May 25, 2018
A severe side (lateral) load on a bicycle wheel is bad news. Wheels are strong for radial (vertical) and torsional (twisting) loads but vulnerable for lateral. Fortunately, high lateral forces are uncommon with single track vehicles that lean through turns. Still, they account for most wheel failures and the actual dynamics remain poorly understood by many.
Let’s examine an extreme lateral load and discover how a wheel responds. How can a tensioned structure with balanced, triangulated bracing warp instantly into an unrideable potato chip shape?
Familiar shape with a bit of frost.
A lateral force usually arrives from the tire-ground contact, perhaps from skidding. The load moves the tire to one side which, in turn, pushes the rim to the side. The rim resists the force with both bending and torsional stiffness. The force is felt by spokes in the immediate region.
A spoke on the the force side tends to maintain its tension. A spoke opposite the force loses tension. The rim does not budge until the opposite side spoke reaches zero tension. At zero tension (all within milliseconds) all forces still balance out, and the rim is undeformed.
lateral load sequence
Once the opposite side spoke buckles, the rim begins moving. Would be helpful if the force side spoke, tight from the beginning, could increase its tension to resist the force. However, due to the low relative strength of bicycle rims, the rim begins moving away from the load in an arc whose radius is the force side spoke. The rim section swings at the end of the force side spoke as a yo-yo swings on its string going “around the world.”
Bent!
In practice, the force side spoke cannot increase tension to keep the rim stationary. The rim is too elastic and swings rather than remaining the same distance from the wheel’s theoretical center. In this example, the lateral force is extreme and our wheel now has a pronounced side bend at the site of impact. Neighboring off side spokes are unloaded as the rim moves their way. Their reduction in tension makes for a positive push that creates two bends that are reverse of the side load. Such “wings” also occur next to broken spokes.
Depending on the magnitude of lateral force, the flexibility of the rim and the amount of spoke tension; a sine wave can propagate around the wheel, driven by the reduction of spoke tension in half, or more, of the spokes. All energetic states seek a lower potential. The loss of spoke tension drives the sine wave, bending the rim into a potato chip shape. This has been triggered by the initial extreme lateral force, but the eventual collapse is an implosion of the tensioned structure.
© The Bicycle Wheel, J. Brandt
This potato chip shape, also known as a pretzel or taco, is technically a hyperbolic paraboloid. You can trace the edges of one on the Dumbo ride at Disneyland. When Dumbo swings low, its radial arm acts like a spoke that is maintaining tension. Swinging high is the same, but like an opposite side spoke.
Dumbo rises and falls as the ride rotates.
Hyperbolic paraboloid—Wikipedia
In wheels with extremely springy rims that do not easily take a permanent set, a potato chip wheel can sometimes be fixed by banging sideways on the ground. A reverse extreme lateral force can cause a sine wave that neutralizes the deformation. It’s a chancy strategy but if you witness one, you’ll know it was special. Steel and wood rims are better for this than aluminum or carbon.
If you travel around the rim like a bug (or Dumbo) it will be obvious the rim is deformed left and right but also twisted. It’s a torsional deformation, not simply left-right. Rims with great torsional rigidity resist taco shapes much better. Torsional rigidity increases as the 4th power of the radius of the largest inscribed circle that fits in the rim section.
The rim above (from 15yrs ago) can fit a large circle in its cross section, giving it extraordinary torsional rigidity. It is nearly impossible to twist into a taco shape. It’s not just the little dude inside making this rim strong. Many deep carbon fiber rims have high torsional rigidity. Pushed by an extreme lateral load they either bounce or break. Notice how many of today’s more enlightened rims feature large open space in their profiles? Good design!
A taco wheel often displays four lobes, two in one direction, two in the other; and one is usually larger than the others. Safe to assume the extreme side load was delivered at this spot and the other three lobes formed as a consequence. Trying to true this wheel is wasted time if the rim has taken a permanent set.
Loosening spokes will reveal how extreme the bend is. Once de-tensioned, the true rim shape appears. If you must use the rim again (think: remote location expedition) try and make it as straight as possible without spoke tension. Be very careful to not introduce kinks or dents as you lever the rim to flat. Once the rim is flat, it will support spoke tension again and have no residual tendency to return to a taco. Truing without first bending the rim makes an unbalanced structure prone to deform again.
Before we leave the world of tacos, pretzels, and potato chips, let’s notice one further way a wheel can assume a multi-lobed deformation—excess tension. A rim can only support so much total tension, in proportion to its mass and shape. We used to build a favorite rim to 100kgf per spoke, with 36 spokes. The same rim with 48 spokes could not support 100kgf on each spoke.
An over tensioned wheel can “pop” suddenly into a wavy pattern. It’s the same principal as extreme side loads. Such a deformation will have many (not just 4) lobes, each small deflections. If you lower the tension total, with luck, the rim may behave as if nothing happened. It was just trying to reach a lower energy level. In its wavy state some spokes lost tension, others maintained. The total was lower.
Whether you ever undertake such truing, it is important to understand the forces involved. A wheel can suddenly become a taco shape with an extreme side force. In slow motion, this begins at one spot and a sine wave of deformation travels around the wheel often leaving a 4-lobed taco shape.
When it comes to metal bending and tension, most everything is reversible so, even if impractical, such wheels can be repaired. With these principles in mind, try your hand at it. You may not succeed but the exercise is always informative. Experience at the fringe of possibilities is what makes developing world bike mechanics so resourceful. Hone your own skills, don’t let them have all the fun!
