also note that he is using the 4.1 final drive which we probably will not be getting here. Thank you CAFE.

I doubt it, current fuel economy regulations in Europe/Japan are probably stricter than they are in the US but 2016 will be different. Higher final drive doesn't hurt city test economy much anyways. What I want to see is a crazy 0.6 6th gear with 4.100 final drive, best of both worlds. Probably something like a 10-15% fuel economy increase on the highway as it'll decrease rpms by 14% compared to the 3.727 final drive even. With a 3.727 final drive you'd be getting into like 260-270g/kwh cruise which is great but you'd lose first gear acceleration.

looks like only Cd was used not CdA.

1/2 * VFA * CoD * rho * V^2

rho varies depending on temp, elevation, etc but I used 0.00235 slugs/ft^3

I used VFA of 23.68 ft^2 for the WRX (found from google) and approximated the BRZ as 20.5 ft^2. I think the VFA I initially used for the BRZ was a bit too low, so I changed it and added more notes to the plot.

I used this WRX dyno:
http://www.clubwrx.net/forums/engine...yno-pull.html:

I know nothing about rolling resistance, but I based my numbers on the formulas I found at http://www.mayfco.com/aero1.xls which was discussed at http://www.rx7club.com/showthread.php?t=541682

Other links:
http://www.miata.net/garage/tirecalc.html
http://www.mayfco.com/mazda.htm
http://www.engineeringtoolbox.com/ca...on-d_1309.html
(I used the last two linkes to make sure my numbers were in the right ball park)

Rolling resistance is a constant value, good estimate is about 0.008 of the car's weight.

For force, yes. For power, it scales linearly with speed.

Oh, and LRR prius tires FTW. :)

The stock Prius tires are in the 0.006xx range :O Michelin Primacy tires all look to be a tad over 0.008, and there is some Bridgestone tire that is 0.00615, pretty ridiculous.

Yeah at legal speeds rolling resistance ends up being close to 0.008 * weight, but according to that spreadsheet it starts increasing around 80 MPH and it's significant above 100 MPH.

The formulas in the spreadsheets are:

fs = Speed Effect Coefficient
V = speed (mph)
Fd = force rolling drag (lbs)
fo = 0.008
W = weight (lbs)

fs = 0.00195 + 0.000024833 * (V - 150)
Fd = (fo + 3.24 * fs * (V/100)^2.5) * W

From what I've read, though the force required to offset rolling resistance isn't related to velocity, at high speed the additional heat increases the coefficient of friction. I got curious about the formula's numbers and the 5/2 exponent, so I clicked around the domain where the spreadsheet came from and found rolling drag at http://www.mayfco.com/keith.htm

DR = W * (fo + 3.24 * fs * (V * (60/88)/100)2.5 (where 60/88 is just a conversion)

It's also mentioned at
http://www.physicsforums.com/archive.../t-321017.html
http://www.ffcars.com/forums/17-fact...top-speed.html

At some point I might dig my old textbooks out of the basement to look it up.

Anyway, while putting this together last night, it also occurred to me that the FT86's "Prius" tires ought to be advantageous for this. Everyone bashes them, but if steering feel is as good as the reviews say, then I think they make sense.

Coefficient of friction doesn't matter as long as the tires don't slip...?
I'd think that at higher speeds the tire actually becomes stiffer since it experiences strong centripetal forces...

I think the reason why it apparently takes extra power at high speeds could be the fact that C_d changes a bit as speed changes. I'm not sure about this but for example a fastback whose rear windshield is angled at 20 degrees could have attached flow at 40mph, but at 120mph the flow will have significant separation and a much larger wake. With FlowIllustrator (a 2d fluid dynamics thingy) turning up the reynolds number definitely has this effect.

The extra heat is not the cause, it is the effect. Rolling resistance isn't caused by friction, but rather by hysteresis in the rubber. Basically, as the tire rolls forward and a certain patch of rubber comes into contact with the pavement, that rubber gets squished and stores up energy like a spring. As the tire continues to turn and the patch of rubber starts to lift off of the pavement it pushes away from the road and releases most of the stored energy, most but no all. The difference in energy has been absorbed by the tire as heat.

If I had to make a wild guess about that exponential velocity component, I'd say it comes from the viscoelastic nature of rubber. The faster you try to squish it, the harder it is to squish, and presumably the higher its hysteresis becomes.

Good stuff. So, basically 25% less accelerative force most of the legal-speed-limit time in the BRZ vs. WRX. That's fine.

Thanks for the interesting comments serialk11r and old greg, especially regarding the tires' hysteresis.

GTI

Tire is 23.9" effective diameter
 

The ETRTO rolling circumference for a 215/45R17 tire is 1907mm so the effective tire diameter in inches is 1907/25.4/pi or 23.9".

Any toe whatsoever and the effective rolling resistance goes up significantly. ~.012 is going to be more realistic than .006-.008 for a real-world RR figure including a small amount of toe and less than ideal surface.

Regarding Cd and Reynold's number effects, you can assume constant Cd for cars at realistic real-world speeds.

Are you sure? If you take Cd and compute how much power it theoretically takes to reach top speed vs. the actual top speed at which cars top out, I think it's usually off by a bit. For example, a GTR tops out at 193mph, which going by the formula would take far less than 400hp to do. Especially for 200mph+ cars, it looks like they have way more power than they need, but that's not the case.

I'm sure, at 200mph Cd hasn't changed.
There's more going on than aero drag and rolling resistance, btw. There's also loss to tire slip, not insignificant at 200mph. Should be accounted for in wheel hp.
Gearing will also play a HUGE role.

I created one vs the 2004 WRX, which made me doubt the validity of the comparison:

https://lh6.googleusercontent.com/-1...celeration.png

It's not that I don't think the BRZ will be faster than the 2.0L WRX... I expect the BRZ to have better top-end, and if launched abusively might even almost match it in the 1/4 mile. I'm just surprised how much of an advantage that plot gave the BRZ.

I think part of the problem is that published power curves often show more low-end than dynos. So I plotted again, but this time vs the BRZ dyno screencap. Because the scale of the dyno screencap is unknown, and the curve doesn't quite match the published dyno, some guesswork is needed. Here's what a couple users speculated in the screencap thread:

https://lh4.googleusercontent.com/-_...celeration.png

Because it has significantly more midrange output than the published curve, I'm dismissing it as unrealistic.

Next up are plots using a more conservative estimate of the screencap scale. It's also questionable because some runs appear to go way past 7500 RPM (but I didn't use them):

https://lh3.googleusercontent.com/-J...celeration.png

This is more like what I've been expecting all along, at least in the mid and high RPM range. This as probably the worst case scenario, and I won't be surprised if it's in-between this and the other plots.

Again, all of this is speculative.

Here are plots with the conservative dyno scale vs the current GTI and WRX:

https://lh3.googleusercontent.com/-x...celeration.png

https://lh6.googleusercontent.com/-i...celeration.png

170whp is an appropriate estimation of the 2L WRX. They dyno between 160whp-180whp depending on transmission and other factors.

200mph vs. 60 is a 11 fold difference in Re. Let's consider airplanes which will start to have separated flow when the upper surface of the aerofoil is at just a little over 10 degrees. Most cars have rear windshields that will slope a bit more than that, and I could see the case being that at 60 they can get away with it but bump the speed up to say 150 and the flow can no longer stay attached. (not saying this is correct, just possible) And since supercar top speed is a major advertising point you'd think they care about getting 6th gear to hit the top speed. Are you sure about the tire slip? Seems unlikely to me...

Not saying you're wrong necessarily, it's just hard to believe these things.

Changes in Reynold's number are quantified on a log scale. 10x difference isn't really that great once you're in turbulent flow and well below sonic.
But anyway, Reynold's number at 200 is only a 200/60 or 3.33x increase. Not a big deal.

Re = density * velocity * characteristic length/viscosity
changes *linearly* with velocity, not with the square.

You don't start seeing significant drag rise until you're approaching transonic velocities. 200mph is definitely in the same flow regime as 60mph or even 30mph.

Hmmm okay thanks for explaining..
But where does the extra drag come from then?

Didja look into GEARING like I mentioned? I'm guessing not...

So are you saying the GTR could do 220mph if they geared it right?

WHAT?! I don't see how anyone could have read my posts and come up with that conclusion!

Well, if you use the drag equation with constant Cd, then it appears that the GTR has a huge excess of power right?
The tires can't be absorbing 100hp for sure. So you mentioned gearing...so is that to say gearing prevents it from reaching a higher top speed?

Very few cars can exceed the 200 mph mark. Other than power and gearing vs drag, there's just a ton of extra engineering that needs to go into making sure the whole car doesn't start tearing itself to pieces/doesn't lose traction/can actually come to a stop.

An unlimited GT-R could probably manage to make it to something approaching that number, depending on gearing -- I'm sure someone has top unlimited speed data somewhere on the internet.

It is at redline in top gear at 193mph.

The BRZ graph is in kW not hp. 2ZZ is not more powerful.

^Yup. The HP peaks should be touching at least (that would be whp) or the BRZ should be higher.

After finding out that the USDM car will indeed have the 4.10:1 rear end ratio, I was curious how it worked out when mixed with the HKS DynoJet data. I tried my hand at Torque to the tire contact patch chart through all 6 gears, using a visually transferred power curve from the HKS video. The HKS video has been interesting as it markedly differs from the advertised power curve, falling off sharply at higher RPM. Does this represent final engine spec? Who knows 'til production models start hitting the dynos, but for now, here's my graph. I'm using 844 rev/mi for tire rolling circumference, FWIW.

Notice that for peak acceleration, you'll need to:
hit redline [7450 RPM] in 1st
upshift at 7250 in 2nd
7K upshifts in 3rd and 4th
final upshift at 7250 from 5th into 6th [at 130 MPH, mind you]

This is strange for a gasoline production car, to have to upshift prior to redline to get peak accelerative force. Hopefully the production car will breathe a bit better at the top end of the RPM band. Note this was taken from the "wheel HP" data, so drivetrain losses are already approximately accounted for. The only thing missing is aero drag implementation, something Deslock already impressively did in his previous charts.

So when you account for aero the higher the speed, the more drag, so the lower the acceleration, so each of those lines starts to go down a little, and the shift points move up a bit, but on Deslock's chart there is still the shift before redline phenomenon.

I guess the weird drop off >7000rpm is something that can only be explained when the cars start arriving.

Doubtful. For your plot, you used one of the early guesses for scale of the the screencap. I used the same scale for the plot titled "2004 WRX and BRZ (unrealistically optimistic) Estimated Acceleration vs Speed" (in post 175).

I threw that plot out because it shows the car making its peak power too early, and working backwards the engine would need to make 167-171 lbf*ft for 4500-6300 RPM. So either that's not the right scale, or the dyno is from early testing, or this engine is way under-rated. I wouldn't count on the last one, and I only included that plot in my post to illustrate why that guess for the scale appears to be wrong.

It's likely just the wrong scale. Try plotting again with the scale shown in the revised first post in that thread (where peak power is actually at 7k) and you'll get more reasonable results (like my "conservative dyno" plots).

Though it's still not quite right... we won't know exactly what the story is until we see some properly labeled dynos.


The shift points don't change due to drag. You upshift when you put down less power in the lower gear than you will in the higher gear. The only plot of mine that shows shifting before 7450 is the one I discarded, for the reasons mentioned above (all my other plots show the car being shifted at redline).

Sorry, brain fart you're right Deslock.

Thanks for the insight. Indeed, something isn't right. The HKS dyno doesn't come close to matching the advertised engine power graph, even with the alternate 8500 RPM scaling. It ends up missing a whole bunch of low RPM torque, with an improbable torque slope below 3k RPM that wouldn't be caught dead in any recent-times OEM engine.

Indeed, we'll have to wait and see what the real production engine puts out.

The conspiracy of the missing torque continues... Heh...

The missing torque below 3k is hardly a surprise. The cam has to have enough duration for good power at 7k :) The 2GR-FSE has no variable duration, so it has a similar drop (or shall I say nosedive) before 2k. Torque at these ranges is limited by VE, which is limited by the amount of cam advance which is limited by internal EGR.

I want someone to hook up an ODB scanner and log the throttle plate and either confirm or debunk the rumor that the high rpm torque dropoff is Subaru closing the throttle to reduce stress on the engine.

And that is why I will always prefer a throttle cable.

LOL, yes it appears it does.

For the time being, I'm going to make a blanket assumption that the HKS dyno data is unrepresentative of the production engine. Who knows what random yet-fine-tuned parts they had already slapped on the car...or how they were able to induce two separate RPM redlines?

I know Subaru/Toyota don't have to have the engine SAE certified, but it would be very shameful if they didn't....and Japanese aren't very willing to accept such public shame. Considering both Scion and Subaru are advertising 200HP in the US market, I'm willing to bet the engine makes no less than 201HP peak on a poorly broken-in engine [i.e. BMW-style break-in], and upwards of 220HP on a properly broken-in engine. These days, having an engine that doesn't average more than the SAE rating just doesn't cut the mustard. Just for the record, however, I can't substantiate this other than basing it on the current state of the industry.