Choosing Bike Wheels— Coast-Down Tests Provide a Quantitative Measure Stephen J. Derezinski, Ph.D. Wheels are arguably the most important single component of a bicycle. The right wheels even on a mediocre frame (however, one that does fit) will make the most dramatic difference in performance. Every serious biker, whether racer or recreational, should first pursue the best wheels when deciding to modify his bike to improve performance. So, what is the best bike wheel? This, of course, will depend upon the type of riding or competition for which it is used; 1) road race, 2) critirium, 3) time trial, and 4) short or long touring or serious recreational use. Wheels have several physical characteristics that suit them to these specific uses. Here, the physical characteristics are defined as they relate to usage, and measurements are used to evaluate, compare, and recommend the best wheels. The variety in selection is based primarily on the number of spokes, their size and shape, and their lacing pattern. Performance Characteristics The performance of a wheel depends on the energy consumed by the wheel. This will include the aerodynamics of the wheel, its weight, its inertia, and the friction of the bearings. Rolling friction of the tires is important, too, but it is not part of this study. Of the factors considered here, aerodynamics is the over-riding factor for wheel energy, and it becomes increasingly important at higher speeds (speeds above 25 km/hr). High speed will be developed by high bike speed and/or by the addition of head wind. Aerodynamics. The time trialer needs to obtain the most aerodynamic wheel. Weight and inertia are secondary. Paradoxically, some advantage from added inertia could be obtained for a time trial course with wind gusts or slightly rolling terrain. That is, the wheel inertia will store energy in the wheels (acting as flywheels) that will help maintain a constant speed for a short period of time when wind gust or short upgrade is encountered. Maintaining a constant speed is a key factor in posting a good time trial. Weight would become more of a factor for a very hilly time trial course, in which case it would be have second priority. For a very hilly time-trial course, wheel weight would gain equal importance to aerodynamics. However, typical time trial courses are relatively flat, and aerodynamics is paramount. Rotational Inertia. The need for low inertia wheels would be most desirable for sprinters, as in a road race or critirium. Also, air drag in a road race or critirium is less of a factor because drafting in a pack of riders greatly diminishes the contribution of air drag losses. The frequent acceleration and maneuvering typically in a road races and critiriums makes wheel inertia for these applications most important. The fraction of a meter advantage that low inertia wheels would provide in the final sprint often could win the race. Weight. For the recreational rider and for touring, overall weight is the most significant issue (after durability and comfort). Low inertia will accompany low weight wheels, but not necessarily, if the weight is distributed in the tires. This may often be the case for a good recreational wheel because added tire weight means a larger tire (more comfort) and a thicker tire and tube for more reliability. Good aerodynamics would be advisable, too, for bucking head winds, but not a paramount factor, especially for pure recreational use. Bearing Friction. Bearing friction is a small factor, but applies to all applications. It is typically so small that it has minimal impact as compared to the other factors. Rolling friction of the tires is another issue, but it is not part of this study. Therefore, four primary factors are used here to evaluate wheels: 1) air resistance, 2) inertia, 3) weight, and 4) bearing friction. Table 1 suggests the priority that each has for the different applications. It is clear from the table that each application will best be served by a wheel with different characteristics. Table 1 Priority of Wheel Factors Air Inertia Weight Bearing Resistance Friction Recreation and 2 3 1 4 Touring Road Racing 2 1 3 4 Critirium 3 1 2 4 Time Trial (flat) 1 3 2 4 Method A system of evaluating bike wheels has been developed, which evaluates their performance based on the loss in energy during spinning. It requires their measured weight, rotational inertia, and speed lost during coast-down. Coast-down is the decrease in wheel speed when it is spun in a stationary test stand. Weight. The total weight of the wheel is measured with the tire, but without the skewer. Skewer weight is not included because in does not turn, and front wheels are primarily considered. Inertia. The inertia of the wheel depends on its mass and the radial distribution of the mass. Mass near the rim creates the most inertia, and the mass at the very center has minimum inertia. The effect of mass distribution on inertia is disproportionate to its radial location. A gram of mass at the rim will increase the inertia by a factor of 4 over the same gram of mass at ½ of the wheel radius. Therefore, tire weight is critical to inertia of the wheel. For the tests here, the inertia is accurately calculated from the mass of the wheel and its period of rotation. Mass was first obtained by weighing the wheel and tire without the skewer. The period of rotation is obtained by hanging the wheel in a horizontal position with three strings of accurately known length, as shown in Figure 1. The wheel is then made to oscillate freely about its axis (hub), and the period of oscillation in seconds is timed. The mass of the wheel, kg, and the period are then used to accurately calculate the inertia, kg-m2. No knowledge or calculation of the distribution of mass is needed by determining the inertia with this method. String attached to ceiling Wheel Figure 1. Setup to measure the rotational inertia of a bicycle wheel. Three strings are attached to the ceiling and support the wheel. The wheel is slightly turned and released. The period of its oscillation is used to calculate the rotational moment of inertia of the wheel. Coast Down Energy. The bike wheel is mounted in a stationary fork, and it is spun to a speed equivalent to about 50 km/hr bike speed or about 400 rpm. It is then allowed to coast down, and the speed of the wheel is recorded as it slows to stopping. At any moment in time, the speed can be used to accurately calculate the energy in the wheel, because the energy of the wheel is proportional to the product of the speed and inertia of the wheel. Coast Down Power. The rate of change of the energy of the wheel as the wheel slows is numerically calculated from the data of the coast-down test. The rate of change of energy is a result of the power lost by the wheel (Watts) as it slows. The loss in power is then given as a function of wheel speed converted to equivalent bicycle speed, km/hr. The resulting curves of lost power in Wattage versus bicycle speed can then be used to compare different wheels. Figure 2 shows the results for several different wheels. Wheel Bearing Friction. Bearing friction is most easily determined by the energy loss as the wheel approaches stopping by assuming that air resistance is negligible at this point. It can then be made proportional to the speed and subtracted from the total power at the speed to obtain the net air-drag power of the wheel. This was done for the results in Figure 2. Wheels Tested The wheels are described in terms of spokes and rims. The number, length, diameter, and shape of the spokes and the size and type of rim are included. Materials used are also noted. The overall diameter is that of a 700 c wheel, and wheels considered are primarily front wheels. Size and type of hub are not considered. A compilation of the factors is given in Table 2. Power Consumption Air Drag on Spinning Wheels No Forward Motion 6 Zipp, 18 Aero Spokes 5 Spinergy, 8 Blades Rolf, 14 Aero Spokes 4 Radial, 32 Flat Spokes Disc Watts Radial, 16 Flat Spokes 3 Std. 3x 36 Front Wheel Std. 4x 36 w/cassette 2 1 0 0 10 20 30 40 50 Spinning Speed, km/hr Figure 2. The air drag power consumption of eight wheels as a function of bicycle speed. Test done in still air, so results are for comparison purposes only. Rotational speed is given in terms of bicycle speed for the applicable wheel diameter.