RZR White Paper
Wheel Performance, By Paul Lew
Director of Technology and Innovation, Reynolds Cycling
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The following article is excerpted from a white paper authored by Paul Lew. The article is presented to provide context and background for the new RZR 46 all-carbon wheel. Reynolds Composites Studio engineers, headed by Paul Lew, introduces the new RZR, an innovative carbon fiber & boron wheel set, representing nothing less than a new paradigm in bicycle wheel design. The result is RZR 46T: at 875 grams per pair, seven patents pending, and a host of design innovations, it’s The World’s Lightest Wheel.
Wheel Performance
Three factors define wheel performance: 1) mass/ inertia, 2) mechanical efficiency, and 3) aerodynamic drag. Unlike the mass of components like the bicycle frame, forks, handlebars, the mass of a wheel contributes to bicycle performance in two ways. Wheel mass contributes directly to the overall mass of the system in the same way that other components contribute. While mass value of most components is static, the dynamic nature of a wheel creates an additional performance aspect known as angular acceleration or inertia.
Inertia
Unlike components such as frames, forks, and handlebars, whose performance is evaluated on a static basis, a wheel is evaluated based on inertia. Low inertia significantly and directly affects the power (watts) required to accelerate the bicycle. The contribution of wheel inertia is significant; it is approximately 3.2 times the effect of the mass of a static component, such as the frame.
The effect of inertia is continuous because a bicycle is constantly accelerating and decelerating. Due to the nature of cycling, a bicycle does not accelerate or decelerate only when a rider consciously decides to increase velocity, or slow velocity. Acceleration and deceleration are continuous through every rotation of the pedal stroke. Therefore, wheel inertia is always a significant factor in bicycle performance. In a comparison test the lowest weight wheel typically results in the lowest inertia. However, it is possible for a wheel of slightly higher overall mass with lower perimeter mass (low rim mass) to produce lower inertia than a wheel that has lower overall mass, lower center mass (hub mass), but higher perimeter mass. Of course, lowest overall mass, and lowest perimeter mass is the best combination of all.
Aerodynamic Testing
The purpose of aerodynamic testing of a bicycle wheel is to determine its drag value, or to determine the amount of drag reduction it contributes
to the bicycle system. A complete bicycle system, which is composed of a cyclist and a bicycle, is a complex combination of structural and mechanical components designed to function in an efficient, reliable manner. Characterization of efficiency can be described as, optimization of the bicycle system to reduce the amount of effort required by the rider to move it forward. Many components of the bicycle system can be
defined scientifically. One such component is the wheel.
Typical aerodynamic wheel testing protocol has been based upon relative comparison of drag data of individual wheels using identical fixtures and tires for every wheel in an attempt to maintain consistency of variables. There are many reasons this type of test protocol will yield results of little to no value.
Testing a wheel in a fixture independent of the bicycle system is similar to expecting to achieve valid structural bicycle frame data independent of a load. No engineer would ever construct a frame and claim that it has been structurally validated without applying a load simulating the dynamic load of a cyclist riding the bicycle. Why then test a wheel independent of factors that interact with it and ultimately define its performance? When was the last time a bicycle wheel raced without a
frame or a rider?
All Reynolds wheels are designed to work as the lowest drag, lowest mass, and lowest inertia wheels for the best real-world performance, not to perform as an individual wheel.
The test data indicates that Reynolds wheels offer the best performance. The best performing wheel does not mean only the lowest aerodynamic drag value, but the wheel inertia must be considered. Because all competition does not occur at 30 MPH, and because climbing and acceleration are factors in bicycle racing, wheel inertia becomes an important factor in wheel performance. The combination of aerodynamic performance and low inertia results in an overall performance value.
Rim Design
The leading edge of the wheel is very important. The leading edge of a bicycle wheel shares some common characteristics with the leading edge of an aircraft wing. Because low drag is the goal, not high lift (the higher the lift, the higher the drag), the widest part of the wheel should not be at the leading edge. Low drag airfoil design typically places the thickest portion of the airfoil at about 33% of the chord line, or approximately 1/3 of the distance from the leading edge to the trailing edge. Most low drag airfoil designs adhere closely to the 33% chord line rule. Tire selection plays an important role in achieving an airfoil shape that closely adheres to the 33% chord line rule so it is possible to choose a tire that is compatible with the rim for optimal low drag performance. The most common mistake is choosing a tire that is too wide for the rim which will move the widest part of the airfoil shape too far toward the leading edge as opposed to 33% of the chord line.
Rim designers have used an “ovoid” shaped rim section combined with a 21 – 23 mm tire to closely adhere to the 33% chord line guideline. See Illustration 2.0. Another method for creating the widest part of the airfoil at the 33% chord line mark is shown in Illustration 2.1. 33% Chord line mark is shown in Illustration 2.1 using the Reynolds Swirld Lip Generator.
Vocabulary
Kinetic Energy: In Joules, is the energy required to change the speed of an object from A to B. Kinetic energy increases with
the square of hte speed.
Intertia: Interia represents the resistance of an object to remain at rest of keep its momentum. The inertia is a bit like kinetic
energy at a given speed.
Inertia Momentum: Identical to the simple inertia but for a spinning motion.
Second Moment of Intertia: It is a property of a shape which is used to predict it's resistance to bending and deflection (such as spoke).
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