[Joe Johnson]

There are a lot of simplifications to the formula, but this should get you in the ballpark.

The velocity factors that folks use are for hours and hours of continuous duty. We run for a few minutes at a time for a few minutes (in gear life terms) total.

The biggest safety factors are that I put the load at the tip of the tooth and I assume that only one tooth has the load. If you keep your pinions large enough (i.e. with 16 or more teeth, which I know is not possible with the Drill, Jideco and the Chiaphau motors), the contact ratios are large enough that for most of the travel of the gear tooth, more than one tooth is taking the load.

The biggest thing working against you is that no dynamic affects are included. This can be a very big deal.

In the end, we don't have time to really study the teeth to optimize them. Some years, my gearboxes are wearing out by the second regional, some years they are unworn after several post season competitions and hours of driver training.

When you get more experience, you will have better feel for the size you will need and where your approximations will get you in trouble. It also helps to get a few initials after your name ;-)

Joseph Johnson, Ph.D., P.E.