The Relationship Between Tires & Gear Ratios


A long time ago, just slightly after dirt was invented, when I was racing Austin Mini Coopers, a fellow competitor, also a Mini driver, sprung some really big bucks to fly over (then, and maybe still) England's best Mini tuner to work on his car. The legendary Richard Longman arrived with boxes full of new go-fast bits, but, as it turned out, said parts were already installed. So Richard turned to the driveline. As our next National Race was the Chicago Region June Sprints at Elkhart Lake, WI, a 4-mile course I refer to as being in the "Asphalt Dynamometer" category, a 1293 cc Mini (a 4-cylinder with a 5-port head; 2 intake, 3 exhaust, and yes, it ***** just as much as you'd think it would) with 10-inch tires was at a significant disadvantage to its little Fiat and Datsun pals.

"Not to worry," said Richard, "I've got a fix for that." Whereupon he proceeded to open a crate and pull out a mounted set of Dunlop 12-inch tires. Woo. Woo, woo! You may think that any 12-inch tire you've ever seen is pretty small, but they absolutely dwarfed the micromeats we were racing on.

"Polish gear change" (sorry; he never was all that politically correct, being, well, English and all). Huh? But... Hmm. Oh. OH! And that, boys and girls, was how Unc was first clobbered over the head with the concept of the true relationship between theoretical gear ratios, practical or "effective" gear ratios, and tire diameter. Richard had elected to forgo any differential gear changes aimed at better top speed, and chose instead to accomplish the effective change with tire diameter. Which, in retrospect, serious full-sized drag racers were also probably messing with at the time. Guess what? It still works, they're still messing with it, and you can even apply the idea to slot drag cars. Inadvertently, you may already have.


How it works. Exclusive of any tire compression due to weight and any growth at speed, this is really a pretty simple concept. Hypothetical example: let's say you're running a car with a 13:52 (4:1) gear ratio and a 1.000" tall tire. Every tire revolution equals a rollout (for our purposes, the basic circumference of the tire) of 3.1416", or appx. .785" per motor revolution. Change to a 13:54 ratio (4.154:1), and you end up with about .756" rollout per motor rev. However, if you retain that 13:54 ratio and fit a 1.040 tire, you end up with about .786" per motor rev, or approximately where you were with the 1.000" tire and the 13:52 gearing. So? So, if you can maintain the same rollout while changing gear ratios, it follows that you can similarly alter the rollout while retaining the same mechanical gear ratio by increasing or decreasing the diameter of the tire, hence the rollout dimension.

Changing pinion and/or spur gears modifies the number (or fraction of a number) of times the tire revolves per motor revolution. One goes up or down in ratios in an attempt to find the exact ratio that best fits a motor's torque and horsepower curves, based on available track power (not to mention weight, body style and aerodynamics, torque multiplication factors, blah, blah, blah. Ignore those considerations for these purpose.) Unless you guess right the first time - which, of course, you don't actually know unless you change ratios and consequently run worse - you're going to have to do some testing.

 
gears ratio rollout/rev (equiv. dia.) (equiv. rollout)

(circum.)

 

What it means. If you run soldered-in sidewinder cars (and, occasionally, even if you don't), this becomes a major pain, not to mention requiring a lot of gears and patience. Additionally, there are some combinations you can't test due to the common unavailability of parts such as 64-pitch 53 and 55-tooth spur gears. You can, however, achieve the same effective ratio by simply changing the tire diameter. Table 1.0, left, illustrates the basic relationships between "smaller" ("non-scale") tires, in a range of sizes, and spur gears. While not precise to the third decimal place, you can see the close correlation between the degree of change via gear and the degree of change with a larger or smaller tire.


 
13:54 4.154:1 .756 .960 .754 3.016  
.970 .762 3.047  
(13:53) 4.077:1 .771 .980 .770 3.079  
.990 .778 3.110  
13:52 4.000:1 .785 1.000 - 3.145  
1.010 .793 3.173  
13:51 3.923:1 .801 1.020 .801 3.204  
1.030 .809 3.236  
13:50 3.846:1 .817 1.040 .817 3.267  

 
Notes: These are calculated numbers that ignore both weight
compression and diameter growth at speed. All dimensions in inches.
 
Table 1.0 - Diameter-to-Effective-Ratio Relationships
  

If one could legally run significantly smaller tires, the correlation would continue with the same degree of equivalency erosion. Similarly, this "drift" also increases above this range. It's not the mechanics of the deal that causes this, but the mathematics; pick a different base diameter, do the math, and see what happens.

Which leads to Unc's Rough Tire Diameter Rule of Thumb. I figure it this way: on a "spec" 1.000" tire, a .020" increase/decrease in tire diameter equals one tooth on the spur gear. Less diameter increases the effective ratio, and more decreases it.

Why you may already have worked with this idea. Not that long ago, a tire manufacturer introduced a "new & improved" tire with a nominal 1.0" diameter. Lots of people found some meaningful decreases in e.t. by simply putting a new set on. Not being all that eager to leave anything on the table, I picked up a set (even though I normally make my own tires - I'm not foolish enough to ignore someone else's stuff if it might be faster). Then I measured them. They measured between 1.020" and 1.032". Oh. Hmm. At both their original and at a reduced dimension, they performed the same as mine did. As a further experiment, I changed the diameter and the gearing of some of my friends' cars. Similar results. O.k., so maybe some people should have done a little more, uh, testing? Or perhaps a bit more tire measuring?

Slot car motors, even those prepared to the same specs and using seemingly identical components, can have amazingly different torque, horsepower, and performance characteristics. The "starting" gear ratio you may have been given by someone else is exactly that: a starting ratio, one that worked adequately well for one or more people. It may not, however, be the best one for you, your car and combination. What my friends and others "found" was something they probably should have tested for in the first place. Before you're satisfied with the performance of a heads-up car, you might want to make sure you're not missing some relatively "free" performance in this area, either. Put another way: make sure what you think you're looking at is really what you're looking at.

Other random thoughts. In the event you might be wondering about the effect that increasing or decreasing tire diameter has on the amount of tire growth, consider the following. Tire growth (or the absence of it) is a consequence of increasing speed, via increasing centrifugal forces, the nature and dimensions of the material, and any weight and aerodynamic (aka: "downforce") effects. All other things remaining kinda, sorta, mostly equal - they really don't, but cut me some slack here - the percentage of growth remains roughly proportional to rotational speed, at least in the size differences we're talking about here. Take a hypothetical growth number, say 2%. At this number, a .980" tire would grow to approximately .9996", and a 1.020" tire to approximately 1.0404"

Are these real numbers? Nope. Just like everyone else I've ever talked to about this, I can verify that tires grow from "some" to "a lot," based solely on empirical evidence and performance numbers. The actual number of things that can effect growth is amazingly long, so, for "guesstimating" purposes, I choose to ignore it until such time as I can a) effectively understand it, and b) accurately calculate it. At which point I will waste tons of time trying to figure out why I could never get better performance from small-hub, small-section, natural rubber tires, at least on C-can cars, than I could from "conventional" wheel diameters with similar sections, since the reduced rotating mass and theoretically greater growth should mean... uh, you get the point. When and if I ever figure out how to predictably use calculated and verifiable tire growth to accomplish something that nothing else can do (at all or as well), I'll let you know.

 

all contents © 2000 UFIE -  f_eubel@juno.com


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