Steering Geometry
When Retrofitting Checker Disk Brakes
to Pre-1968 Checkers
~~~~~~~~~~~~~~~~~~~~~~
Lane Darnton
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When considering a disk brake retrofit to a pre-disk (1970-earlier)
Checker, one question that comes up is “Which Checker disk brake steering
knuckles will fit my pre-disk Checker?”. Another is “Is there a difference
between ‘rear steer’ and ‘front steer’ Checker hardware in terms of what
will work on my pre-disk Checker?”
The answer to the first question is “any 1968 – 1982”. This means
‘68-‘70 (drum brake) Checkers already have the correct knuckles and steering
arms for a disk retrofit. Note that pre-‘68 cars need a ’68-later lower
A-arm end fitting. This is because Checker flipped the lower ball joint
over in ‘68, with the ball joint body pressed into the steering arm (not
the A-arm end fitting as on earlier cars), so the ball stud pointed DOWN
into the new A-arm end fitting. By the way, one benefit of this change is
that coil spring replacement is rendered trivial, an advantage for fleet
cars such as taxis – and for you!
The answer to the second question is a resounding “yes!” The 1978-1982
“front steer” steering arms will not work on your pre-‘68 Checker. They
do not have the correct angle to the centerline of the car to induce the
right amount of dynamic toe-in when you turn the wheels.
To understand this, let’s review the basics. When you turn your car,
the following things are true:
1) each wheel follows the arc of a circle,
2) these circles have a common center, and
3) each circle has a different radius. For the rear
wheels this is not a problem – they just follow along like a trailer –
but each front wheel must be correctly steered along its separate circle,
or else the front tires fight each other and scrub themselves to death.
Here’s a sketch:
Note that the outside front wheel follows a larger circle than the
inside front, so it needs less steering angle. This dynamic toe-out depends
on the wheelbase and track width of the car (to the center of the tread contact
patch). For Checkers these values are 120” and about 65” respectively for
models A11, A12, & A12W. (A11E and A12E wheelbases are 129”.) Using these
values, one can calculate the required dynamic toe-out as a function of
the inside wheel angle:
Look at the “Neutral” curve. Simple, huh? If only. There are two problems:
1) how do you get the front wheels to do that? and 2) this curve only applies
at extremely low speeds, when there are no cornering
forces.
Let’s address the 2nd problem first. Due to lateral weight transfer
and body lean in corners, the outside and inside wheels do not share the
cornering load equally. The degree of inequality depends on many factors
– the height of the center of gravity, the stiffness of the anti-sway
bar, the car’s speed, spring stiffness, etc. – but the result is
the outside tire takes more cornering load, so it needs to operate at a
greater slip angle than the inside tire. It therefore needs to be turned
IN slightly more than the inside tire (relative to the circle it is forced
to follow), and so its dynamic toe-OUT needs to be LESS than indicated by
the neutral curve. Got that?
How much less? It varies from car to car, but let’s say *roughly*
half (see “1/2 neutral” curve above). Why half? Because the outside front
tire generates *roughly* twice the cornering load of the inside front
tire for a passenger car driven “normally”. The slower the car is cornered,
the higher this value should be (closer to “neutral”). The faster you corner,
and especially if you drift, the lower this value should be (closer to zero
dynamic toe-out). On race cars, the required dynamic toe-out reaches zero
as the inside front wheel lifts off the ground, which is fairly common.
Now back to the first problem: how to get the front wheels to do that.
The answer: by bending the steering arms IN toward the car centerline (for
rear steer cars). Why does this work? Well, the details involve trigonometry,
but the upshot is, it makes the inside wheel steer more quickly than the
outside wheel at all turn angles. Thus, the toe-out increases steadily
(quadratically) with turn angle, as the graph shows is required. The more
the inward slant of the steering arms, the more dynamic toe-out. Checkers
“want” about 1.5 degrees of toe-out at an
inside wheel
steer angle of 20 degrees, as shown by the gray dashed "1/2 neutral" curve.
So, how much steering arm angle produces that much toe-out? Let’s
add to the graph:
The two added curves are labeled: ’68-’77 (rear-steer) steering arm
(on a rear-steer car), and ’78-’82 (front-steer) steering arm (again on
a rear-steer car, but facing aft). The inward slant of these steering
arms is 8.14 and 2.39 degrees respectively, whereas the inward slant that
would produce “neutral” and “1/2 neutral” toe-out are 10.44 and 20.88
degrees respectively. The ‘68-’77 arm is about 1/3rd neutral, which tells
me that Checker believed their taxis were cornered hard enough to shift
3/4ths of the front cornering load to the outside front wheel. The ’78-‘82
arm, if retrofitted to a ’77-earlier rear steer Checker, gives another
factor of 3 less toe-out than that. (So why do they work on ’78-’82 cars?
That’s another story.) Use the wrong arm and you’ll get 3x faster
tire wear, very uncool tire squeal in slow, tight corners, particularly
in parking lots, and worst of all, reduced cornering force because the
tires spend part of their available force fighting each other. My car did
all these things.
So. Imagine you are in Joe Pollard’s Mojave, CA junkyard with a pile
of Checker steering arms in front of you. Which ones do you want? I wondered
this too, since the ones I had were clearly wrong, so I drove out there
and spent four windy hours underneath junk Checkers with a digital camera
and a tape measure, and took home a boxful of arms courtesy of Joe. Check
out these two photos.
The differences in steering stop castings and inward slants are the
clues. Both arms have a steering arm length of 7.5” (ball joint center
to tie rod hole center), but the ’68-’77 arm has a tie rod inboard offset
of 2.25” from the arm mounting surface, while the ’78-’82 offset is only
1.5”. Since the center of the ball joint itself is offset inboard from the
mounting surface by 1.19 inches, the resulting inward offsets from the ball
joint are 1.06" and 0.31", so the inward slant angles (ball joint to tie
rod end) are arctan(1.06/7.5) = 8.14 degrees and arctan(0.31/7.5) = 2.39
degrees respectively, as stated above.
Here’s an interesting side note. In early-to-mid 20th century automobile
design, a quantity known as the Ackerman Angle was used as a guide to what
the steering arm inward slant ought to be. This was the angle the arms
would have if you extended the line formed by the steering axis (i.e. ball
joint or kingpin center) and the steering arm end (tie rod end mount hole),
and made it pass through the center of the rear axle. For a Checker, this
angle is about 14.6 degrees and would produce 70% of neutral dynamic toe-in.
From this we can deduce that those early cars, most of which
had no anti-sway bar, were designed for sedate cornering, and
squealed their tires if you misbehaved, just like in the movies – and the
’51 Buick Roadmaster I drove in my teens.
Now you know why.