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August 18, 2013
No surprise, everything is elastic. Some are profoundly like natural rubber, others microscopically like rock salt. These elasticities define the world around us. Even if unnoticeable, they create limits and rhythms that affect our every moment. The fun of bicycles seems always to return us to the basics because our machine is so lean. A great place to observe and marvel at properties like elasticity.
Remember, every force change (tension, weight) causes a change in length. If the length returns when the force is removed, the change is called elastic. If the change is permanent, then the material's modulus has been exceeded and we have a plastic deformation.
For a wheel, the interesting topic is everyday performance, not plastic deformation like accidents. And when it comes to elasticity the wheel is a busy place. How do bicycle wheels manage all of this without exotic solutions? Some folks don't quite get it.
Conventional wheel spokes are tensioned, which causes them to stretch and the rim to shrink. 100 kgf of tension and a high end stainless spoke elongates over a millimeter. A rim with several dozen spokes at such tension will contract in length several tenths of a millimeter. A clincher tire inflated to 7 bar exerts an additional shrinking pressure on the rim of over 2,200 kg. Thermal expansion of a rim creates opposite, expansive force.
An average rider's body weight unloads bottom spokes as much as 15%, so they temporarily shorten. Pedal torque causes many rear wheel spokes to tighten and stretch and others to loosen and shrink. Lateral forces on the wheel work on the triangular cross section of hub, spokes and rim. One spoke tightens, the opposite loosens and length change make the rim move side to side.
As small as these actual movements, their key is found in stacking. It's never just one element that gives a system its behavior. The more parts involved, the more you often see substantial change as a result of combinations of tiny effects. Together they matter. Riders all testify they can feel the difference between stiff and flexible wheels. This ought not to be possible because the dimensional changes are so small. But combinations are not always the same and they affect your ride.
Gauge affects elasticity and cross section varies faster than diameter. A 15g spoke is only 10% thinner than 14g (1.8mm vs. 2.0mm ∅) but has 20% less cross section. Therefore, it's 20% more elastic. A superlight butted or bladed spoke can have twice the elasticity of straight 14g. Spoke springiness is not a large factor but you cannot ignore differences of that magnitude.
Fairly big events for wheels do not produce large tension changes so, in a very general way, tension does not greatly affect wheel elasticity unless it is extremely low. In fact, loads upon a wire wheel produce tension that strengthens the structure even if absent before.
Shape affects rims more than mass but both determine how the rim will elastically deform during riding. Very deep rims, like the "aero" sort, are less elastic in the radial direction. Wide rims, like MTB downhill, are less elastic in the lateral direction.
Regardless of shape, rims deform tiny amounts at the bottom. In this flattened zone, spoke tension goes down. There are actually much smaller and shorter bulging zones next to the load zone. These are 25 times smaller but make very brief, very small increases in spoke tension. These deformations are part of wheel function, tension variation, and occur continuously as you roll down the road or trail.
They don't vary enough in size to appreciably affect the wheel's behavior. However, the side-to-side flange positions greatly affect lateral movement.
No Free Lunch
Elasticity has both benefit and cost. Radial elasticity gives comfort but too much may increase rolling resistance. It will also have a mechanical price as no spring is perfect. Deformation causes molecular friction, heat, and energy loss.
Side flexibility will improve traction, especially on washboard corners, but detracts from precise control and might interfere with a full out sprint.
All of this should sound like suspension talk. Yup, the wheel is springy, the issues of a suspension. On a very stiff road bike, you can actually feel the springiness, tiny as it is.
Lastly, never overlook a structural element's effect on its neighbors. The wagging of forks (usually treated as an imperfection), tiny deflections of the wheels, the pneumatic inputs, even the bobbing of the stem, these combine and greatly affect the frame. No doubt a fork without flex and a completely inelastic wheel would cause premature fatigue, possibly failure, of a frame that did not anticipate them.
The best bicycles, besides their optimal design and ergonomic match to each rider and terrains, are subtly integrated minimalist structures. Each component characteristic, whether or not a benefit to its direct mission, is an asset or detriment to its neighbor. Bike design has evolved over 150 years to optimize these relationships to a degree few (if any) other devices enjoy.
When you design or appreciate wheels, keep in mind their role as suspension elements. Your choice of components directly affects the outcome.
Why else do we recently see such popularity of lower pressures, larger tires, and shallower (more flexible) rims in road racing? Could it be that contemporary carbon frames are so light and rigid they tend to skitter about and corner less well? Many have noticed how fast they are (sprinting, aerodynamics) but also inelastic. Wheels and tires are filling the gap.
My, aren't we resourceful?
Next up, part 6 - the wheel's central role in the partly understood but deeply studied zone of stability. Wheels help bicycles self-steer. Hear the latest on this timeless conundrum. Two wheel (single track) stability is key to our bipedal nature and the magic of cycling.
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