Scottrik

iTrader: (261)

Sorry guys...he asked.

Roll-out Primer

Here's a bit of a primer on roll-out.

Gearing a foam-tire on-road car is ENTIRELY dependent on the current diameter of your tires. What you're trying to find is how far the car moves forward for every revolution of the motor. To express it any other way is hopeless because of the fact that foam tires change diameter where rubber tires, effectively, do not. Also we'll see why the question "what gear to run" is impossible to answer without some of the other variables answered.

Once you understand the concepts behind roll-out it's a matter of measuring your rear tire dia. and consulting the roll-out chart to find desired roll-out and what size pinion gets that for you. BUT...like a lot of things in life you will gain a FAR better appreciation and understanding for this phenomenon if you do it the hard way a few times. Remember that prior to PC's and easy to download Excell share-sheets we had to manually calculate roll-out and this is a good skill to have because even now I'll end up with an oddball spur gear or a value that doesn't show up on the chart. Or I'll leave my charts someplace. Or... Plus the mathematician/math teacher in me LOVES this stuff!

This is where your high school geometry comes in handy (you remember...the stuff you and every other kid on earth said "but I'll never use it"). Roll out is calculated using good ol' pi (3.14159...). You multiply the tire diameter by pi and that gives you the tire circumference (distance around the tire). Then divide your spur gear by the pinion gear to get your final drive ratio. Finally, divide the tire circumference by the fdr and you have roll-out. The roll-out charts all do this but it is performed on an Excell spread sheet.

What you're usually trying to do is find what pinion to use. If you know your tire dia/circumference, spur gear teeth and desired roll-out value you can identify the pinion size that yields your desired roll-out with a little algebraic manipulation.

The base formula is (remembering that / means "divided by"):

(pi X tire diameter) / (spur teeth / pinion teeth) = roll-out

Let's call (pi X tire diameter) "tire circumference" and (spur teeth / pinion teeth) "final drive ratio" (though we probably won't use this for now).

As I said, the mystery number is usually the pinion teeth so we want to segregate that variable.

Our base formula is now:

(tire circumference) / (spur teeth / pinion teeth) = roll-out

Noting that we have a "double division" in this base formula (basically a fraction in the bottom of a fraction) our first step is to take the bottom fraction, (spur teeth / pinion teeth), invert it and multiply by the tire circumference, giving:

(tire circumference) X (pinion teeth / spur teeth) = roll-out

Now we multiply both sides by spur teeth giving us:

(tire circumference) X (pinion teeth) = (roll-out) X (spur teeth)

Finally, divide both sides by (tire circumference) and we get our desired result:

pinion teeth = (roll-out X spur teeth) / tire circumference

Seems like the long way to get there but THIS is the point where you'll start. This last is the only formula you'll need if you know everything BUT the pinion gear size. I just showed the math to get there as proof. Please note that there are a couple ways to get from there to here but the result will be the same.

So, say you're like me and have a 96T spur gear and new 48mm dia rear tires. You want to be a little conservative so you're going to start with a 40mm roll-out (I think I'm running about 42-43mm in Stock). The pinion you need is found by:

pinion teeth = (40mm X 96 teeth) / (48mm X pi)

Remember that pi is approximately equal to 3.14159 (you can really stop at 3.14, but what's the fun in that?)

pinion teeth = (40mm X 96 teeth) / (150.8mm)

pinion teeth = (3840 mm teeth) / 150.8mm)

When we divide out the right side the mm cancel leaving only teeth AND the desired result.

pinion teeth = 25.46 teeth

NOW...a 25.46 tooth pinion is a bear to find, and it usually doesn't mesh worth CRAP even if you do locate one. You'll need to round up or down, especially since you're nearly exactly in the middle. This little difference probably won't be catastrophic (provided your initial assumption was "conservative" as I did) either way, so I'd probably do a 26T pinion and settle for the 40.84mm roll-out.

NOTICE...the roll-out we "accepted" in this example is almost a full mm more than what our target was. THAT'S how quickly things that seem really small can change things once multiplied back out. This difference is about a 2% variance but such is what we're left with since we can only go to full tooth intervals on pinions. The only alternative would be to true the tires down a nick. I can find that amount (if I was really concerned...in this case I really wouldn't be but will make the entire case for our discussion) by going back a step in our earlier calculation to where we had:

(tire circumference) X (pinion teeth) = (roll-out) X (spur teeth)

And divide both sides by pinion teeth to yield:

tire circumference = (roll-out X spur teeth) / pinion teeth

tire circumference = (40mm X 96 teeth) / 26 teeth

Multiplying and dividing (this time "teeth" cancel) we find that the tire circumference to hit EXACTLY 40mm roll-out would be 147.7mm. Divide this by pi and we see we need to true the rear tires to 47mm...taking a full mm off of them. Again, a bigger result than anticipated, but that result is multiplied by over 3 X to enter the equations.

Once you're comfortable with roll-out we'll tackle ride height adjustment.