11-07-2013, 12:10 AM | #265 | |
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Are you losing faith that the M4 will be all you hope and will be a suitable next car for you, personally?
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11-07-2013, 01:24 AM | #266 | |
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The proof is pretty well in the pudding though... Although one can get bogged down in the large amount of physics involved one can at the same time distill this down to its essence. On a slightly more abstract level - what it say THE 1/4 mile time for any given vehicle? Real world testing involves both controllable and random variables as well as systematic errors. Thus there isn't really a true, single value for such a time. The discrepancies associated with the results from CarTest have been proven across a fairly wide range of vehicles and performance levels to be as small or smaller than the natural variation we observe in testing. Similary it's predictive power to capture a change in performance given a certain isolated change in inputs has also been fairly well demonstrated. The results are certainly immensely more accurate and consistent than say dyno tests... Distilling down to the key inputs they are simply an rpm dependent torque or power curve (or in many cases just peak values and some reasonable interpolation for other rpms) and the vehicle weight. Although gear ratios are important for some individual contests they are not that important for contests across multiple gears such as a 1/4 mi time or trap. Have a look at the possibilities from just a super simple (peak!) power to weight prediction here. This should give you some comfort that most of the other factors you mention are simply higher order corrections to the dominant physics of power to weight. Now specifically I will list which of your concerns are addressed by CarTest. There are plenty more that are included and are critical such as tire losses (see link below). Some are indeed addressed more accurately than others (one specific example is gear ratios and shift times which are certainly handled more accurately than tire friction and tire losses). I certainly appreciate the skepticism here. I was myself initially quite skeptical of the tools ability to capture all of the relevant physics. I even posted about that quite some time ago. Since then I've completely satisfied my skepticism as to the tool satisfying the level of accuracy mentioned above. Despite very small unknowns that remain such as the one that surfaced here - wheel weight vs. wheel inertia, my overall confidence remains quite firm. -Gear ratios and final drive ratio - check -Wheel size (even exact based on rev/mi numbers if you have them) - check -Drivetrain losses including transmission, differential and axles - check -Static and dynamic friction coefficients - check -Shift times - check -Down force - not handled and not required -Center of mass shift with acceleration resulting in changes to peak sustainable wheel force without spin - check -AWD, FWD and RWD - check The full equation CarTest uses was partially quoted above this was the drive force equation. The other forces such as road slope and drag are relatively trivial additions. I've actually modeled a very similar equation simply with V = Vinitial + a * t (i.e. no formal solving of a differential equation) and iterating over a small time interval (inside the context of a huge spreadsheet with a half dozen sheets and thousands of lines...). It's less accurate, less generic and requires the approximation (perhaps even "fudge") discussed herein of using mass factors, but can capture the same complex curves of acceleration vs. time that match very closely with those from CarTest. This post (not mine) shows a variety of screen captures from the software and shows the impressively large number of inputs and outputs one can address with CarTest. Beyond that - buy it, it's cheap and fairly easy to use and I would be happy to let you know which default parameters I have found to need some modifications.
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11-07-2013, 01:28 AM | #267 |
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Thanks for the "atta boy", however, I think "errors" is a bit of a harsh way to characterize the fairly smart skepticism that hotsoup has voiced.
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11-07-2013, 01:52 AM | #268 | |
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Any level of error I've made with regards to gearing should not have a major impact on any simulation results that cover range of gears. Some specific in gear results could though be quite a way off due to this still unknown.
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11-07-2013, 02:18 AM | #269 | |
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Me too, good discussion. Also rewarding that others are interested in this stuff...
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11-07-2013, 12:19 PM | #270 | ||
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So for your example, yes, car 1 will out accelerate car 2. Let's put real world examples to these names. Let's make car 1 an E90 M3 and car 2 an E90 3 series diesel. Pretty similar cars and let's pretend for now they weigh the same (I haven't checked). Car 1 makes ~300 lb/ft of torque and car 2 makes ~425 lb/ft of torque. Which car accelerates harder? Car 1 of course. Why? Because it makes torque at a much higher rpm therefore is able to use higher gearing to more than overcome the engine torque deficit. This is why BMW used to say they loved high rpm motors. With a high rpm motor you can make lots of HP without needing to make tons of torque. This allows lighter smaller drivetrains but requires higher tech machinery. Once you move towards lower rpm turbo motors making tons of HP, you'll end up with much heavier, bulkier transmissions and differentials to handle the extra torque. Pat |
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11-07-2013, 02:04 PM | #271 | ||
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I was using exactly this presumption to establish my "theoretical" optimal gearing for the S55 and was proven wrong by Swamp2 himself . The engine's moment of inertia, gearing and at what engine RPM the power is produced have an impact on how much of that power will be robbed to angularly accelerate the engine instead of accelerating the whole car forward. Last edited by CanAutM3; 11-08-2013 at 07:56 AM.. |
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11-07-2013, 02:30 PM | #272 | |
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Maybe through tweaking of the input parameters, the errors from the losses in the drivetrain efficiency and the errors in inertia happily cancel themselves out in the CarTest acceleration model. Maybe not so in the optimal shift point calculation model . I would not have expected that doubling the FD while halving the gear ratios to have an impact on optimal shift points. The resulting relationship between the car acceleration and engine angular acceleration remains the same and the ratio between gear ratios also stays the same. Last edited by CanAutM3; 11-08-2013 at 07:57 AM.. |
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11-07-2013, 03:48 PM | #273 | |
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Swamp2, thanks for the reply. Some good points to think over. I think we might be talking about two different things if I'm not mistaken. I was focusing on how to identify optimal shift points, and it seems as you're focus is on the macro stuff - predicting 0-60/quarter-mile/etc based on various inputs. For some reason, I was under the impression that shift points were under discussion but if that wasn't the case... oops. Not so crazy about the stuff on the link. Essentially boils down to fitting a curve using regression. It's practical, fairly accurate, easy, and used ALL the time in engineering, but just so inelegant. |
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11-08-2013, 11:58 PM | #274 | |
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Hmmm heading slightly in circles...
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The statement in itself is accurate in the context of the completely incorrect claim that torque is what matters in vehicle performance. Have a look here for my older ramblings on this.
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11-09-2013, 12:07 AM | #275 | ||
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Curve fitting can be dangerous especially when it leads to a conclusion confounded by correlation not being the same as causation. However, in regards to the scaling of ET and times as power to weight ratio to the 1/3rd power there is actually some great basic physics buried in this. Assuming constant power one can derive a close form expression for trap times with (power/weight)^1/3. Thus here we have correlation (curve fitting) and causation.
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11-09-2013, 12:16 AM | #276 | ||
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You certainly don't need to be reminded of this but all of these things being user controlled inputs, along with CarTests ability to do sensitivity studies are overall points that make simulation incredibly insightful and useful. Quote:
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11-10-2013, 10:20 AM | #277 | |
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I think we are saying the same thing, while some losses are torque dependant, some of the losses are speed dependant. Applying a fixed efficiency number that is only torque dependant, as is done in Gillespie's equation, is not really accurate (Gillespie even mentions it himself in his text). Drivetrain losses also vary with other parameters such as temperature, this is why I am saying that they are complex to accurately model. But yes, there are decent enough ways to approximate their impact. Thanks for clarifying that efficiencies are also speed dependent in CarTest, it certainly brings more accuracy. I don't see a "direct" impact (see equations below). However, since the drive shaft would be spinning twice as fast, more power is consumed to accelerate it angularly. This would would slightly reduce the acceleration parameter (ax) in the equation below. But as you said, the impact would be so minimal on optimal shift points, that it becomes negligible in real life. This is why I said I did not expect it to make a difference. Last edited by CanAutM3; 11-10-2013 at 11:50 AM.. |
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11-10-2013, 10:23 AM | #278 | |
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However, I never intended for my comment to imply that you did not understand this. I know you have played long enough with all this to have an in depth comprehension of it all . IMO, one would be off by the ratio of mass factors in the same way as for optimal shift points (see post#263). Last edited by CanAutM3; 11-10-2013 at 10:40 AM.. |
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11-10-2013, 01:10 PM | #279 |
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I think the flaw I'm seeing in this additional derivation is that ηtf, the combined efficiency of the transmission and final drive is rpm dependent. You should also use the 1 and 2 subscripts on ηtf, i.e. η1f and η2f. Although it may not affect your final result, you also have subscript problems in your original derivation. The first t subscript is for transmission gear and the second f is for the final drive ratio. Although your derived equation may determine a condition that is met at the ideal shift point it does not explicitly solve for the shift point. Even ignoring the rpm dependency of ηtf one can't just pick out some terms and say they don't change on both sides and then conclude the shift point is also unchanged. Let me share the way both CarTest and I have implemented this. The value one enters as a fixed percent, say 15% (loss) is scaled according to rpm and redline. As an aside I believe that both correlation with test as well as published loss figures indicate 11% is more accurate for the E92 M3. Let's say we call the 15% number the loss, ℓ Thus ηtf = (1 - rpm x ℓ/redline) (efficiency = 1 - loss) And examining the state of affairs just before and just after any shift ideal or not, the rpm has changed and thus so has ηtf. Originally in my observation and tests in CarTest I just looked at the Nf^2 term in the original equation and realized it isn't invariant under the aforementioned doubling and halfing process. Yes the other primary Ntf term is invariant but there is simply no way everything else in the equation will cancel out this Nf term change precisely. The drive power curves change in both gear n and gear n+1 and there is no way the curves will just happen to intersect at the exact same rpm. The doubling and halfing process will change the ideal shift points, however, again, probably by a fairly small amount. Also as another side note I think this loss is handled a bit differently by different simulators. Some may choose redline or perhaps redline/2, etc. for the constant in the formula above. Unfortunately, this level of detail about CarTest is not available. My spreadsheet simulator uses redline and the formula above. Anyway these differences are significant. They are part of the dominant engine torque term, not part of any inertial (nor equivalently mass factor) terms.
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11-13-2013, 10:14 PM | #280 | ||
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See the new derivation below. The resulting equation does make good sense. When the torque at the transmission output is equal for the two gears, it is the optimal shift point. The key point is that acceleration is still part of the equation. I am still trying to solve the complete equation ax1=ax2 when v1=v2 to remove acceleration from the equation, but the math gets very messy and I have not yet found a path to an elegant and simplified end equation . Last edited by CanAutM3; 11-13-2013 at 10:24 PM.. |
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11-13-2013, 10:29 PM | #281 |
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@ Swamp2
On a different note, I am trying to estimate the various I (Ie, It, Id and Iw) for a DCT E9X M3. In all the simulations you have done, would you have the resulting mass factors for the 7 gears of the DCT? I would also need the assumed weight of the car for those mass factors. |
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11-14-2013, 01:30 AM | #282 |
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^ A much longer reply by PM, getting waaaaay OT...
Anyway for my own spreadsheet simulator I am using mass car = 3537 lb mass driver = 160 lb shift time = 50 ms Mass factors by gear 1 1.19 2 1.17 3 1.15 4 1.12 5 1.11 6 1.10 7 1.10 Although I've done very little validation of acceleration in gears 5-7 Comparing my spreadsheet (light blue) vs. CarTest (purple) for acceleration vs. time I get a pretty nice agreement. Note likely mistreatment of wheelspin after 1-2 shift....
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11-14-2013, 01:36 AM | #283 | |||
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11-14-2013, 08:52 AM | #284 |
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^ I agree on the efficiency. See my new derivation above.
However, for all the other terms that were simplified, they were not simply arbitrarily picked and removed. If, for the condition to be solved, terms are demonstrated equal, they can be simplified. That is mathematically valid. To determine the theoretical optimal shift point, we need to find the intesection point between the two curves, Solve f1(x1)=f2(x2) when x1=x2 So yes, IMO, it does solve for the optimal shift point. Last edited by CanAutM3; 11-14-2013 at 10:41 AM.. |
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11-16-2013, 02:53 PM | #285 | |
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I guess we've probably beat this horse about to death at this point...
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12-12-2013, 05:04 PM | #286 |
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