& once agin, the Cane Rattler sets us all straight!

Amen,

Mr. BZ-Calculus 101? Barely passed

On Mar 16, 2010, at 4:22 PM, Al Knoll wrote:

> Curiouser and curiouser,  What is the best way to figure out the
> revolutions per mile?  Count the revolutions over a smaller distance
> and extrapolate?  Measure the rollout linearly?  And of course what
> accuracy is necessary for the intended use of the number, this will
> perhaps dictate the method used.  If two significant digits is good
> enough almost any method will work.  If one needs 4 or 5 significant
> digits then the measurement becomes by necessity more complex.  If it
> must be within one RCH, it's going to be a long afternoon.
>
> If 5% is close enough, picking a method that yields a deviation in
> that range of values might just do.  1% of 800 is 8 so for all intents
> and purposes the 804-812 value will give you the necessary 1%
> accuracy.  IFF the stated value is accurate.  You can check by doing a
> rollout test yourself and seeing how close to the -specification your
> result is.  5% accuracy is +-3mph indicated on your speedometer or
> 57-63 at an indicated 60 MPH.  Close enough?  Only you can decide.
>
> A rollout of two rotations measured to the nearest 1/4 inch will give
> +- 1/8 inch of circumference accuracy.  Since pi day was recently
> celebrated, you can use the leftover pi to crank the Diameter out of :
> Circumference (what you measured) = pi*Diameter.  The revolutions per
> mile however is the number of circumferences travelled per mile and
> that is a tricky figure to obtain as the tire is not rigid in radius
> but quite rigid in the steel belts that determine the circumference at
> any angular velocity, and air pressure.  Best to approximate under
> vertical load and factor in the rotational expansion for which we have
> no convenient formula.
>
> The end game is that there is a solution space that can be made fairly
> small in the vector space of angular velocity, belt stiffness,
> inflation pressure and vehicle mass.  This solution space is populated
> by the various experimental results obtained by measurement of one
> particular tire.  The space grows larger as other particular tires of
> the same manufacture and the same size are added and measured.  At the
> end of the day the results should resemble a circular scatter diagram
> like you see on 12ga enhanced road signs.  Your best choice in that
> population is likely near the center of the pattern.
>
> I maintain that that solution space cannot be reduced to a single
> solution but only to an acceptable collection of solutions.   Only you
> can decide how close is close enough, or whether it is important at
> all.
>
> "No matter how elegant the hypothesis, or how eloquent it's
> presentation, if it doesn't agree with the measured data, it's wrong"
> -- Feynman
>
> Pensionerd.  Fan of RCH's in years gone by.
>
>
> On Tue, Mar 16, 2010 at 2:28 PM, mark drillock <mdrillock@cox.net>
> wrote:
>> You can look up any number of manufacturers rev/mile for a given
>> size.
>> You will find they tend to group together in a range and then you
>> will
>> see that the Miata Tire Toy program calculates a value for that size
>> that falls outside of that group. You could say that none of the tire
>> companies can count or measure but I would say the Miata Tire Toy
>> program makes erroneous assumptions and then gives false results.
>>
>> Also, axle center to ground distance is a poor way to measure tires
>> for
>> revs/mile purposes as inflation pressure affects that static
>> measurement
>> to an extent that greatly exceeds its effect on true revs/mile while
>> rotating.
>>
>>
>> Mark
>>
>>
>> John Bange wrote:
>>
>>>
>>> I would love to trust the manufacturer's quoted numbers, but when
>>> the Revs
>>> per Mils and the diameter they state don't match, it's hard to
>>> take them
>>> completely seriously. I suspect they might use the largest possible
>>> diameter, and the smallest possible rolling radius. Given that, I
>>> tend to
>>> use the mathematical number initially, and then actual physical
>>> measurement
>>> after they're on the vehicle (axle center to ground, and GPS
>>> mileage vs
>>> miles clocked that assume 805 RPM).
>>>
>>> --
>>> John Bange
>>>
>>