Bicycle Wheel

Bicycle wheel

Read here about the wire spoked bicycle wheel, considered as a tensegrity structure.

Not included here are various bicycles constructed as tensegrity stuctures; instead, see Bicycle.

The Wire-spoked Wheel Conforms To Tensegrity Structural Principles

The discussion below is based on a presentation by Levin.

The hub of a wire wheel is suspended in a tension network. The axle load is hung from the top of the rim that tries to belly out. Additional tension spokes are added horizontally to resist the bulge. For circumferential stability, the additional spokes are added.

Bicycle engineer and mechanic comment, added 4/2019: If you take a normal well-tensioned bicycle wheel (where no spokes go slack under load) and load the wheel by adding weight to the handlebars(1) of the bike, you will find that the only spokes that change tension are the bottom ones. This can be determined by experiment easily, since the tension is directly related to the note produced by plucking the spokes. When the wheel is loaded, only the bottom few spokes lower in pitch. (1) Use a front wheel because it is symmetric left-right, unlike dished rear wheels that have unequal tension for the left and right spokes.

I believe the first time this was described in writing is in the excellent book, "The Bicycle Wheel" by Jobst Brandt. This book includes both practical tips on wheel building and engineering analysis with computer modeling of the stresses and strains (deflection) in bicycle wheels. The above result occurs because normal bicycle rims (the hoop, without spokes) are relatively flexible compared to the loads they carry when built into a tensioned wheel. Brandt presents a thought experiment that may help to visualize this--imagine that you are holding a wheel (of any construction) by the axle and press the tire against a vertical wall--wouldn't you expect the part to be in contact with the wall to be the part that deflects? (End of bicycle engineer comment).

In a bicycle wheel, at any given moment the hub is suspended, hanging from the topmost spoke. Imagine if there was one wire spoke only. Its downward force would cause the thin, weak rim to buckle. What keeps the rim from buckling in a standard wheel? The other wire spokes constantly pulling in on the rim circumference--they keep it round.

All the spokes are under constant and equal tension. The tensions are preset and do not vary with the load (Bicycle engineer again--this is trivial to disprove, just load & unload a well tensioned wheel and pluck spokes as described above--the bottom spokes will give a lower pitch under load). It is an integrated structure with each spoke depending on every other to share the load at all times. The compression of the ground to the rim is distributed through the tension spokes to the hub. Therefore, there is no direct compression link between the load on the bicycle frame and the ground reaction force. The bicycle is suspended off the ground in a tension spoke network, hanging like a hammock, and the same system works equally well in a unicycle as a bicycle or tricycle. In a cycle wheel, the hub and rim are compression elements kept apart by tension spokes. There are no bending moments in the tension spokes, which are pre stressed, under constant tension. The cycle wheel exists only as an integrated structure. One spoke will not hold up under the weight of the load.

Once constructed this way the tension elements remain in tension and compression elements remain under compression no matter the direction of force or point of application of the load. It makes no difference where you compress the rim of the cycle wheel; the load is equally distributed through the spokes to the hub. The rim of the bicycle is a geodesic, connecting the many points of the spoke attachments, the more spokes the rounder it gets.

The Bicycle Wheel As A Tensegrity Icosahedron Within A Torus

Levin conceptualizes the bicycle wheel's outer rim as a tensegrity torus, and the hub as a tensegrity icosahedron. Tom Flemons rendered these thoughts in a model hosted at Levin's gallery [1]]

Image width="340" height="375" caption="Tensegrity model of Bicycle Wheel, icosahedron in a torus, by Flemons, based on Levin's concept."

Contrasting the wire-spoked bicycle wheel and the solid wagon wheel

Wagon wheels vault from spoke to spoke. A wagon wheel transmits the wagonload to the ground through the axial compressing the spoke between it and the ground. Compression in a column creates shear stress. Therefore, the column must be thick, stiff and strong.

The spoke has to be strong enough to withstand the full weight of the wagon; it gets no help from the other spokes, which, at that moment, sustain no load. Besides the compressive loads, internal shear is created within the spoke. When loaded each spoke acts as a column with compression and shear.

The intervening rim acts as the pedestal of the columnar spoke and has to be equal to the task of being crushed by the full weight of the wagonload. As the wheel rotates it vaults from spoke to spoke. Halfway through the transfer of compressive load from one spoke to the next the rigid rim acts as a lever, creates bending moments, and has to be strong enough to withstand the additional loads. At any one instant in time, the structures are locally loaded and the remaining elements can be stripped away without seriously compromising the structural integrity. (The wheel just could not roll on.)

The Human Pelvis Considered As a Bicycle Wheel

Carsten Pflüger wrote, "Levin imagines/envisages the pelvis as a bicycle wheel. This wheel is also a tensegrity structure described by Buckminster Fuller. If the difference of the wheel of a vehicle and the wheel of a bicycle is observed, according to Levin the difference between Newton’s mechanics and tensegrity mechanics can be seen clearly. The wheel of a vehicle distributes the load onto compression elements which are directly connected. The wheel of a bicycle however transfers the weight of the frame onto the hub which is suspended in the network of the spokes. These spokes are under continuous tension (they are pre‐stressed), the compression elements are discontinuous and the compression forces are distributed around the rim. The rim is comprised by the tension of the spokes. Levin regards the pelvis as such a construction whereby the pelvic ring forms the rim and the sacrum forms the hub. The surrounding myfascial structures are pre‐stressed spokes. The sacrum is suspended in a myofascial shell as compression element and divides its load in this network. Thereby an omnidirectional stability is achieved whilst simultaneously mobility is allowed. The coccyx and the pelvic floor form the hub in this structure and are important for the stand and stability during everyday functions." [5]

Criticism Of Labeling The Wire-spoke Wheel A Tensegrity

Motro deliberately crafted his definition of tensegrity structure in order to exclude tensile structures like the bicycle wheel. His definition is "as a system, in a stable, self-equilibrated state that contains a discontinuous set of components in compression inside a network of components in tension." [2]

Snelson categorizes bicycle wheels and hub-and-spoke radiating domes as "solid rim, exsoskeletal structures" not tenesgrities. [1]

Levin responds: All tensegrities have part of their compression on the outer shell of the construct. They may be the tips of the rods, the nodal points, but they are there. If you put those tips close enough together, it will look solid, but function as a tensegrity. In a BW it is clear that the hub is a compression in a network of tension, a 'floating compression', and it is clear that it is a closed structural system whose compression struts do not touch each other, forming a firm, prestressed, tension and compression unit. It is my belief that the force vectors are triangulated.

Links and References

[1] Snelson letter to Jáuregui, in Gómez Jáuregui's thesis, Appendix D., p.140 [2] Motro R., and Raducanu V. (2001), “Tensegrity Systems and Tensile Structures,” Extended Abstracts International Symposium on Theory, Design and Realization of Shell and Spatial Structures, H. Kunieda, Nagoya, 314-315, quoted in "Adjustable Tensegrity Structures" by Fest, E., Shea, K., Domer, B. and Smith, I.F.C."Adjustable tensegrity structures", J of Structural Engineering, Vol 129, No 4, 2003, pp 515-526. [5]