DMF 

Personal preference aside, there is an engineering justification for 5-armed spiders on road cranks.

The analysis is the same that dictates the use of 5 "feet" on a swivel chair. With 4 feet the chord between feet is 90°, placing the tipping point closer than the 72° chord of the 5-footed chair. (Try it; you'll see what I mean.) Historically, swivel chairs had 4 feet because until the advent of cheap casting and NC machining a 4-armed base was easier to manufacture. Now 5-footed bases are ubiquitous because they solve the problem better.

A crankset is different in three ways. First, mass (weight) is much more important. Second, there is a structure around the circumference - the ring. As the chord span* increases the ring itself must be made stiffer to oppose flex (as cs1 notes above). With more arms it is possible to make each slimmer and lighter. I don't know if (more arms x less arm mass) produces a net savings (doubt it), but adding the mass savings of lighter rings certainly does.

Third, with a chair, the diameter of the base is roughly fixed by the length of the human femur and 5 has been found an optimal number. Chain rings, OTOH, have a rough maximum diameter, but can be considerably smaller. As tooth count decreases the ring needs less strength (mass) to oppose flex, but a ring has a minimum chord mass because it also has to support the teeth against the (roughly constant) torsional force of the chain. Instead, fewer arms makes more sense. Thus, 4-armed spiders.

I wonder at what tooth count a solid disc makes more sense than crank arms?


* Chord span is the length of the chord at the rim; it is not the BCD. Chord span is a direct function of tooth count and arm count. The mounting flanges of the chainring act as arm extensions. For our purposes arm length = (ring diameter - hub diameter).