On Friday, November 30, 2001, at 10:42 , TeamZ06@aol.com wrote:
> In a message dated 12/1/01 12:11:27 AM Central Standard Time,
> Kevin_Stevens@pursued-with.net writes:
>
>
> > The equation:
> >
> > Diameter * pi * toe in degrees/ 360
> >
> > has absolutely nothing to do with calculating toe measurements.
> > Somebody is confused.
> >
> > Mark
>
> You're wrong, and if you weren't being snotty about it I'd offer to
> demonstrate. Figure it out yourself.
>
> It was no more my intention to be snotty than it was probably your
> intention to call the kettle black. The somebody confused could just
> as easily be me as anybody else.
Ok, pax.
> Using my equation:
>
> tire diameter 25.6"
> total toe measurement 3/8" ---> 3/16" per side
>
> angle = arcsin [(0.5*0.375) / 25.6]
> angle = 0.420 degrees
>
> Using your equation with the units above:
>
> Diameter * pi * toe in degrees/ 360
> [25.6 * 3.142 * 0.42] / 360 = 0.094 or approx. 3/32"
>
> Where did I go wrong?
Well, your choice; either your definition of "toe", or your triangle
base. You're calculating the short side of a triangle with hypotenuse
equal to the diameter, which isn't normally how you do it; you perform
calculations from the center of a circle, not the opposite point of the
circumference. So for your calculation you'd use 12.65 instead of 25.6,
and come out with around half your value in degrees (don't have a sci
calc handy), which would correspond to my calculation. That's for one
wheel, multiply it by two for both wheels. Multiply it by two again if
your using a definition of "leading edge track minus trailing edge
track", because you're measuring both the variance in front and the
variance in back (which will be equal if your rims are true!).
> The reason I don't understand your equation is because
>
> [(diameter) * (pi)] = circumference
>
> and I don't understand what the tire circumference has to do with
> calculating a toe measurement. It looks to me that this equation is
> calculating the partial angular measurement of a treadface
> circumference.
>
> [partial angle / 360] * circumference = partial circumference
> measurement for a given angle.
Sure - it's the same thing. Stand a tire on edge and look down on it
from above. This particular one is 25.6 inches in diameter. If you
spin it all the way around you've compassed 360 degrees of toe. You've
also covered pi*D distance as you described the circumference of a
circle. So pi * D = 360 degrees. Divide and multiply as you need to
get whichever units you need.
As someone pointed out much earlier, toe really should be measured in
degrees, like camber. You're measuring to what degree (literally) the
wheel is altered from pointing straight ahead. When you do it that way
this method is intuitively correct. Measuring in inches makes all
methods seem a bit wacky.
KeS
PS - thinking about it, your triangle base is wrong in any case. You
can't perform trig (well, directly) from one side of a circle to the
other; you won't have the requisite right triangle on which the trig
values are based. You would have to perform your trig function on the
radius, and then multiply the result by two, which will produce a very
slightly different result. Probably not noticeable in this situation,
but still...)
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