The science behind spokes
These thin strands of wire perform a relentlessly tough job, being stretched and compressed repeatedly with every single revolution of our wheels. They also carry the acceleration forces of pedalling from hub to wheel rim and transmit braking forces too. Their role in the very fact of us being able to ride a bicycle at all is almost magical – such thin strands supporting such huge loads. So we felt it was high time that the humble spoke took some credit, where a whole load is due.
The genius of the spoked wheel is that it can transfer the often very large forces created by the rider, bicycle and varying road surfaces into these skinny rods, each being systematically compressed as the wheel turns and the loads transfer from one spoke to another, and so it goes on,’ says Professor Mark Miodownik, director of the Institute of Making at University College London, author of Stuff Matters, TV presenter and keen cyclist. He continues, ‘It’s a beautiful way to optimise the weight, cost and performance of a wheel.’
Spokes, once under tension, in essence brace the rim using the hub as the central anchor. In a perfect-world scenario each spoke pulls with equal tension to distribute the load evenly throughout the wheel while also holding the rim true and circular. The spokes must support the wheel against lateral flex and deformation of the rim and also resist the wheel effectively being squashed by vertical loading (radial compression). No small task. It’s little wonder that since the advent of the wheel, very few other solutions have been explored.
Now things start to get technical, and you won’t be alone if what follows is a little confusing and counterintuitive.There’s vigorous disagreement over whether a bike in effect hangs from the upper spokes (those above the hub as you view the bike from the side) or rather is being supported by the lower ones, acting like tiny pillars. ‘The latter view, odd as it seems, is definitively the case,’ says Jim Papadopoulos from Northeastern University’s College of Engineering in Boston, USA, and the co-author of Bicycling Science.
While it’s easy to believe a bicycle spoke would simply collapse under the weight of bike and rider, he goes on to explain that the tension created in a spoke during the wheel building process (called ‘pre-tension’) is what allows the lower spokes to bear the load without buckling, as they would if there was no pre-tension. ‘Every spoke on the unloaded wheel has a tension of the order of 100lb [445N]. When the axle is pressed towards the ground with a force of 100lb, the only significant effect on spoke tensions is to reduce those directly below the hub – typically, one reduces to about 50lb and spokes to each side of that one reduce to about 75lb. This is exactly what one would see with solid wooden spokes like an old wagon wheel – the bottom one would carry 50lb and those to either side of it would carry 25lb. The difference with wire spoked wheels is that a wire spoke cannot carry a compression load – it will collapse. So all spokes are ingeniously pre-tensioned. A wire cannot carry a compression load of 50lb, except when it already carries a tension load exceeding that.
Of course a bike wheel will collapse if the upper or horizontal spokes are removed,’ Papadopoulos adds. ‘But that is essentially because the altered structure has a very different load path, and furthermore is unable to supply the required pre-tension. We can’t use that collapse to conclude that the typical wheel carries load through the upper spokes.’ If that leaves your head spinning, you’re not alone. So let’s move on to the more straightforward area of spoke material.
Spokes are predominantly made of steel, a choice of material that, as Miodownik tells us, ‘basically comes down to the ability to have a reliable thread. Steel wire is great because even with a very small amount of fastening area, such as where the nipple holds the spoke at the rim, you can put quite a lot of tension on them without stripping the thread. Stainless steel is the ideal material as it has the right mix of high strength and low weight, while also being affordable.’
Stainless steel has been the metal of choice for spokes since the late 19th century because of its high tensile strength, which allows spokes to remain relatively thin and lightweight while coping with the forces placed on them. ‘Mild steel spokes would have to be twice as heavy and thick,’ says Chris Hornzee-Jones, director at structural engineers Aerotrope. He designed the ground-breaking Lotus carbon fibre mountain bike and worked on one of the largest tension-spoked wheels ever made – the 60m diameter structure suspended beneath the roof of the Millennium Dome, used as a platform for aerial performers. ‘By adding chromium and molybdenum into the iron and carbon of mild steel, the resulting stainless steel alloy is much more resistant to fatigue.’
Fatigue is a spoke’s nemesis. If you think your quads are being repeatedly put under strain from the repetition of your pedal strokes, then pity your spokes, being pummelled with every single wheel revolution. Each spoke in the wheel comes under compressive load only for the fraction of a second that it is directly underneath the hub, and for that moment it gets compressed before the pressure comes off and it can return to its normal length. It’s a relentless cycle that can be the undoing of a poorly built wheel, literally.
A wheel is like a fatiguing treadmill for spokes, which is made all the harder for them by having had a thread added at one end and [in most cases] a bend and/or head at the other,’ says Hornzee-Jones. ‘The thread is a concentrator of stress and the load transfer occurs mostly through the first few threads. What’s more, the nipple is comparatively stiff and, as it tries to sit perpendicular to the rim, it rarely aligns perfectly with the angle the spoke arrives at, which can be the cause of additional concentrated stress. At the other end the J-bend flexes minutely and, after hundreds of thousands of normal wheel rotations, any tiny surface flaws, only microns deep and completely imperceptible to the human eye, may start to open up. It’s a slow process at first but will eventually lead to a spoke breakage.’
Steel is not the only material used for spokes, however. Mavic and Campagnolo (as well as Campagnolo’s sister company Fulcrum) have long been advocates of aluminium spokes. Aluminium has one third of the density of steel but about one third of the stiffness too, so spokes need to be thicker, which means they are potentially less aerodynamic, require larger-diameter nipples and, subsequently, bigger holes in the rims, which can reduce rim strength and stiffness. Aluminium spokes also tend to use a straight-pull design as a J-bend in aluminium would be highly likely to fail under stress.
Another limitation is that aluminium doesn’t hold a thread as easily. Mavic’s solution is to thread the nipples directly into the rim, instead of onto the spoke. Campagnolo suggests it chooses aluminium spokes that weigh the same as steel versions, but by comparison improve the ride feel of its wheels, however this is a largely subjective matter in which spokes play only one part, with tyres, rims and hubs also significant players, let alone the rest of the bike.
Given the various stresses that spokes endure, carbon fibre may not seem like a likely choice at all, but Mavic, along with several other high-end wheel brands, such as Lightweight and Reynolds to name two, have found ways to harness its tensile strength in spokes, with obvious weight savings up for grabs. Mavic’s R-Sys SLR, for example, uses hollow carbon tubes to provide stiffness under tension and resistance to compression. ‘The spoke stretch is much lower than steel or alloy because carbon is stiffer’, says Mavic’s Michel Lethenet. ‘Being tubes, they resist compression, which helps maintain the stiffness of the wheel, although some metal parts are required, which are bonded at each end to make the attachments at the rim and hub.’ An alternative method is employed in Mavic’s Cosmic Carbone Ultimate, in which bladed carbon spokes go from one side of the wheel to the other, connecting with the hub flange, and crossing other spokes en route.
There are a few other pieces of received bicycle wisdom relating to spokes that Peter Marchment, materials scientist and director of Hunt Bike Wheels, is happy to dispel. ‘A wheel using a deeper rim with shorter spokes is often seen as “stronger” but this is usually down to the inherent added stiffness in the rim,’ he says. ‘Also, many people believe that a higher spoke tension means you get a stiffer wheel, but this is not the case. Wheel stiffness is affected by many things besides tension alone, including spoke count, bracing angle and rim depth.
Actually a spoke will elongate by the same amount when loaded, regardless of the pre-tension applied, meaning that increasing the spoke tension doesn’t make the wheel stiffer.’ Marchment continues, ‘Putting spokes under the right tension is crucial. At extremely high tensions the rim and spokes are more liable to be damaged because they are effectively being pre-loaded with a high force. But low spoke tensions are also a problem because the nipple is more likely to come loose [unwind] when they are de-stressed through impacts or road vibrations, causing the wheel to come out of true.’
Whatever the tension and pattern, there’s a vast array of spokes from which to choose, not to mention many variations in the quality of the wire from which they’re made. Sapim, one of the leading spoke manufacturers, produces 300 million spokes a year, and shops around to maintain quality and stay competitive across its product range. ‘Sixty to 70 per cent of the price of a plain gauge spoke can be in the material, so it’s important to get that right, but the most important thing for all of our spokes is the performance of the wire,’ says Sapim’s sales manager, Klaus Grüter. ‘We’re looking for a wire that’s bright and shiny and that has a tensile strength of 1,000 to 1,050N/mm2 with good fatigue data and importantly, excellent corrosion resistance.’
Grüter tells us samples are lab tested for tensile strength, bending and torsion resistance. Once accepted, the wire off the spools is straightened by machine and cut. Plain gauge wire can also be made into butted spokes (where the central portion is made narrower) by drawing the wire through a die. Once butted, the head of the spoke and the J-bend are forged and the thread at the other end is rolled (not cut). Finished spokes are inspected both by machine vision systems and by human eye and hand. One machine is able to make 20,000 butted spokes a day, which explains why different labour costs have little impact on the price of a finished spoke and why manufacturers worldwide can sell at similar prices.
But why butt a spoke anyway? Jonathan Day of Strada Wheels explains, ‘Butted spokes are better at handling torque than plain gauge. They are wider in the plane of the wheel, which is the direction of the torsional force, so there is more material to resist it. Also, they flex a little more in the perpendicular plane, so they are better at distributing the compression load across the wheel.’
The traditional spoking pattern of a bicycle wheel comprised 32 (or sometimes 36) spokes, crossed three times. The interwoven pattern of the spokes in a traditionally laced wheel, far from being just a pretty kaleidoscopic arrangement, is actually a functional part of the wheel design.
In terms of lateral rigidity the points where the spokes intersect allow each one to brace against another as it is placed under tension, as well as support it as it is compressed. The most vital role of the three-cross lacing pattern is in a rear wheel, where the spokes must transmit pedalling power from the hub. In this case the spokes are loaded with much greater torsional loads thanks to the twisting force from the drivetrain. Spokes on the cassette side, leaving the hub tangentially, transfer a rotating force (torque) from the hub to the rim. Radial spokes (which follow a path from the centre of the hub directly to the rim, without crossing another) are much less able to cope with this type of loading and would be more likely to fail.
When torque isn’t an issue, such as on a front wheel with rim brakes, using radial spokes makes sense. This saves weight, as the spokes can be shorter and fewer are needed to create a laterally stiff wheel. It looks good too. Disc brakes cause significant torsional loading, however, making radial spoking all but impossible. ‘Getting the lacing pattern right is key because spokes share the compression load by squeezing against the neighbours they cross, so spokes should be laced to be leaders or trailers,’ says Day. ‘You have to make sure a leading spoke takes the strain first on the drive side. On a 32-spoke wheel you want 16 leading spokes to share the load. If you get the lacing wrong you’ll end up with only eight doing the work.’
Remarkably, spoking patterns have remained one of the least challenged aspects of wheel design, despite some massive leaps forwards in materials and manufacturing technology over recent decades. It’s a truly tried-and-tested methodology and as the saying goes, if it aint broke
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