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12-13-2009, 12:55 PM | #133 | |
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"...it's not about the money and not about the brand of the car, it's about handling,performance and passion......And that, no other car has all together like an M3........when you talk about the most complete car the M is invincible." --Tony Kanaan. |
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12-13-2009, 01:08 PM | #134 | |
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WARNING - A LONG FORMULA FILLED REPLY FOLLOWS. Power to weight is the single most important factor, both at the track and at the strip, not the torque curve. It is simpler and it actually contains more information. What is confusing you is that the area under the torque curve (T vs. time in an actual WOT run) is what is important and that is very well approximated by peak power. Torque curves either vs. rpm or in gear curves vs. speed only give you instantaneous views of an event that occurs over time. Sure in gear torque curves vs. speed can be sort of scrolled through and visually integrated sort of in a time stepping fashion but the problem with that is you need to move much quicker on the left hand part of the plot than the right since the time between any two speeds is constantly increasing. I am going to spell this out at clearly as I possibly can, with only very basic math and physics. 1. Instantaneous acceleration is the drive force delivered to the wheels (not the torque) minus non drivetrain losses (quantified as forces) divided by mass. This is Newton's second law. 2. Typical ICE engine torque curves are, to a crude but decent approximation are flat and their power curves are therefore typically rising linearly with rpm. The latter comes from P = T x ѡ (SI units, ѡ for angular velocity) or the same relationship, hp = T x rpm / 5252 when using hp and ft lb units. These relationships are nothing more than the basic definition of power for rotating devices. This is for the engine, not the vehicle obviously. 3. At low speeds aerodynamic losses and wheel losses can be roughly ignored calling them a second order effect. This is a reasonable approximation across a typical 2nd or 3rd gear run. Based on these we can write (SI units): Vf = Tw / (rw*m) x t This is Newton’s 2nd Law again with an integration along with the definition of torqe from force, T = r x F. Here is the importance of torque indeed, but we can not neglect time. The formula says in an acceleration run (in gear, starting from 0 speed, and with constant torque) the final velocity is the wheel torque divided by (drive wheel radius x vehicle mass (both just constants)) times the time duration of the acceleration. Clearly to maximize Vf you need to maximize t (since Tw is already constant). In this case, in a single gear, t is then just the time spent in that gear. And the higher the redline the longer you can stay in gear. 4. Torque at the wheels is proportional to engine torque x gear ratio (or gear ratios multiplied in the case of a transmission and final drive). Here we are only considering in one gear so we can say Tw α Te x FD (final drive ratio). This is simply the well known torque multiplication by gearing. 5. When Vf is maximized, at redline, the time spent in gear is proportional to redline / FD, it is simply how long (or far) the engine can spin ratioed with the final drive ratio. Again, this only technically holds for constant accelerations beginning at zero speed. 6. Putting #4 and #5 into #3 we have: Vf max α (Te x FD) x (redline / FD)/(rw x m) Again this is proportional to, not equal to and since all comparisons here are relative the constants and or conversions factors will be the same across the two or more hypothetical cars. So now Vf max α Te x redline /(rw x m) 7. Since Te is constant. Te x redline αpeak hp. So Vf max α peak hp /(rw x m) And with a slightly different constant of proportionality (we can just drop the wheel radius for now). Vf max α peak hp / m This should be plenty to convince one that maximum overall acceleration through multiple gears then also requires the maximum peak power to weight ratio. Neither the instantaneous nor overall acceleration value is actually proportional to this ratio (this prior value varies smoothly vs. time in each gear) they are simply jointly maximized. Q.E.D. Peak power to weight provides maximum acceleration Now you can attempt to argue that torque is never constant; that you must include all sorts of losses; aerodynamic, drive train, wheels; include gear shifts; etc. But all this does is take this the basic key concept here and make you use a bit of calculus and numerical integration to see the same effect or to get more accurate results. The concept still holds. I am happy to share some numerical examples both simulations and real world ones as well to further prove my point. Here is a the first of four counter examples to your thinking. This one is based on detailed simulation since obviously no such car exists: A. What is faster a DCT M3 stock or with the following?
The torque and in gear torque curves look better for the latter car. Nonetheless the standard M3 is faster, it will trap about 1.5 mph faster and cross 1/10 second earlier in the 1/4 mi (pretty much a wash on time). I chose the numbers specifically to illustrate this case. Other details about the two cars: The std. car will:
You can make a basic spreadsheet to show the various formulae and values here and see this yourself. Of course without simulation you can't actually get the 1/4 mile results or others that occur across multiple gears. B. You can see this same thing happen in the real world (if those are the only examples that appeal to you) when you compare cars like prior year base Corvettes vs. the current M3. More torque in the Vette by a huge margin, a bit better power to weight in the Vette, more peak power and much higher redline in the M3, yet very comparable performance. These may not be the best examples as in these comparisons the M3 seems to be over performing just a bit based on its power to weight. Either way the example works to make the point herein. C. Take any large database of performance metrics such as 0-100 time, 1/4 mi. time, 60-130 time, track lap time, etc. Don’t use 0-60 since it highly depends on traction, also don’t choose any single gear metrics and don’t choose any metric involving very high speeds or top speed since those are governed nearly solely by drag, tire losses and peak hp. If everything else is constant between two top speed contenders you will find that peak hp is the only thing that dictates the top speed. An ancillary reason why hp is a better metric. Now plot your chosen metric vs. power to weight. Also plot the metric vs. some measure of torque; some feature of the torque curve, peak torque, peak in gear torque. You will find that power to weight gives the best prediction (technically speaking it will give the best R^2 value for a curve fit) for the data. D. Double the power, weight, redline and FD of any car, leaving its torque unchanged. Guess what will happen to its 1/4 mi. time and trap speed - they will be nearly unchanged. Sure the power monster will begin to really pull away at high speeds but You won't be able to find a simple torque based metric (that doesn't actually have power hidden in it already) that can make this prediction. Force to the wheels works perfectly well but that takes calculations. Hp / weight simply works and it right on the money. Call this my treatise on torque vs. power. Well at least from a message board perspective it is a treatise. I hope this helps. P.S. There is nothing in this analysis that dictates that manufacturers will always choose suitable gearing. If you change an engine from a high power to a high torque design the latter typically comes at the expense of the high redline which in turn necessitates re-gearing. If you purposefully bugger up the gearing for a car my analysis will indeed fall apart. In this case just go back to wheel force (minus losses) divided by weight. As it turns out for sporty cars they typically do choose the gearing quite well. There is also nothing here that claims anything to the contrary to the statement that having the same torque curve extended to a higher rpm with no changes to gearing isn't better - that is simply more power. Last but not least this all is highly related to analyzing the case of alternate (typically higher) FD ratios (rear end swaps). You can improve the in gear torque and acceleration with this mod but you reduce the time spent in each gear, thereby reducing the total time spent at higher accelerations. Just this difference in the DCT M3 is a reduction by about 1/3rd of comparing the average acceleration in 1st vs. in 2nd. That is huge, you really need to balance gearing torque multiplication vs. the need to maintain this very strong 1st gear acceleration for absolutely as long as possible. You can think of it sort of like taking a 33% reduction in power as you shift to second. The combination of the better in gear punch combined with getting through the gears quicker give a very false sense of actual overall improvement in performance across any length of time involving one or more shift. I've beat that horse pretty dead in other posts.
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12-13-2009, 01:25 PM | #135 |
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Radically shortened: you shift to maximize velocity, and change of velocity varies as the square root of work. Work is basically the area under the graph of thrust over distance. Power is the slope of that area (d/dt). Therefore, shift late for maximum acceleration - staying as close as possible to peak power is the key.
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12-13-2009, 01:46 PM | #136 | |||
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Yes, it is a joke. We are witnessing an evolution-this is akin to what happened to the (American) automotive industry back in the '70's. Quote:
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12-13-2009, 01:49 PM | #137 | |
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The above reply sounds like it came from someone in his teens and has a very idealistic option of things. |
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12-13-2009, 02:27 PM | #139 | |
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W is the area under the graph of force vs. distance not force OVER distance. What is thrust anyway, is if force? The latter has a precise meaning, technically thrust is for rockets and jets only. Have you even seen a graph of force vs. distance for a car to actually integrate it. I never have. I've seen torque vs. rpm, torque vs. speed and force vs. speed but never force vs. distance. I would like to see one. I should work on that. The time rate of change of power is work so P is the time integral of work, not the slope. I do not at all see how "shift late" follows directly from your other statements. Perhaps a shortened version is stay in low gears as long as possible since they have such a high mechanical advantage and hence high acceleration yet at the same time do not cause more total force to occur just after any upshift. That however is not really rigorous.
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12-13-2009, 02:30 PM | #140 | |
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imo a racecar experience is about ruthless acceleration, impeccable braking abilities, creating enough downforce to make your eyeballs want to fail and fall out whilst cornering at insane speeds, unforgiving and will bite your head off if you fk up and the list goes on... the sound is just a bonus. Whilst i agree that a muted engine note will certainly detract from the overall experience, but what good would a "performance" car with a ferrari-like engine note be if it corners like a pickup, brakes like a bus(a tad extreme, but you get the picture) and accelerates like the high revving rx8. Do you think the 99% of people that you mention would own these cars? And, there are probably 100 more reasons why many buyers would end up with the ferrari over the Viper |
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12-13-2009, 02:42 PM | #141 | |
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Thrust is the force exerted by the tires on the road (in the plane of the road). I don't do "touch feely" anything. Last edited by BimmerBoomer; 12-13-2009 at 03:31 PM.. |
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12-13-2009, 03:03 PM | #142 |
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Precisely DiVinci, that is why I maintain that there is far more to a sportscar's experience then simply the engine. If you were to believe it's solely the engine that's important then the ideal M car would be either the M5 or M6 with their mighty V10 and their brutal acceleration but no one here would place either ahead of an M3.
It's the complete package that makes cars like the M3 so special. And that is why I reckon 330CI and his opinion came from someone relatively new to driving performance cars and is more at home dreaming about the ones in the posters. When you have driven enough performance cars you realise how important the 'feel' makes to the experience, far more than the actual note or acceleration. |
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12-13-2009, 03:49 PM | #143 |
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Still calling it.
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12-13-2009, 04:53 PM | #144 | |
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Atleast, I drive a 3-series BMW that was developed and modified by the M-division (steering rack, headers, exhaust, flywheel, gear ratios, final drive and the redline) that in some people's opinion could handle even better than a stock E46 M3 around a autoX circuit as opposed to you that drives a diesel Jaguar that has nothing to do with BMW so you need to keep your foolish analogies to yourself.
I am fine with you not personally finding it significant, but don't undermine the importance of it for majority of the people who consider themselves "performance enthusiasts". It is certainly no less or more important than braking, handling or acceleration. The sound is a huge part of the "total race-car experience" a high-performance car and as integral as other components. That is why a Porsche GT3 997 is the dream of even GT-R owners because the GT3 screams "race car" while the GT-R does not. How else would someone justify all the praises and price premium a Ferrari Italia 458 or a Lamborghini LP560-4 receives over the Viper ACR when the ACR beats the Ferrari or the Lambo in every possible performance category? Both cars are equally uncomfortable and impractical. It is all about the soul-stirring experience that the Ferrari gives with the flat-plane crank V8 that the Viper is simply unable to match. By saying such ignorant things I have given examples and I told you before you are in the minority if you think the car's sound is not a huge part of the experience. Like I said before, that is why companies like Ferrari, Lamborghini, Porsche and Pagani etc. have acoustic engineers that develop and tune the engine's sound, sound channels in the cabin and resonance in various corners of the cabin. Quote:
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12-13-2009, 05:21 PM | #145 | |
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12-13-2009, 06:41 PM | #146 | |
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I've only seen one M3 in our area.
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12-13-2009, 08:50 PM | #147 | |
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I still do not see in one single way how your conclusions about when to shift follows from th decriptions you provided. Help me out. Again technically speaking the term thrust only decribes the reactive force from the ejection of mass, typically done by a jet or rocket. I suppose you can use it to mean force but not a jargon choice I would make.
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12-13-2009, 08:57 PM | #148 | |
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12-13-2009, 09:07 PM | #149 | |
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Thanks swamp. Yes, I did once hear about Harley Davidson trying to trademark their V-twin sound.
I recently was reading the LF-A chief engineer's interview in which he had mentioned how people have perceiving Lexus to be "boring, appliance like vehicles" that are "too numb, too comfortable and too quiet". Even Lexus had admitted that the Lexus cars are too boring and numb to drive because they do not entertain the senses of the driver with exciting sounds. In order to address this stereotype, Lexus just did not want to build a supercar that performs extremely well with the LF-A, but they created a total F1 racing car experience and they hired Yamaha acoustic engineers from the Yamaha sound system engineering section to completely create and tune the engine sound, exhaust sound, the ducting inside the cabin to create and route sound channels and to completely resonance in the car. The result? Lexus created a magnificent exotic machine that is getting the attention of everyone with the sound being the key to the sheer attention because of its sound being as good as the Porsche Carrera GT. Quote:
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12-13-2009, 09:07 PM | #150 |
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I love my M3 and don't look back for a moment. BUT...I've had a 996 and 997 and the P-car, while different isn't a downgrade. There's no driving experience like the M3. AND there's nothing like a 911. But Porsche is going the same direction as BMW in the efforts to reach a more diverse market. I'm just thankful, so far, BMW remains committed to the engineering that went into this car. Those days may be short for anybody looking for this type of performance outside of exotics. Hopefully not, but...
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12-13-2009, 09:33 PM | #151 | |
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P = F x v F = m x a then a = F / m = (P/v) / m = P / (m x v) So at any given speed you should shift to maximize power. However, I prefer to look at it through the whole shift sequence, plotting power against time. Clearly the area under this graph is work. Maximize this area and you maximize acceleration. It follows that you should shift past the power peak, in order to take minimize the power loss on upshifts. Last edited by BimmerBoomer; 12-13-2009 at 10:23 PM.. |
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12-13-2009, 10:18 PM | #152 |
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I came from two small displacement (for the US) turbo cars before the M3 - 2.7L biturbo and 2.5L single turbo. When I drove them both the way I wanted, the gas mileage was pretty crappy. If I was taking it easy on them, the mileage was much better; but you need to stay out of positive boost and off heavy throttle. My M3 is obviously worse, but it also has 139HP and 104HP on the two cars respectively - it needs more fuel. |
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12-13-2009, 10:31 PM | #153 | |
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As an example, the EJ257 STi engine has unequal length headers and a distinctive subaru rumble stock. Some choose to switch to equal length headers which results in a loss of the rumble and more of a racy sound. You can also seriously influence the sound of the engine by changing the catback, so there is a lot of tuning to be done. In general though I do agree that high performance NA engines typically sound better than turbos, but not always. |
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12-13-2009, 11:01 PM | #154 | |
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His house? 1.5 Million dollars. |
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