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If you’ve gotten this far , you’re either curious, skeptical or both.
The following justifies the benefits of nipples at the hub. It is
presented in a “no frills” technical manner. Enjoy!
The figure below shows the in-plane free body diagram of a rear bicycle wheel subject to a chain force (applied by the rider).
The forces between the bike and the wheel are ignored since they are
not of concern for this analysis. The forces in the vertical direction,
while illustrated, are not considered during further analysis, since it
is assumed that they are always in equilibrium. The horizontal forces
are relevant and are as follows:
1) Fchain = force from chain onto sprocket
2) Fground = force from the ground onto the wheel (friction)
The other parameters are as follows:
1) d = effective radius of sprocket (distance from center of wheel to chain force)
2) rw = effective radius of wheel (distance from center of wheel to ground)
3) m = mass of wheel
4) ω,α = anglular velocity, angular acceleration respectively
5) x,v,a = displacement, velocity, acceleration respectively
Summing forces in the x direction yields:
Summing moments about the center of the wheel yields:
Assuming that the rear wheel rolls without slip, the flowing kinematic relationship holds:
These three equations in three unknowns can be reduced to the single equation that relates chain force to acceleration:
The term meq is the effective mass, since it
is the term that relates the force supplied by the rider (through the
chain) to the acceleration of the rear wheel.
To simplify the effective mass expression, it can be assumed that d is small compared to rw . Exercising this assumption changes the prior equation to:
This expression, though a slight approximation for the rear wheel, is exact for the front wheel where d does indeed equal zero.
The importance of I is clear. Just like mass, for a given force, acceleration will be greater for lower I.
Moment of inertia is defined as,
where rm is the distance from the rotational axis to the differential mass element dm
. As indicated, this can be approximated by a finite sum of masses
times the square of the distance each mass is from the rotational axis.
In either case it is clear that that the total moment of inertia is
simply the sum of the moments of inertia of each component, because of
the distributive property of the integral. Thus, the contribution to
the total moment of inertia of each component can be analyzed.
To estimate the contribution of the spoke nipples to the total moment of inertia, the finite sum approximation is used.
Traditional wheel:
Spoke nipple mass (standard brass spoke nipple): 0.9 grams
Distance of spoke nipple from axis of rotation: 294 mm
Thus for a 28 hole wheel:
Cane Creek wheel:
Spoke nipple mass (Cane Creek alloy nipples with Nylock): 0.27 grams
Distance of Cane Creek spoke nipple from axis of rotation: 22 mm
Effect of Decreased Moment of Inertia
Clearly, moving the nipples to the hub drastically reduces their moment
of inertia. Test data has shown that high performance wheels have
moments of inertia that range from around 34 g • m2 to about 57 g • m2 . Thus, the spoke nipples can contribute from 4% to 6% the total moment of inertia.
The effect of this on angular acceleration is readily acknowledged from the relationship,
For a given torque, the Cane Creek design will accelerate 4%-6% faster,
assuming all other things are equal. Alternatively, it requires 4%-6%
less torque to achieve the same angular acceleration with a Cane Creek
wheel than with a traditional wheel.
Some effects beyond angular acceleration might not be so obvious. Consider the energy in a spinning wheel,
Now consider two wheels with identical rims, hubs, and spokes. On one
wheel, the patented Cane Creek nipple at the hub design is used. The
other wheel is built the traditional way, with brass nipples at the
rim. Simply because the Cane Creek wheel has nipples at the hub, it
will require 4%-6% less energy, depending on the wheel, to achieve the
same angular velocity as the traditional wheel.
Another way to look at it is: If two riders were able to able to put
out the same amount of energy into spinning the wheels, the Cane Creek
wheel would be spinning 2%-3% faster.
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