Friday, May 17, 2013

What cars should be faster/slower around EVO's racetrack?

Lap times are dependent on such variables as horsepower and weight. More horsepower will correspond to a faster lap time while more weight will lead to a slower lap time. However, there are many other variables not in the specs that can effect the lap time. For example; some cars are hard to handle on the limit and will make the driver cautious / slower around the track. Conversely a more confidence inspiring car will make the driver push the car to its limits and have a quicker lap time. Other factors such as; steering feel, power delivery, weight transfer through the corners, etc. will effect the lap time to a degree that the specs of a car do not.

What cars should be faster or slower on a racetrack given their own specifications?

Using EVO Lap times and variables including; Number of Cylinders, RPM @ max RPM, HP, RPM @ max LBFT, LBFT, Engine Size, and Weight, I made a regression model and looked at those that over/underperformed given the model.

This then, is just looking at the residuals and seeing what cars should be better. This may sound stupid at first. After all no one says "Well..yea you're car is 5 seconds faster, but it really should be 10 seconds faster!". Then again most of comparisons involve residuals. Whenever anyone says "Good for the price" they're talking residuals given a price. Here I'm talking residuals given HP and Weight figures.


Below are the cars and how fast they went around the EVO lap in seconds. (Other data can be found here)




Car
Lap Time
Ferrari 458 Italia
79.3
Caterham Levante VS
79.6
Porsche 997 GT2 RS
79.9
Lotus 2-Eleven GT4
80.1
Caterham Superlight R500
80.2
McLaren MP4-12C
80.6
Noble M600
80.8
Porsche 997 GT3 RS 4.0
81
Lamborghini Murcielago LP670-4 SV
81.3
Ariel Atom 3 Supercharged
81.5
KTM X-Bow (300bhp)
81.5
Ferrari 430 Scuderia
81.7
Porsche 997.2 CT3 RS (3.8)
81.9
Brooke Double R
82.5
Lamborghini Gallard LP560-4
82.5
Lamborghini Murcielago LP640
82.9
Porsche 997.2 GT3
83.3
Porsche Carrera GT
83.3
Porsche 997 Turbo S
83.5
Nissan GT-R
83.6
Lotus 340R (190bhp)
84.2
Caterham Superlight R300
84.3
Maserati GranTurismo MC Stradale
84.5
Mercedes-Benz SLS AMG
84.6
Porsche Boxster Spyder
84.7
Ferrari California
85
KTM X-Bow
85
BMW E92 M3 Coupe
85.1
Mercedes-Benz SL65 AMG Black
85.2
Audi RS5
85.4
Audi R8 Spyder V8
85.5
Porsche Cayman R
85.5
BMW M5 (F10)
85.7
Aston Martin V12 Vantage
85.8
BMW 1-series M Coupe
85.9
Mitsubishi Evo X FQ-400
85.9
Mitsubishi Evo X RS 360
86.1
Renaultsport Megane 265 Trophy
86.1
Audi TT RS
86.3
Aston Martin DBS
86.4
Porsche Panamera Turbo
86.5
Jaguar XJ220
86.7
Mercedes-Benz E63 AMG
86.8
Porsche Cayenne Turbo
86.9
Lotus Evora
87.1
Nissan 370Z
87.1
Porsche Panamera S
87.3
Lotus Elise SC
87.7
Mercedes-Benz C63 AMG Coupe
87.7
BMW E46 M3 C5L
87.8
Renaultsport Megane R26.R
87.8
Vauxhall VXR8 Bathurst S
87.8
Audi RS6 Avant
87.9
Jaguar XFR
87.9
Honda Civic Type-R Mugen 2.0
88
Lexus IS-F
88.1
Porsche Boxster S
88.1
Subaru WRX STI
88.3
Jaguar XJ Supersport
88.4
SEAT Leon Cupra R
88.7
Bentley Continental Supersports
89.2
Lotus Elise Club Racer
89.2
Maserati Quattroporte S
89.5
Renaultsport Megane 250 Cup
89.9
Honda NSX
90.1
Nissan 370Z Roadster
90.3
VW Scirocco 2.0 TSI
90.4
Ford Focus RS (Mk2)
90.8
Renaultsport Clio 200 Cup
91.9
VW Golf GTI [Mk6)
92.4


Below is a Pairs Plot of each of variables.



I ran a step regression with Lap Time as dependent and all other variables (excluding weather since there all except 3 were Dry). The process lead to a model including; HPRPM, Engine Size, BHP, and Weight and is shown below. 

Coefficients: Estimate Std. Error t value pvalue
(Intercept) 88.2097659 2.1478362 41.069 approx zero
hprpm -0.0005044 0.0002497 -2.02 0.0475
CubicCenti 0.0003122 0.0002945 1.06 0.293
Bhp -0.0207499 0.0027082 -7.662 1.16E-10
Weight 0.0056975 0.0008757 6.506 1.28E-08




Residual standard error: 1.974 on 67 degrees of freedom
Multiple R-quared: 0.6635 ADJ R-squared:0.6435
F-statistic:33.03 on 4 and 67 DF


Using this model the residuals

Car Residual
KTM X-Bow (300bhp) -2.93487945
Lotus 2-Eleven GT4 -2.83245965
Nissan GT-R -2.66665528
Ferrari 458 Italia -2.57420938
Porsche 997.2 CT3 RS (3.8) -2.55684266
Mitsubishi Evo X RS 360 -2.50226452
Maserati GranTurismo MC Stradale -2.46471552
Renaultsport Megane 265 Trophy -2.44615874
Porsche Cayenne Turbo -1.91766928
BMW 1-series M Coupe -1.83047226
Porsche 997 GT3 RS 4.0 -1.81502563
Caterham Superlight R500 -1.77237657
Porsche Boxster Spyder -1.6582512
Porsche 997.2 GT3 -1.54770591
Lamborghini Murcielago LP640 -1.35574562
Porsche 997 GT2 RS -1.28253206
Audi TT RS -1.27050135
Porsche Panamera Turbo -1.17816797
Lotus Evora -1.10761578
Porsche Panamera S -1.04072814
Porsche 997 Turbo S -0.83654924
Ferrari 430 Scuderia -0.82185243
Audi R8 Spyder V8 -0.68468002
Porsche Cayman R -0.68457919
Lamborghini Gallard LP560-4 -0.67647912
KTM X-Bow -0.63837555
Nissan 370Z -0.62867383
BMW E92 M3 Coupe -0.58344003
Audi RS5 -0.56349199
Renaultsport Megane R26.R -0.50017286
Lotus 340R (190bhp) -0.44282995
McLaren MP4-12C -0.40117778
Brooke Double R -0.3714648
Ferrari California -0.33430501
Caterham Superlight R300 -0.3061938
Lamborghini Murcielago LP670-4 SV -0.24397178
BMW M5 (F10) -0.18196681
Mitsubishi Evo X FQ-400 -0.18097319
Ariel Atom 3 Supercharged -0.10631631
Subaru WRX STI -0.08331381
Aston Martin V12 Vantage 0.02661749
Mercedes-Benz E63 AMG 0.11885765
Mercedes-Benz SLS AMG 0.33430532
SEAT Leon Cupra R 0.47876336
Mercedes-Benz C63 AMG Coupe 0.48358713
Aston Martin DBS 0.54115489
Lexus IS-F 0.55513591
Porsche Boxster S 0.67495797
Maserati Quattroporte S 0.67528337
VW Scirocco 2.0 TSI 0.7166074
Mercedes-Benz SL65 AMG Black 0.87429901
Renaultsport Megane 250 Cup 1.0633422
Honda Civic Type-R Mugen 2.0 1.24547732
Noble M600 1.30749315
Jaguar XFR 1.33734955
Bentley Continental Supersports 1.38429526
Audi RS6 Avant 1.61605625
Vauxhall VXR8 Bathurst S 1.76433676
Lotus Elise Club Racer 1.84730036
Jaguar XJ Supersport 1.86583708
Porsche Carrera GT 2.00596389
BMW E46 M3 C5L 2.03663438
Honda NSX 2.27324813
Nissan 370Z Roadster 2.37761095
Lotus Elise SC 2.53179383
Ford Focus RS (Mk2) 2.94808301
VW Golf GTI [Mk6) 3.02997026
Renaultsport Clio 200 Cup 3.87547123
Jaguar XJ220 3.90086627
Caterham Levante VS 4.13508509


Jaguar XJ220 should be faster (underachiever) while Ferrari 458 should be slower (overachiever). Makes some sense.


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