Regression analysis to estimate performance
#1
Regression analysis to estimate performance
I read interesting article at Autospeed.com, which uses regression to derive 0-100 km/h times based on Kw per tonne ratio. Formula is y=240.89x^(-0.7332). Correlation coefficient is 0.91. x is kw per tonne ratio-for Protege5 it's going to be 75 kw/tonne
Putting formula into excel gives 0-100 of 10.13 seconds-seems fair considering 0-60 of high 9's posted by magazines.
So 170 hp Mazdaspeed Protege should do AROUND 8.3 sec and 210 hp custom turbo will be 7.1 sec 0 to 100 km/h
Please do not trash this method unless you're really sure what regression , correlation and their drawbacks and benefits are.
I will not post graph due to possible copyright violation, but try to look for atricle on Autospeed website.
Alex
Putting formula into excel gives 0-100 of 10.13 seconds-seems fair considering 0-60 of high 9's posted by magazines.
So 170 hp Mazdaspeed Protege should do AROUND 8.3 sec and 210 hp custom turbo will be 7.1 sec 0 to 100 km/h
Please do not trash this method unless you're really sure what regression , correlation and their drawbacks and benefits are.
I will not post graph due to possible copyright violation, but try to look for atricle on Autospeed website.
Alex
#2
It makes sense that there would be a high correlation in the 0-100km/h (0-62mph) arena. Drag is less of an issue at these points which is what would throw a formula like that off. The article looked okay from a distance (I didn't see anything obviously wrong, didn't have time to read the whole article).
#3
So 170 hp Mazdaspeed Protege should do AROUND 8.3 sec and 210 hp custom turbo will be 7.1 sec 0 to 100 km/h
Unfortunately, I think there are just too many variables like gear ratios and powerband for a formula to be very reliable. I've seen reviewers use formulas to predict the 0-60mph times for the '99 ES. They always came up with high 9's to low 10'. As you can see, they were way off. While accurate for one car, it can be totally off for another. The Mazdaspeed better run quicker than 7 seconds 0-60mph... if they want to keep the name in such high regards.
-Jerry
#4
Yep and when Mars is coaligned with the angular perpindicular roatational intertia of Saturn, well then the hypotenuse of the tangent quadrant force becomes a huge vector in the moment of acceleration of the new Mazdaspeed 3 causing great performance times that will surely astound and amaze.
#5
Originally posted by jstand6
The Mazdaspeed better run quicker than 7 seconds 0-60mph... if they want to keep the name in such high regards.
-Jerry
The Mazdaspeed better run quicker than 7 seconds 0-60mph... if they want to keep the name in such high regards.
-Jerry
Look at Sentra Spec v. It barely breaks into 8 sec with 175 hp.
Do not buy it. It's ****. But question is-did you ever manage to race and spank one with your 8 second 99 ES?
Alex
#6
Originally posted by Sweedenhouse
Yep and when Mars is coaligned with the angular perpindicular roatational intertia of Saturn, well then the hypotenuse of the tangent quadrant force becomes a huge vector in the moment of acceleration of the new Mazdaspeed 3 causing great performance times that will surely astound and amaze.
Yep and when Mars is coaligned with the angular perpindicular roatational intertia of Saturn, well then the hypotenuse of the tangent quadrant force becomes a huge vector in the moment of acceleration of the new Mazdaspeed 3 causing great performance times that will surely astound and amaze.
Last edited by sandman; June-11th-2002 at 09:40 AM.
#7
Re: Regression analysis to estimate performance
Originally posted by obender66
Please do not trash this method unless you're really sure what regression , correlation and their drawbacks and benefits are.
I will not post graph due to possible copyright violation, but try to look for atricle on Autospeed website.
Please do not trash this method unless you're really sure what regression , correlation and their drawbacks and benefits are.
I will not post graph due to possible copyright violation, but try to look for atricle on Autospeed website.
There are WAY too many variables involved in a 0-100 kmh (or 0-60 mph) acceleration run to use one formula based solely on power-to-weight ratio. Any time-to-speed acceleration run that ends at a relatively low speed (like 100 kmh) is HIGHLY dependent on the car's ability to get off the line quickly, which depends on (to name a few variables) tire selection, front and rear suspension design, gearing, differential type, drivetrain layout (FWD, RWD or AWD), engine torque, engine power, weight distribution, and overall vehicle weight. (Did I forget anything?) There is simply too much to consider.
Just about the only performance measurement that can be boiled down to a simple formula is 1/4 mile (or 0-400m) trap speed. Unless a car's gearing really, REALLY sucks, trap speed is almost purely a function of weight and horsepower. However, almost all other commonly quoted performance measurements (0-100 kmh, top speed, lateral g's, slalom etc.) depend on so many variables that any attempt to reduce them to a simple formula are
#9
Look at Sentra Spec v. It barely breaks into 8 sec with 175 hp. Do not buy it. It's ****. But question is-did you ever manage to race and spank one with your 8 second 99 ES?
The Spec-V will consistently run 0-60mph in 7.1-7.4 seconds. The '99 and '00 Protege ES will consistently run that same sprint in 8.3-8.6 seconds. This is not from some fancy calculation. This is from actual testing and correlating times between between the likes of Car and Driver, Road and Track, Motor Trend, etc., and not some newspaper reporter that takes the car on a little jaunt through their neighborhood.
Have you ever taken a '99 Protege ES on the track? Ever run a slalom and acceleration run comparison test between the Protege and it's competitors such as the Sentra, Civic, Corolla? I have been to so many Mazda Ride and Drive courses, new model launches, and Product Master classes to make my head spin.
But, according to your times, the Protege is one of the slowest cars in its class. Why did us idiots spend money on them? If the Mazdaspeed is only going to run 0-60mph slower than a Toyota Echo then Mazda must be the most idiotic manufacturer in the world. Heck, the Metro runs faster 0-60mph times than you claim for the Protege. Hello? We must sell all of our cars now before the world realizes how stupid we are for buying cars that can't even outrun a minivan!
What's next? A formula for handling? Braking? Seat comfort?
#10
Well Jstand, TheMan has posted some dynos of his car in pretty much stock form and they looked pretty similar to the ones you posted after you put your CAI on. I don't get how you can knock the 2.0L:
1.8L Engine
HP 122 @ 6000RPM
TQ 120 @ 4000RPM
2.0L Engine
HP 130 @ 6000RPM
TQ 135 @ 4000RPM
Seems like I've got apprx. 8hp and 15lb/ft on you there buddy. Little bit of extra weight maybe, but not much.
Anyway, if the formula were perfectly able to calculate a vehicles 0-100 time it would have a 1.00 correlation coefficient, which it doesn't. The .91 leaves room for variables providing that a good driver was at the wheel, which is where they got their data. They used peak times not nimrod driving at the track times.
1.8L Engine
HP 122 @ 6000RPM
TQ 120 @ 4000RPM
2.0L Engine
HP 130 @ 6000RPM
TQ 135 @ 4000RPM
Seems like I've got apprx. 8hp and 15lb/ft on you there buddy. Little bit of extra weight maybe, but not much.
Anyway, if the formula were perfectly able to calculate a vehicles 0-100 time it would have a 1.00 correlation coefficient, which it doesn't. The .91 leaves room for variables providing that a good driver was at the wheel, which is where they got their data. They used peak times not nimrod driving at the track times.
#11
Well Jstand, TheMan has posted some dynos of his car in pretty much stock form and they looked pretty similar to the ones you posted after you put your CAI on. I don't get how you can knock the 2.0L:
102.1 hp
112.1 ft-lbs
YellowPR5 2.0L (stock except for 18" wheels):
100.0 hp
107.7 ft-lbs
Jstand6 1.8L (totally stock):
102.8 hp
105.0 ft-lbs
Jstand6 1.8L (stock except Injen Racing Division CAI):
107.8 hp
111.2 ft-lbs
Not only is power fairly similar, but look at the power curves. The 2.0L's torque and horsepower curves fall quickly after their peaks. The 1.8L's torque curve remains fairly flat throughout, and the horsepower curve is very linear all the way to the rev limiter cut-off. My first clue was driving the two of them. The 2.0L felt sluggish compared to the 1.8L. The 2.0L had a little bit more power off the line, but power fell off quickly. The 1.8L pulls hard all the way to redline. Plus, the sounds the two engines make are pretty different. The 1.8L growls all the way to redline, where the 2.0L sounds like it is just being worked too hard. I was just pretty disappointed in the 2.0L... it is better for the automatic, though.
We calculated optimum shift points in another board. For the 1.8L, optimum shift points were redline in each gear. For the 2.0L, it varied... redline was for the first gear only. By the time you shift out of 4th gear, the optimum shift point was just under 6,000rpm. That's a testament to the different power curves between the engines. The 2.0L just drops off too fast.
-Jerry
Last edited by jstand6; June-11th-2002 at 12:54 PM.
#12
Well, I'll be sticking with 2.0L. But I'll be damned if that 1.8L can do an 8.4.
Plus the magic of statistics is that they are, here is the surprise, ESTIMATES. You will always run into data that does not fit your formula. But it usually sits pretty close.
Plus the magic of statistics is that they are, here is the surprise, ESTIMATES. You will always run into data that does not fit your formula. But it usually sits pretty close.
#13
Originally posted by Sweedenhouse
Yep and when Mars is coaligned with the angular perpindicular roatational intertia of Saturn, well then the hypotenuse of the tangent quadrant force becomes a huge vector in the moment of acceleration of the new Mazdaspeed 3 causing great performance times that will surely astound and amaze.
Yep and when Mars is coaligned with the angular perpindicular roatational intertia of Saturn, well then the hypotenuse of the tangent quadrant force becomes a huge vector in the moment of acceleration of the new Mazdaspeed 3 causing great performance times that will surely astound and amaze.
Post.
Ever.
#14
Well, I'll be sticking with 2.0L. But I'll be damned if that 1.8L can do an 8.4.
1999 Mazda Protege ES
November 1998
Ever driven the two? I've driven probably over a hundred of each, including the older BP 1.8L. What's my favorite? Well, from just a fun-to-drive standpoint, I love the BP. That engine loved to rev and was way smoother than either the FP or FS. There's a reason the BP is still found under the hood of the Miata. The FP and FS feel like old truck engines in comparison. I looked into buying the 2.0L when it came out. However, not even the 0% could get me to give up the FP for the FS. And you will hear this same sentiment from anyone that owns an FP or has upgraded from the FP to the FS or from anyone that owns both.
Personally, what I really miss is a good ole 13B rotary. Now that's an engine who's sound, feel, and smoothness blow everything out of the water! (IMO of course)
-Jerry