Date: Tue, 16 Mar 2010 15:22:55 -0700
Reply-To: Al Knoll <anasasi@GMAIL.COM>
Sender: Vanagon Mailing List <vanagon@gerry.vanagon.com>
From: Al Knoll <anasasi@GMAIL.COM>
Subject: Re: Revs per mile , was: 15" VS. 16' WHEELS
In-Reply-To: <4B9FF7E0.4030904@cox.net>
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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
>>
>
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