All tensegrity structures have stored energy; the energy is in the form of stored mechanical energy. Other terms used to describe this energy are “spring energy” or prestress. This little-known feature is essential to the function of tensegrity structures. These articles will give clear examples of that spring energy and why stored energy important to understand the behavior of these structures.

Artillery wheel
The bicycle wheel with spokes, invented around 150 years ago, is a tensegrity structure. Buckminster Fuller noted the “evolution” from thick wooden spokes to thin metal spokes; Amy Edmondson comments on that in A Fuller Explanation:

The wheel’s use of tension enables a far more efficient and lightweight structure than could be produced with compression spokes. Tension materials are inherently smaller and lighter than compression materials carrying equivalent loads.The wheel was originally an exclusively compression structure starting with the cave man’s stone cylinder and progressing to slightly more sophisticated designs like “the old artillery wheel” cited by Fuller in Synergetics.

Engineer and master wheel-builder Jobst Brandt writes about building strong, robust wheels in The Bicycle Wheel (3rd edition, p. 35):

A rigid rim combined with many thin spokes will give the longest load-affected zone and the best stress distribution. By lengthening the load-affected zone, a strong rim distributes loads over more spokes than a weaker rim can. Since thin spokes are more elastic than thick ones, they absorb larger rim deflections without becoming slack. The more spokes carrying the load, the stronger and more durable the wheel can be. Wheels used by professionals in classic road races have a good balance between strength and weight. […] If its spokes are tensioned to 1000 N [about 225 pounds], a 36-spoke wheel will support approximately 400 kg. This is considerably greater than the average rider’s weight. However, loads of 400 kg or more sometimes occur when a wheel strikes a bump in the road at high speed.

Brandt doesn’t speculate what sort of loads a wheel where all the spokes were threaded but untensioned could support. I’m guessing such a wheel would have about 10% of the strength of a properly tensioned wheel. Even if a very light rider could mount a bicycle using wheels with untensioned spokes, the bicycle would be unrideable and the wheels would rapidly be destroyed. The stored mechanical energy — about 1000 N worth per spoke — is essential for a strong and resilient bicycle wheel. Brandt provides a graphical way to think about this spring energy (p. 95):

Warning. Tensioning spokes can be dangerous. A spoke can rupture under tension and shoot from the rim, like an arrow from a crossbow, into your eye. Never face directly into the line of the spokes while tensioning a wheel. Installing a rim tape [before tensioning the spokes] will prevent this from occurring.

To create a strong and long-lasting wheel, the spokes must be brought up to tension in a systemic fashion. The forces must ultimately be balanced, and they must be balanced at all steps in the tensioning process. The final part of the tensioning process is called truing the wheel: repeated measurement of the wheel’s shape and alignment alternating with very small adjustments to the tension of particular spokes. The Wikipedia article on the bicycle wheel describes the truing process this way:

In wheel truing, all these factors must be incrementally brought into balance against each other. A commonly recommended practice is to find the worst spot on the wheel, and bring it slightly more into true before moving on to the next worst spot on the wheel.

The Wikipedia article also has some general commentary on the material properties of spokes and how plucking can be used to approximate tension:

In addition to the three geometrical aspects of truing, the overall tension of the spokes is significant to the wheel’s fatigue durability, stiffness, and ability to absorb shock. Too little tension leads to a rim that is easily deformed by impact with rough terrain. Too much tension leads to overstressed spokes which have a short life. Spoke tensiometers are tools which measure the tension in a spoke. Another common method for making rough estimates of spoke tension involves plucking the spokes and listening to the musical tone of the vibrating spoke. The optimum tension depends on the spoke length and spoke gauge (diameter). Tables are available online which list tensions for each spoke length, either in terms of absolute physical tension, or notes on the musical scale which coincide with the approximate tension to which the spoke should be tuned.

There is a certain range of tension for tensile materials. For a bicycle wheel, too little spoke tension makes the structure soft, squishy, and unable to carry a load. Too much tension makes the structure stiff, inflexible, and prone to component failure. Goldilocks would not be pleased with either! She would prefer something in the middle: robust, resilient, and with the ability to absorb shock with little to no damage. This “just right” range of tension is the high art of wheel-building.

In the next part of this series, we will explore the stored energy in a different kind of tensegrity: the Swiss Ball and hot air balloons.

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