Gear ratio is an often misunderstood topic and when used by itself it is found to be a meaningless number.  Let me explain.  It is the first half of a complex variable in your slot car and if it is not linked to tire diameter and engine speed then it can be very misleading.

A Tale of Bob and John

Let's take two cars owned by Bob and John.  They have the same gear ratio and same motor.  John has more top end, but Bob has more torque off the corners.  Why is this so?  John's tire has a greater diameter than Bob's and that gives him more top end. Bob has smaller wheels and tires and so his car has more power.  How can they be rectify this difference without changing motors or using all the same parts?  They change their tires and/or gears. In my strange story John chooses a completely different ratio and tire than Bob, but now the cars are exactly the same in acceleration and top end. How does this work?  OK, let's do some math to show how this happens.

We will start by identifying the variables.

1.    D = Tire Diameter.  Diameter is the height of the tire when mounted on the wheel.
2.    P = Number of teeth on the pinion.  The pinion is the gear on the motor.
3.    C= Number of teeth on the spur (sidewinder) or crown gear (inline).  This is the gear on the axle.
4.    ADR = Adjusted drive ratio.  This is the distance a car will go per 1000 revs.

Now the formula is 1000 x D x 3.1416 x P / C = ADR.  What is this in human language?

1.    Multiply 1000 times the diameter of the tire.  Multiply the answer by 3.1416 (which is PI). Finally multiply the last number by the number of teeth on the pinion. What is the 1000 for?  I hate decimals and so I multiply by a 1000 each time I do the formula just to get a number that is meaningful to me.

2.    Take the answer you get in step one and divide by the number of teeth on the spur/crown gear.  This number is what you will use in comparing setups.

Next we identify the setup on each car.

John's Car: He has .803" diameter tire, a nine tooth pinion, and a 28 tooth crown gear.

Bob's Car: He has the same setup except he was running a .744" tire.

Bob is happy because he is beating John on the infield and short straights and is not losing much on the big end of the long straight. John is not happy because he is getting his butt kicked. What are his options besides going out and getting the same tire?  Well if he does get the same tire then his car will drag. What he wants is an adjusted drive ratio equal to Bob's 751.3" of travel in a minute for every 1000 revs of the engine..  With his old setup John was getting 810.9 inches per 1000 revs.  The higher the number the more top speed you have, but less power.  A lower number equals more power, but less top speed unless neither engine is winding itself tight.  A lower number also gives better brakes. Somewhere there is a delicate balance.

John has decided he is going to keep his old wheels and tires. First he drops a tooth on the pinion.  When he does the math he gets a rating of 720 inches per 1000 RPMs, but he now has killed his top end.  He puts the old pinion back on and decides to add a tooth on the crown by putting a 29 tooth  gear in which would give a rating of 782.9 which is closer, but then he realizes nobody makes a 29 tooth crown.  You can only use what is available! OK, now he calculates using a 30 tooth crown gear and gets a rating of 756.8 inches per 1000 RPMs and that is close enough for government work.

He now shows up with his new setup and runs better, but Bob still beats him because Bob is a better driver.

Chet vs. Dyno Tom: A Family Feud

Chet wants to beat his daddy so badly that he buys a Falcon IV motor. His car is set up identically to his father's. He notices almost immediately that the Falcon does not come close to running out of RPMs even on long straights.  It is also apparent his car with its 47000 RPM wonder does not have the get up and go of his dad's SlotIt V12 in the infield portion of the track.  Since the two cars are using radically different motors Chet needs to plug the actual RPM rating of his and the rating of his dad's motor into the equation and not the 1000 that was used in the preceding story where the motors were the same.  He also needs to change gears and tires to match the characteristics of the new motor to the track.

Now let's look at the setup of the two cars after Chet makes some changes.

Tom's Setup: 9 tooth pinion, 27 tooth crown, .803" diameter tires, and a 25000 rpm motor.  This gives a top end of 21022 inches of travel per minute.

Chet's Setup: 7 tooth pinion, 30 tooth crown, .744" diameter tires, 47000 rpm motor. This gives 25633 inches of travel per minute.

Chet's car now has several advantages over his dad's.  First of all he has about 20% more top end speed.  He also has fantastic acceleration and braking. Why?  On the acceleration he is converting RPMs to power because of the lower ADR and his braking is better because of the ratio as well.

Tom's ADR is 841 inches per 1000 RPMs, but Chet has an ADR of 545.  The lower the ADR the more power and better brakes a car will have.  If  the motor is not wound tight at the end of the straight. then it needs to have its ADR lowered by changing the gears or tire diameter.  If it runs out of steam half way down the straight then its ADR needs to be a higher number.   With the changes Chet now beats dad because he has a better car and always was a better driver, but dad is a much better engineer and goes back to the drawing board.

RULES

1.    The lower the ADR the more power and brakes you have, but to get top speed you need more RPMs.

2.    The higher the ADR the more top speed you have, but the brakes and power are not as good.

Old Fart of a Driver vs. Sam

Sam is the better driver and so old fart follows safety rule #1 which is never tell Sam a thing.  Rule #2 is to lie to Sam about what you are doing.

Conclusions

1.    Don't buy or change parts until you have played with the numbers on paper.  Make changes one at a time.  Making one change will affect the whole system.

2.    Never fight a land war in Asia.

3.    Never enter a battle of wits with a Sicilian unless you want to eat pizza.

Comments on Numbers and Ratings

Numbers are only of value for rating anything if the way of achieving a number can be replicated.  They are always relative to each other.  If someone chooses to change the 1000 in the above equation to 18000 then that is OK as long as he does it consistently.  If the motors are different types then put in the actual numbers for the RPMs.

---

The names in this article are totally fictitious and refer to no person living or dead, but rather to the undead who are nocturnal creatures of habit who lurk in the back alleys of Ward's Corner.