The bicycle wheel: basic geometry and dynamics

Still to this day, in an age of widespread and freely available knowledge, I keep reading a load of “tosh” about something as simple as a bicycle wheel. Of course, for a complete lowdown, you should read the excellent book by Jobs Brandt, but if you are time crunched, I will hereby try to explain the very essential. I want to point out that the following ONLY applies to spoked bicycle wheels which rely on tension. Trispokes, lens-like disc rear wheels and wheels with rigid spokes that are not in tension work on different forces and are not discussed in this article.

The first myth to debug is that strength of a wheel and “durability” of a wheel are the same thing. They are not, if your rim cracks, this has nothing to do with the wheel being weak.

The strength of a wheel is the ability to carry load: the more load a wheel can carry, the stronger it is. The strength is down to geometry and dynamics. The amplitude of the bracing angles alpha and beta in the technical drawing below determines by and large the strength. Wide angles stabilise and strengthen the wheel. Then of course, the wheel is only as strong as the tension loaded on the spokes, therefore the average tension of the spokes multiplied by the number of spokes is proportional to the ability of a wheel to carry load. A somewhat less important parameter is spoke deflection: spokes with larger section (gauge) show less deflection and therefore increase the load capability of a wheel. There are drawbacks in large gauge spokes, but we will examine this later.

In the first instance, for a strong wheel you want large bracing angles, high tension and many thick spokes.

Bracing angles alpha and beta are a function of the distance AD, or in other words the diameter of the wheel: a smaller wheel has wider bracing angles and is therefore stronger. To a lesser extent, it is possible to increase the bracing angles by having a larger BC distance, so a wider distance between the two flanges of a hub. To an even lesser extent, it is possible to increase the bracing angles by having “taller” flanges, but given the shape of the ABD and ACD triangles, the effect is negligible in any but the smallest wheels.

Strength can be increased by placing more load (tension) on each individual spoke or by increasing the number of spokes. Spokes on the drive and non drive side side will ALWAYS show a tension ratio which is the reciprocal of the ratio between the respective bracing angles. So, in simple words, while having a wide alpha bracing angle will increase strength, it will also lower the relative tension of the non drive side of the wheel. This is down to geometry and with one exception, the only way to change the ratio between the drive side and non drive side tensions is to either change the relative distances BD and CD or moving the point of attachment A, using an asymmetric rim. A rim hole offset to the left will result in less tension difference (less difference between the bracing angles) and viceversa.

The exception is the number of spokes: the two sides of the wheel are in equilibrium by having an equal load times bracing angle. However, the load is spread among a number of spokes in tension. If the number of spokes on one side of the wheel is halved, then the resulting tension on each spoke is doubled. This type of spoke lacing is called 2:1 or triplet lacing. Triplet lacing does not per se increase the strength of a wheel, but it makes for equal tensions on each spoke of the two sides of the wheel, which can be beneficial, as we will explore later.

A common myth you might read on the web is that tension spread between the two sides of the wheel can be altered using spokes with different gauge. This is, excuse my French, total bollox. Tension is the load placed on a spoke and is not affected by the size of the spoke. Different spokes with the same tension show different” deflection” when measured with a tensiometer, but the load is identical. Don’t mix up tension and deflection!

Once we have cleared the air about the basic geometry and dynamics at play, we can look at what happens in the real world. Of course we would like wide alpha and beta bracing angles, possibly identical, huge tension and a lot of spokes to spread the load.

While there is no theoretical limit to the number of spokes, the general rule is that the bigger the wheel, the higher the spoke count. A 16 inch Brompton could survive well with 12 spokes per wheel, but a 29er MTBike might need 32 per wheel. A high enough number of spokes means the average tension can be kept a bit lower, which is beneficial for rims and hub flanges. If the spoke count is too low, then the tension needs to be cranked up to maintain the same level of strength (load bearing capacity). Bear in mind the size of the wheel that count is the internal diameter of a rim, therefore a 700c road wheel with a rim depth of 60 mm, will give the same bracing angle of a much smaller wheel and will require fewer spokes to be strong.

Generally speaking, wheels do not collapse, but fail by fatigue. Fatigue is the damage produced on the components by cycles of loading and unloading (turns of the wheel). Fatigue is always a finite quantity, nothing lasts forever, but of course you want to maximise the number of turns a wheel can do before a spoke or other component fails. The general rule is that a strong wheel will fatigue slower than a weak wheel given the same load. In addition spokes are not all born equal, while a spoke with great gauge gives more strength to the wheel, it is not designed to absorb load and unload cycles in the same way as a butted spoke, so paradoxically, it might last less. Spoke fatigue life is directly proportional to the tension load on the wheel (average tension times the number of spokes), so for a spoke to last a long time, tension needs to be high. There is a limit to how much tension can be placed on the spokes, as other components will suffer and the order by which they will fail due to excessive tension is roughly as follows: rims first, then hub flanges/nipples. Again, to keep a healthy tension and have a long spoke life, the number of spokes is critical.

This is, to my knowledge and experience, pretty much all there is to know about a spoked bicycle wheel. Anything else, like spoke lacing pattern, is somewhat less important and can by and large be discounted.