[Note: this is #8 of a series of 20]
We refer to the World's predominant spoke shape as "J-bend," which couldn't be more self explanatory. What escapes discussion is the precise geometry of the bend. For low end wheels and short distance riders the only concern is whether a spoke can be attached to a hub quickly and stay put in service. The situation is different for high end wheels and competitors, where every effort is made to minimize weight without losing strength.
Besides punctures, spoke breakage is the most chronic headache for wheels used in competition and serious training. The majority of spokes break at the elbow, hence our concern with the geometry. A broken spoke means instant, major wheel wobble and the repair becomes elaborate if both tire and cassette removal are required. You might be able to ride home but one brake will need to be open to a point that renders it useless, an unwelcome distraction on any outing. In a worst case, the wheel won't rotate without contact with the frame or brakes often knocking a racer completely out of contention.
A spoke elbow has three critical dimensions. First, the radius of the bend, usually close to the wire's diameter. The example below has a radius of 2mm. Second, the bend angle. In this example it's 100º. Last, the elbow height, here 5.1mm. These dimensions differentiate spoke brands, greatly affect the ease of wheel building, and define spoke-to-hub contact area.
The three most important elbow dimensions.
Elbow radius needs to be as large as possible. Less bend leaves more fatigue life in the spoke itself. A radius too large means a spoke might not fit easily in a hub with a small hole and thick flange. 2mm is about as large a radius as modern, high end hubs will tolerate.
Spokes intended for mass market wheels are designed to be easy to assemble into wheels. A tall elbow height makes for a quick fit in any hub. Short elbows might not fit thick hubs, requiring manual bending to reach the angle required for the wheel. A 90º elbow will fit both inside and outside (of the hub flange) orientations. Technically, elbow outside spokes need to be 90º or less, while elbow inside are greater than 90º. If the spoke is 100º, for example, it will need to be bent further to lie correctly when placed in an elbow outside position. This requires extra wheel building time. An elbow of 90º usually needs no additional bending.
Spoke fatigue tests show that greater hub contact area is in the spoke's favor. Since hubs come with a variety of materials and flange dimensions, spoke makers play a guessing game. In general, large spoke radius, large elbow angle, and smaller height act to increase contact area but force the builder to manually bend the spoke to shape.
It's easy to see what an advantage it is to design the spoke AND the hub at the same time. If they anticipate each other, these issues can be perfected. Such a hub can have holes with radii rather than simple countersinks. A radius that matches the spoke would maximize contact area. So it's baffling to me why hubs and spokes so rarely match even when the same company is responsible for both. It suggests that basic spoke design principles are not well understood. Even in the 21st century, spokes are largely taken for granted, like staples or paper clips. They shouldn't be. Within their choice of material and geometry lies the key to longevity, and spoke life is the key to wheel reliability.