The nice thing about rennlist is that there really rarely seem to be the typical internet flamemasters that seem far more concerned about winning an argument than eating. Stay away from m3forum.com as there are some recent graduates of the Evo forum when it comes to netiquette.

Anyway, I let myself get suckered into arguing with one of these idiots thinking that reason, logic and good, sound math might crack the shell of nonsense. No such luck, I got called (variously) a "dik" a "frat boy" and a "lunatic" for making the following argument.

It's about Nring times and power to weight. I think you guys might enjoy it. Have a great weekend and happy new year! -dc

I normally don't geek out this much, but we were having a lively debate in the E92 forum on track times. I ended up putting together some data and might as well share it (since it's done now) with some fellow track nuts that would probably be more interested in this technical super-geek, track stuff.

Long story short, I put together a worksheet that compared Nurburgring times to power to weight ratios. I ran a regression model (I didn't regress any other variables than power to weight) and came up with a linear formula for a guess at a time around the Ring.

((kg+100)/ps)*14.72 + 425 will give you a guestimate of your cars capability at the Ring in seconds. You HAVE to add 100kg to your cars weight for driver and fluids to make the math work.

Interesting data points:
1) the standard error of y is 9 seconds, which basically means about 67% of the data points are within 9 seconds of the guestimate based on the formula above.

2) of the total sample of 65 cars in the database, 44 (68%) were within +/- 1 standard error of y (SERY)

3) of the 12 cars slower than 1 SERY, 6 were fat (over 1600kg dry) and 3 were underpowered (less than 250hp can't achieve the speed on the straights and included the Caterham, the s2000 and the Civic Type-R, the exige was close, but barely made it; still slow due to low power).

4) so weight, independent of power, is clearly one of the variables in lap times (duh!). there were only 3 "light" slow cars, the diablo SV, the ferrari 355 and the C6 tested by sport auto (the Z51 C6 driven by dave hill was inside the band). Interestingly, there were several "sport auto" tests of several different cars that came out on the slow side (although still in the band).

5) of the 9 cars faster than 1 SERY, 6 were Porsches!!! Wow, think Walter knows what he's doing? Maybe there is something to that rear engine on that particular track. The other three were the BMW CSL (obviously an awesome track car), the WRX Sti spec C and the Lambo Murcie (just barely made it outside the band by about 0.5 second).

6) Of the 9 "fast" cars, at least 5 we can guess were very well setup for the track with lowered suspensions, lots of static negative camber and probably some really sticky tires (including the GT2, (2) GT3s, the WRX STi C and the CSL). The remaining cars were all "regular" porsches like the 997TT, the CGT and the Cayman. The 993TT was actually on the really slow side (change in tire technology in the last 10 years?)

There are, of course, lots of variables other than power to weight that impact lap times. However, the interesting thing to me is that the data is highly correlated to just power to weight.

If you pull out the "fat" cars (over 1600kgs), the underpowered cars (under 250hp) and the "track" setup cars like the CSL, STi and the GT2 and GT3s, the SERY drops to only 7.4 seconds. If your car fits in that category, the revised regression formula is (kg+100)/ps * 14.195 + 426 (answer in seconds).

So for a "regular" street high performance car like a boxster, the new M3 or a 997S here are the predicted values vs. actual recorded times (guess/actual):
1) 997S (7:59/8:02)
2) New M3 (8:04/8:05)
3) Boxster (8:23/8:23)

The fatter your car, the more time you've got to add in reality vs the model
Viper (8:04/8:10) - 1567kg -seems a little slow anyway, maybe no ABS?
M5 (8:01/8:13) - 1844kg

The porsches AVERAGED 6.2 seconds faster than the regression formula, or nearly a full standard error of Y. If you want to go fast with low hp, buy a porsche!

4wd seems to help some as most 4wd cars are faster than the straight math, and lighter cars at the same p/w (cars with less weight and HP) are a little faster (to a point, really low weight and low hp (ie caterham) is pretty slow on this long, high speed track.


Anyway, here's the chart (line on the low side that got blotted out is the 997TT):



Here's the link if it isn't showing up: http://forums.rennlist.com/upload/m3chart.jpg


Again, there are obviously lots of factors that impact performance. I'm just surprised that tires, suspension and balance only have (on average) about a 7.5 second impact on performance for a given p/w ratio. Again, that just means that tires/suspension/etc. are only responsible for about a 15 second total band at each p/w point, not that tires aren't significant (look at the CSL and GT3)

My guess is that this is the case because modern sports cars ALL have good tires, fairly good balance, good brakes and a pretty good suspension with a fairly low CG. So for the purposes of this chart, they are somewhat close to constants.

The breakout cars on the low side pretty much all have really tight (almost unacceptable on the street) suspensions with really soft tires. I would imagine they are setup with quite a bit of static negative camber too (CSL, Gt3, etc.) to take advantage of those tires.

Bottom line, if you want to go fast with relatively less horsepower at the Nurburgring, buy a porsche or a CSL (or just hire walter to drive you).

One other interesting point, the math would imply an absolute limit (no car has a p/w ratio of ZERO) of the y-intercept or about seven minutes and five seconds. So, barring downforce (ie a radical or racecar that can generate a lot more than 1g in a corner), no regular car is going to break 7 minutes with existing tire technology no matter what the p/w ratio.

Sorry for the long, blabbering, geeky post, but the work was already done. Let me know what you guys think.

And, again, I'm NOT saying there aren't other factors. I'm saying it's interesting that the other factors have less of an impact than we probably imagine given a reasonably well engineered sports car with pretty good brakes and tires (that fact is pretty much absolute in the math). And this is cleary a horsepower track.

Happy New Year.

 

Just mention Fernando Alonso a few times and that will change.

 

Ok, I'll bite on the geek thread. I suspect part of the spread in the data has to do with different track and/or weather conditions. I wonder if you end up with slightly different correlations if you split it up by engine location (front, mid, rear)?

 

yeah, I looked at a couple of different factors. The problem is that the equation is so dominated by the power to weight ratio that it's difficult to isolate the other variables. How do you objectively measure "balance" anyway?

Is it tires? tire width? balance? All have an impact, but the correlation with p/w is SO high.

You've got to get enough data points in each time range to remove the effect of power to weight and look to see what otherwise might be impacting the results.

-dc

 

the other thing you forgot to mention in your equation is your PS (Hp) used in your equation RW or crank hp?
If crank then my car should be able to see 7:59 laps, if RW 8:09

Now the one factor you left out is the driver not all are equal.

 

This is a fun, real world, application of regression modeling. It's not geeky it's something every MBA should know...or have known at some point. I suspect there are a fair amount of MBA's on this board.

I know you didn't regress any other variables but you do need to rule them in or out before your accept your model. You can't really work on a hunch with this stuff.

Thanks for doing this. It's an interesting read.

 

Now you've done it. Don't diss Alo or Wayne will have to come in here and bust some heads....

 

Great thread and good work, Derick. Not bad for a lunatic frat-boy (j/k!).

Neat how even with tossing out the 10,000 other variables of The Ring, including really big ones like "Who's Driving, and on What Tires?" and "Rainy Day?", the absolute importance of Lightness comes shining through.

You know, with the popularities of The Ring and Teh IntraNet we could probably gather a lot more data. It's be great to enter into this chart a time for each car that is an average derived from a ton of data points for that car model (different drivers, conditions, etc) so we negate the "Walter On Slicks" vs "Journalist On Cellphone" effects.

 

It's crank hp.

I DID factor in the driver, just in an off-hand manner. I'm enough of a porsche fan to believe there's some "special sauce" in a porsche that makes it faster than pure numbers would dictate, but I'm sure the majority of that time difference can be accounted for by Rorhl (the real special sauce).

I'd also assume that most of these times were set by very, very competent drivers thus mitigating *most* of the driverness independent variable. I'm sure there are still some variances, no doubt.

If you start testing the numbers by using the model and adding about 5 to 10 seconds for overweight or underpowered and subtract about 10 seconds for a very well setup suspension with sticky tires, I think you'll find it applies to every single car and is accurate to within about 7 or 8 seconds.

Again, my guess is not that tires/suspension/balance/driver don't make a difference in how a car performs, just that they don't make much of a relative difference in this particular company of very competent machines.

-dc

 

You're exactly right. The real irony is I think statistical modeling is far, far over-used. Have you ever read "the black swan" ? It's a great example of the ridiculous overestimation of the power of regression.

However, with more isolated variables (on a racetrack vs the stockmarket), it appears to have some merit.

-dc

 

Think he may run a daily search for that term to see who's dissin' who?

 

the driver counts for a lot! the best time ive seen is 8:39 and thats bridge to gantry, with the car wearing michelin pilot sport 2s, 1480 kg with a full tank and 394ps. ive been round the ring about 70 times, im confident i can remove 10 seconds more relatively easily and a LSD might help as well! after that i will want the security of stickier rubber.

 

nick,
I'm sure the driver matters a TON. definitely THE most important factor.

However, I think we can safely assume that all these various manufacturers and tuners found some pretty damn good drivers when making an attempt at a fast ring time, so for purposes of this analysis, it's not as BIG a factor as for you and me.

 

derick, i am actualy impressed by the numbers you have managed to generate and the way they aproximate real life. good stuff!

 

MBAs know how to do regression? I thought all they knew how to do was lunch

Yeah, I'm an engineer, I know, no social skills and an overdeveloped sense of how funny I am.

BTW, Derick, thanks for the analysis and the thoughts - doesn't seem like a dikly thing to me, although maybe a bit lunatic for doing it.