Suspension Geometry

[Scott Fisher <sefisher@xxxxxxxxx>]

Graham Hilder basically gets it on the nose, not once but twice:

> stiffening up the front of an Alfetta/GTV6/etc will
> reduce its understeer, rather than increasing it 

Without getting into the arcana of weight transfer, this can often a
good rule of thumb for most cars with factory-designed built-in plow. 
Most cars understeer in their stock form, with the understeer
progressing due to the suspension geometry, which is where the duck
comes down yet again for lucky Graham:

> the use and the particular layout of unequal length
> wishbones which gives the camber result Chris describes

Precisely.  The key, for me, was in understanding the words "camber
curve" -- realizing that a car's suspension is a moving system that
reacts on a curve, rather than in a straight line, and that camber
changes as the car's body rolls on its suspension.  (We'll ignore
MacPherson struts for this discussion, as they're not part of the RWD
Alfa equation.)

For unequal upper/lower A-arm suspension, the following dimensions have
an effect on the camber curve:

  - the length of each arm
  - the angle, at rest, of each arm
  - the angle, at rest, that both arms make

There's more in real life, but it helps to begin by visualizing just
these three things, plus one more: as the car itself rolls in a corner,
this changes the reference point for the tire because the car -- what
the suspension is connected to -- has now moved.

Let's take a car where the upper arm is slightly shorter than the lower
and both arms are parallel to the ground.  Furthermore, imagine three
planes that are vertical with respect to the car's body and parallel to
its direction of travel.  One plane is in the body's Centerline (and
perpendicular to the ground, at rest); one plane runs through the center
of the outboard end of the Upper A-arm, and the last runs through the
center of the outboard and of the Lower A-arm.  We're now going to
consider two lines: UC, from the Upper A-arm to the Centerline, and
another, LC, from the Lower A-arm to the Centerline; imagine that these
lines remain perpendicular to both planes they connect, no matter how
the car rolls.

In such a system, as the car's body rolls in a corner, consider what
happens:

1.  The shorter, upper arm describes a smaller, tighter arc as the car
leans.  This means that line UC gets *smaller* as the car leans, and it
does so *more quickly* than line LC.

2.  The longer, lower arm describes a larger, looser arc as the car
leans.  This means that line LC gets smaller as the car leans, and it
does so *more slowly* than does line UC.

3.  The net result is that the top end of the kingpin moves *inboard*
relative to line C.  

Basically, this suspension causes increased negative camber under body
roll.  The degree to which this happens depends on the ratios of UC to
LC, which in turn are based on the lengths and angle of the arms.  

What happens when you change the resting angle of the suspension arms? 
Consider now this option:

1.  The short, upper arm is angled so that the inner end is below the
outer end.

2.  The long, lower arm is angled so that the inner end is above the
outer end.

3.  In *this* geometry, increasing body roll causes line UC to shorten,
but it causes line LC to *lengthen*. 

Basically, this second suspension causes increased negative camber under
body roll but *much* more quickly than the former, because it actually
moves the outboard end of the kingpin out while moving the inboard end
in -- but only up to a point.

When the long, lower arm is raised to the point where it's above
perpendicular to the car's vertical axis, *it starts pulling the lower
end of the steering kingpin inboard again.*  (One of us may actually
have to draw this part, it's very subtle till you "get it.")  This dials
in more *positive* camber as the car's lean increases -- even if only by
reducing the negative camber enough so that the cumulative angle of the
suspension movement plus the car's body roll means a positive value
(that is, the top of the tire is leaning out away from the car).

So here, let's consider that suspension design #2 is set up with the
lengths and angles such that as a car tilts a few degrees, the wheel is
kept vertical (negative camber).  However, after a little *more* tilt of
the car, the wheel begins to be tilted so that the top tilts outboard a
bit (positive camber).  That would be one way for the suspension
designer to build in responsive initial steering feel, yet provide for
"safe" understeer as the cornering load increased.

Graham's final comment is also important:

> how would his 15 degrees figure be altered if the car 
> is lowered, with consequent changes to the wishbones' initial
> angles?  

Precisely.  Lowering a car by inserting shorter springs means that the
car retains the same camber curves dictated by the suspension arms --
but you start *at a different point* on the camber curve.

Let's take the example of our car that provides increased negative
camber for the first few degrees of body roll and then starts to provide
increased positive camber.  With stock springs, this car will feel
nimble and responsive as you enter a corner, and then will become more
stable as roll progresses; finally, if you really overcook it, the car
will simply understeer off course nose first.

Now you lower it, oh, let's say 1.5" is enough to do the trick.  You
enter a corner and you're immediately in the understeer phase of the
curve, so you dial in more steering and more steering and eventually you
either scrub the outside of the front tires all the way off or you bitch
about the spring manufacturer making junk. 

One solution for the problem of a car for which the camber curve
eventually goes positive: stiffer anti-roll bars with stock ride-height
springs.  These win in the following way:  When you enter a corner, the
car resists roll, meaning the suspension geometry stays in the negative
portion of the camber curve for longer.  As you go faster, the car still
rolls, but it takes higher speeds for this to happen.  Finally, if you
get to a very high degree of body roll, you will get the stabilizing
effect of understeer, but typically where you want it, at a higher rate
of speed -- always assuming, of course, that the geometry at the rear
hasn't made life interesting by breaking free first.

This posting is getting long enough, so I'll merely hint that the
factors affecting rear-end geometry, at least on production rear-drive
Alfas, have nothing to do with the unequal A-arm approach.  On solid
axle Alfas, there is actually a little rear-steer effect built into the
system, which may be a surprise to people who only started reading about
rear-steer effects when they were added, at the cost of great
complexity, to FWD cars about seven to ten years ago.  But that's a
whole separate tome.

- --Scott Fisher

------------------------------

End of alfa-digest V7 #122
**************************