Regression analysis for kg/hp vs. Ring laptimes

[lucid]

Originally Posted by jaiman

So I added cd and skidpad numbers to the regression and now get an Adjusted R Square of .87 with good significance on the new variables. The GTR goes from a 21 second outlier to a 12 second outlier. if i can figure out how to post up the excel file, i'll do that this evening. I'd like to add some metric for brake performance and see if that helps.

I also tried a dummy variable for AWD but it didn't really add anyhitng at a level of significance that was worthwile.

You need to zip the spreadsheet and upload that. Also, it would be easier to discuss a chart. You can just copy the chart from excel to any graphics program like Paint or PhotoEditor, save it as a jpg, and upload that.

[sdiver68]

Originally Posted by footie

I think we all have to eat humble pie here.
That's sounds like special tyres to me.
P.S.
This was posted by the same guy on RS6.com by the way. He might not have been the fool we all thought.

Well humble pie needs to be eaten, but most likely not by us.

We've discussed the tire controversy stirred by that article ad naseum in this forum and others, and the consensus is a translation issue. The car is claimed by Nissan to be on stock 20" Bridgestone REO70A RFT, developed specifically for the Nissan GT-R. Nissan was challenged on this issue by several reporters in several different interview sessions and only the 1 report from the 1 source is "cut-slicks". Furthermore, if you read the whole paragraph, cut-[racing]slicks doesn't make any sense in context.

[sdiver68]

Originally Posted by jaiman

So I added cd and skidpad numbers to the regression and now get an Adjusted R Square of .87 with good significance on the new variables. The GTR goes from a 21 second outlier to a 12 second outlier. if i can figure out how to post up the excel file, i'll do that this evening. I'd like to add some metric for brake performance and see if that helps.


I also tried a dummy variable for AWD but it didn't really add anyhitng at a level of significance that was worthwile.

Thanks! Did you add cd assuming a constant frontal area?

[swamp2]

Originally Posted by jaiman

So I added cd and skidpad numbers to the regression and now get an Adjusted R Square of .87 with good significance on the new variables. The GTR goes from a 21 second outlier to a 12 second outlier. if i can figure out how to post up the excel file, i'll do that this evening. I'd like to add some metric for brake performance and see if that helps.


I also tried a dummy variable for AWD but it didn't really add anyhitng at a level of significance that was worthwile.

Sounds quite exciting. Looking forward to your post! I am sure you already know the following, but just some friendly reminders...

1. THE most significant variable will be a boolean. DOT legal race tires or street tires. That would remove most of the outliers below the regression prediction.

2. Next, like I mentioned before, Cd WITHOUT frontal area is IRRELEVANT. The drag force is what is relevant and it is proportional to Cd x A x v^2.

3. Skidpad number is a good variable to include as well.

Let's see the data and graphs!

[enigma]

Originally Posted by swamp2

1. THE most significant variable will be a boolean. DOT legal race tires or street tires. That would remove most of the outliers below the regression prediction.

Skidpad data will mostly cover this and a good chunk of suspension. This of course assumes that the skidpad data is for the same tires as the ring time.

[footie]

Originally Posted by swamp2

Sounds quite exciting. Looking forward to your post! I am sure you already know the following, but just some friendly reminders...

1. THE most significant variable will be a boolean. DOT legal race tires or street tires. That would remove most of the outliers below the regression prediction.

2. Next, like I mentioned before, Cd WITHOUT frontal area is IRRELEVANT. The drag force is what is relevant and it is proportional to Cd x A x v^2.

3. Skidpad number is a good variable to include as well.

Let's see the data and graphs!

Surely then braking distances at say 60mph and 100mph if possible would again be of value, plus acceleration figures to say 150mph.

I think if you can add all of these to your figures then you will see things getting even more exact.

[enigma]

Originally Posted by footie

Surely then braking distances at say 60mph and 100mph if possible would again be of value, plus acceleration figures to say 150mph.

I think if you can add all of these to your figures then you will see things getting even more exact.

You do realize that power to weight determins acceleration and probablly projects times better than 0-60 because it removes the error and imprecision of the launch?

Also, braking numbers are usually very noisy compared to the signal. Every production car today has brakes capable of locking up the wheels, at that point its just a measure of the surface and tire combo.

[sdiver68]

Originally Posted by swamp2

Sounds quite exciting. Looking forward to your post! I am sure you already know the following, but just some friendly reminders...

1. THE most significant variable will be a boolean. DOT legal race tires or street tires. That would remove most of the outliers below the regression prediction.

2. Next, like I mentioned before, Cd WITHOUT frontal area is IRRELEVANT. The drag force is what is relevant and it is proportional to Cd x A x v^2.

3. Skidpad number is a good variable to include as well.

Let's see the data and graphs!

2) Isn't Cd without frontal area the same as Cd with an assumed constant frontal area as would be expected from similar sized cars? I think I disagree that Cd alone is worthless as long as the compared vehicles are similar.

[enigma]

Originally Posted by sdiver68

2) Isn't Cd without frontal area the same as Cd with an assumed constant frontal area as would be expected from similar sized cars? I think I disagree that Cd alone is worthless as long as the compared vehicles are similar.

yes, assuming same aera. The approximation is probably good enough, with the only issues being some of the small 2 seat cars.

[swamp2]

Originally Posted by sdiver68

2) Isn't Cd without frontal area the same as Cd with an assumed constant frontal area as would be expected from similar sized cars? I think I disagree that Cd alone is worthless as long as the compared vehicles are similar.

Again the total drag force is the only thing relevant and it is

F = 1/2 x air density x area x Cd x v^2

Each is absolutely equally relevant. Typical Cd numbers vary from about .25 - .35 in these cars, which is about 40%, typical frontal areas vary from about 1.6 m^2 to 2.2 m^2 which is also 40%.

If one really wants to do it right, simply regress against Cd x A, just like in the formula.

[footie]

Originally Posted by enigma

You do realize that power to weight determins acceleration and probablly projects times better than 0-60 because it removes the error and imprecision of the launch?

Also, braking numbers are usually very noisy compared to the signal. Every production car today has brakes capable of locking up the wheels, at that point its just a measure of the surface and tire combo.

Fair point, I didn't think of that before I put fingers to keyboard.

[sdiver68]

Originally Posted by swamp2

Again the total drag force is the only thing relevant and it is

F = 1/2 x air density x area x Cd x v^2

Each is absolutely equally relevant. Typical Cd numbers vary from about .25 - .35 in these cars, which is about 40%, typical frontal areas vary from about 1.6 m^2 to 2.2 m^2 which is also 40%.

If one really wants to do it right, simply regress against Cd x A, just like in the formula.

I'm not completely disagreeing, other than mentioning the practical issue that frontal area will be very hard to come up with for all these cars, but I'll look around. However, the fact remains that Cd alone improved the model, which confirms my theory.

And not to bring up another variable that is almost impossible to find good data on, and varies by speed anyway, but downforce

[swamp2]

Originally Posted by sdiver68

I'm not completely disagreeing, other than mentioning the practical issue that frontal area will be very hard to come up with for all these cars, but I'll look around. However, the fact remains that Cd alone improved the model, which confirms my theory.

And not to bring up another variable that is almost impossible to find good data on, and varies by speed anyway, but downforce

Agreed. Frontal area may be tough to get for many of these cars but I have found it fairly widely available. Since each factor comes in about equally, indeed one parameter alone, either Cd or area will improve the model, it will just leave outliers based on extreme frontal areas, large or small.

Also +1 on downforce - a huge factor in how hard you can push through the fast corners at a high speed circuit like the ring. Almost impossible to get this data!

[footie]

All of this equations are missing one vital thing, they are all based on each car's behaviour in relation to how the suspension copes with each bump, camber etc of every corner being the same. I am sure there is numerous people which experience of the ring which will tell you just how bumper it is, it's the reason why manufactures do their handling development there in the first place, but you also have to remember that all car's suspensions isn't signed off after the ring either, like everything there is a compromise made between handling, comfort and safety. Each car receives a certain amount of understeer which is dialled in to let lesser drivers know when the limits are being approached, plus the suspension is usually made a bit softer as most people wouldn't want the best setup option for the ring as it would be way to hard.

So like I said, the relationship between the suspension and the road surface is a major determining factor on how hard you can corner on any track as bumpy as the ring is and it's something which each manufacture has a differing opinion of importance of.

Just a thought from the rambling of an old man.

[sdiver68]

Originally Posted by footie

So like I said, the relationship between the suspension and the road surface is a major determining factor on how hard you can corner on any track as bumpy as the ring is and it's something which each manufacture has a differing opinion of importance of.

Just a thought from the rambling of an old man.

While what you say is true, statistics in this case are an attempt to predict the unknown variables based on what is known. Unless you have some extensive and specific data logs on each of these cars, I think suspension is just an unknown. Other than the fact each of these cars are performance cars and it is assumed that each manufacturer went through a significant effort to get the car to handle well, we just can't measure suspension bump absorption very well or even the data from any tests that would help measure that.

To your point, though in the case of the GT-R and M3 and some other cars, semi-active suspension in various guises would help.

The biggest unknown imho is driver skill. Even a 1% difference there is good for ~5 seconds on a large track like the Nordshleife.

[enigma]

Originally Posted by sdiver68

I think suspension is just an unknown.

Tune, yes. Type, no

Adding strut VS double A arm or multilink would be good to have.

[footie]

All I was trying to show was while interesting and entertaining it's never going to be as exact as to prove why some cars are quicker than others.

That's all.

[swamp2]

jaiman: Where is the data and plots? I am a greedy data whore. Give me the precious.

Seriosuly, very keen on seeing the data and results. If you are having trouble posting or plotting just post a text file and lucid or I can help out.

[jaiman]

Originally Posted by enigma

Tune, yes. Type, no

Adding strut VS double A arm or multilink would be good to have.

i tried that as well, but didn't get anything of use.

[jaiman]

Ok, so here is the regression and raw data. Cd is only significant at the 97% level, i'd expect adding frontal area would help, but it would take a lot of work to find it for each car. The skidpad numbers came from internet sources, so i'm not sure how acurate they are and i wasn't able to find numbers for a bunch of the cars.

sorry it took so long, i've been on vacation from work and haven't touched my computer at home until today.

[enigma]

Originally Posted by jaiman

i tried that as well, but didn't get anything of use.

Hmm, another good grip aproximation is:

(Avg rim width) / (LBS)

The idea being its not simply weight but weight per area of tire on the ground that deterimins grip. The Nissan, Lotus, Z06 and some Porsche have really wide wheels for their weights.

[swamp2]

Originally Posted by jaiman

Ok, so here is the regression and raw data. Cd is only significant at the 97% level, i'd expect adding frontal area would help, but it would take a lot of work to find it for each car. The skidpad numbers came from internet sources, so i'm not sure how acurate they are and i wasn't able to find numbers for a bunch of the cars.

sorry it took so long, i've been on vacation from work and haven't touched my computer at home until today.

Thanks, files seem to be garbled. Have a look at the data in a text editor. Can you post in .csv format? I thought you were going to try a multi-variable regression? If you get me the data in a readable format I will certainly do it.