Acceleration Mods - What to expect?

[BTZ461]

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.

Do it

[Vanne]

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?

[just-right]

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.

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.

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

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?

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

[beanie]

Do it

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

[just-right]

Do it

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

And all that brass would make you loose acceleration

[beanie]

And all that brass would make you loose acceleration

It’s a lose lose situation

[Aulday]

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.

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.

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

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?

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

For arguments sake, if one adjusted the diff ratio so much that 3rd gear now started where 2nd gear did, and 4th, now where 3rd did, and so on and so forth, so you've shifted the whole transmission such that 1st gear neon doesn't exist. What are the gains?

This is just to help me better understand the benefit. As once the engine is in the power band and you're past 1st gear, wheel hp should be roughly the same there after?

I have a 2004 2.5i, I'm planning on a 75 NOS install (if insurance isn't too bad). Then thought how about the diff, but then the fact of wheel HP remaining the same makes, me wonder 'how' the car could be any quicker. Or is this just a more convenient place to have the gear changes for spirited driving?

[Aulday]

Or is it because it technically shortens the gear ratios relatively, and makes for use of a tighter RPM-powerband?

[Smartbear]

Or is it because it technically shortens the gear ratios relatively, and makes for use of a tighter RPM-powerband?

Lowering the gearing increases the torque at the wheels
Rob

[Aulday]

Or is it because it technically shortens the gear ratios relatively, and makes for use of a tighter RPM-powerband?

Lowering the gearing increases the torque at the wheels
Rob

But at lower wheel RPMs, so same wheel HP.

Basically the new found wheel torque you now have at the beginning of 3rd, is wheel torque you had previously at the end of 2nd, and at the same wheel RPM. So I don't quite understand the logic.

[Smartbear]

Or is it because it technically shortens the gear ratios relatively, and makes for use of a tighter RPM-powerband?

Lowering the gearing increases the torque at the wheels
Rob

But at lower wheel RPMs, so same wheel HP.

Basically the new found wheel torque you now have at the beginning of 3rd, is wheel torque you had previously at the end of 2nd, and at the same wheel RPM. So I don't quite understand the logic.

If you accelerate side by side against an otherwise identical car, the car with the lower gearing will beat it.
Rob

[Vanne]

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.

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.

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

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?

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

I appreciate the response and the trouble you went through to try to explain it to an old sea dog like myself.

Thank you.

Just shows you that there is always something left to learn.

[Aulday]

Lowering the gearing increases the torque at the wheels
Rob

But at lower wheel RPMs, so same wheel HP.

Basically the new found wheel torque you now have at the beginning of 3rd, is wheel torque you had previously at the end of 2nd, and at the same wheel RPM. So I don't quite understand the logic.

If you accelerate side by side against an otherwise identical car, thcar with the lower gearing will beat it.
Rob

I can imagine this being true from the stand still in 1st gear. But I don't make sense of it once you change gear. The lower geared car will be changing slightly sooner, but ending each gear at a slightly slower speed. I must be wrong here but it makes no logical sense.

Say if two cars with different ratios did a 3rd gear pull side by side, the lower geared car pulls ahead momentarily as it's at higher rpm and thus more HP, then it changes to 4th and accelerates more slowly, meanwhile the other car is at the top of 3rd so catches up, and so on and so forth.

I must be wrong somehow, but my brain doesn't like the logic

[Aulday]

Well, if it makes a big difference I want to do it What's the average cost on a 2004 2.5i?

[Aulday]

Perfectly explained, different ratio'd cars will hit different speeds first, so I think it's staggered like I was imagining: https://youtu.be/DHhY_z1bYA4?t=121