By Paul Lew, Director of Technology and Innovation
Reynolds Cycling, LLC
UNDERSTANDING WHEEL DYNAMICS: A THREE PART SERIES PART 1: WHEEL STIFFNESS
In the world of wheel dynamics, the qualifications for a "good" wheel always incorporate stiffness and compliance, or more specifically,wheels that are laterally stiff and vertically compliant.
What does this mean? In engineering terms, this means that the wheel has minimal deflection side-to-side and at the same time moderate to large deflection in the down direction.
In this article, I’ll discuss the relationship of these dynamic variations and the contribution of the hub, spokes, and rim as influencers of these wheel characteristics.
The HUB – The hub of the wheel is its central point, or anchor. It determines forty percent of a wheel’s stiffness and compliance. The key components of the hub are the hub shell and flanges. Regardless of whether they’re straight pull or bent the hub flanges play the same role and have the same effect.
A hub shell and flanges can expand as much as 0.5 mm under high spoke tension. With 100 – 130 kg of tension on each spoke, a total force pulling the hub outward can exceed 2000 kg. This force can create structural challenges that can range from expanding the bearing seat to cracking the hub flange. As a result of the high force, bearing tolerances must be carefully considered. The bearing fit in a hub shell before and after spoke tensioning is an important consideration in the hub design and specification process.
A well-designed and manufactured hub will not suffer from the static and dynamic forces of a high-tensioned wheel and it will serve as a strong and reliable anchor point for the high-tensioned spokes. Wide flange spacing contributes to the desirable characteristics of a wheel. A wide flange spacing decreases side-to-side deflection and at the same time increases vertical deflection, both contribute to a well-riding, "good" wheel.
The SPOKES – Spoke stiffness and spoke count are also responsible for forty percent of wheel stiffness; however spoke crossing patterns and spoke tension do not have a significant impact on stiffness. Increasing the spoke count in a front wheel from 16 spokes to 20 spokes will increase the wheel’s resistance to deflect laterally by approximately thirty percent. Increasing the spoke diameter and profile from a 2.0/1.8/ 1.5 mm triple butted spoke to a straight-gauge 2.0 mm spoke will increase the wheel stiffness approximately thirty five percent. The combination is additive, so increasing the spoke count from 16 to 20 spokes and the spoke diameter to a 2.0 mm straight gauge spoke will increase overall wheel stiffness by sixty five percent.
Unlike the hub, which is two-dimensional and can contribute favorably to both lateral and vertical performance, the spokes are one-dimensional. So, a stiff spoke (one that resists bending) decreases side-to-side deflection and at the same time decreases vertical deflection, whereas a flexible spoke (one that is easily bent) decreases side-to-side deflection and increases vertical deflection.
Some cyclists believe that a crossing spoke pattern will increase vertical deflection while minimizing lateral deflection, but this is not true. Crossing spoke patterns typically increase vertical deflection and increase side-to-side deflection.
Additionally, spoke tension is over-estimated as an influence on wheel stiffness, and in fact only plays a minimal role. Stay tuned for more discussion of spoke crossing patterns and spoke tension in Part 2 of this article.
The RIM – the rim determines twenty percent of wheel stiffness. Rim stiffness, in turn, is a function of the rim section geometry and hoop stiffness.
As a wheel designer it is common to think of a rim in terms of "aspect ratio". Hoop stiffness, or the tendency of the hoop to deform from a circle to an oval or egg shape, is influenced by section aspect ratio as well as material selection, but section aspect ratio is the largest influence.
A high aspect ratio rim has a height dimension greater than the width dimension. A low aspect ratio rim has a width dimension greater than the height dimension. A neutral aspect ratio rim has equal height and width.
Typically, a low aspect ratio rim contributes favorably to a desirable ride quality with minimal side-to-side deflection and moderate to high vertical deflection.
While a low aspect ratio section rim may be reasonable for MTB wheel designs, a high aspect ratio rim section is more desirable for road and triathlon wheels due to the requirement to optimize aerodynamics. The high aspect ratio resulting in high hoop stiffness requires fewer spokes, which also contributes to aerodynamic optimization.
While rim stiffness can be independent of material, meaning that an engineer can design an equally stiff rim from any material so long as rim weight is not a design consideration, carbon fiber has the unique quality of low mass, stiffness tune-ability, high strength, and an unlimited fatigue life not possible to achieve with metal alloys which makes it an ideal material of choice for high performance rims and wheels.
Part 3, in March, I will examine the dynamic characteristics of the hub, spokes and rim as a wheel completes a 360 degree rotation under power.
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