Date:         Tue, 20 Oct 1998 20:47:05 -0700
Reply-To:     Vanman <mckayaa@OIT.EDU>
Sender:       Vanagon Mailing List <vanagon@vanagon.com>
From:         Vanman <mckayaa@OIT.EDU>
Subject:      Re: Yokohama tires: math lesson
Comments: To: vanagon@VANAGON.COM
Content-Type: text/plain; charset="iso-8859-1"

-----Original Message-----
From: Budd Premack <bpremack@WAVETECH.NET>
To: vanagon@VANAGON.COM <vanagon@VANAGON.COM>
Date: Tuesday, October 20, 1998 8:01 PM
Subject: Re: Yokohama tires


>According to my tire diameter table (attached), the 205/70R14 tires have a
>diameter of 652 mm, while the 195/60R14 tires have a diameter of 590 mm.
>This means the 205s are about 10% larger in diameter, thus 5% larger in
>radius, thus 15% larger in circumference (C=3.14xR).
>
>If my math is correct, this would mean Jim's Passat would have a 15% error
>in the odometer and speedometer if his new 205s were to replace his old
>195s.  This would mean an indicated speedometer reading on the Passat of 60
>mph would actually be 69 mph once the 205s were installed.
>
>Budd Premack
>86 Syncro, 73 Super
>Minneapolis, MN (Land of Sky-Blue Waters)
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I would have to disagree with your math.  The diameter of the 205's is about
10% larger than the 195's (110% the size, in calculations, I will use 1.1),
however, the formula for finding your circumference is 3.14 x Diameter.
Also, your math that found that the radius is 5% larger is also wrong.

R=RADIUS, D=DIAMETER, C=CIRCUMFERENCE

R+R=D -> 1.1(R+R)=1.1D -> 1.1R+1.1R=1.1D

This shows that the radius must also increase by a factor of 1.1 (10%
increase).  In the same way, the circumference must also increase by a
factor of 1.1.

C=3.14 X D -> 1.1C=1.1 X 3.14 X D -> 1.1C=3.14 X (1.1D)

The last term shows that with a 10% increase in diameter, you get a 10%
increase in circumference.  It is this way with all linear functions, where
if you change the variable on one side by a factor, then your final product
also changes by that factor.  For example, if you buy 1 apple, it costs you
$.10, if you buy 2 x 1 apple, it costs you 2 x $.10, or $.20.  Therefore if
you buy Y x apples, you will pay Y x $.10.  Where this changes is if you are
calculating surface areas.  There, if you double your perimeter, you
quadruple your area, and if you increase your perimeter by a factor of 3,
your area increases by a factor of 9, and so on.

If there is anyone out there that found any blatant mistakes with my
reasoning, please correct me promptly.  Heck, if anybody knows how to
differentiate and integrate, why not help me add something on to enlighten
the mathmatically impared on vanagon.com.  You know, start with the basics,
and work from there.

lim    f(x+h) - f(x)   =  f'(x)
h->0         h

-Aaron Mckay
                                 mckayaa@oit.edu
                                 college student in mechanical
                                 engineering at Oregon Institute of
Technology
                                 '85 vanagon GL