Akkana gave us a nice description of practical ways to do alignment. This
is a short followup to that. (Thanks, Akkana. (I always forget whether
your name is Akkana or Akanna.))
She suggested sticking pins in the tires at some arbitrary height in the
tires. (No, of *course* you don't want to stick pins all the way into
the tread. That might let the air out, much akin to letting the smoke
out of your electrical system. So I'm not going to talk about that.)
Toe-in is supposed to be the difference between the front and rear of
the tires (tyres), measured at the axle center (centre). Let us assume
zero camber (cambre), meaning the axle is exactly horizontal (an admittedly
weak assumption, but not a problem for our purposes).
. .
.A ------- O ------- B.
|. .|
| .C D. |
| . E . |
| ... |
-----------------------
<---------d----------->
Ideally the toe-in should be measured at the two points a distance d apart,
where d is the tire (tyre) diameter (diametre). [All this English spelling
is getting to be a problem!] This would mean using points A and B. However
had you used point C instead of point A, then the distance between the tires
(tyres) would be different by some small amount. (Well, if you really want
to know, the total distance you should see at each point will be
track + sin(toe-angle) * sin(rotation-angle) * diameter
where track is measured at E and rotation-angle is measured from vertical,
as in the angle EOC. Camber adds more terms, but we can still ignore it.)
For zero toe-in, all this would make no difference, since the distance between
the wheels will be constant for all points A-E. However, for non-zero toe-in,
if you measure it at C (and D) instead of A and B, you'll get a smaller
value, and thus are likely to set toe-in to be larger than it ought to be.
("Smaller" and "larger" are used here in an absolute-value sense.)
Now, this is not a *serious* problem, and almost none at all if you are going
for zero toe-in. The reason it isn't so serious (and also the reason we can
ignore camber) is that the errors this produces are quite small compared to
the accurace you really need. In other words, you don't need to be exactly
at A and B, and anyway, you need to work at some point that has clearance
around the body and frame. But the closer you can get to the height of the
axle, the better your results will be, with increasing importance for desired
toe-in further from zero (either positive or negative).
If you do have to work at some height significantly removed from axle height,
you could compensate. Use an rotation-angle that is symmetric front to rear,
and figure that your measured toe-in will be reduced from what it "really" is
by a factor of
2 * d * sin(rotation-angle).
Even for desired zero toe-in, measuring at C and D reduces the precision of
your measurments. So it is best if you work as close as possible to axle
height.
This message brought to you by the Physic-For-A-Better-(And-Boring)-World
Society. Hi, Akkana.
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