Acceleration Mods - What to expect?

I have been looking at a few performance mods for the M. I have wondered what kind of change could be expected in acceleration time. Considering last week’s bad weather I had some time to write a little program that simulates a Z4M in acceleration all the way up to top speed. I thought some of you might be interested in the results.

In OEM spec the figures are not too far off real life data (). They would be pretty close accounting for shifting:
0 – 100 kph : 4.91s (4.9 – 5.0)
0 – 200 kph : 16.73s (17.0)
400 m : 13.06s (13.2)
1000 m : 23.51s
Vmax : 281.1 kph
Max g : 0.63

First look is at different final drive ratios, comparing the stock 3.62 (Blue) to 3.91 (Red) and 4.1 (Green). A shorter final drive is a bit quicker across the board and helps top speed as well by being closer to max power.
0 – 100 kph : 4.91s -> 4.82s -> 4.81s
0 – 200 kph : 16.73s -> 16.46s -> 16.34s
Vmax : 281.1 kph -> 284.5 -> 285.4 redlining 6th gear



First gear acceleration is similar to stock as you are grip limited (dotted line). Acceleration after that is slightly better for the shorter final drive ratios when you are in the same gear and drops off where the gears are offset (i.e. 3rd gear on 4.1 and 2nd on 3.62 ratio). The time delta and the delta of longitudinal tyre force shows this behaviour and their relationship quite well.





The original gear and final drive ratios would theoretically allow a top speed of over 300 kph. The OEM 6th gear and final drive combination is mainly chosen to keep the cruising RPM and fuel consumption a bit lower. The RPM drop is defined by the gearbox ratios and therefore do not change.



Overall, shortening the final drive looks like a pretty solid step. I will have a look at some other options, like increased power and weight reduction.

IMO the only real S54 choice for a noticeable S54 acceleration upgrade is Nos or a Supercharger, though not for me.

Otherwise a cheaper(ish) alternative to slightly changing the drive ratios is also to use 19” rims with 30 profile 265x19 tyres, as the rolling circumference is smaller than 255x35x19 or the standard 255x40x18

Jembo said:

IMO the only real S54 choice for a noticeable S54 acceleration upgrade is Nos or a Supercharger, though not for me.

Otherwise a cheaper(ish) alternative to slightly changing the drive ratios is also to use 19” rims with 30 profile 265x19 tyres, as the rolling circumference is smaller than 255x35x19 or the standard 255x40x18

Click to expand...

Going to 19”s might not help so much as the wheels are generally heavier than 18”s and can slow acceleration because of this :?
Rob

Smartbear said:

Jembo said:

IMO the only real S54 choice for a noticeable S54 acceleration upgrade is Nos or a Supercharger, though not for me.

Otherwise a cheaper(ish) alternative to slightly changing the drive ratios is also to use 19” rims with 30 profile 265x19 tyres, as the rolling circumference is smaller than 255x35x19 or the standard 255x40x18

Click to expand...

Going to 19”s might not help so much as the wheels are generally heavier than 18”s and can slow acceleration because of this :?
Rob

Click to expand...

I’d normally agreed with this had I not found the 19” CSL’s i put on are lighter than the OEM 224 18”

Grip limited in first gear? Sticky tyres will sort that. Though your drivetrain wont last as long. And less weight will definitely help, simple force = mass x acceleration.

Weight is the key. Z4M is a bit of lard a#se. Start with a Caterham and modify that. :wink:

Shorter gearing? I’d like it longer if anything!

I think on the road it'll make a massive difference as most of the time you're in 3rd on a nice b road, and the top of 3rd is very illegal as standard.

buzyg said:

Weight is the key. Z4M is a bit of lard a#se. Start with a Caterham and modify that. :wink:

Click to expand...

Best weight reduction I've done with my M is lose 3 stones myself :rofl:

Argenta said:

I’d like it longer if anything!

Click to expand...

Wouldn't we all? :? :lol:

Ha!

You walked straight into that one Argenta! :lol: I think slightly shorter gearing, especially in 3rd gear could be quite nice on some winding B-roads. The time from 100 to 150 kph is not far of 5% quicker.

Damn that old Newton dude: more power less weight, simples. I had a quick look at some weight sensitivities, removing 20 kg (Red) and 20 kg from the rotational assembly (Green)

0 – 100 kph : 4.91s -> 4.87s -> 4.86s
0 – 200 kph : 16.73s -> 16.54s -> 16.48s

The acceleration time deltas are not ground breaking, as will be the case with a lot of the parameters in relatively small quantities. Now if we were to remove 200 kg (Red) you can expect a decent improvement.

0 – 100 kph : 4.91s -> 4.59s
0 – 200 kph : 16.73s -> 14.86s

Obviously around a race track a 20 kg weight reduction in braking and cornering in addition to the acceleration benefits will easily yield a few tenths a lap.

Adding some good old power this time in the form of a uniform 20Nm increase (Red) at any rpm and the fitment of a ESS VT2-525 supercharger (Green) The 20 Nm increase results in about 22 hp at peak rpm.

0 – 100 kph : 4.91s -> 4.79s -> 4.46s
0 – 200 kph : 16.73s -> 15.76s -> 12.24s

Hitting 525 crank HP is not too bad 8) You should theoretically be able to hit the rev limiter in 6th gear as well.

just-right said:

Hitting 525 crank HP is not too bad 8) You should theoretically be able to hit the rev limiter in 6th gear as well.

Click to expand...

Only if we assume you also remove the software-controlled 6th gear speed limiter, otherwise more power will simply get you to that limiter faster - and your VMAX will still be in 5th gear

I think the standard gearing is pretty well judged and looking at the data, it seems I’d be far better off telling the girlfriend to catch the bus and saving her weight and luggage. :lol:

beanie said:

I think the standard gearing is pretty well judged and looking at the data, it seems I’d be far better off telling the girlfriend to catch the bus and saving her weight and luggage. :lol:

Click to expand...

Do it

I think this data is missing the point, no one drops in 4.10 gearing for straight line performance. Lol. It's for coming in and out of turns where this really shines.

Also not sure how you came up with this, but Def not correct..

Vmax : 281.1 kph -> 284.5 -> 285.4

Your getting a higher top speed with 4.1? Maybe you got those figures inversely proportional?

Vanne said:

I think this data is missing the point, no one drops in 4.10 gearing for straight line performance. Lol. It's for coming in and out of turns where this really shines.

Click to expand...

Not quite, as you would have seen I included several graphs with the final drive ratio changes. I didn't add these with power and mass alterations because the effects are more uniform. The graphs are to illustrate the effects throughout the speed range i.e. acceleration out of a corner. Some of the other forum members highlighted the benefits of acceleration in 3rd gear on a nice windy B-road for example. :driving:

Coming out of a given corner you are transitioning from lateral to longitudinal g's and once you are not grip limited the figures and graphs posted are very much valid whether it is pure straight line performance or accelerating between corners (even if it is not exactly straight) Depending on the track it should help people choose the final drive to match the corners

Vanne said:

Also not sure how you came up with this, but Def not correct..

Vmax : 281.1 kph -> 284.5 -> 285.4

Your getting a higher top speed with 4.1? Maybe you got those figures inversely proportional?

Click to expand...

Not quite, the original post states that it is due to operating closer to max power at vmax as the original 6th gear is too long in the interest of cruising rpm and fuel consumption. I'll try and explain.

Power is a function of torque and rpm, so equally torque is a function of power and rpm. To obtain torque at the wheels, the torque from the engine is multiplied by the gear ratio and final drive ratio, i.e. shorter final drive is more torque at the wheels. Then the torque is converted to a longitudinal force at the wheels by the effective rolling radius. There are obviously drive train losses as well.

At top speed there are no acceleration effects so all the resistance is formed by the aerodynamics, tyres and some other smaller contributors. The aerodynamics are dependend on the speed squared and the tyres to a very small effect are also dependent on the speed. The engine is linked to the speed through the aforementioned gear ratios, rolling radius etc.

What you want to do at vmax is be at maximum power. This is where the Z4M fails in its original configuration as we are some ~1000 rpm away from this. By shortening the gear ratio you improve the forces at the wheels two fold, get closer max power and increase the drivetrain torque multiplication.

I understand it can be a bit of a head scratcher and for some cars shortening the gear ratios will not result in the same outcome. I hope the explanation helps

BTZ461 said:

Do it

Click to expand...

If my balls were that big I wouldn’t fit in the car anyway!

beanie said:

BTZ461 said:

Do it

Click to expand...

If my balls were that big I wouldn’t fit in the car anyway!

Click to expand...

And all that brass would make you loose acceleration :rofl: