose traction you will slide in the
direction you were traveling at the time the slide starts. So long as
you have traction you will travel in the direction the contact patch
points, not the tire. Slide angle is the angular difference between
the direction inertia sends you and the direction your tires are
pointing while slip angle is the angular difference between the
direction your contact patch is pointed (thus, the direction the tire
moves) and the direction the tire is pointed.
Decreased
traction reduces slip angles and increases slide angles!
What
else affects slip angles? Acceleration and braking, tire profile size,
belt wrap direction, and tire camber.
Acceleration and braking affect traction primarily because of weight
transfer.
A 'low profile' tire has sidewalls that do not flex as much as
normal tires - hence, less torsional deformity (ie, less slip
angles.)
Radial tires are belted with the belt threads running radially while
standard tires are biased at an angle or circumferentially. In
addition, radial tire sidewalls are constructed to strongly resist axial
deformation. In other words, radial tires produce smaller
slip angles than do the others. (This means that it is critically
important that you NEVER have one tire be a radial and the other be
standard construction. Corner handling will be almost
unpredictable!)
Compared to the rear tire, since the front tire of a motorcycle is
narrower and has greater camber, its camber thrust is greater.
Camber thrust attempts to turn your wheel into a turn. Thus, greater
camber thrust yields smaller slip angles.
For
these reasons you should expect that your rear tire is almost always
operating with a greater slip angle than your front tire. (ie, your
motorcycle tends to oversteer.)
What
changes a slip angle into a slide angle? Excessive slip angles!!! That
is, a slip angle is so called because the part of the contact patch
that is to the outside of your turn is moving faster than the wheel
itself is in the direction it (the contact patch) is pointing while
the part on the inside is moving more slowly. (Exactly like camber
thrust.) Since the outside part is moving faster than the tire it must
be slipping. The inside part is gripping better than it would if
moving in a straight line. For this reason the contact patch 'walks'
itself into the turn.
The
greater the slip angle, the larger portion of the contact patch that
is slipping. At some point there is so little part of the contact
patch that is not slipping that traction is lost and the tire begins
to slide. Until shortly before a slide traction increases. Note,
however, that traction is generally not lost all at once. Rather than
an abrupt loss of traction, it tends to be lost gradually.
(Thankfully!!!)
So now
you know how it is that oversteer means that the rear tire has a
greater slip angle than does the front one, thus it probably has more
traction, yet despite that greater traction, it is the first tire to
slide while in a curve.
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