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Date: Thu, 3 Jul 2008 07:58:27 -0700 (PDT)From: "Duncan Granger" <dmgranger@yahoo.com>

To: Classic Rendezvous <classicrendezvous@bikelist.org>

Subject: [CR]rotating versus non-rotating mass on bicycles

okay, let me start by saying that I find adding lighter (but still period c
orrect) wheels to my on-topic bikes really does improve their performance.

and it's not just less weight: yes, a lighter wheel accelerates faster,

and when you think about it, since your velocity is rarely completely cons
tant, you are decellerating and accellerating all the time... but I also

think lighter wheels take less effort to maintain momentum once they're up

to speed (even if it is constant). but i'm not a scientist, and in fact

i suck at math, so my opinion ain't worth much on this issue..
however,
found an interesting entry in wikipedia (yes, i know, many of those entries

are rife with errors) that seems to make pretty good sense...
Kinetic en
ergy
Consider the kinetic energy and "rotating mass" of a bicycle in orde
r to examine the energy impacts of rotating versus non-rotating mass.
The

translational kinetic energy of an object in motion is:[7]
,
Where E
is energy in joules, m is mass in kg, and v is velocity in meters per secon
d. For a rotating mass (such as a wheel), the rotational kinetic energy is
given by
,
where I is the moment of inertia, \u03c9 is the angular veloci
ty in radians per second, r is the radius in meters. For a wheel with all i
ts mass at the radius (a fair approximation for a bicycle wheel), the momen
t of inertia is
I = mr2.
The angular velocity is related to the tran
slational velocity and the radius of the tire. As long as there is no slipp
ing,
.
When a rotating mass is moving down the road, its total kinetic

energy is the sum of its translational kinetic energy and its rotational k
inetic energy:
Substituting for I and \u03c9, we get
The r2 terms cancel
, and we finally get
.
In other words, a mass on the tire has twice th
e kinetic energy of a non-rotating mass on the bike. There is a kernel of t
ruth in the old saying that "A pound off the wheels = 2 pounds off the fr
ame."[8]
This all depends, of course, on how well a thin hoop approximate
s the bicycle wheel. In reality, all the mass cannot be at the radius. For
comparison, the opposite extreme might be a disk wheel where the mass is di
stributed evenly throughout the interior. In this case and so the resultin
g total kinetic energy becomes . A pound off the disk wheels = only 1.5 p
ounds off the frame. Most real bicycle wheels will be somewhere between the
se two extremes.
One other interesting point from this equation is that f
or a bicycle wheel that is not slipping, the kinetic energy is independent
of wheel radius. In other words, the advantage of 650C or other smaller whe
els is due to their lower weight (less material in a smaller circumference)

rather than their smaller diameter, as is often stated. The KE for other r
otating masses on the bike is tiny compared to that of the wheels. For exam
ple, pedals turn at about the speed of wheels, so their KE is about (per
unit weight) that of a spinning wheel.
so i personally will continue to s
eek out lighter wheels for both my on-topic and off-topic rides...
Duncan

Granger
avoiding work in
Austin, TX