E90Post
 


 
BMW 3-Series (E90 E92) Forum > BMW E90/E92/E93 3-series General Forums > General E90 Sedan / E91 Wagon / E92 Coupe / E93 Cabrio > Mathematical Performance Model (328i, 335i, M3)



Reply
 
Thread Tools Search this Thread
      09-08-2009, 11:36 PM   #1
dougman
Second Lieutenant
 
dougman's Avatar
 
Drives: '07 E92 328 --> 2010 E92 M3!
Join Date: Apr 2007
Location: Bay Area

Posts: 227
iTrader: (0)

Mathematical Performance Model (328i, 335i, M3)

I used to design vehicles; now I design computers for a living. But since I still love cars I got some of it out of my system this weekend with a simple mathematical model in Excel for our cars. Here's how it works and some of the results:

Vehicle Inputs:
- Vehicle weight
- Drag coefficient and frontal area
- Axle and gear ratios
- Tire size
- Torque curve (one point every 1000 rpm)
- Driveline efficiency
- Weight distribution and cg height
- Max tire friction

And also:
- shift RPM (when to shift)
- shift delay (how long to shift; I used 0.5 s)
- RPM for clutch dump

Then the program calculates the torque to the wheels and corresponding force to accelerate the vehicle, checks to make sure it's not friction limited (and reduces as appropriate). Then it subtracts the forces for aerodynamic losses, figures out the change in velocity, increments the time, and calculates a new torque, and so on...

I did three runs using the data for 328i, 335i, and M3. I adjusted driveline efficiencies slightly (but within reasonable values of 80%-90%) to get close to published data for the vehicles. The model delivered these results:
- 328i: 0-60 in 6.1s; 1/4 mile in 14.6s
- 335i: 0-60 in 4.9s; 1/4 mile in 13.5s
- M3: 0-60 in 4.1s; 1/4 mile in 12.5s

If anyone's interested I provide more info (or maybe I should sell it!). But here are some screenshots:

1) Input sheet and some results for M3:


2) speed vs. time graphs for all three:


3) Acceleration vs. speed for 1st three gears: (red=M3; green=335i; blue=328i)


4) Acceleration vs. speed for gears 4 - 6 (red=M3; green=335i; blue=328i)


Interesting to look at these last graphs and think about how and when the M3 can pull on the 335i. Also, it's interesting to see that you should shift the 335i from 4-5 and 5-6 before redline (when the acceleration graphs cross). The 328i and M3 should be shifted at redline.

Enjoy. I make NO claims as to the veracity of these models; I did them purely for the fun of it.

But I'm happy to run some "what if" analyses--i.e. driveline ratio changes, etc. etc. Could make for some fun "virtual" drag races.
dougman is offline  
0
Reply With Quote
      09-08-2009, 11:45 PM   #2
blue2fire
Brigadier General
 
blue2fire's Avatar
 
Drives: BMW 135i
Join Date: Jan 2009
Location: Location, Location, Location

Posts: 4,289
iTrader: (8)

Very interesting, thank you for taking the time.
__________________

BMW CCA
Member #420568
Quote:
Originally Posted by Gordon Murray View Post
Being a fan of Honda engines, I requested that they consider building for the F1 a 4.5 liter V10 or V12. I asked, I tried to persuade them, but in the end could not convince them to do it, and the McLaren F1 ended up with a BMW engine.
blue2fire is offline   Cayman Islands
0
Reply With Quote
      09-09-2009, 12:02 AM   #3
visor
BMW, can I have some LSD please?
 
visor's Avatar
 
Drives: '13 F30 328xi
Join Date: Jun 2005
Location: Vancouver, Canada

Posts: 1,538
iTrader: (0)

Quote:
Originally Posted by dougman View Post
I used to design vehicles; now I design computers for a living. But since I still love cars I got some of it out of my system this weekend with a simple mathematical model in Excel for our cars. Here's how it works and some of the results:

Vehicle Inputs:
- Vehicle weight
- Drag coefficient and frontal area
- Axle and gear ratios
- Tire size
- Torque curve (one point every 1000 rpm)
- Driveline efficiency
- Weight distribution and cg height
- Max tire friction

And also:
- shift RPM (when to shift)
- shift delay (how long to shift; I used 0.5 s)
- RPM for clutch dump

Then the program calculates the torque to the wheels and corresponding force to accelerate the vehicle, checks to make sure it's not friction limited (and reduces as appropriate). Then it subtracts the forces for aerodynamic losses, figures out the change in velocity, increments the time, and calculates a new torque, and so on...

I did three runs using the data for 328i, 335i, and M3. I adjusted driveline efficiencies slightly (but within reasonable values of 80%-90%) to get close to published data for the vehicles. The model delivered these results:
- 328i: 0-60 in 6.1s; 1/4 mile in 14.6s
- 335i: 0-60 in 4.9s; 1/4 mile in 13.5s
- M3: 0-60 in 4.1s; 1/4 mile in 12.5s

If anyone's interested I provide more info (or maybe I should sell it!). But here are some screenshots:

Interesting to look at these last graphs and think about how and when the M3 can pull on the 335i. Also, it's interesting to see that you should shift the 335i from 4-5 and 5-6 before redline (when the acceleration graphs cross). The 328i and M3 should be shifted at redline.

Enjoy. I make NO claims as to the veracity of these models; I did them purely for the fun of it.

But I'm happy to run some "what if" analyses--i.e. driveline ratio changes, etc. etc. Could make for some fun "virtual" drag races.
Cool exercise!

Yah, with the 335i you don't have to be close to redline to wring out the most power; shifting somewhere just before 6000rpm is good enough. It's because forced induction doesn't work as well at higher rpms, and also because the fat torque curve/plateau from 2000rpm up to 5500rpm.

Whereas the M3 by design has to be wrung out to just short of its 8300rpm redline in order to get the most power.
__________________
2006 330i | TiAg | Black | Al | 6MT | Sports Package | Logic 7 retired
2008 335i | AW | Black | Al | 6MT | Sports Package | Logic 7 retired
2013 328xi | Red | Gray | Al | 8AT | Sports Line | Premium | Executive | Heat Pkg
visor is offline   Canada
0
Reply With Quote
      09-09-2009, 03:15 AM   #4
Gill72
Enlisted Member
 
Gill72's Avatar
 
Drives: 09' 335i xDrive
Join Date: Nov 2008
Location: Expat in Europe

Posts: 32
iTrader: (0)

Interesting. I have driven the BSR in Virginia, but never in a performance car, so I am not a guru in getting the most out of a performance engine.
I have paddle shifters and have not been able to take the BMW drivers course here in Europe, due to the fact they charge a fortune. I have wondered at what points I was supposed to be shifting and I now know that I have been doing it a bit wrong. Once in a while I like to do a quick 0-60 just to remind myself what's under the hood. I will follow your input the next time and shift before 6000 during higher torque and see if it pulls a little stronger.

Thanks for the time you put into this. You may have just improved my appreciation for this engine.

Gill.
Gill72 is offline   Belgium
0
Reply With Quote
      09-09-2009, 10:04 AM   #5
BK
Smiling politely
 
Drives: 330i
Join Date: Feb 2006
Location: Washington DC

Posts: 7,916
iTrader: (0)

Garage List
2006 330i  [4.50]
Very cool thread. This gets my vote for one of the more interesting threads we've had in quite some time. Maybe I'm just a geek for data. It would be cool to add the E90 330i and 325i on there while you are at it.

A bit OT, but your meticulous attention to detail and fluency with computers reminded me of another impressive thread I remembered from years ago. Not the same topic, but another guy with a love for these cars and some computer fluency, doing a CAD model of the E90 based solely on photos he'd seen in brochures and online: http://www.e90post.com/forums/showthread.php?t=10074
__________________


330i | Black Sapphire | Beige + Burl | Sport | Premium | Cold | Nav | CA | Sat prep
BK is offline   United_States
0
Reply With Quote
      09-09-2009, 08:49 PM   #6
dougman
Second Lieutenant
 
dougman's Avatar
 
Drives: '07 E92 328 --> 2010 E92 M3!
Join Date: Apr 2007
Location: Bay Area

Posts: 227
iTrader: (0)

Thanks for the feedback gentlemen.

Any requests for simulations? New axle ratio on the M3? Race on the wet (half friction)? All cars shift at 5000 RPM; does 335i beat M3? Effects of weight reduction programs? Effects of cutting shift time down (i.e. DCT)?

I can run any of these through--while the model may not be spot-on accurate, it should be pretty good at predicting changes in performance.
dougman is offline  
0
Reply With Quote
      09-09-2009, 08:58 PM   #7
Alpine 335i
Banned.....not!
 
Alpine 335i's Avatar
 
Drives: Alpine White 335i Sedan
Join Date: Feb 2008
Location: Bakersfield, Cali

Posts: 1,023
iTrader: (1)

good info indeed.
__________________
JuiceBox3 1.4 Map 5, AR Design CL DPs, BMS Filter, LUX 4.0, 8k HID fogs, Matte Black Grill, Matte Black Badges, Black/White Roundels, Blacklines, Matte Black Finishing Rods, MFD Matte Black Scoops, Amber Overlays, Tinted Sidemarkers, Tinted all around, LED Courtesy Lights
Alpine 335i is offline  
0
Reply With Quote
      09-09-2009, 09:17 PM   #8
lsdless
Private First Class
 
lsdless's Avatar
 
Drives: E92 335i 6MT
Join Date: Jan 2009
Location: Atlanta, GA

Posts: 184
iTrader: (0)

You got some skills.
lsdless is offline   United_States
0
Reply With Quote
      09-09-2009, 09:19 PM   #9
jopa489
BMW/Detailing Addict
 
jopa489's Avatar
 
Drives: Estoril F30 335i 6MT
Join Date: Mar 2009
Location: New England

Posts: 6,561
iTrader: (8)

Wow, awesome information! I love statistics and visuals like these, very cool!

Thanks for taking the time to do this and share with us.

Subscribed for future reference (and in case you add more).
__________________

jopa489 is offline   United_States
0
Reply With Quote
      09-09-2009, 09:26 PM   #10
Prowess Symphony
Major General
 
Prowess Symphony's Avatar
 
Drives: ///Mistress
Join Date: Nov 2008
Location: WV

Posts: 5,860
iTrader: (12)

Garage List
Nice. But would it be hard to add a 335 with a tune to the list. It would be great to see jb+, jb3 and procede all next to eachother on that list.
Prowess Symphony is offline   United_States
0
Reply With Quote
      09-09-2009, 09:29 PM   #11
jeremicium
Captain
 
jeremicium's Avatar
 
Drives: 2009 335i coupe
Join Date: May 2009
Location: Olympia, Wa. USA

Posts: 926
iTrader: (0)

Garage List
i'm so ashamed. When I have rare free time, and a computer is involved, i'm usually looking at porn.

j.k.


kind of.
__________________
09 E92/Montego Blue/Black leather/Dark burl trim/6MT/Premium/Sport/19" Matte Black Avant garde M310 Wheels/Nav/Comfort access/COBB stage 1
jeremicium is offline   United_States
0
Reply With Quote
      09-09-2009, 09:33 PM   #12
blk335i08
Second Lieutenant
 
Drives: 335i e92
Join Date: Nov 2008
Location: usa

Posts: 288
iTrader: (0)

Quote:
Originally Posted by jeremicium View Post
i'm so ashamed. When I have rare free time, and a computer is involved, i'm usually looking at porn.

j.k.


kind of.
haha
blk335i08 is offline  
0
Reply With Quote
      09-09-2009, 09:42 PM   #13
dougman
Second Lieutenant
 
dougman's Avatar
 
Drives: '07 E92 328 --> 2010 E92 M3!
Join Date: Apr 2007
Location: Bay Area

Posts: 227
iTrader: (0)

Quote:
Originally Posted by Prowess Symphony View Post
Nice. But would it be hard to add a 335 with a tune to the list. It would be great to see jb+, jb3 and procede all next to eachother on that list.
Sure. All I need is the torque curve.
dougman is offline  
0
Reply With Quote
      09-09-2009, 09:43 PM   #14
dougman
Second Lieutenant
 
dougman's Avatar
 
Drives: '07 E92 328 --> 2010 E92 M3!
Join Date: Apr 2007
Location: Bay Area

Posts: 227
iTrader: (0)

Quote:
Originally Posted by jeremicium View Post
i'm so ashamed. When I have rare free time, and a computer is involved, i'm usually looking at porn.

j.k.


kind of.

Both are hard-core... Plus I have the joy of 12-hour flights to China every few months...
dougman is offline  
0
Reply With Quote
      09-09-2009, 09:44 PM   #15
Prowess Symphony
Major General
 
Prowess Symphony's Avatar
 
Drives: ///Mistress
Join Date: Nov 2008
Location: WV

Posts: 5,860
iTrader: (12)

Garage List
Quote:
Originally Posted by dougman View Post
Sure. All I need is the torque curve.
Well this could get interesting. Who has the tune torque info?
Prowess Symphony is offline   United_States
0
Reply With Quote
      09-09-2009, 11:25 PM   #16
Kroy
Brigadier General
 
Kroy's Avatar
 
Drives: E90
Join Date: Jul 2009
Location: Los Angeles, CA

Posts: 3,035
iTrader: (1)

That was interesting!
Kroy is offline   United_States
0
Reply With Quote
      09-10-2009, 12:47 AM   #17
jlstyle
Major
 
jlstyle's Avatar
 
Drives: E92 335i
Join Date: Jun 2008
Location: nj

Posts: 1,317
iTrader: (0)

Damn look at that g difference at first gear!!!
I need the facking M!!!!!!!!!!!!!
__________________
09 E92 335i Coupe
Jet Black/Coral Red/Sports Pkg/Prem Pkg/Cold Weather/Navi/PDC/Ipod/6MT
jlstyle is offline  
0
Reply With Quote
      09-10-2009, 01:20 AM   #18
Prowess Symphony
Major General
 
Prowess Symphony's Avatar
 
Drives: ///Mistress
Join Date: Nov 2008
Location: WV

Posts: 5,860
iTrader: (12)

Garage List
Wheres the tuners to give out the necessary info? I wanna see how the tunes stack up against stock and the m3.
Prowess Symphony is offline   United_States
0
Reply With Quote
      09-10-2009, 01:24 AM   #19
lcs
Lieutenant
 
Drives: 328i LCI
Join Date: Apr 2009
Location: GTA

Posts: 520
iTrader: (2)

sticky!!
lcs is offline  
0
Reply With Quote
      09-10-2009, 04:50 AM   #20
Borsig
Captain
 
Borsig's Avatar
 
Drives: '09 335i ///M-Sport
Join Date: Dec 2008
Location: NC

Posts: 883
iTrader: (3)

the minority of us i think are stock with our 335i...

I agree - add tuned 335i and stock 330i to the list.. I used to own a 330i. It was much quicker than the 328.
Borsig is offline   Germany
0
Reply With Quote
      09-10-2009, 08:51 AM   #21
Derek Zoolander
Banned
 
Drives: 09 E90 M-Sport
Join Date: Aug 2009
Location: Nashua, NH

Posts: 1,876
iTrader: (0)

Quote:
Originally Posted by dougman View Post
Also, it's interesting to see that you should shift the 335i from 4-5 and 5-6 before redline (when the acceleration graphs cross). The 328i and M3 should be shifted at redline.
Turbocharged cars make more power/torque in lower RPMs, and taper off to redline. It should be no surprise that you should shift before redline because you're losing power..
Derek Zoolander is offline   United_States
0
Reply With Quote
      09-10-2009, 11:40 AM   #22
bbbuzzy
Lieutenant
 
Drives: '06 330i ZSP,ZPP
Join Date: Mar 2009
Location: north of Boston

Posts: 416
iTrader: (0)

Thanks OP for the great info. A couple ideas for additional comparisons:

e46 M3, manual transmission
e90 330i, manual transmission
__________________
'06 330i MT, sport,premium
'05 XC70 (family truckster)
'05 Sienna XLE LTD AWD (road tripper)
bbbuzzy is offline  
0
Reply With Quote
Reply

Bookmarks

Thread Tools Search this Thread
Search this Thread:

Advanced Search

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Forum Jump


All times are GMT -5. The time now is 09:30 AM.




e90post
Powered by vBulletin® Version 3.7.0
Copyright ©2000 - 2014, Jelsoft Enterprises Ltd.
1Addicts.com, BIMMERPOST.com, E90Post.com, F30Post.com, M3Post.com, ZPost.com, 5Post.com, 6Post.com, 7Post.com, XBimmers.com logo and trademark are properties of BIMMERPOST