Weight is not the whole story
Moment of Inertia is white-coat, taped-glasses technical jargon for
“rotating weight”. For cyclists, it is as closely related to
performance as weight, and should be heavily considered when choosing
big components that spin, like wheels.
More specifically, Moment of Inertia (denoted I by
the engineering community) is a measure of resistance to change of
angular velocity. It is a function both of weight (or mass) and how the
weight (or mass) is distributed. It takes more torque to accelerate an
object (like a wheel) with a large moment of inertia than an object
with a smaller moment of inertia. In this sense, moment of inertia is
like mass; it takes more force to make something massive move faster.
However, even if two rotating objects have the same weight, the one
with the smaller moment of inertia takes less torque to accelerate.
That is why Cane Creek wheels accelerate so quickly: they are not just
lightweight, they also have a low moment of inertia because of the
patented nipple at the hub design and lower spoke count.
So clearly, this moment of inertia thing is a big deal. Let’s work out the details. Newton’s
second law of motion states:
That is, the sum of the forces on a body is equal to the mass of
the body times the acceleration of the body. However, this only applies
to rectilinear motion, i.e. to things that are not spinning. A cyclist
might think of this equation as follows:
I can generate a certain amount of force, therefore if my
bike weighs less I have a greater acceleration. Greater acceleration
means I get to the finish line sooner, I get to work faster, and I can
finally outrun that angry dog!
If nothing on your bike was spinning, this would be the end of the
story. Since rolling bicycles are much faster than sliding
bicycles, there is more to this story. Newton’s second law also applies
to rotational motion. For rotating objects it states:
where τ = torque, I = moment of inertia, α = angular acceleration. In words, torque equals
Moment of Inertia times angular acceleration. A cyclist might think of this equation as
follows:
I can generate a certain amount of torque, therefore if my wheels have a lower moment of
inertia, I can make them accelerate faster. More acceleration means I can get to the
finish line sooner, I get to work faster, and I can finally outrun that angry rabid dog!
To tie these two concepts together, we can use the fact that on a bicycle there is a
fundamental relationship between acceleration and angular acceleration. Specifically,
which comes from the fact that bicycle wheels do not slip on the ground as they roll. In the above equation, r
is the radius of the inflated tire. Using this relationship, and a
small assumption about how chain force is transmitted to the hub (see Advanced MOI ), allows us to obtain the following more insightful equation.
With this equation a cyclist is finally in a position to think clearly.
I can generate a certain amount of force. To increase my
acceleration, I need low weight AND low moment of inertia! If my bike
is light and my wheels have low moment of inertia,
I can cross the finish line first, sleep in late since I can get to
work so quickly, and after that angry rabid dog sees how fast I am,
he’ll never chase me again!
As can be seen, moment of inertia is just as important as mass. Indeed the quantity
is often referred to as “equivalent mass”, since it is a true measure
of how force is related to acceleration when the force acts on bodies
that both translate and rotate. Cane Creek has addressed this
fundamental property with our patented wheel design.
By combining the best rims technologies and the best spokes with
our proprietary low moment of inertia nipple at the hub design, Cane
Creek wheels get you there faster.
The story does not end there. The same “equivalent mass” concept that
relates force to acceleration also applies to deceleration.
Consequently, Cane Creek wheels not only accelerate faster, they also
require less force to stop. To the rider this translates into less
force at the brake levers and decreased stopping distances. A cyclist
can interpret this as:
Since my Cane Creek wheels stop faster with less effort, I
can stay at speed longer without worrying about overcooking the corner,
I can have a fighting chance to avoid T-boning that SUV that just
turned in front of me, and I can stop short of smashing that cute
little puppy.
As though better acceleration and deceleration are not enough, the low
moment of inertia design of Cane Creek wheels make turning and
cornering easier. Since the same physics apply to turning and cornering
as apply to accelerating and decelerating, less force is required at
the handlebars to change the direction of the bike.
For more details on this analysis, a complete derivation of the
equations, and some arguments on energy saved due to lower moment of
inertia, please see Advanced MOI .
|
