Few mechanisms are built at the edge of feasibility. It's expensive to make stuff and we require some measure of reliability. Hence, over-design. However, cycling and aviation seem to push those limits like no one else. For very different reasons, each fights an uphill battle to succeed. Human safety is a big consideration for both. For more on the cycling-aviation relationship, check here.
When you push structures to the limit you deal with materials: their strength, stiffness, endurance, hardness, thermal properties, elasticity, etc. With bicycle wheels, arguably the leanest and most efficient structure in general use, this is particularly true. Lately, I've been reflecting on elasticity.
A bike wheel consists of pneumatic tire, rim, spokes, and hub. The elastic behavior of the tire is easy to grasp. A rubber coated textile is soft in the hand until inflated. With substantial air pressure, a tire becomes firm and capable of supporting the vehicle at speed. If struck with high force, the elastic nature of the tire enables it to deform momentarily, absorbing shock and avoiding damage.
The rest of the wheel - aluminum, carbon fiber, steel - seems rigid and inelastic by comparison. No rubber here. If you closely examine the dynamic performance of a wheel you discover a world of elastic movement that is core to the structure's effectiveness.
Hubs seem to be simple spools that rotate and connect spokes and frames. In fact, they withstand many forces extreme enough to change their shapes. The trusty quick release develops huge compression force, approaching 1,000lbs. The hub axle actually contracts with this force and hub designers need tricks to keep the bearings running free.
Spoke tension on an aluminum hub stretches the body, enlarging the bearing seat. A good fitting bearing can fall out loosely once spokes are tensioned. The bearing seat must be made undersized to compensate for tensioned induced deformation.
Lateral forces at the rim become magnified due to geometry once they reach the hub. Larger diameter axles are sought to help keep the hub from flexing.
No bicycle component is regularly stressed so close to its failure point as spokes. The static load of a spoke can be 1/3 of its breaking strength. This requires spoke wire to be extremely strong and uniform. Tensile strengths and consistency are the highest in all of engineering for these materials.
Under the extreme tensile load of a bike wheel, spokes stretch. A straight gauge steel spoke will elongate more than 1mm during a wheel build. Butted spokes stretch more and it affects comfort, fatigue life, and nipple retention. The elasticity of spokes is part of the calculation of a successful bike wheel.
Rims, especially aluminum, are built to be rigid. Loaded with 20 to 32 tensioned spokes, they become an amazingly firm, almost brittle structure. But to look closely, rims elastically deform in dramatic ways.
When spokes are attached, a huge compressional force is applied to the rim hoop. It can be 600lbs, measured at a rim joint. Due to the small mass and density of the rim, the hoop actually becomes temporarily smaller. Clincher tire pressure pushes rim beads outward. You can use calipers across the brake track to see those surfaces change. With pressure, parallel brake tracks become angled more than one degree.
Inflation pressure spreads the rim at the brake which affects the rim "belly" below. For many rims, the change to the belly is enough to increase spoke length and change tension over 20%. Deflate the tire and brake track springs back and spoke tension rises.
With riding, all these elastic deformations combine to define wheel behavior. It's not just the tire that's in constant elastic motion. A structure as light as a standard bicycle wheel is a complex, dynamic structure. No wonder there are so many opinions and observations about the zillion combinations of components, spoke tension, tire pressure, and riding.
The more I learn about wheels, the more secrets are revealed. I discovered the elastic properties of spokes while studying them at Wheelsmith in the 1980's. Now it's clear that all wheel components have elastic properties that affect their neighbors and wheel performance. This elasticity is substantial and you should bear its contribution in mind whenever designing, building, or riding these magnificent structures.