How much does
a wheel's weight, rotating inertia, and drag affect performance?
Topics on this page:
Magnitudes of the Forces
and Measurements
Wheel
Aerodynamics
Table of Coefficients
of Wheel Drag
Wheel
Rotational Inertia
Table
of Wheel Inertia and Mass
Equations
of Motion
Forces
on Rider
Wheels are a small portion of the forces on
a bike and rider. The differences between wheels are small. Ordinarily
power can be measured to what is normally a small tolerance,
say plus or minus 3%, maybe plus or minus 1% under ideal conditions.
As the table below shows, a typical difference between wheels
may be 1% or less. Clearly, another approach, other than direct
power measurement, is needed.
The table below gives typical values for the
forces on two riders. The Standard Rider is on 32 hole standard
wheels and the Test Rider is on Specialized trispokes. Forces
are in grams of force since such forces are often quoted that
way.

Standard Rider 
Test Rider 

Force (gmf) 
% 
Force (gmf) 
% 
Speed (m/s) 
10.76 

10.76 

Total Force on Rider 
2337 
100 
2287 
100 
Wind Resistance 
1811 
77.5 
1811 
79.2 
Rolling Resistance 
304 
13.0 
304 
13.3 
Gravity Force 
0 
0 
0 
0 
Drag on Front Wheel 
127 
5.4 
98 
4.3 
Drag on Rear Wheel 
95 
4.1 
74 
3.2 
Wheel
Aerodynamics
A paper by D. I. Greenwell, et. al., entitled
"Aerodynamic Characteristics of LowDrag Bicycle Wheels", Aeronautical J., Vol. 99, No. 983, Mar. 1995, pp.109120,
has a good discussion of the aerodynamics of bicycle wheels.
Conclusions by Greenwell et al:
 The total drag of the wheels is in the range
of 10% to 15% of the total drag on a bike. Drag improvements
between wheels can reduce this by 25%, or 2% to 3% of the total
drag.
 Axial drag forces are difficult to measure
precisely. Most single valued measurements should be suspect.
 Deep section aero wheels are better than
a conventional 36 spoke wheel and are all about the same within
the limits of measurement. Disk wheels are better yet. (Don't
run a disk in front if there is any chance of wind.)
 The rotational drag on a wheel does not change
as speed changes or with different wheels.
 The drag on the rear wheel is reduced by
25% due to the seat tube.
 The forgoing applies to zero yaw angle. Read
the paper if you want to know the results for nonzero yaw angles.
Coefficients of Drag Reported for Various Wheels (1)
Wheel 
Cxo 
Conventional 36spoke 
0.0491 
Campagnolo Shamal 16spoke 
0.0377 
HED CX 24spoke 
0.0379 
Specialized trispoke 
0.0379 
FIR trispoke 
0.0382 
HED disk (lenticular) 
0.0361 
ZIPP 950 disk (flat sided) 
0.0364 
Please note that for the coefficients given
in the above table, the conventional wheel is significantly different
from the deepsection wheels, and deepsection wheels are significantly
different from the disk wheels. However, there is no significant
difference between the deepsection wheels or between the disk
wheels.
Wheel
Rotational Inertia
It's easy to calculate a wheel's rotational
inertia using a kitchen scale, a stopwatch, and a tape measure.
The general approach is to measure the time
period for a wheel swinging at the end of a pendulum. See Figure
1. From the time period of a swing, one can calculate the rotational
inertia of the wheel about the point of rotation of the pendulum.
The rotational inertia about the point of rotation of the pendulum
can be transformed into the rotational inertia about the center
of gravity of the wheel.
Most of the error of the method comes from
measuring the period. Timing 100 swings and dividing by 100 gives
a good estimate. This minimizes the error of starting and stopping
the stopwatch by hand. A pendulum has the property that its period
is constant as it slows down.
Take care that the wheel swings in the same plane at all times.
The method will be invalid if it does not. Go to Calculation
of Inertia to calculate rotational inertial for your own
wheels.
Data on some wheels is shown in the following
table. Wheels were complete, meaning they had tires, tubes, rim
strips, rims, spokes, hub, skewers, free wheels, just like they
would be ridden. As individual components, rims lend themselves
to calculation of rotational inertias; tires and tubes don't.
There is a large variation between advertised weights and actual
weights as manufactured. More realworld, meaningful results
come, in my opinion, from measuring wheels in an "as ridden"
state. Hence the values here are for fully rideable wheels, just
like the ones handed to you from your support vehicle.
Rotational Inertia and Mass for
Various Wheels
Wheel 
Details 
Ic
(kg m^2) 
Mass
(gm) 
Wire Spoke 
Rear, Std Rim, 700, track, 36 spokes, w/o tire,
w/ axle, nuts 
0.0528 
1177 
Wire Spoke 
Front, Std Rim, 700, 32 spokes, w/ tire, tube,
rim strip, axle, skewer 
0.0885 
1264 
Wire Spoke 
Rear, Std Rim, 700, 32 spokes, w/1221 cassette,
tire, tube, rim strip, axle, skewer 
0.0967 
1804 
Specialized
trispoke 
Front, 700, w/ tire, tube, axle, skewer 
0.0904 
1346 
Specialized
trispoke 
Rear, 700, w/ 1221 cassette, tire, tube, axle,
skewer 
0.1032 
1771 
Specialized
trispoke 
Front, 650, w/ tire, tube, axle, skewer 
0.0683 
1207 
Mavic 
Front, Std Rim, 650, 28 Bladed Spokes, w/ tire,
tube, rim strip, axle, skewer 
0.0632 
1179 
MTB 
Front, 32 Spokes, w/ tire, tube, rim strip, axle,
skewer 
0.1504 
1847 

Equations of Motion
Wheel weight and wheel rotational inertia
matter when a rider and bike are accelerating. Drag matters whenever
a rider and bike are moving. It is not enough to estimate rider
and bike performance under constant conditions. Differential
equations are used to describe motion under transient conditions.
Such equations let us evaluate the combined effect of wheel weight,
rotational inertia, and drag.
The following differential equation, with
an appropriate starting point and initial speed, describes the
position, speed, and acceleration of a rider over time. Using
this equation, a comparison can be made between a "Standard
Rider" and a "Test Rider" to see the effect of
various alternatives. This is the equations that is evaluated
in each of the case studies presented here.
