"Taller diff ratio = slower acceleration"- really?

[LuckyP]

OK guys, I would like to hear some educated and well-reasoned arguments on this one...
Wasn't sure which section to put this one in, but settled for tech help in the end, as I perceive this to be a technical subject.

I often read on the Zone that taller gearing equals slower acceleration. For my type of driving, I don’t necessarily agree.

Right from the start, I'd like to make one thing clear;
I fully agree that all other things being equal, acceleration time in any given gear (between two given speeds) will be subdued with a taller diff, providing both speeds are obtainable in that gear.

But what about if those speeds are adjusted?
Nobody ever mentions the extra mph you have available in each gear when running a taller diff. For a while, you're using lower overall gearing (e.g. between 55 and 65mph you might be using second gear with a taller diff vs third gear with a shorter diff), so for that while your acceleration will be improved when using the taller diff.

In summary; when accelerating through the gears, at some speeds your acceleration will be worse, and at some speeds your acceleration will be better. I suspect these two factors may cancel each other out, providing the start and finish speeds are wide enough apart to include a gear-change or two.
Might this mean that a given engine will produce similar acceleration times no matter what the gearing (within reason)?

What would be really interesting (at least to me) is if anyone access to some relevant real-world data to either support or disprove my theory. Data from any car would be suitable, not necessarily an E30.


The reason I have raised this is my opinion that both of my cars (one of which is a 325i touring) are under-geared, to the point that I rarely use first gear in either of them.
I have recently bought a taller diff for the E30 (quite a bit taller, actually) in an attempt to make first gear useable. I might expand on this if some good replies are posted.

Anyway, I look forward to hearing your thoughts.

Pete.

[kam-325i]

Quick answer.......

Yes, each gear will have a higher terminal speed, But it will take longer to get there...

[kam-325i]

Long Answer.........

If your current differential ratio is 3.15, and your desired ratio 3.46:

3.46 - 3.15 = 0.31
0.31 / 3.15 = 0.098
0.098 x 100 = 9.80 (or 9.8%)

Your difference is 9.8%. Now, you can take your current RPM at any given speed and add 9.8% to see your new engine speed. If you are currently turning 3000RPM at 70mph with a 3.15:1 differential, you will be turning 3294RPM with a 3.46:1 differential.

The major gain here is getting the engine into it's peak power band at a 10% lower road speed, which translates to faster acceleration.

With a taller diff, it takes the engine longer to reach peak torque.
If the engines torque was constant throughout the rev range (I wish !!!)then your original statement would be true(ish).

[LuckyP]

Numbers ... now we're talking.

Kam, I agree with some of your post.
Assuming our starting engine speed is relatively low, then yes, the shorter diff means the engine reaches the torque band at a 10% lower road speed. But this only translates to faster acceleration until the engine runs out of puff - which will also be at a 10% lower road speed.
It is this last 10% of road speed where I suspect the taller diff reclaims the ground lost earlier.

It is this last 10% that is at the heart of my theory, and that I feel is ignored by people who blindly claim that taller gearing equals slower acceleration.

It may pan out that the taller diff never quite reclaims all of the ground lost. I don't know for sure, but I think it would be extremely close.

After a gear change at a given engine speed, the new engine speed is always the same no matter what the diff ratio (it's only the road speed that's different).
This means that in both cases the engine will be operating over the same rev range, and hence will be outputting the same torque.
Of course, with a taller diff the driven wheels see less torque, but only until the shorter diff would have necessitated a gear change.


I'm not claiming that any particular ratio is better or worse than any other. I am suggesting that most sensible ratios would have a minimal effect on actual acceleration times between two diverse speeds.


Pete.


Edited for clarity - maybe it's not worth the effort!

[kam-325i]

I can see the point you are trying to getting over.

The driven wheels will allways see lower torque due to the taller ratio....

What matters is the torque output of the diff....

[LuckyP]

Will,

My wandering mind is thinking it's not so simple!

I understand your point, but you have assumed that a single overall gear ratio is being used.
But overall gearing is a function of gearbox ratio and final drive ratio.

For example, after the 4:1 car has had to shift from second to third gear, the 3:1 car is still in second gear and now has the leverage advantage.
Assuming a flat torque curve, the 3:1 car is now accelerating faster, and will continue to do so until it too must up-shift.


As I said in my original post, at some speeds the acceleration will be worse, and at some speeds the acceleration will be better.

I am wondering how these two scenarios counteract each other, with respect to time and distance.

Pete.

[kam-325i]

Will,
I understand your point, but you have assumed that a single overall gear ratio is being used.
But overall gearing is a function of gearbox ratio and final drive ratio.

Which will give an overall single ratio of the "Gear Chain"

The input torque to the diff will be the same, but the output will be lower.

Using your flat torque "curve" example, everthing equal for both cars, except diff

car 1: 2nd gear 4000rpm 150Lbft 3.63 dif 40Mph
car 2: 3rd gear 3000rpm 150Lbft 4.1 dif 40Mph

which of the above will have higher acceleration ?

In a world with no load, the taller diff would give more accelleration.

But car 1 & 2 have a load on them, the same load.

[Dave_M3]

Only place where a taller diff appears to be faster is on paper where you pick a speed before a gear-shift...

Lets say, 0-60 times etc as the shorter diff needs to change gear.

But leave it run until 80 and you'll see that the taller diff has lost out again as it dropped out of the power band.


I see what you are saying in real world terms, a taller diff could be faster for example in not having to shift up a gear in things like overtaking etc but really the shorter the diff, the quicker the car is whichever way you cut it in the end.

It's the actual gear-ratios and the range between them in the gearbox itself that can have a strange effect by making certain gears longer or shorter.

[mrLEE30]

i think you need to rephrase your question as the simply answer is yes a higher ratio diff will accelerate faster to an achievable speed, as said above, but what i think you are getting at is will the car with a higher ratio arrive at a destination before one with a lower one, and this makes a big difference especially if the distance to be arrived at is some distance away.

Take a simple engine such as on a boat which has one forward gear and the "diff ratio" in this case if the propeller pitch, a boat with a 17inch pitch will reach its terminal speed - dictated by engine power vurses resistance quicker, so in this case the speed is limited to how fast the engine can turn which is normnally dictated by the engine management, so lets say 6000rpm, now take a boat with a 21 pitch prop which never may reach its terminal speed as the engine is not powerful enough to turn the prop fast enough to over come the reisistance, but if the boat with a 21 pitch is powerful enough to reach its terminal speed and this is only dictated by the rev limit again then at this 6000rpm erev limit it will obviously be moving at a faster speed than the 17 pitch at the same rpm. so if we say the terminal speed of the 17 pitch is 40mph and the 21 pitch is 50 mph then this can be said. the two crafts side by side will see the 17 pitch boat reaching 40 mph faster then the 21 pitch, but the 21 pitch will reach 50 mph faster than the 17 pitch (which cannot reach this speed) so at some point which can be shown graphically the 21 pitch will overtake the 17 pitch and arrive at a destination earlier then the slower but faster accelerating boat.

so we can say the following from the above.
the 17 pitch will accelrate to 40 mph fastest.
the 21 pitch will accelerate to 50 mph fastest.
given enough distance the 21 pitch wil reach a given point earlier.

thus with a car diff ratio it is the same issue, and if the above scenario is repeated around a track then there will be an optimum diff ratio for a fastest lap, and if this perfect ratio is found then no matter what other ration you have either taller ot lower you will not beat the perfect ratio, but the selection of this ratio is based on the track, long straights may require a taller ratio.

How this translates to real life driving is the same, but as we are limited to speed limits which are reachable with any available diff the higher ratio will be quicker, but at the expense of fuel.

does that help or just confuse more!!??

[LuckyP]

Thanks for your replies guys, but I’m still not convinced.

The boat propeller argument and the gear-chain argument both only examine a single-ratio scenario. And Willnz's comment that "the engine output is constant ... as we change through ratios", whilst true, does not take into account the torque multiplying effect of the transmission, which is different at all times.
I have already accepted that in a single gear, the shorter diff accelerates faster due to the higher torque available at the driven wheels - as Willnz said, it’s simple physics.

My point is that the simple physics will also tell you that this higher acceleration happens for a shorter time. Once this time is over, the taller diff now takes it’s turn with the shorter gearing and the resultant better acceleration.
Net effect: the overall acceleration of the two cars in real-world situations will be very similar. By real-world I mean up-shifting during acceleration ”“ this is something I tend to do.


If we could try and quantify all this for a minute”¦
Most people seem to think that taller gearing results in slower acceleration.
So if I changed my diff for one 15% taller, how many percentage points slower do you think my acceleration would be?
15%? More than 15%? Less than 15%? Perhaps you would like to explain your choice?
Between two speeds that both diffs can reach in the same gear, I would expect my acceleration to be 15% slower, because the gearing has reduced my effective torque at the driven wheels by 15%.
But accelerating through the gears, that’s a different story. The result has more to do with the speeds you pick than anything else.

Say our engine’s gearbox ratios and rev-limiter dictate changing gear at 6000rpm, and achieve 4200rpm in the next gear. These two numbers will be the same for both diffs.
These are not unrealistic figures, but it is true to say I chose them for convenience.
We’re only using a rev-range of 1800rpm, which is 30% of the 6000rpm maximum speed.
Due to the different gear change speeds, each car has a 15% gearing advantage for half of the speed range (half because of the numbers 15 and 30 above). This is not an isolated point, this is 50/50.
If my starting speed is such that the car with a taller diff can use a lower gearbox gear, then I think the car with the taller diff should win overall. If the same gearbox gear is used at the start, the shorter gear should win. But in either scenario, I would expect the difference to be small.
If my maths or methos is incorrect, please feel free to correct me.


To me it boils down to the engine output. Any differential I choose will use the same rev-range as I go through the gears. The advantage of lower gearing see-saws from one car to the other, as gear-changes occur at different road speeds.
Of course, in the real world torque curves are not flat. I’m now thinking it’s down to how the torque curve matches the overall gearing that is important, not how long or short your gearing is.


The whole point of the OP is that when I have read that shorter gearing equals slower acceleration, I think to myself ”ano, not necessarily”a.
And I still do.


Pete.


P.S.
The way this thread has developed makes it look like
a) I want to win the traffic light grand prix
b) I am claiming that taller gearing is somehow better or faster.

Neither of these is true.
a) I can’t remember the last time I side-stepped the clutch from a standing start. This doesn’t interest me any more. I have deliberately steered clear of ”a0-60”a or ”a0-100”a arguments. The variables induced by starting at zero (such as clutch slip and wheelspin) make comparison difficult.

b) I think that between some speeds, a shorter diff is indeed faster. But between other speeds, a longer diff is faster. These swings and roundabouts might (more or less) cancel each other out.

[e301988325i]

LuckyP, you're not alone, I feel my 325 is undergeared too. I'm running 3.64, and would like to try a 3.46 or 3.25, but it's all money, I can't justify.

With a shorter final drive, time spent in a gear will be less as the engine has less work to do and will reach the limiter quicker, but you'll be going slower.

There is a sweet spot for an engine, and gearing depends on the power/torque band that engine produces vs the cars weight/drag.

A 325 that needs 4 gear changes (1st to 5th) to get to 100, may well get beaten by one that only needs 2 (1st to 3rd).

It's swings and roundabouts, and frankly one set of ratios will beat another at certain points in the speed range.

If you feel it's undergeared, then it probably is for how you choose to drive and you may well, on top of that have a particularly strong engine that could cope with some extra gearing.

Alex

[Gunni]

Simple answer.

Higher Average HP over a given time means higher accelaration rate.

So as soon as you change your gear ratio by switching up a gear the car with the shorter gear ratio will produce less HP(less rpm). While the one with the longer gearing will make more HP and at that time will accelarate faster then the one with the shorter. Until it has to change gear and they will do this until they reach there terminal speed.

This scenario can be assumed if.

both cars start in the best gear (one in 3rd perhaps and the other in 2nd).
If both must start in the same gear because of a specific speed then the one in higher rpm will out accelarate the other one.

[DRIFTBOY]

Interesting topic, and one which I often discuss with a mate of mine who always thinks he needs the shortest final drive ratio he can possibly get, which I disagree with.

I have recently swapped my M30 turbo E30's diff from a 3.73:1 to a 2.93:1, quite a jump.

My findings, aside from the obvious nicer motorway cruising, are these:

- I can now use first gear usefully

- Traction is better, it's really calmed down unwanted wheelspin

- Holding gears for longer can, in a lot of situations, save changing gear while overtaking or being 'between gears' coming out of corners on the track, although I realise that's not always going to be the case.

- It stays in the engine's sweet spot (around 3000-5500rpm) for longer, so it's a little less 'punchy' but also less frantic to drive quickly.
As such, the car FEELS slower and a bit less exciting, but in real terms I don't think it's lost much at all, and I won't be swapping back.



I think the negative aspects of swapping to longer gearing are less of a problem if the engine has a lot of low-mid range grunt.

I can't imagine a high revving peaky engine, like a Honda V-Tech, would deal with very tall gearing well, but a supercharged V8 might do.

It's a pity it's not feasable to do back to back tests on one car with different ratios to measure these differences.

[djk]

Interesting topic - I generally agree with your original point regarding the gearing on e30s being to short/high.

Couple of points here using my layman's knowledge.

Say our engine’s gearbox ratios and rev-limiter dictate changing gear at 6000rpm, and achieve 4200rpm in the next gear. These two numbers will be the same for both diffs.

This is incorrect, although with the sort of changes to final drive we are talking about, the differences won't be huge. The lower the final drive ratio, the wider the spacing of the gears overall in terms of your 'drop in revs' - you are, in effect, 'amplifying' the difference between each gear. Imagine a really high final drive - say 10:1 or something ridiculous - 1st and top would be a lot closer together than in a normal 4:1ish ratio final drive. I could go and work out the maths, but I can't be bothered to look up all the figures right now!

Anyway, I'm in general agreement that acceleration is about many more factors than final drive. Also, in the real world, any significant change in final drive will result in you using different gears for various circumstances. Say 5th became too tall to use at all at under 35mph, you would drive around in 4th at this sort of speed, likely at a shorter overall gearing than previously in 5th and therefore enjoying improved acceleration response, potentially at the cost of fuel economy (depending on whether the engine is in an efficient rev range or not in either gearing circumstance).

Regarding fuel economy, often people conform to the view that 'less revs = less fuel', although that is not always the case - generally speaking, if the engine has to labour outside it's torque band to pull a taller gear at a given speed, it will use more fuel per set distance than an engine not forced to labour so, all other things being equal. Basically, I can see how most e30s could get away with gearing that was almost 'one gear taller' in all circumstances. 1st could be almost as tall as second is overall on a 4.1:1 final drive and still be adequate for pulling away in all but the more difficult circumstances, so one could generally use each gear's lower neighbour in normal driving, but then with a useful motorway overdrive in top.

I'm sure my 320i doesn't need to be doing as much as 3900rpm at an indicated 80mph in order to be efficient - a final drive that gave an indicated 80mph at, say 3000rpm or less, would likely give more economical cruising with little lost performance wise elsewhere except in 'traffic light grands prix' - something I, like many, have simply grown out of. It's worth remembering here that the first e30 320is were supplied with a 3.45:1 final drive on the same gearbox ratios - I tend to think the final drive ratio was only increased to give better 'cor, boot it in second gear' performance to motoring journos who were perhaps less than complimentary about the intermediate model's perceived acceleration. In truth, my suspicion is 0-60 was probably better on the lower ratio due to only needing one gearchange, but 0-Vmax was probably significantly slower in percentage terms. But how often do you accelerate from 0 to maximum speed inas little time as possible? It's basically irrelevant.

[e301988325i]

Changing gear wastes a lot of time which is why manufacturers make cars do 60 in 2nd, some even have higher rev limiters in 1st and 2nd to achieve this! The Maclaren F1 did 60 in 1st to get the numbers!

By the book A standard 325i does 60 in 7.2 and needs 3rd, that would be a lot quicker if it could do it in 2nd. without the time wasted changing gear across the gate. The taller ratio being faster in that instance.

[mrLEE30]

thats why i said the question needs rephrasing, the answer to the question is simple, the answer to the question of which is faster is extreamly complicated hence why the answer is to gear your car for the application in the same way race teams swap diff ratio to suit a track, for the record i also think my 325 is undergeared and it reaches the limit in 1 and 2 too easy, i also have the sport ratio making it even worse, others disagree saying the standard 260 box with a 3.91 (i have a 3.64) is better. as it happens i do have a 3.46 in the garage which i am tempted to try next as i as the original poster belive that by gearing to a lower ratio i will be able to get to a certain point faster although the car will not accelerate faster in first, but yes once the next gears become a factor then this is where i also think it will be better as i can hold the gear longer and shift less

good discussion by the way, i only hope it is not knackered later on by idiots coming on and posting silly arguements or single line comments on howw they raced a nove last week etc etc

mrlee

[daimlerman]

I have played about with overall gearing on my cars.
My 316i touring came with a 4.27(60mph at 3000rpm).I swapped in a 4.1(65mph at 3000rpm).
Gains were quieter cruising at motorway speeds and a small improvement in fuel economy on the motorway.No apparent loss in traffic,but no gain in overall fuel consumption over a week's normal usage.
My M50'd touring started with a 3.45(85mph at 3000rpm).
Was noticably quicker in 1st gear away from the lights than my 2.7 running a 3.64...down to being able to reach a higher speed in 1st gear.
BUT,on zone roam touring up the west coast of Scotland I found myself spending most time in 4th,the car was over-geared.Overall fuel economy for the trip was around 33mpg.
This car is now running a 3.64,feels quicker throughout the rev. range with no significant loss of refinement at motorway speeds,overall economy in general use is 32mpg.
My 2.7 on the 3.64 'feels' about right,when fitted with a 4.1 I could pull away in third....
Overall this car returns 33/34mpg week after week,with a 'best ever' week at 37.8mpg.
The cabbie that is being re-built at the moment will try the 3.45 with the 2.7 engine first,see how it runs!
When considering gearing,do not forget the effect of body shape,insignificant wind resistance up to say,30mph,then rapidly this will start to take effect,as I found with the second touring,running relatively high gearing.

[djk]

I have played about with overall gearing on my cars.
My 316i touring came with a 4.27(60mph at 3000rpm).I swapped in a 4.1(65mph at 3000rpm).
Gains were quieter cruising at motorway speeds and a small improvement in fuel economy on the motorway.No apparent loss in traffic,but no gain in overall fuel consumption over a week's normal usage.
My M50'd touring started with a 3.45(85mph at 3000rpm).
Was noticably quicker in 1st gear away from the lights than my 2.7 running a 3.64...down to being able to reach a higher speed in 1st gear.
BUT,on zone roam touring up the west coast of Scotland I found myself spending most time in 4th,the car was over-geared.Overall fuel economy for the trip was around 33mpg.
This car is now running a 3.64,feels quicker throughout the rev. range with no significant loss of refinement at motorway speeds,overall economy in general use is 32mpg.
My 2.7 on the 3.64 'feels' about right,when fitted with a 4.1 I could pull away in third....
Overall this car returns 33/34mpg week after week,with a 'best ever' week at 37.8mpg.
The cabbie that is being re-built at the moment will try the 3.45 with the 2.7 engine first,see how it runs!
When considering gearing,do not forget the effect of body shape,insignificant wind resistance up to say,30mph,then rapidly this will start to take effect,as I found with the second touring,running relatively high gearing.

Interesting real world experience Malcolm. I'm very tempted to try a 3.64 in my 320i, but I don't want to find that I'm going everywhere in an unnecessarily short 4th, rarely using 5th and getting worse economy as a result. I average 28mpg on the 4.1:1, with quite a lot of motorway mileage - best ever was 38mpg, most of a tank used up on one 50-60mph cruise in traffic/poor weather.

The myth I really want to dispel is that lowering the gearing makes your car 'faster', in the same way that increasing power will. If you only ever have a certain amount of power, all the gearing does is change how you use it. Do these people really drive everywhere at WOT to the limiter in every gear? If not, and they want lower gearing, why don't they just use_lower_gears ?

[daimlerman]

Bearing in mind the relative lack of torque lowdown on a 320i,3.64 is way to high IMO.
3.91 would be my choice,little effect on acceleration,but a noticable drop in engine speed on the motorway should show a small mpg improvement.

[hongkongfuey]

i have a 325 and do a lot of town driving, the only motorway driving is normally on a meet, otherwise i use the 316

standard it came with a 3.64 diff, i swapped it with a 3.91 as it was the only one they had at the time in the scrappy,
i found that round town and country it felt better as sometimes at 30mph or now 20mph the gearing is now at the middle of the gear instead of being at higher revs on a lower gear or too low on the higher gear.

i have tried 3.73 as well,

as i understand, the final drive ratio is how many turns the prop has to turn to turn the road wheels once,

and speed, can't remember the 3.64, but the 3.73 at 3000rpm was about 300 revs less than the 3.91, probably 500 rpm difference between the 3.64 and 3.91,
so top speed would be lost abit but acceleration would be gained , but i didn't do it for that reason in the first place, but am happy with the setup

[djk]

Bearing in mind the relative lack of torque lowdown on a 320i,3.64 is way to high IMO.
3.91 would be my choice,little effect on acceleration,but a noticable drop in engine speed on the motorway should show a small mpg improvement.

Yeah, I need to do some maths before I get carried away. I was just thinking 3.91:1 isn't very far from 4.1:1, and changing a diff would be a big job for someone of my mechanical experience - I don't want to go changing it and finding that there's little difference. I'm ever mindful of those tall-diffed chromies - really, I'd like to try an early 320i on a tall diff and see what it's like, but my feeling is they were probably alright. I also know StuBeeDoo ran his 320i Touring on a 3.64 for a long time and really liked it. I guess I'll have to suck it and see though, as it's so subject to individual driving styles, not to mention individual expectations.

[hongkongfuey]

djk, i would try a 3.91 or 3.73 but no lower

[daimlerman]

BMW seemed to gear the cars for acceleration,I was suprised to find a 4.45 under the project cabbie! There again,a bit of digging confirmed it left the factory as a 318i auto,but I bet it was very quick off the mark!Need good gearchanging skills around town,though!
Diff swap is not too difficult,bear in mind the things are heavy and require lifting and supporting both in and out,if you drop one on your hand it will hurt....

[f4stjay]

if you drop one on your hand it will hurt....

Speaking from experience perhaps?

Not wanting to play devil's advocate here but I have studied this thread quite carefully (mostly because it is VERY informative and interesting to the various forum geeks, myself included).

One thought has occurred over and over with each post. There are clearly some intelligent and well-informed E30 owners on here; there must be to in order to understand and, moreover, articulate their views and opinions on the physical laws that bind us all. I have; however, noticed that nobody (yet) has taken into account that BMW themselves also employ their own set of "boffins" to discuss exactly this...

Not having studied Physics, in any great detail at least, for the past ten years since leaving school I started a seperate thread to try and reacquaint myself with the various laws and properties governing gearing, differentials and final drive. I believed that the lower the diff ratio the quicker a car would accelerate, when in fact - as willnz so vehemently argued -it would only cause the same car to rev through the entire rev range quicker and not actually get to any given speed quicker.

It is physically impossible to make the same car with a longer diff ratio ACCELERATE faster than the same car with a shorter diff ratio. END OF STORY!!!

Again, playing devil's advocate, does this not beg the question...have the BMW "boffins" perhaps not already had this conversation and concluded that the diffs they have produced their cars with are those best suited to the car they're in from day one?

Case in point: my car left the factory with a 3.91 LSD and so this is the most suitable differential for my car (based on the engine being standard and running a standard gearbox). I had toyed with the idea of putting a lower ratio diff in my car in order to gain better acceleration but surely all other things remaining constant would that not throw other things out of balance? It would seem that (due to the those pesky laws of physics) I couldn't actually make my car go any faster than those clever chaps at BMW designed it to go purely by changing the differential.

Am I correct in assuming this or have I just sealed my status as the forum "chump" for misunderstanding every single point put forward on this thread?

[e301988325i]

The BMW boffins would have achieved the goals they were set, whether I want what the marketing men did is another question. . . Also, your 325i sport has a 3.91 and a shorter 1st 2nd and 3rd gears, my 325i 2dr has a 3.64 from the factory, we've identical engines. Why did BMW make them different? Do see where I'm coming from?

[djk]

Well, that's kind of where I'm coming from - I sort of assume that BMW knew best, but they seemed to play around quite a lot with final drive ratios throughout the e30 production run - hence the various diff options. I've never driven a Sport, but I can imagine the box ratios and 3.91 diff combine better than almost any other stock configuration for most circumstances. Indeed, the Sport gearbox throws up a whole load more discussion, particularly in the light of people like me finding the standard 260 box's ratios to be a bit strangely chosen.

I'm annoyed now that I don't have a .jpg of the final drive chart, that shows exactly which e30s had which diff at which point in the production run. It's been on the forum loads of times, and would be particularly useful here.

One thing I have been thinking since my last post is this: a change in final drive will have less real world effect on 1st than on 5th, so I'm guessing performance in the first three gears is not enormously blunted by a small lowering of the final drive ratio that gives a noticeable improvement in motorway cruising. That is to say, a diff that gives say, a 500rpm drop at 80mph didn't ought to make 1st gear feel enormously different in use, and as the OP and I both feel first is too short, any change in usability, for us, ought to be for the better.

I'm going to have to get my calculator out. If anyone could save me some searching by posting both the 240 and 260 box's ratios on here, that would be a massive help.

EDIT: Here is the diff chart

http://www.e30zone.net/e30zonewiki/inde ... ferentials

[f4stjay]

The BMW boffins would have achieved the goals they were set, whether I want what the marketing men did is another question. . . Also, your 325i sport has a 3.91 and a shorter 1st 2nd and 3rd gears, my 325i 2dr has a 3.64 from the factory, we've identical engines. Why did BMW make them different? Do see where I'm coming from?

I do indeed see where you're coming from and agree with you in principle. BMW will definately have marketed my car to a different demographic than yours...proving your point that the marketing chaps would have had a significant say in how the cars are set up.

I believe the point of the thread though is that with the same car (technically speaking our cars are not the same as the gearboxes - ratios more than likely although I'm sufficiently 'green' that I'm unable to prove this with hard eveidence - differ) where all other things remain constant, simply changing the diff would not provide any difference as far as acceleration is concerned.

[LuckyP]

Well there’s a bonus ... I arrive home from work to find that some people might actually agree with me!
This thread appears to be moving to the more practical side ”“ this is a good thing since I think the theory side has little new ground to cover.

Just one point I would like to pick up on before we move on though...

djk, the point I made regarding the new revs after an up-shift at a given rpm being the same no matter what the diff ratio is correct, and it is important to the theory that it is correct.
This change in gearing happens irrespective of diff ratio.
For example, shifting from second to third in my E30 changes the gearbox ratio from 2.2:1 to 1.4:1. This drops the engine speed by 37% (1-[1.4/2.2] = 0.37). This percentage is constant as it is defined by the number of teeth on the gear wheels in the gearbox.
No matter what your diff ratio, or your wheel size, or even the engine speed before you changed gear, the revs will always drop by 37%.
This is important to the theory because it results in the engine starting at the same point on the torque curve in the new gear [as the car with the other diff ratio], after changing from second gear at any given engine speed, not just the red line. This means that direct comparisons can be made between the two scenarios.
The only difference the diff ratio makes is to the road speed at the time of the gear shift. Of course, the effect of air resistance slowing the car down more during a shift at a higher speed will have a small effect.

You are certainly not alone though; before I sat down and did the maths, I was of the same opinion as you. In fact it was this little discovery that got me thinking on the whole subject.


Alrighty, I need food before I can type any more drivel...

[StuBeeDoo]

I also know StuBeeDoo ran his 320i Touring on a 3.64 for a long time and really liked it.

I did and you're right - I felt it was a great improvement.
Pre-facelift 320is came with a 3.64 as standard, so I can't see what all the fuss is about.
From a 0-60 point of view, it should have been quicker as it would do over 60 in 2nd - less time wasted on a gear change.
I found that in day-to-day driving with the original 4.27, 1st gear was a waste of time, and an overall 20mph/1000rpm in 5th shocking!
A lot of the overall feel has to do with the torque/power characteristics of the engine as well. When I had the 2.7 fitted to my touring (with the exception of 1st) the car felt as though the ratios in the 'box were a lot closer. It's because the engine pulls much harder from much lower revs.

[johnl320]

I've got a silly tall diff on my M30 conversion a 3.07. Although taller and theoretically slowly on acceleration. It makes my first gear now useable instead of just lighting up the rear and also allows me to cruise at 70mph at just 2436rpm

Surely you can't argue with science, the only way, for example to reach 60mph with a taller diff is by omitting the requirement to carry out as many gear changes.
But you will have to change gear at some point and thats when the shorter diff will reel you in I suppose. Thats my take on it.

I did run a 3.64 on my standard 320i ( it was a 4.10) Purely because of the motorway miles I was doing. Very effective at cutting fuel costs AND ACCELERATION

[djk]

djk, the point I made regarding the new revs after an up-shift at a given rpm being the same no matter what the diff ratio is correct, and it is important to the theory that it is correct.
This change in gearing happens irrespective of diff ratio.
For example, shifting from second to third in my E30 changes the gearbox ratio from 2.2:1 to 1.4:1. This drops the engine speed by 37% (1-[1.4/2.2] = 0.37). This percentage is constant as it is defined by the number of teeth on the gear wheels in the gearbox.
No matter what your diff ratio, or your wheel size, or even the engine speed before you changed gear, the revs will always drop by 37%.

Fair enough, you're right. I was imagining graphs rather than actually thinking of the arithmetic - it's obvious when you think about it, though I did have to write down an imaginary set of ratios and do the maths before I got my brain in gear(excuse the pun)! I really want the gearbox ratios of the 240, 260 and Sport boxes so I can do a table with all the overall gear ratios in each gear with each diff ratio, corresponding to road speed range from say, 1000 - 6000rpm - that way I can see the true differences in each gear with each final drive. I can then use the 'arse dyno' feeling that the 320i's torque curve seems to have steps at both 3000 and 4500 to decide if a final drive change is really what I want.


EDIT: Duh, I've just realised the ratios are in the handbook

[hongkongfuey]

i think at the end of the day you can look at charts and numbers all day long, the thing is it's not going to matter utill you try one. If you put in a longer one you could say its great, but so could a shorter one too. And unless you plan to race your car ??? The other thing to look at is is your diff broken?? Is your gearbox tight, have you changed oils ,done a service lately, wheel bearings good? Lightened flywheel? Then engine mods bbtb,fiters,ecu(chip) etc. I'm not being pissy about this i just think basically its now all been said about diffs ???