# Mathematics of Gearing

23 replies to this topic

### #1 Ali_G

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Posted 05 May 2022 - 13:31

I don’t think I’ve ever seen discussed in here.

Just wondering if anyone is familiar with how maths work vis-a-vis gearing in a race car. I assume that back in the day, teams would determine what were the best ratios to run depending on some sort of mathematical formula, bearing in mind the nature of the circuit.

At a guess, I assume the maths is similar to compound interest? The more regular you compound, the more interest you get. It’s a diminishing return with continuous compounding getting you 2.718 (e) times more than getting paid interest at the end of the year.

Assume the maths here is very similar with a CVT being the optimum solution. Assume (e) also features somewhere. Also assume that the biggest difference between gearing and compound interest is that each gear change takes time. Adding more gears improves from a ratio point of view but you are adding more time when you are changing gears and off the gas?

### #2 Bloggsworth

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Posted 05 May 2022 - 17:46

Hewland gear ratio charts, experience, visualisation of the circuit were a good starting point - Clearly the GP circuit at Silverstone was not going to have the same gear-set as Lydden Hill or Cadwell Park. You would know the rev limit of your engine, one run down the fastest part of the circuit would tell you if you had it right. 400rpm down, consult the gear chart and adjust accordingly. Aim for the best possible compromise for the twisty bits (you didn't want to be changing gear half way round a corner with the older gearboxes).

### #3 MatsNorway

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Posted 07 May 2022 - 21:45

Probably a integral/area under the graph. In other words just like drag racing you want to focus a lot on the acceleration to get the average speed up as quick as possible.

Is there exceptions? Probably, a jet fighter might be one of them.

Edited by MatsNorway, 11 May 2022 - 15:24.

### #4 Fat Boy

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Posted 09 May 2022 - 23:08

I don’t think I’ve ever seen discussed in here.

It has...extensively. Solve for optimizing (area under the curve) engine power or thrust at the tire. They're both measures of the same thing and you can take any number of paths to get there.

The truth is, though, if you're doing gears on a road course car, then you're much more interested in gearing to the corners than for ultimate acceleration. Top gear is based on your longest straight. First gear is based on the slowest corner and/or for standing starts. Everything in between is either based on a higher speed corner or a shorter speed straight. You look at the 'optimum' to see the best acceleration, but it's very rare that the best straight line acceleration is ever chosen, because it will be slower around an actual lap.

Edited by Fat Boy, 09 May 2022 - 23:14.

### #5 GreenMachine

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Posted 10 May 2022 - 04:10

... a jet fighter does not loose torque as you swap in a higher gear,

Maybe I am missing your point Mats, but last time I looked jet fighters don't have gears

### #6 gruntguru

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Posted 10 May 2022 - 04:37

No wonder they don't lose torque.

### #7 Charlieman

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Posted 10 May 2022 - 12:53

Maybe I am missing your point Mats, but last time I looked jet fighters don't have gears

External starter gear?

### #8 desmo

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Posted 10 May 2022 - 14:00

When I was a kid racing karts, I'd just go see what sprocket the fastest competitor was running. My father told me to stop as it was cheating. I still remain slightly dubious.

### #9 Fat Boy

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Posted 10 May 2022 - 16:22

When I was a kid racing karts, I'd just go see what sprocket the fastest competitor was running. My father told me to stop as it was cheating. I still remain slightly dubious.

Imitation is the most sincere form of flattery.

### #10 Fat Boy

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Posted 10 May 2022 - 16:25

Probably a integral/area under the graph. In other words just like drag racing you want to focus a lot on the acceleration to get the average speed up as quick as possible.

Is there exceptions? Probably, a jet fighter does not loose torque as you swap in a higher gear, so if acceleration is closer to linear top speed would matter more.

Mats,

Stop trying to explain stuff you've never done.

### #11 desmo

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Posted 11 May 2022 - 02:01

Imitation is the most sincere form of flattery.

I don't think he actually used the word "cheating", I think the word was "dubious" and I just took it that way. When that happened we were about the only direct-drive kart at most races, which *definitely* made the idea dubious in more than any moral sense. Also made any flex pipe or expansion chamber-related stuff other racers in the class were using pretty irrelevant for us. Back then, the rule of thumb was to start by using a gear that would top out about 3/4 way down the longest straight and go from there.

### #12 MatsNorway

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Posted 11 May 2022 - 15:20

Maybe I am missing your point Mats, but last time I looked jet fighters don't have gears

Put in a dont somewhere. It was funny tho.

### #13 MatsNorway

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Posted 11 May 2022 - 15:21

Mats,

Stop trying to explain stuff you've never done.

Stop visiting this forum. You are just going after people. In this thread and the one other thread in technical. You are just an ass.

### #14 Fat Boy

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Posted 11 May 2022 - 17:18

Stop visiting this forum. You are just going after people. In this thread and the one other thread in technical. You are just an ass.

OK, Mats, whatever. Look, guy, if it weren't for bad information, you'd present none at all. I wasn't *just* an ass, I also explained how it's actually done in practice and the path to get there in theory.

You have never done this stuff, which makes it a bit daft for you to be so quick to offer advice. I've probably set gears 1000 times, which means I've looked at 10x that many scenarios. Is is really such a stretch that I might able to offer a little insight into the process?

### #15 Canuck

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Posted 11 May 2022 - 17:19

Meh. People go after each other on here all the time. When everyone agrees on something, this place goes deadly quiet and all but dies. The only posts come from the free energy people.

He does have a point even if you didn’t like the delivery. There are people here who do and have done exactly what the OP asked about, it’s their domain knowledge. Certainly not mine even if I’ve read books and talked about it.

### #16 desmo

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Posted 11 May 2022 - 18:54

I've wondered if the rather odd discrepancies in top speed between the Ferrari and RB F1 cars so far this season is as much about differing gearing philosophies as aero or power differences.

### #17 Joe Bosworth

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Posted 11 May 2022 - 20:19

Guys, relax!  The reality is that Fat's post #4 above probably gives as succinct an explanation to heart of  the issue as needed and someone can go off to the track and put it into practice.

If one is good enough at physics and programming and has a reasonably accurate HP/Torque curve for the engine being used they can create a quite accurate speed/time curve which can be changed to a speed/distance curve.  Having done that they can play the gears thing to their hearts delight.

I figured this out back in about 1953 in my drag racing days.  Won a US mid west class championship at Half Day Illinois driving a car with 4.11 gears in the dif and my closest competitor must have had about a 3.06. On flag fall I was through all my gears and in top gear while he was just getting into second gear and many car lengths behind.  I then sat back and watched my rear view mirror while he came at me at a much greater top speed only to fail to catch me at the 1/4 mile point.

All of this stuff became important in my F Ford days in the 1970s when I had a box full of gears for my Hewland and I had to gear differently for every track and sometimes for which way the wind was blowing.

If you want to baffle yourselves go to a bicycle road race some day and check the rear wheel derailiers on the competitors.

The principles stay the same for all of these examples; the physics never change.

Regards

Edited by Joe Bosworth, 11 May 2022 - 20:20.

### #18 Joe Bosworth

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Posted 11 May 2022 - 20:22

Desmo, re post #16

Check the F1 rules and see if they do not fix gearbox ratios at the beginning of the season!

### #19 Joe Bosworth

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Posted 11 May 2022 - 20:38

PS  to posts  #11 and 14

The fixed gear karting guys are constantly playing exhaust system lengths and final gearing to play off torque off of tight corners before long straights versus still getting rear wheel torque at the overrun at end of straights.

The exhaust configuration gives you almost infinite alternatives as does gear selection.  The winners mostly come to the same end points so , , are all at work.

### #20 Fat Boy

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Posted 11 May 2022 - 20:54

Desmo, re post #16

Check the F1 rules and see if they do not fix gearbox ratios at the beginning of the season!

Almost everyone is limited on gear ratios presently. Indycar and DPi are a couple of the few exceptions, but there aren't many left.

What we tend to see with ratio changes is not a difference in end-of-straight speeds, which is more a product of drag vs. power, but elapsed time, and, even then, it's never as big as you want it to be. As Joe says, a minor gain in acceleration makes a big difference in terms of elapsed time, because it has a compounding effect. This is one of the reasons that drag racers obsess about their 60 foot time (and I obsess about low-speed corner exits). A small gain at that end of the track is a big gain on the other one. This is also why it's more beneficial to deploy hybrid power out of slow corners which lead to long straights. A small advantage at a low speed can be quite large proportionally.

### #21 Lee Nicolle

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Posted 18 May 2022 - 01:38

Almost everyone is limited on gear ratios presently. Indycar and DPi are a couple of the few exceptions, but there aren't many left.

What we tend to see with ratio changes is not a difference in end-of-straight speeds, which is more a product of drag vs. power, but elapsed time, and, even then, it's never as big as you want it to be. As Joe says, a minor gain in acceleration makes a big difference in terms of elapsed time, because it has a compounding effect. This is one of the reasons that drag racers obsess about their 60 foot time (and I obsess about low-speed corner exits). A small gain at that end of the track is a big gain on the other one. This is also why it's more beneficial to deploy hybrid power out of slow corners which lead to long straights. A small advantage at a low speed can be quite large proportionally.

Big time motorsport with fixed gear ratios, fixed tyres, fixed brakes, fixed vehicle weight and if that does not work fix the drivers!! And teams.

The reason so much modern racing is BORING.

As a budget tintop racer I still managed to have 3 diff ratios and 2 gearboxes with different ratios. May not have been perfect but within reason covered the tracks I ran at.  Tight twisty Mallala, even tighter Winton, high speed Sandown and then more technical Philip Island with steeper hill up and down. As well as the AGP circuit where I raced twice.

And I do remember a well known competitor telling me early on that you gear for the corners before the straights. Very true on both ovals and road race.

On dirt ovals in my classic Supermodified I can beat most of the better V8 cars simply with gearing, both diff ratios as well as at times tyre size because it jumps off the corners harder, is as quick through them. This with 250hp Holden 6 against 6 litre Chevs, Fords and Mopars.

Then it depends on the engine, generally the more power you make and the more rpm you turn to make that power means all your ratios will change. Usually the diff ratio first.

### #22 Fat Boy

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Posted 18 May 2022 - 18:38

Lee, I wish I could argue with you, but you make some completely reasonable points.

The question about 'boring' or not is a matter of perspective. Changing the gearing might keep the engineer entertained, but the fans don't care, the team owners don't want to carry a drawer of unused gears around, the team owners don't want to pay for a dedicated gearbox mechanic (which is necessary in pro racing if you're changing gears) and, in more advanced racing, all the cars tend to run similar ratios in the end, regardless.

If I'm driving a racing kart, I'm the one being entertained and part of that is working on the kart (and changing gears). If I'm racing professionally, it stopped being about me 'having fun' a long time ago. That's actually one of the mental shifts which must be made. It's no longer recreation; it's work. The person being entertained is now some combination of the driver (if of the gentleman variety) and the crowd (live and/or TV). You don't do it because it's fun; you do it because it's hard.

### #23 Lee Nicolle

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Posted 25 June 2022 - 06:37

Lee, I wish I could argue with you, but you make some completely reasonable points.

The question about 'boring' or not is a matter of perspective. Changing the gearing might keep the engineer entertained, but the fans don't care, the team owners don't want to carry a drawer of unused gears around, the team owners don't want to pay for a dedicated gearbox mechanic (which is necessary in pro racing if you're changing gears) and, in more advanced racing, all the cars tend to run similar ratios in the end, regardless.

If I'm driving a racing kart, I'm the one being entertained and part of that is working on the kart (and changing gears). If I'm racing professionally, it stopped being about me 'having fun' a long time ago. That's actually one of the mental shifts which must be made. It's no longer recreation; it's work. The person being entertained is now some combination of the driver (if of the gentleman variety) and the crowd (live and/or TV). You don't do it because it's fun; you do it because it's hard.

Modern racing is BORING. All the cars look the same sound the same and change gears at the same time.

The reason EFF ONE down has less crowds. Here in Oz our Stupidcars all have the same power, same gears, same brakes so they piss around with running different compound tyres and how much fuel the car has.  Ditto F1. Boring, the punter on the mound doesnt know so it is only for TV.

Crowds are well down, TV viewing is well down.

And 10 lap tyres says nothing about the manufacturers product, says they are no good as they are not fast and wear out.

I would sooner have a box of gearbox ratios, far cheaper than 3 sets of tyres for a 45 min race.

I seldom go to modern racing,, and if I do it is state level usually with different cars achieving similar ends from several ways. 'Franchise' racing in tintops as well as some open wheel classes is boring,, or a crash fest as the cars all go the same speed.

The Sports Sedans I used to race had generally outright 6 litre engines though at times a turbo rotary or 4 on the pace. Where I was most of the time in the back half of the top ten defenitly had all of this, some were faster than me on a single lap but  a simple carby Chev more often than not beat them. Though some could make the tyres live better so ended up in front of me towards race end. Everyone was different making a more entertaining race. Our historic sedans also are bit lo this with Fords or Chevs fastest but a gaggle of slower V8s, Torana XU1 sixes, very good twin can Escort, rotaries, V6 Capris all making up the mix. And again they look different, sound different, and make speed in different areas

### #24 Fat Boy

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Posted 29 June 2022 - 22:11

Modern racing is BORING.

But you, Lee, are not! I honestly don't find many gripes with your post. Screaming at the sky doesn't change much, so I play in the sand-boxes which exist as opposed to those which I would prefer.