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Gearing explained 11
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Gearing explained Tips & Tuning
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Part 1 - Teaching Granny to Suck Eggs (the very basics)
I'll keep this section short....
Slot cars support multiple pinion and crown sizes.
Manufacturers supply cars with a gearing that can work reasonably on most tracks.
Performance can be significantly improved by setting gearing to be optimal for the track upon which you are competing.

Crown ÷ pinion gives you a basic ratio.
Eg 27 / 9 =3 The motor turns 3 times to make the wheels turn once.
-Higher numbers can make a car accelerate and brake more quickly but reduce the top speed because they result in a shorter distance per motor turn.
-Lower numbers can make a car accelerate and brake more slowly but increase the top speed because they result in a longer distance per motor turn.

Part 2 - Beyond the Basics. Wheel and Tyre size
Accounting for wheel sizes, also known as "roll out" gearing.
Pi x diameter ÷ ratio = distance traveled in one turn of the motor.
"Longer" gearing results from lower ratio numbers.

Gearing matrix chart.
It's easy to create a gearing chart with a spreadsheet program.
Below is a link to my "test tools" which includes a link to a chart I generated.

Part 3. Speed and Torque.
-Motor speed and ratio
You may intuitively think that the ideal ratio is related to speed and that when changing your motor, you can make a calculation so as to make the car's performance equivalent to the older motor as a start point.
Eg I'm changing my NSR king22 to a king30 to improve performance
22/30 = 0.73
This might lead you to want to change your ratio from (for example) 3 to 4.1 (so that the rear wheels will top out at the same speed) but this would be a mistake.
Gearing is less related to motor RPM than is is to torque.
So if changing a motor that's optimally geared, to a faster one of the same G/CM rating, the existing ratio should provide a good start point.

-Torque and ratio
Torque : A measure of how hard the motor will pull.
If you have two motors of equivalent speed spec (rpm) but different torque ratings:
The motor with the higher torque rating (eg NSR king-25 at 350G/CM) is likely to be able to pull a longer mm/rev than (for example) a Slot.IT FlatSix RS at 240G/CM
However, basing your gearing decisions on manufacturer torque numbers is problematic.
Testing of the torque of several motors has shown me that some manufacturers are "glory running" in this respect (over stating) and others are "sandbagging" (under stating) . Manufacturers don't all test at the same voltage. Some don't even quote the voltage that their torque numbers are representing.

Part 4. Advanced : "What goes on in your head, Wilkinson ?"
A. Gear preparation
There is much more to be gained by diligent gearing installation and preparation than from changing ratios.
I know racers who rarely change their factory ratios but their equipment prep is certainly a thing to be admired.
- Backlash is an important factor. Set by the spacing between crown and pinion, a fit that is too close or too loose will waste energy.
For inlines, ensure you use axle collars or spacers to maintain an ideal mesh.
For Angle winders, adjust the pinion and crown toward (or away from) the centre of the car to loosen or tighten the mesh (respectively)
For sidewinders you are at the mercy of the gear manufacturer. This partly explains a growing trend for some manufacturers to create sidewinder pods with a greater and greater angle. It also partly explains why there is a current fashion with some racers to fit short can motors into anglewinder pods with motor adapters.
- Running-in your gearing can also bring performance enhancements.
Toothpaste or other abrasive products can be used at slow speeds to get the crown and pinion to mesh nicely, but do be sure to scrub this gunk off the gears and apply a dry lube before racing.
A noisy gear is a slow gear. If your car is screeching its way around the track, you are wasting energy and losing speed.
If you are not using feeler gauges to Install your axles, I suggest you do. Slot.IT manufacture a nice set of axle washers and gauges on an acid etched foil. Axles Installed to tightly or too loosely agaist the bearings are wasting power and costing you performance in friction or resonance.

B. Non fixed pitch.
A dirty little fix employed by slot car manufacturers to maintain a fixed motor to axle distance.
Ideally, all of the tooth wheels that are running together would be of identical pitch (represented as a TPi "teeth per inch " number)
However, Companies like NSR and Slot.IT play fast and loose with gear pitch, especially on angle winder and sidewinder gears so that they can avoid having to design a system where the motor would have to be on a sliding mount to account for the different gear diameters that such a fixed pitch design would require.
Instead, the manufacturers stretch and squeeze extra teeth or fewer teeth onto the same diameter gear.
Practically, such designs work but if the mismatch is pushed too far, the gears cease to work efficiently.
These compromises can completely overcome any advantages you may get from altering ratios.
The manufacturers do not publish their TPI numbers, you will have to take measurements and make calculations.
If you can, try to stay in the sweet spot where pinion and crown are of similar pitch.
My father used to cut gears for RollsRoyce Gearboxes.
I would listen intently to his stories of optimising gear faces for silent running , right out of the factory.
(The stories always came with shed loads of comments about supervisors and managers who simply had no idea what was really happening on the 'shop floor)
Slot car gears and their variable pitch would have triggered some consternation I think.

C. Counter Intuitive Effects
Often the ratio changes that you plan and deploy don't have the required effect.
Rule1 : "A junk motor is a junk motor".
No amount of gear tweaking will make such a motor perform well. Dump it!
Rule2: "Acceleration and top speed are not a perfect trade off.
Sometimes a longer mm/rev will make your car more sluggish (expected) but bring hardly any additional top end speed (and vice versa)

D. Power band
Its sometimes easy to forget that electric motors have a very flat power band.
Internal combustion engines are "peaky" requiring the driver to keep the motor inside a certain rpm range to get the optimal power.
The peaky power band is the reason that IC engine cars require multiple gears.
Electric motors do not really need a gear box.
(The policar gearbox is not really a gearbox, it's a fixed ratio layshaft, but more about that later)

E. Mass of the Car.
In theory, the lighter the car, the better.
Each extra gram on your car is mass that needs power to accelerate and decelerate it.
lighter cars can run longer mm/rev gears and still accelerate like a kicked cat.

In practice, Other factors come into play that may make a heavier car perform better.
The car may well overcome the tyres' capability to put the power down.
The car may exhibit start line "power DeSlot" or other such bad behaviours.
Be aware that rotating mass (wheels, tyres, gears, armatures) has more of an impact than non rotating mass (body chassis)
1g removed from the wheels will have a larger impact than 1g removed from the chassis or body.

F. Mismatched gear manufacturers.
Many believe that you should never mix and match gears from different manufacturers.
Mixing is asking for trouble because each manufacturer has gone to some length (some more than others) to design the crowns and pinions to engage and disengage each other cleanly and smoothly.
Practically, some gears will play well together.
Eg. I have AllSlotCar pinions driving Slot.It inline crowns without any problems at all.
All you can do is try it and see.

G. Psychology
An age old adage states that "Races are not won on the main straight. Races are won in the corners"

Having said that, hammering down on your opponents on the straight can have a negative impact on their state of mind.
Even if you are barely as quick in the corners, they know you are coming at them in spades on the straight and it can cause them to push too hard on the infield and leave their braking too late at the end of the straight.
Ferrari F1 deployed this psych-weapon in 2019 but underestimated how methodical and hard headed the Mercedes F1 team really are.
Infield short straight "punch" can also act as a psych-weapon. Against an over geared car , this kind of performance can push an opponent into trying to enter a short straight too quickly in the hope that you won't punch past them. Once their car gets out of shape, they are unable to get traction out of the corner to defend their position.

H. Oddities
The Policar F1 GEARBOX.
A very unique slot car drive solution designed by Maurizio Ferrari of Gallileo Engineering SRL.
The design employs a lay-shaft so that a large and unsightly protruding inline crown wheel is not required, making the Policar range of classic 1970's formula 1 cars more aesthetically pleasing.
There are no pinion options. Only the factory fit 9 tooth pinion is available.
There are no layshaft options.
The final drive ratio axle has three options. 16, 17 and 18
17 is the factory fit.
18 results in a higher ratio number and a shorter mm per motor revolution number.
16 results in a lower ratio number and a longer mm per motor revolution number.

Tyre size changes have far more impact on the final mm/rev than any of the gear options.
This design is crying out for a better spread of gears and I would guess that we might see that if and when the "policar generic modern f1" car comes to market.

As above, diligent prep of the policar gear box brings far more performance improvement than ratio changes.
The right spacers, diligent run-in and application of lubricants are critical to good performance.

In summary,
Gearing options are a useful tuning technique but require experimentation.
Setting up your factory ratios in a diligent way can bring just as much improvement and sometimes more.
Track testing and competition is absolutely required to fine tune your gearing.

Final thoughts
Why am I obsessive about car setup and tuning ?
In short, its because my driving skills are "sub optimal" (Ron Dennis speak for "not good enough")
I compensate as best I can with better and better car preparation.

Now... If someone has a technical fix for my sub optimal eye to hand coordination....
Or maybe those highly skilled guys should be made to wear boxing gloves during racing ....

As always, comments are welcome, especially if I've made a technical error in the details above.