BMW M3 M4 RPM Redline Visual, Finally

[CanAutM3]

Originally Posted by catpat8000

Changing wheel radius changes inertial loss in every gear. So I don't see how wheel radius affects shift point from this formula.

If you calculated F in gear 2 at an rpm in which F was higher than in gear 3 at the same velocity, it would all still be true with larger wheels. i.e. the propulsive force in a given gear would drop when increasing Iw but it would drop in all gears and by an amount which kept the optimal shift point constant.

Inertial loss is proportional to the acceleration of the car. Changing the wheel radius is like changing gears. For a given whell inertia, a bigger wheel radius will result in lower acceleration and lower inertial loss in the overall drivetrain.

[catpat8000]

Originally Posted by CanAutM3

Inertial loss is proportional to the acceleration of the car. Changing the wheel radius is like changing gears. For a given whell inertia, a bigger wheel radius will result in lower acceleration and lower inertial loss in the overall drivetrain.

It doesn't make sense to me to say "for a given inertia". A larger radius will produce a larger inertia unless you change the material of the wheel.

My main point is that at the output shaft of the transmission, there is a certain amount of torque present at every rpm in every gear. The affect this has on the car can be altered by changing aspects of the car not related to the engine or transmission. But you can't alter the torque available at the output shaft by altering aspects of the car not related to the engine, like changing wheel size. How does the engine or transmission know to alter the torque available in a specific gear at a specific rpm when the wheels change? It doesn't, this question makes no sense. That's why it can't affect shift points.

So back to my question. Assume a specific torque available at the transmission output at an rpm in gear 2. Assume further that there is a lower torque value available in gear 3 at the same velocity. Obviously you want to keep the car in gear 2 until either you hit redline or the torque relationship changes.

Now do the same experiment with larger wheels. Neither value of torque output at the transmission output changes. So why would you shift earlier? If you did shift earlier, you'd see lower torque out of the transmission with more inertia present from the wheels. The car would be even slower to accelerate.

[CanAutM3]

Originally Posted by catpat8000

Yes, I quite agree. And this will be equally true in every gear

Not quite, since the inertial loss in the engine varies with the square of the gear ratio, the loss is not the same in every gear.

Originally Posted by catpat8000

so therefore won't affect shift points.

I am still on the fence if it has an impact on the optimal shift points though. Intuitively, I don't think it does. But I am not able to demontrate it mathematically...

[catpat8000]

Originally Posted by CanAutM3

Not quite, since the inertial loss in the engine varies with the square of the gear ratio, the loss is not the same in every gear.


I am still on the fence if it has an impact on the optimal shift points though. Intuitively, I don't think it does. But I am not able to demontrate it mathematically...

I originally mis-read what you posted and responded to something I thought you said but didn't. I have since changed the post to which you refer above. Pls re-read and see if you agree.

The experiment I understand us to be running is to test whether changing wheel size, and thereby increasing inertial loss due to increased wheel size, changes optimal shift points. So when I am talking about changing the inertial loss, as above, I mean the loss due to changing wheels, which does not change with transmission gear ratio.

Pat

[catpat8000]

Originally Posted by CanAutM3

I am still on the fence if it has an impact on the optimal shift points though. Intuitively, I don't think it does. But I am not able to demontrate it mathematically...

OK, I thought about this on the way to work and I've changed my tune. Now I think swamp2 is correct.

Here is how I thought about it: when you change the wheel size on a car, all other things being equal, you'll change the rate of acceleration. When the car's acceleration changes, the rpm acceleration of the engine and transmission reciprocating mass changes. Therefore the inertial loss in the engine and tranny changes and these changes are not constant per gear. The loss is higher in lower (numerical) gears.

Therefore you can affect output power by changing the car's acceleration which means you can affect shift points.

The total power produced by the engine doesn't change but more of it is lost to accelerating the engine and transmission internals when the car accelerates harder.

And when I think back to the discussion, this is what swamp2 has been saying all along. So thanks swamp2, I learned something today that I never knew before!

Pat

[swamp2]

CanAutM3: One major problem with your attachment with the math is the following: We are discussing two hypothetical vehicles identical except for Iw thus minimally you need Iw1 and Iw2 and they are not equal.

Also in regards to your statement,

"While I underestimated the impact of drivetrain inertia on optimal shift points, I still think that Cartest overestimates the impact by using the mass factor rather than the actual inertia."

CarTest, according to direct correspondence with the author, does not use mass factors. The software makes the assumption that all cars have the same I's for various drivetrain components and explicitly calculates the inertial terms. Although this assumption clearly is not strictly correct, it certainly appears to be a suitable approximation so as not to cause significant errors in its predictive capability. However, in the other extreme, the error of entirely leaving out the inertial terms, is very significant. Again for a car like the M3, easily equal to 20% of a cars weight in 1st gear.

[CanAutM3]

Originally Posted by swamp2

CanAutM3: One major problem with your attachment with the math is the following: We are discussing two hypothetical vehicles identical except for Iw thus minimally you need Iw1 and Iw2 and they are not equal.

Please have another look at the math, I still believe it is sound. The math is to find the optimal shift point for a given hypothetical vehicle; solving for the intersection point between two "tractive force" equations. It is not to compare two different vehicle conditions. Since the wheels are not changed during a gear change, Iw in a given gear equals Iw in the next gear, hence Iw1=Iw2.

As I stated in my post, acceleration is still part of the equation though; and acceleration varies with Iw. So I concede that shift points will vary with wheel inertia. But it also implies shift points would vary depending on mass, incline, towing, etc... Which is becoming much more complex than I anticipated.

Next step for me is to introduce the equation of acceleration in the formula and see where I can reduce it to... just need to find some free time to doodle more with the math

Originally Posted by swamp2

Also in regards to your statement,

"While I underestimated the impact of drivetrain inertia on optimal shift points, I still think that Cartest overestimates the impact by using the mass factor rather than the actual inertia."

CarTest, according to direct correspondence with the author, does not use mass factors. The software makes the assumption that all cars have the same I's for various drivetrain components and explicitly calculates the inertial terms.

Thanks for this clarification. I should not speculate on CarTest without seeing the code. From here though, it should be an easy step for the author of CarTest to add the various moments of inertia as input parameters. This could make the software even more powerful.

Any clue if CarTest uses fixed values of I or values of I that are proportional to the weight of the car?

Originally Posted by swamp2

Although this assumption clearly is not strictly correct, it certainly appears to be a suitable approximation so as not to cause significant errors in its predictive capability. However, in the other extreme, the error of entirely leaving out the inertial terms, is very significant. Again for a car like the M3, easily equal to 20% of a cars weight in 1st gear.

While I agree that the impact is significant in the lower gears, it is much less so in the higher gears. I figure about a 4% difference in torque for the 3-4 shift and less than 1% for the 6 to 7 shift.

Most (not to say all) of the shift point calculations I have made in the past always yielded very obvious red line shifts in the lower gear. Since the error is much smaller in the higher gears, despite my calculations being off, they were close enough not to see a difference in real life. This is most likely why I never realized my error of ignoring engine inertia.

I am still confused as to why CarTest comes up with very similar shift points (7200RPM) in all gears in the simulation in post #195. If the impact of engine inertia gets lower in the higher gears, shouldn't the shift points be progressively closer to red line with higher gears (equal ratio between ratios here)?

If I can understand it properly, I could recalculate gear ratios that would yield redline shifts while optimizing the power plateau. Which is where this whole discussion started .

[swamp2]

Originally Posted by CanAutM3

Please have another look at the math, I still believe it is sound.
...
So I concede that shift points will vary with wheel inertia.

I do not see at all how these statements are consistent.

Originally Posted by CanAutM3

Any clue if CarTest uses fixed values of I or values of I that are proportional to the weight of the car?

Except for an option to vary the wheel weight, it uses fixed I's for various drivetrain components. Not a great approximation. I would better guess these might scale well with the vehicles peak torque rather than vehicle weight.

However, this may have been the simplest approximation that was still able to yield small errors and suitable accuracy. I can't say I've worked through this enough to be certain of it. I don't have access to the source code.

Originally Posted by CanAutM3

While I agree that the impact is significant in the lower gears, it is much less so in the higher gears. I figure about a 4% difference in torque for the 3-4 shift and less than 1% for the 6 to 7 shift.

If using a mass factor approach I have reasonable evidence that in the E92 M3 in the M-DCT in 7th gear the mass factor is still as large as 5-10%. So I'm not quite sure what you mean but "difference in torque" again the mass factor is how much heavier the vehicle must be to account for drivetrain interia.

Originally Posted by CanAutM3

If I can understand it properly, I could recalculate gear ratios that would yield redline shifts while optimizing the power plateau. Which is where this whole discussion started .

Knock yourself out, BMW does not care about making cars that require redline shifts in each gear and thus such ratios are not going to see production .

[pkimM3r]

Short shifting would be boring as hell though. At least within 100s of revolutions to redline. Not 1000s.

[swamp2]

Originally Posted by pkim1079

Short shifting would be boring as hell though. At least within 100s of revolutions to redline. Not 1000s.

Pretty much the point I (and others) have been making here. A very direct consequence of BMW Ms new path with turbo charged engines is rapidly falling torque above a relatively low rpm threshold. This leads to (IMHO) a considerably less frenetic and exciting engine character due to the combination of a lower redline and even lower shift points because redline shifts are not required in all gears to extract maximum performance.

[solstice]

Originally Posted by swamp2

Pretty much the point I (and others) have been making here. A very direct consequence of BMW Ms new path with turbo charged engines is rapidly falling torque above a relatively low rpm threshold. This leads to (IMHO) a considerably less frenetic and exciting engine character due to the combination of a lower redline and even lower shift points because redline shifts are not required in all gears to extract maximum performance.

+1

The power delivery of the S55 seems to be very close to most modern turbo engines. More specific the curves and power levels seems very close to the N63. The N63 has a lot of power and able to propel the 550s, 650 and even the 750 with gusto but what it's not IMO is an exciting engine. I drove several 650s ( GC, Coupe, Vert, rwds and Xis) and 750s ( 750i and 750 il ) on track and drag strip. While strong there is definately turbo lag and the engine feel like it's losing breath above 5500 rpm. You can go very fast, smooth and effortless but there is no traditional race character to it at all. The power is undeniable though if that's the main concern, I put down a 13.3s at 109.55 mph strip time with the 750iL, just flooring it from idle rpms. This power in a 3500 lbs car with some M fairy dust should make for quite a beast, but will it be nearly as exciting, responsive and predictable as the S65, cause the N63 sure isn't even in the same realm. We'll see.

[pkimM3r]

Originally Posted by solstice

+1

The power delivery of the S55 seems to be very close to most modern turbo engines. More specific the curves and power levels seems very close to the N63. The N63 has a lot of power and able to propel the 550s, 650 and even the 750 with gusto but what it's not IMO is an exciting engine. I drove several 650s ( GC, Coupe, Vert, rwds and Xis) and 750s ( 750i and 750 il ) on track and drag strip. While strong there is definately turbo lag and the engine feel like it's losing breath above 5500 rpm. You can go very fast, smooth and effortless but there is no traditional race character to it at all. The power is undeniable though if that's the main concern, I put down a 13.3s at 109.55 mph strip time with the 750iL, just flooring it from idle rpms. This power in a 3500 lbs car with some M fairy dust should make for quite a beast, but will it be nearly as exciting, responsive and predictable as the S65, cause the N63 sure isn't even in the same realm. We'll see.

yes, this sucks...but since M listens to its customers, and 99% aren't on these forums and are complaining about certain things which would sacrifice some of the things we love about the current car, we will get the short end of the stick. Im hoping though that overall, the car will be great...i really really hope the lag in throttle response has been 99% addressed.....i keep watching reviews on the m5/6 and its always "throttle response is great given that its a turbo".....wtf does that mean?! I wish Chris Harris would have just said that it was either responsive or just plain ole crap, not something in the middle. I've asked some of the 1m guys on 1addicts and they have honestly said that it does lag.

[solstice]

Originally Posted by pkim1079

yes, this sucks...but since M listens to its customers, and 99% aren't on these forums and are complaining about certain things which would sacrifice some of the things we love about the current car, we will get the short end of the stick. Im hoping though that overall, the car will be great...i really really hope the lag in throttle response has been 99% addressed.....i keep watching reviews on the m5/6 and its always "throttle response is great given that its a turbo".....wtf does that mean?! I wish Chris Harris would have just said that it was either responsive or just plain ole crap, not something in the middle. I've asked some of the 1m guys on 1addicts and they have honestly said that it does lag.

At the same track event I also drove the M6 GC, Coupe and Vert. The throttle response is much better than in the N63 but it's not nearly as good as the S65. Is it acceptable, yes I think so but it's not enough to make the S63TU as exciting as the S65 even if it has wayyyyy more power. It really shows that at this power levels it's more important how power is delivered than how much. I'd be slightly disappointed if the character of the S55 resembles that of the S63TU but if the rest of the car is top notch and everything works together with usual M3 perfection it can still be a very, very nice car.

[pkimM3r]

And that is without any special electronic gizardry right? So hopefully itll be that much better.

I also hope you wont have to be in "sport plus" mode so to only have no laggy response only when its an on/off throttle. Guess ill have to start adapting now. Sport plus throttle settings at the next track day. Im gonna give it a go. My heel toe will be WAY off for a while

[hotsoup]

Honestly, I feel there are just too many variables when you try to theoretically, accurately model the acceleration of the car over the course of several gear shifts. I am curious about the approximations and assumptions made from user input parameters, and differential equations used in their (CarTest's) numerical method (assuming they're using something like Runge-Kutta to solve the ODEs). Also would like to see the differences between the experimental and theoretical data. I'm no mechanical engineer (chemical engineer), but off the top of my head there are a crazy amount of not-so-insignificant variables besides gear ratios, torque specs, and horsepower - there's drivetrain losses as a function of angular velocity, anti-parallel drag forces as a function of velocity, static coefficient of friction of the tire rubber, normal (down)forces as a function of velocity, etc.

To achieve what we want (find optimal shift points), it might be best to go with empirical data (as another person has mentioned in this thread) which would be much more reliable, accurate, and easy to gather. I imagine something like CarTest (or any other simulation engine) would be better if one were planning to build out an engine without having one handy in order to make some design decisions before committing on specs/parts. If you have the car you want to get optimal shift points for on hand, I'd try plotting acceleration (g's on a straightaway) vs speed, assuming you are at full throttle when testing. Get the curves for each gear. There are many methods to get them, but ultimately you'll want a curve for each gear that starts at the lower speed end and the upper speed end of that gear (again, you must create these curves at full throttle). Qualitatively, the curves should look like concave down parabolas, with each successive gear producing a similar parabola shifted to the right of the previous gear's curve. Since the end goal of optimal shift points is... well, going as fast as possible in the shortest period of time, that translates to the goal of maximizing the area under the acceleration vs. speed curves. In order to do this, we travel along the curve of first gear until we hit the intersection of the first gear curve and the second gear curve. You can then either note the speed for this intersection point and decide to shift at this speed, or back-calculate using gear ratios and tire radius to get the RPM you need to shift at. Then repeat this for the next shift point, and so on. No need for crazy models and is lightweight-enough for the average person to pull off with a smartphone app and a bluetooth OBD connection.

I could also be completely wrong with all this. Thought it would be a nice thought experiment to distract me from consulting.

Note: I chose speed as the independent variable because if you know the gear (and gear ratio) and assuming full throttle, it directly determines a wide number of factors such as engine RPM, torque, drag forces, etc.

[turbolag]

Originally Posted by pkim1079

And that is without any special electronic gizardry right? So hopefully itll be that much better.

I also hope you wont have to be in "sport plus" mode so to only have no laggy response only when its an on/off throttle. Guess ill have to start adapting now. Sport plus throttle settings at the next track day. Im gonna give it a go. My heel toe will be WAY off for a while

DCT is the answer.

[CanAutM3]

Originally Posted by hotsoup

Honestly, I feel there are just too many variables when you try to theoretically, accurately model the acceleration of the car over the course of several gear shifts. I am curious about the approximations and assumptions made from user input parameters, and differential equations used in their (CarTest's) numerical method (assuming they're using something like Runge-Kutta to solve the ODEs). Also would like to see the differences between the experimental and theoretical data. I'm no mechanical engineer (chemical engineer), but off the top of my head there are a crazy amount of not-so-insignificant variables besides gear ratios, torque specs, and horsepower - there's drivetrain losses as a function of angular velocity, anti-parallel drag forces as a function of velocity, static coefficient of friction of the tire rubber, normal (down)forces as a function of velocity, etc.

To achieve what we want (find optimal shift points), it might be best to go with empirical data (as another person has mentioned in this thread) which would be much more reliable, accurate, and easy to gather. I imagine something like CarTest (or any other simulation engine) would be better if one were planning to build out an engine without having one handy in order to make some design decisions before committing on specs/parts. If you have the car you want to get optimal shift points for on hand, I'd try plotting acceleration (g's on a straightaway) vs speed, assuming you are at full throttle when testing. Get the curves for each gear. There are many methods to get them, but ultimately you'll want a curve for each gear that starts at the lower speed end and the upper speed end of that gear (again, you must create these curves at full throttle). Qualitatively, the curves should look like concave down parabolas, with each successive gear producing a similar parabola shifted to the right of the previous gear's curve. Since the end goal of optimal shift points is... well, going as fast as possible in the shortest period of time, that translates to the goal of maximizing the area under the acceleration vs. speed curves. In order to do this, we travel along the curve of first gear until we hit the intersection of the first gear curve and the second gear curve. You can then either note the speed for this intersection point and decide to shift at this speed, or back-calculate using gear ratios and tire radius to get the RPM you need to shift at. Then repeat this for the next shift point, and so on. No need for crazy models and is lightweight-enough for the average person to pull off with a smartphone app and a bluetooth OBD connection.

I could also be completely wrong with all this. Thought it would be a nice thought experiment to distract me from consulting.

Note: I chose speed as the independent variable because if you know the gear (and gear ratio) and assuming full throttle, it directly determines a wide number of factors such as engine RPM, torque, drag forces, etc.

Yes, in principle obtaining the acceleration curve in each gear via an empirical method would work. The caveat is that real world testing often includes variables that are not always easy to control. Ask me how I know (I am an aerospace engineer that spent most of his professional career on real world testing). For accurate results, multiple runs would need to be done and the results averaged once the outliers are eliminated. This can be quite tedious.

The combination of real world test data combined with analytical models usually yields the most valuable results. Plus, it's also fun to play with the numbers. It allows one to better understand what happens in the real world .

[Never Convicted]

Originally Posted by hotsoup

Honestly, I feel there are just too many variables when you try to theoretically, accurately model the acceleration of the car over the course of several gear shifts. I am curious about the approximations and assumptions made from user input parameters, and differential equations used in their (CarTest's) numerical method (assuming they're using something like Runge-Kutta to solve the ODEs). Also would like to see the differences between the experimental and theoretical data. I'm no mechanical engineer (chemical engineer), but off the top of my head there are a crazy amount of not-so-insignificant variables besides gear ratios, torque specs, and horsepower - there's drivetrain losses as a function of angular velocity, anti-parallel drag forces as a function of velocity, static coefficient of friction of the tire rubber, normal (down)forces as a function of velocity, etc.

To achieve what we want (find optimal shift points), it might be best to go with empirical data (as another person has mentioned in this thread) which would be much more reliable, accurate, and easy to gather. I imagine something like CarTest (or any other simulation engine) would be better if one were planning to build out an engine without having one handy in order to make some design decisions before committing on specs/parts. If you have the car you want to get optimal shift points for on hand, I'd try plotting acceleration (g's on a straightaway) vs speed, assuming you are at full throttle when testing. Get the curves for each gear. There are many methods to get them, but ultimately you'll want a curve for each gear that starts at the lower speed end and the upper speed end of that gear (again, you must create these curves at full throttle). Qualitatively, the curves should look like concave down parabolas, with each successive gear producing a similar parabola shifted to the right of the previous gear's curve. Since the end goal of optimal shift points is... well, going as fast as possible in the shortest period of time, that translates to the goal of maximizing the area under the acceleration vs. speed curves. In order to do this, we travel along the curve of first gear until we hit the intersection of the first gear curve and the second gear curve. You can then either note the speed for this intersection point and decide to shift at this speed, or back-calculate using gear ratios and tire radius to get the RPM you need to shift at. Then repeat this for the next shift point, and so on. No need for crazy models and is lightweight-enough for the average person to pull off with a smartphone app and a bluetooth OBD connection.

I could also be completely wrong with all this. Thought it would be a nice thought experiment to distract me from consulting.

Note: I chose speed as the independent variable because if you know the gear (and gear ratio) and assuming full throttle, it directly determines a wide number of factors such as engine RPM, torque, drag forces, etc.

Over/under on how many errors Swamp finds in this is 7. Place your bets.

[catpat8000]

Originally Posted by Never Convicted

Over/under on how many errors Swamp finds in this is 7. Place your bets.

I've used CarTest a lot in the past to model some mods I did to a C6 corvette I used to own and I found it to be pretty accurate, once all the parameters were accurate. I don't think we know all the M3/M4 variables we need to know yet.

I also think the accuracy depends what you are trying to model. If all you want are 1/4 mile trap speeds and ETs, I think CarTest does this well. Yes there are lots of variable but their contribution to the final result varies significantly.

In my view, Swamp knows what he is talking about and I have familiarity with the tool so I have some confidence in the results.

[pkimM3r]

Originally Posted by turbolag

DCT is the answer.

that is of absolutely no help.....you know DCT has nothing to do with the gas pedal!!

[CanAutM3]

Originally Posted by swamp2

I do not see at all how these statements are consistent.

I don't see why not.

The outcome equation (quoted below) for optimal shift points is mathematically valid. It indicates that when torque at the transmission output minus the inertia loss in the engine and transmission are equal in both gears, it is the optimal shift point.

Since the inertia losses are proportional to acceleration, Iw has an impact of optimal shift points. And so does vehicle mass, road slope, wind direction, etc... which is something I never anticipated.

Originally Posted by swamp2

If using a mass factor approach I have reasonable evidence that in the E92 M3 in the M-DCT in 7th gear the mass factor is still as large as 5-10%. So I'm not quite sure what you mean but "difference in torque" again the mass factor is how much heavier the vehicle must be to account for drivetrain interia.

When establishing shift points, IMO, it is the relative change of equivalent mass between the gears that needs to be considered, not the absolute value.

Using Gillespie's blunt approximation formula for mass factor on a DCT E9X M3, we would have a mass factor of 1.076 in 6th and 1.065 in 7th. Therefore, the drivetrain has 1% less equivalent mass to accelerate in 7th compared to 6th. Hence the 1% error (the actual error is most likely even lower than that).

The "difference in torque" I am referring to is the torque consumed by the engine inertia in one gear compared to the torque consumed by the engine inertia in the other gear.

Originally Posted by swamp2

Knock yourself out, BMW does not care about making cars that require redline shifts in each gear and thus such ratios are not going to see production .

Agreed, it will most likely never see production. Playing with the math does help one to better understand and learn though; like I did on the ramifications of inertia right here .

BTW, thanks for entertaining the discussion in this thread, it is much appreciated on my part. There are not that many people out there that have the ability to dive in such details

Still no thoughts as to why CarTest has shift points around 7200RPM in all gears for the simulation in post #195?

[Kadema]

Also thanks for this discussion, although unfortunately I'm not able to contribute much by myself, but I do enjoy reading!

IMHO, BMW might care a little more about (near) redline shifts this time, or at least they should, because afaik this is their first turbo engine that has a power plateau ending just about 100-200 rpm before the red line.