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Date:         Thu, 23 Sep 2004 22:20:38 -0400
Reply-To:     Dennis <guskersthecat@YAHOO.COM>
Sender:       Vanagon Mailing List <vanagon@gerry.vanagon.com>
From:         Dennis <guskersthecat@YAHOO.COM>
Subject:      Re: Tire Question / low profile tires

After replying to a few pmails on the subject I figured I'd yank my old physics text and try the issue of rotational moment of inertia on for size. So here goes:

"The moment of inertia of a system about some rotational point is the measure of an object's resistance to a change in the object's angular acceleration due to the action of a torque."

There are multiple formulas to calculate this and they vary depending on the type, and symetry of a rotating mass. The distribution of mass in a rotating object determines what formula you use. A hub/brake/rim/tire combination obviously has mass distributed all over the place and would be thus difficult for a mere mortal as myself to model. So to simplify I just chose to look at a hoop of material with a given width and mass. Think of a big cheerio. You can use I = 1/2M(R1^2 + R2^2) where M is mass in kg's, R1 is the distance to the inside of the hoop, and R2 is the distance to the outside.

Given a hoop with 7 inch radius and 13.5 inch outside radius, with mass of 20kg (about 44 pounds) one gets a value of 1.46. Thats approximating a 14 inch rim with stock rolling diameter (27 inches.

Now with a hoop of 8.5 inch radius with the same 13.5 inch outside radius and 20KG (about 44 lbs) one gets a value of 1.61. That's approximating a 17 inch rim with stock rolling diameter (27 inches).

Torque = (Moment of Inertia)x(Angular Acceleration)

Angular acceleration is the same in both scenarios, as we are concerned with spinning the same 27 inch diameter wheel system in both cases. So we can ignore it and compare the two torque values required based on the moments of inertia.

Assuming both hoops have the same mass, you would need about 10% more torque to achieve the same angular velocity change on the 17 inch hoop.

Ahh, but some of you are thinking that I'm assuming both hoops have the same mass. Keep in mind that a 17 inch rim has more metal in it than a 14 inch rim, but less rubber assuming stock rolling diameter. I've also ignored the moment of inertia of the two wheel faces which can be calculated using the formula for a symetrical disk (I=1/2MR^2). The 17 inch rim has a larger wheel face, thus a higher momemt of inertia. If you upgraded to larger brakes, another moment of inertia increase.

For the record, I really like the looks of a 17 inch rim on a vanagon. I would be personally inclined to upgrade based on the handling and aesthetic difference ... with the acceptance that my van would probably be a bit slower to accelerate.

Brian sent this link..what a transformation! HP be dammed.

http://pg.photos.yahoo.com/ph/nobleman36/album?.dir=464f&.src=ph&store=&prod id=&.done=http%3a//pg.photos.yahoo.com/ph//my_photos


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