That's an ingenious experiment, but it doesn't look as if he ever shows how to compute the rotational inertia of the wheel based on the wheel's design, only how to measure it. The key seems to be the factor mr2, that is, if the weight of the wheel had been concentrated at the wheel's center, the measured rotational inertia would have equaled the mass of the wheel times the square of the radius of the pendulum. The weight of the wheel, however, is distributed in a complex manner over various radii from the axle, which is why it is easier to measure its inertia than to compute it. His formula implies, however, that the rotational inertial of any component of the wheel is equal to its mass times the square of its distance from the axle. This is just a more precise way of saying the same thing that has always been said about wheel design: THE WEIGHT OF THE RIM AND TIRE IS CRUCIAL; THE WEIGHT OF THE HUB IS IRRELEVANT. Gee, basic physics hasn't changed since I was in engineering school, even if my memory of the physics is often faulty. Guess the guys who rode sewups in the old days knew something after all, even if they didn't have physics or engineering degrees.
Regards,
Jerry Moos
-----Original Message----- From: dave bohm [mailto:davebohm@home.com] Sent: Sunday, April 22, 2001 7:31 PM To: John Joseph Taglia; Jerry & Liz Moos Cc: RMAugust@aol.com; classicrendezvous@bikelist.org Subject: Re: [CR]Re: Reducing the "Polar Moment of Inertia"
You may like this website:
http://www.analyticcycling.com/
It has lots of calculators for just this kind of thing and many others.
Dave Bohm Bohemian
----- Original Message ----- From: John Joseph Taglia To: Jerry & Liz Moos Cc: RMAugust@aol.com ; classicrendezvous@bikelist.org Sent: Sunday, April 22, 2001 3:19 PM Subject: Re: [CR]Re: Reducing the "Polar Moment of Inertia"
This is interesting, but fails to take into account the only acceleration that is material: the acceleration of bike and rider. Unitl I see an equation, I will continue to believe that weigh of bike is pretty much immmaterial, and that wheel matters no more than any other.
I guess I don't think it is too much to ask for proof via an equation. (And the skater analoqy is flawed as speed stays constant--larger radiusx slower rpm=smaller radius x higher rpm. So no net change in enery or speed.)
On Sat, 21 Apr 2001, Jerry & Liz Moos wrote:
> Thanks, Randy, guess I won't have to find my Engineering Dynamics book
after
> all. To elaborate, the inertia is a product of the weight (actually
the mass)
> and the distance from the axis of rotation, and inertia determines the
ease with
> which the wheel can accelerate or decelerate (brake). Since the hub is
very
> close to the axis of rotation, its weight is almost irrelevant. Since
the rims
> and tires are at the greatest distance from the axis, a small decrease
in their
> mass leads to a large decrease in inertia, so their weight is
all-important.
> Also, since the weight of the bike and rider acts thru the axle, it
isn't
> important in acceleration either. Total weight does play a small role
in riding
> at a steady pace, as it does affect rolling friction of the tires
somewhat. It
> matters a lot in climbing, since neglecting friction and wind
resistance, the
> energy required to lift the bike and rider to the top of the climb is
the product
> of the total weight and the vertical distance climbed. This is why
track
> sprinters, or road sprinters for that matter, are usually heavily
muscled types,
> since they have more power output, and their weight is no handicap, as
the weight
> of the rims and tires and the power applied mostly determines
acceleration. In
> climbing, however, it is the ratio of power to weight that matters, so a
130 lb
> rider only has to have 2/3 of the power output of a 200 lb rider to make
it to
> the summit first. Never thought polar moment could explain why
Cipollini
> thrashes Pantani in the sprint, but Pantani destroys him on the l'Alpe
d'Huez did
> you?
>
> Regards,
>
> Jerry Moos
>
> RMAugust@aol.com wrote:
>
> > << Why doesn't someone offer some proof that weight matters all that
much to
> > begin with and that rim and tire weight matters more. All I see are
> > unsubstantiated claims. I say until some one can prove different
rotating
> > weight doesn't matter more, and that weight in general doesn't matter
all
> > that much.
> > >>
> > Given two wheels of equal weight, one with a greater proportion of its
weight
> > in its rim and tire will have a greater polar moment of inertia which
> > therefore will accelerate at a slower rate of speed. A good example of
this
> > is an ice skater rotating with arms extended (high polar moment) and
then
> > moving the arms in very close to the body (lower polar moment). The
result is
> > that the speed of rotation increases dramatically.
> >
> > Wind resistance plays a small role in this but mainly it's the
reduction of
> > the polar moment. In the case of wheels, reducing the polar moment
makes a
> > bike feel more fleet and in competition can give one an actual speed
> > advantage off the line. That's the proof of why reducing rim and tire
weight
> > matters more than reducing weight in general.
> >
> > As to reducing weight in general, I think it's generally known that,
given no
> > other variables, a lighter bike will be more efficient to move owing
to fact
> > that less calories are required to fuel it.
> >
> > Randy
> > Corral De Tierra, Ca.
> >
> > _______________________________________________
> > Classicrendezvous mailing list
> > Classicrendezvous@bikelist.org
> > http://www.bikelist.org/
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