Login






BMW Garage  BMW Meets  Register  Search  Today's Posts  Mark Forums Read 

BMW 3Series (E90 E92) Forum
>
Mathematical Performance Model (328i, 335i, M3)


09092009, 12:36 AM  #1 
Second Lieutenant
12
Rep 228
Posts 
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: 060 in 6.1s; 1/4 mile in 14.6s  335i: 060 in 4.9s; 1/4 mile in 13.5s  M3: 060 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 45 and 56 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" analysesi.e. driveline ratio changes, etc. etc. Could make for some fun "virtual" drag races. 
09092009, 01:02 AM  #3  
BMW, can I have some LSD please?
46
Rep 1,564
Posts 
Quote:
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 

Appreciate
0

09092009, 04:15 AM  #4 
Enlisted Member
4
Rep 32
Posts 
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 060 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. 
Appreciate
0

09092009, 11:04 AM  #5 
Smiling politely
108
Rep 7,933
Posts 
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 
Appreciate
0

09092009, 09:49 PM  #6 
Second Lieutenant
12
Rep 228
Posts 
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 throughwhile the model may not be spoton accurate, it should be pretty good at predicting changes in performance. 
Appreciate
0

09092009, 09:58 PM  #7 
Banned.....not!
16
Rep 1,023
Posts 
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

Appreciate
0

09092009, 10:19 PM  #9 
BMW/Detailing Addict
74
Rep 6,562
Posts 
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).
__________________
'15 i3 REX // Capparis // ZGW // ZTD // HK // 20"
20% Tint, Coding, LED High Beams/Signals, Painted Reflectors, MAX2 Hardwire Past: F30 335i, E90 328xi 
Appreciate
0

09092009, 10:26 PM  #10 
Major General
149
Rep 5,891
Posts
Drives: ///Mistress
Join Date: Nov 2008
Location: WV

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.
__________________

Appreciate
0

09092009, 10:29 PM  #11 
Major
79
Rep 1,162
Posts 
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.
__________________
2016 SO/SO three pedal M4

Appreciate
0

09092009, 10:42 PM  #13 
Second Lieutenant
12
Rep 228
Posts 

Appreciate
0

09092009, 10:43 PM  #14 
Second Lieutenant
12
Rep 228
Posts 

Appreciate
0

09092009, 10:44 PM  #15 
Major General
149
Rep 5,891
Posts
Drives: ///Mistress
Join Date: Nov 2008
Location: WV

Well this could get interesting. Who has the tune torque info?
__________________

Appreciate
0

09102009, 02:20 AM  #18 
Major General
149
Rep 5,891
Posts
Drives: ///Mistress
Join Date: Nov 2008
Location: WV

Wheres the tuners to give out the necessary info? I wanna see how the tunes stack up against stock and the m3.
__________________

Appreciate
0

09102009, 05:50 AM  #20 
Captain
28
Rep 883
Posts 
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. 
Appreciate
0

09102009, 09:51 AM  #21 
Banned
42
Rep 1,876
Posts 
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..

Appreciate
0

09102009, 12:40 PM  #22 
Lieutenant
9
Rep 468
Posts 
Thanks OP for the great info. A couple ideas for additional comparisons:
e46 M3, manual transmission e90 330i, manual transmission
__________________
'11 X3 xdrive35i
'05 XC70 (family truckster) '05 Sienna XLE LTD AWD (road tripper) '06 330i MT, sport,premium (retired) 
Appreciate
0

Bookmarks 
Thread Tools  Search this Thread 

