Originally Posted by padailey
Spur/pinion * internal ratio = FDR
This would really be expressed as (spur/pinion)*internal ratio = FDR . In the given example the order of operations takes care of itself, but this would not necessarily always be the case (one could commutatively change to internal ratio * spur/pinion which would yield an incorrect answer) so a couple parens ("grouping symbols") never hurt anybody and yield the correct answer regardless the order taken.
Now, to make this formula a bit more useful for you, lets segregate the unknown variable (probably pinion) rather than a known variable (in this case, FDR). I'm assuming you know what spur you have, you know your internal ratio, and you know the FDR you are targeting (4.2), thus the unknown variable (as it usually is) is what pinion size you need.
Multiplying both sides by pinion gives us:
spur * internal ratio = FDR * pinion
Then dividing both sides by FDR yields:
(spur * internal ratio) / FDR = pinion
Thus solving for the unknown in the equation.
Using my TC5 as example which has an internal ratio of 2.0 and mine has a 108T spur (64p gears).
(108 * 2.0) / 4.2 = 51.42t pinion to give a FDR of 4.2
An IMPORTANT consideration is that in these cases you MUST round down or you have exceeded the allowable roll-out. Yes it's a comparatively small amount, but the simple fact is it would technically be cheating. Round down, then there's NO doubt. So I install a 51t pinion for an FDR of 4.24.
Or my TC3's (which sounds like you've got one). The internal ratio is 2.5, my cars have 100T spur and we're still shooting at a 4.2 FDR
(100 * 2.5) / 4.2 = 59.52t pinion.
Again, you'd need to round down, but in this case it is pointless...that gear combo won't fit in a TC3. If I were running 21.5 option I'd need to install a significantly smaller spur gear to make this work. In fact in the (iir) VTA tuning thread there is a fellow who posted some pics of the Dremel work and gear combos needed to get a TC3 to the 4.2 FDR. BUT...the fact remains that the equation is more useful in most cases expressed in this slightly re-oriented fashion.