[GeeTwo]

While weight of the bull gear would eventually be an issue, the decision to go from single-stage to double (or triple) stage is more commonly driven by geometric considerations (the SIZE of the gearbox, esp. relative to the wheels). Pinions for most of the FRC motors typically have 10-15 teeth. Smaller numbers of (spur gear) teeth would result in poor pressure angles. Gears with more than about 50 or 60 teeth (again, in FRC-typical sizes) are often larger than the wheels they drive, leading to untenable gearboxes. That is, at somewhere around 3.5:1, a two-stage gearbox is preferable to drive wheels of 4" or larger. At somewhere around 14:1, a three-stage gearbox is preferable to drive 4" or larger wheels.

With planetary gearboxes, these ratios are somewhat different, of course. Planetary gearboxes can reduce up to 10:1 (theoretically a bit higher, but no more than 14.9:1) per stage.