comparing cars of different weight?

[jeffgoddin]

At first I took it for granted that the key to judging relative performance among vehicles was to look at them when they have the same weight to power ratio (and similarly whatever vehicle has a lower weight to power ratio will probably be more competitive), but in practice I've found that when you compare a 2750lb 275 hp Atlantique 300 to a 1450lb 145 hp Elise this assumption appears ridiculous. Though they both have a weight to power ratio of 10lbs/hp, the Elise just doesn't have the oomph at high speed or the traction from weight on the wheels to compete in the 400m, 1000m, or on any track that I've tested.

Looking around I've found Parnelli Bone's GT2 racing guide very helpful in identifying the weight to power ratios and parts which will make for a good race in the various events. One thing he notes in many cases is that light weight cars need to have lower power to weight ratios to remain competitive in these races. I had a guess already that in fact what remains constant is not simple weight/power but perhaps weight/power^2. When I analyzed Parnelli's guide what came out of it is that in fact from his experience what remains constant is weight/power^3.

So according to this that 1450lb Elise should have more like 215hp to remain competitive with the much heavier 276 hp Atlantique 300.

I'd like to be able to compare cars of different weights, but without a good understanding of the relationship between performance and weight and power I can really only confidently compare cars of the same weight and power.

Just wondering if anybody else has looked at this seriously and what they decided?

Also, it seems like the flywheels and driveshaft translate directly into hp if anybody has thoughts on that or other parts like tires or clutch.

 

[jeffgoddin]

Was fiddling around with some physics equations today and made a remarkable discovery which relates to this thread.

If you want to calculate theoretical top speed for a given vehicle with changes in horsepower, and you assume that top speed happens when peak horsepower is equal to drag*, then you get a relationship which says top speed is proportional to the cube root of horsepower.

For example, the drag coefficient of the 180sx can be found online, and the more useful CdA, the coefficient times the relevant cross-sectional area. Using the density of air at 1 atmospheric pressure and 86deg F (not sure what PD uses, density would be higher at lower temperatures) I can then calculate theoretical top speed given hp under these conditions.

For 153hp, the top speed would be 160mph. Track testing with track stated 153 hp, it'll go up to 152mph and still gradually climbing when you cross the finish. For 307hp stated on the track, the top speed would be 202mph, though I found I only had enough room to push it to 188mph before cornering cost me all the speed I'd gained on the straight (running backwards this time.) In both cases it's easy to imagine a ceiling very close to the theoretical prediction, especially if we guess a lower air temperature/higher density which means slightly less top speed predicted.

When you are accelerating, you're always pushing against inertia, related to mass, and your ability to do so is directly related to your horsepower. So especially at low speeds, where drag is less of an issue, performance is more or less related to your power to weight ratio. At high speeds, where drag is a greater factor than inertia, your performance will have less to do with your mass, but will be strongly related to the cube root of your horsepower.

What I really find interesting is that this theoretically corroborates what I found in Parnelli Bone's empirically determined suggestions for competitive racing, where lighter weight vehicles need to have relatively more hp, and the best line fit I found for his suggestions was a cube proportional.

Well I'm sure not too many people are going to jump for joy when they read this, but it just struck me as really exciting when I was playing around with equations and realized that they strongly supported what Parnelli was saying (whether he knew it or not...)

*Edit: just thinking about this a little more, I realize that I've left out the rolling resistance of the tires. So, not sure what percentage of hp has to go towards overcoming this, and how much is left to push through the wind. As far as tires go, I'm not sure that posted CdA's for cars include the tire's CdA or if that's extra since it's variable (you can change tire widths and therefore change tire CdA.) Bottom line, maybe only 90-95% of available hp will go to pushing through wind resistance at the limit, and so actually I would predict lower top speeds more in line with what I saw in testing the 180SX above.

 

[Parnelli Bone]

Wow, somebody else is into math? Lol.

Some random thoughts. I would say weather is always a perfect 70-80 degrees in the lands of GT2, so far as your calculations go. Low humidity. I'm not sure what weather is typically like in Japan. For instance, in Maryland it's typically humid and muggy to some degree during spring and summer. In the winter it's typically dryer.

When I lived on the west coast (Portland, Seattle), there's an opposite effect. Summers are very dry, while fall, winter, and spring there's a lot of rain.

My GT2 racing guide is actually very simplistic compared to my GT4 racing guide, which at this point is pages and pages long (with multiple links in between, lol). I managed to fit the entire GT2 guide onto one online page, in comparison.

The reason for this is rubber-banding I think. Most any race in GT2, the majority of cars will fall within certain parameters or something, especially during most of those sprint races that last 2 to 5 laps. This made it easy for me to use a single mathematical ratio (or 2 or 3 logarhythmic ratios in extreme cases) and pretty much find competitive racing for just about any car that fell within that race's horsepower qualificatoin.

I haven't messed around that much with drag coefficients or wheel speed, and how it relates to GT, although I do take this information down (especially drag, frontal areas, and Cx) if I can find it. I can't always find this stuff here online, though.

 

[jeffgoddin]

Sounds like I have your GT4 guide to look forward to once I finally get into that game. Never had a PS2, but I've bought about 3 PS1's over the years pretty much just to play Gran Turismo 1 and 2.

So here are some sites I've found which list Cd's and CdA's:

http://en.wikipedia.org/wiki/Automobile_drag_coefficient (of course)
http://ecomodder.com/wiki/index.php/Vehicle_Coefficient_of_Drag_List (link off wikipedia)
http://www.tercelreference.com/Downloads/CdA_List.htm
http://www.mayfco.com/tbls.htm (lots of older figures)

If you have or can reasonably guess Cd, you can get A pretty easily. Not sure why it's factored down, but it's 0.84*height*width. Cd is generally 0.26 to 0.38 for the cars we race, and most of them are 0.32-0.36. Since Cd remains relatively constant, most of the difference in drag is because of the more highly variable frontal area.

Trying this out with some more cars using the assumption that 90% of your hp will be available to push through wind resistance the calculations have been spot on, I'm happy to report. Not sure where PD got their numbers, but they seem to agree with the figures I've used very well.

 

[Parnelli Bone]

^Sweet! I'm bookmarking those sites now.

If you ever get to GT3 or GT4, wind definitely does start to become more of a factor. Not wind, but drafting and aerodynamics. There are some cars in GT2 for instance that aren't as fast in GT3 or 4 because their aerodynamics are factored in more accurately with these later games. You really onlly notice this sort of stuff at the Test Courses, though.

Off-topic: where did you get 3 PS1s over the years? I'm assuming eBay?

 

[jeffgoddin]

It's been a long time, so hard to say for sure, but either Gamestop or EB Games. 1st two went bye-bye due to life-changing moves/events maybe a year and a half apart (1st in 1999? then 2000-1?). Last in like 2004-5 and haven't lost it this time.

But on the subject of comparing cars of different weights, I'll just record here the details of what I concluded while doing the comparison of 80's cars.

Basically, given a weight to power ratio, decide what your "anchor" weight is, and for every 40kg/90lbs a car is above or below that weight, increase or decrease the power to weight ratio by 1%, then figure what hp that means to tune to for that weight, and if you run these cars against each other, you can be fairly sure you're comparing skill and fundamental car quality, and not just seeing the unfair advantage higher hp gives at high speeds, where weight no longer matters nearly as much.

Example: pick 2800lbs, 10:1 ratio = 280hp. You've got one car with 3250lbs, =5 x 90lbs over 2800, so ratio goes up by 5% = 10.5 to 1 ratio now = tune to 309 or 310 hp, not 325 for a fair comparison. Similarly a 1900lb car = 10 factors of 90 less means reduce your ratio by 10%, so 9:1 now. Tune to 1900/9 = 211hp instead of the 10:1 ratio of 190hp.

As you can see, this is a real difference. Like a poor Levin getting an extra 21hp and whacking 15hp off of a fat Lexus SC400 and then letting them go at each other. Try it out, I think you'll be surprised what a difference this makes in determining a fair match.

Yes you will probably need a calculator to do this.

This would actually be interesting to see applied to online racing to get fair competition set up. And it would probably apply to real life and could be used to determine ballast requirements given hp for an event.

 

[Parnelli Bone]

^Holy christ! I'll have to try those formulas at some point.

 

[loulou221]

This formula is truly interesting. But I think they aren't available when your cars drive at high speeds, because of the aerodynamics.
Weight is an important parameter to determine overall performance. However, performance depends also on suspension setup, weight balance, engine response (or torque if you prefer)...
To quote your example, If you take the Levin and the SC400, and compare them past 100 mph, because of its greater weight, the Lexus will go faster. But in the corners, it will feel heavy, because it's not really a sports car, but it is more a luxury car, unlike the high-revving Levin.
But similar calculations are interesting, and I admit they can help setting fair competition.

 

[jeffgoddin]

Was just reading back through some old posts and this one caught my eye again.

In anyone's curious to see how well this formula sets up close competition, look over at the "lap time challenge" thread here. All the events are set up using this formula. I think given that different cars actually have different base performance potential, the results are well withing boundaries expected from close competition (when you look at how relatively close the best lap times are for each different car despite frequently having very different stock weight.)

 

[Parnelli Bone]

Well that's cool. Let me know when that wagon thing starts up. I should be doing some laps at Rome this weekend.