http://www.analyticcycling.com http://www.analyticcycling.com/AnalyticCyclingLogo.gif http://www.analyticcycling.com/WheelsConcept_Heading.gif 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 tri-spokes. 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 100Wind Resistance 1811 77.5 1811 79.2Rolling Resistance 304 13.0 304 13.3Gravity Force 0 0 0 0Drag on Front Wheel 127 5.4 98 4.3Drag on Rear Wheel 95 4.1 74 3.2 Wheel Aerodynamics A paper by D. I. Greenwell, et. al., entitled "Aerodynamic Characteristics of Low-Drag Bicycle Wheels", Aeronautical J., Vol. 99, No. 983, Mar. 1995, pp.109-120, 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 non-zero yaw angles. http://www.analyticcycling.com/WheelsConcept_WheelFor1Blue.gif Coefficients of Drag Reported for Various Wheels (1) Wheel CxoConventional 36-spoke 0.0491Campagnolo Shamal 16-spoke 0.0377HED CX 24-spoke 0.0379Specialized tri-spoke 0.0379FIR tri-spoke 0.0382HED disk (lenticular) 0.0361ZIPP 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 deep-section wheels, and deep-section wheels are significantly different from the disk wheels. However, there is no significant difference between the deep-section 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. http://www.analyticcycling.com/WheelsConcept_WheelFor2Blue.gif http://www.analyticcycling.com/Figure1.gif 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 real-world, 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 SpokeRear, Std Rim, 700, track, 36 spokes, w/o tire, w/ axle, nuts 0.0528 1177Wire SpokeFront, Std Rim, 700, 32 spokes, w/ tire, tube, rim strip, axle, skewer 0.0885 1264Wire SpokeRear, Std Rim, 700, 32 spokes, w/12-21 cassette, tire, tube, rim strip, axle, skewer 0.0967 1804Specialized tri-spokeFront, 700, w/ tire, tube, axle, skewer 0.0904 1346Specialized tri-spokeRear, 700, w/ 12-21 cassette, tire, tube, axle, skewer 0.1032 1771Specialized tri-spokeFront, 650, w/ tire, tube, axle, skewer 0.0683 1207MavicFront, Std Rim, 650, 28 Bladed Spokes, w/ tire, tube, rim strip, axle, skewer 0.0632 1179MTBFront, 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. http://www.analyticcycling.com/WheelsConcept_DiffEqMotionBlue.gif