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      07-11-2015, 07:57 AM   #1
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!X3 Acceleration Files - Master List!

A much larger project than first anticipated, here is the first installment of the Acceleration Simulation as discussed in an earlier thread, and what better way to get it started than to share data on the hypothetical 'M' and '40i' models.

To be clear, this is an approximated simulation and cannot account for the infinite variables present in real world dynamics (temperature variances, custom tire coefficients, individual gearing and torque parameters at different speeds, etc), but Matthew Snare, Dr. Hesham Rakha and their colleagues developed (and verified) a remarkably adept construct in 2002 which appears to model maximum acceleration rates well, and their contribution to this subject is much appreciated. I have tried my best to develop a series of Excel spreadsheets using their recommended equations and have been careful in my attempts to avoid errors. Given the complexity and sheer volume of this data, however, especially for one not versed in this field, it is possible mistakes in the construct (and/or my methodology) have been made. If so, I apologize in advance.

As it takes a lot of time for me to perform these different simulations I am going to add the additional models as time allows, but at least we will have one centralized repository for this information. Once I have completed each model type's four simulated runs, I will then be able to compare across the models, which was the central reason for this project in the first place.
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      07-12-2015, 05:39 AM   #2
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      07-12-2015, 03:07 PM   #3
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      07-13-2015, 04:35 AM   #4
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      07-13-2015, 10:08 AM   #5
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      07-13-2015, 02:46 PM   #6
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wow that's lots of detailed calculations... makes my eyes pop!

Btw, if you are really into the precision of your numbers ( i assume you are, as the numbers are in decimal places), there are couple additional things you need to consider:

1. The engine is rarely making its peak power, you would be flooring it all the time.

2. For merging situations, transmission downshift time ( you probably need 2-3 downshifts from cruising RPM to the RPM that gives you full 240HP on a N20). And it is not just the time of the physical shift itself, but also the time that the computer needs to determine that you need a shift (or two).

3. Turbo spool up time (turbo lag), it was around 1.5 to 2 second for the N54 engine at low RPM (from no throttle to full torque output). N55 should be a bit better, probably around 1 to 1.5 second. Downshift to higher RPM will shorten this lag. Higher altitude will lengthen this time.

4. Inertia of the drivetrain and wheels, the HP is not only used to make car go faster, but also the wheels spin faster. That's why small/light wheel/rim combination can sometimes provide better acceleration. The higher the speed, the larger the kinetic energy (square of speed). 70mph to 90 mph is not slow.
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      07-13-2015, 03:43 PM   #7
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Thank you for your comments, exon.

All of your points are indeed very sound, and I suspect the folks who design professional vehicle modelling software implement coefficients and/or equations which can capture those concepts. As much as I would like to have the knowledge base (not only in Physics and Engineering but also computer programming) to incorporate such variables, as I mentioned in my introductory statements, 'this is an approximated simulation and cannot account for the infinite variables ...'. The model developed by Matthew Snare and Dr. Rakha, however, provides a reasonable and practical solution which fits quite nicely into the goal set forth initially - to be able to paint a broad picture of a vehicle's 'maximum acceleration rates' while (whilst) varying load, grade, altitude, and Cd. And I must admit I have been quite surprised to find it agreeing fairly closely with published times for 0-60 mph and 1/4 mile times as published by BMW and Automobile Catalog in Model (A) simulations.

As I was unable to find such information (how these variables affect our X3s) anywhere online, this at least provides us with a construct with some validity behind it to show how all these come together. And one point on the 'precision'. I always get confused over the terms 'precision' vs 'accuracy'. As this model makes calculations every 0.1 sec for 88 seconds, and the same construct of equations (and thereby methodology) is used for every simulation of the (A), (B), (C), and (G01) types, I think the precision should actually be quite good. What is clear, however, is that the 'accuracy' of the data points (in comparison to real-life measured data) is most certainly off to some extent. Matthew spend a lot of time proving this model provides a reasonable validation with actual field numbers in the 13 cars he and his team tested, so I am comfortable with using it for our purposes here.

And I'm not sure if you have had a chance to read Matthew's thesis yet, but he took it even one step beyond just the maximum vehicle acceleration model, by trying categorize 'acceleration behavior of drivers'. That is way beyond the scope of this thread, but clearly is also another important variable when it comes to merging in real life.

Thanks again for reading. Up next, the 20d and 20i models when I get some time.
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      07-14-2015, 01:25 AM   #8
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My real world problem is this: overtaking a 40 feet trailer on a windy secondary road in a forest. This is a valid exampel in the UK and Sweden.

As mentioned above: using AUTO would mean a delay and then downshift, comined with a nasty jerk. To minimise time in wrong lane AND make a "nice" overtake, I will use MAN and downshift to 3500-4000 RPM prior to overtaking, hence utilising my Power Band (35i), and will pass the trailer with no or just one upshift.
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      07-14-2015, 06:32 AM   #9
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      07-14-2015, 12:33 PM   #10
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      07-14-2015, 03:08 PM   #11
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      07-15-2015, 06:03 PM   #12
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Wow this is great. but the 1/4 times on the larger engines seem way off, not even like a second, but much more.

My stock X3 35i does 13.8 sec at 99 mph in the 1/4 nearly every single time in 75 deg and over type of weather and fairly low elevation. On a colder night such as 30-40 deg with no wind my car can do it in 13.6-13.7 seconds at around 101 mph

Can you change some variables to reflect more realistic 1/4 times?
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      07-16-2015, 04:15 AM   #13
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Quote:
Originally Posted by Crashnbrn5 View Post
Wow this is great. but the 1/4 times on the larger engines seem way off, not even like a second, but much more.

My stock X3 35i does 13.8 sec at 99 mph in the 1/4 nearly every single time in 75 deg and over type of weather and fairly low elevation. On a colder night such as 30-40 deg with no wind my car can do it in 13.6-13.7 seconds at around 101 mph

Can you change some variables to reflect more realistic 1/4 times?
Thanks, Crash. I'm not sure which of the Simulation Settings you are referencing which are way off at the 1/4 mile times. Remember only (A) [which is unladen, 0% grade, and 1 meter altitude] would be applicable to your situation. Simulations (B) and (C) indicate what performance might be expected to be like for +250 kg load, 3% grade, 2000 m altitude and +500 kg load, 6% grade, and 3000 m altitude, respectively, and they are consistent with what one would expect. Going up a mountain side with a significant grade and a heavy load would slow those times. (G01) reflects what we might can expect in our next generation X3s with their lower weight (here estimated to be 100 kg less) and improved Cd (from 0.35 to 0.32), which BMW was able to shave off in the X5s new style.

In (A), the numbers agree within a few tenths of a second across the board for the 1/4 mile times. And such agreement is also found in the 0-60 mph times, except for the 20i and 20d, in which the simulation appears to make them faster out of the blocks by at least 0.5 seconds c/w BMW's numbers. I have spent quite a bit of time looking at that and can't figure why the smaller engines aren't being modeled as accurately early in the curves as all of the larger engines. As mentioned before, though, there are a lot of complex equations which go into this, and for continuity I did not wish to try to change things up for one engine vs another. In a comparison analysis, which was the intent of this project, I wanted to make sure all equations and coefficients remained the same across the board.

I'm attaching here a more 'zoomed-in' look at the 60 mph and 1/4 mile times here, with dashed lines highlighting the X3-M, X3-40i, and X3-35d/35i (which nearly superimpose in this construct) for clarity:
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      07-16-2015, 08:40 AM   #14
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Quote:
Originally Posted by Max Well
Quote:
Originally Posted by Crashnbrn5 View Post
Wow this is great. but the 1/4 times on the larger engines seem way off, not even like a second, but much more.

My stock X3 35i does 13.8 sec at 99 mph in the 1/4 nearly every single time in 75 deg and over type of weather and fairly low elevation. On a colder night such as 30-40 deg with no wind my car can do it in 13.6-13.7 seconds at around 101 mph

Can you change some variables to reflect more realistic 1/4 times?
Thanks, Crash. I'm not sure which of the Simulation Settings you are referencing which are way off at the 1/4 mile times. Remember only (A) [which is unladen, 0% grade, and 1 meter altitude] would be applicable to your situation. Simulations (B) and (C) indicate what performance might be expected to be like for +250 kg load, 3% grade, 2000 m altitude and +500 kg load, 6% grade, and 3000 m altitude, respectively, and they are consistent with what one would expect. Going up a mountain side with a significant grade and a heavy load would slow those times. (G01) reflects what we might can expect in our next generation X3s with their lower weight (here estimated to be 100 kg less) and improved Cd (from 0.35 to 0.32), which BMW was able to shave off in the X5s new style.

In (A), the numbers agree within a few tenths of a second across the board for the 1/4 mile times. And such agreement is also found in the 0-60 mph times, except for the 20i and 20d, in which the simulation appears to make them faster out of the blocks by at least 0.5 seconds c/w BMW's numbers. I have spent quite a bit of time looking at that and can't figure why the smaller engines aren't being modeled as accurately early in the curves as all of the larger engines. As mentioned before, though, there are a lot of complex equations which go into this, and for continuity I did not wish to try to change things up for one engine vs another. In a comparison analysis, which was the intent of this project, I wanted to make sure all equations and coefficients remained the same across the board.

I'm attaching here a more 'zoomed-in' look at the 60 mph and 1/4 mile times here, with dashed lines highlighting the X3-M, X3-40i, and X3-35d/35i (which nearly superimpose in this construct) for clarity:
Okay I see now on this chart it looks more accurate. I do remember reading through the tables not the graphs where I saw that the times are off. But when you draw the dashed line vertically on the graph you can see much easier the simulated numbers
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      07-16-2015, 10:33 AM   #15
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Quote:
Originally Posted by Tjalle View Post
My real world problem is this: overtaking a 40 feet trailer on a windy secondary road in a forest. This is a valid exampel in the UK and Sweden.

As mentioned above: using AUTO would mean a delay and then downshift, comined with a nasty jerk. To minimise time in wrong lane AND make a "nice" overtake, I will use MAN and downshift to 3500-4000 RPM prior to overtaking, hence utilising my Power Band (35i), and will pass the trailer with no or just one upshift.
Valid example in U.S. too. My 35i does not know how to properly use its powerband.

Typical situation is: pedal down -> hesitation/ engine lugging -> nasty downshift & jerk -> too much acceleration and neck snap.
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      07-17-2015, 01:39 AM   #16
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Quote:
Originally Posted by exon
Quote:
Originally Posted by Tjalle View Post
My real world problem is this: overtaking a 40 feet trailer on a windy secondary road in a forest. This is a valid exampel in the UK and Sweden.

As mentioned above: using AUTO would mean a delay and then downshift, comined with a nasty jerk. To minimise time in wrong lane AND make a "nice" overtake, I will use MAN and downshift to 3500-4000 RPM prior to overtaking, hence utilising my Power Band (35i), and will pass the trailer with no or just one upshift.
Valid example in U.S. too. My 35i does not know how to properly use its powerband.

Typical situation is: pedal down -> hesitation/ engine lugging -> nasty downshift & jerk -> too much acceleration and neck snap.
No hesitation on mine (I drive in Sport or Sport +). Do you have DHP?
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      07-17-2015, 12:28 PM   #17
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I am not talking about hesitation: if in AUTO, gearbox has to downshift, before acceleration - means delay and jerk.

If in SPORT, of course the downshift, delay and jerk will be slightly less - but no way as smooth as if using MAN- and properly prepare for overtake.

Note: I was not thinking - should be 80 footer! Even the UK has shifted into the Metric system!
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      07-28-2015, 03:32 PM   #18
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G01 Models at 1/4 Mile Zoomed:

Here is the summary graph illustrating how the G01 models might be expected to perform at the 1/4 mile mark in this approximated simulation. I've also included the analyses for the 'M' at 484 HP and at 516 'tuned' HP as requested by 'jt2' in the 'Wish List for G01 (3rd Gen) X3 2017' thread, http://x3.xbimmers.com/forums/showthread.php?t=1015499 .
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      07-29-2015, 07:06 AM   #19
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X3 35i Sim vs Crashnbrn5 at Island Dragway:

As Crashnbrn provided two of his drag slips in his previous thread 'X3 35i Vs. E55 AMG at Island Dragway, NJ' http://x3.xbimmers.com/forums/showthread.php?t=1144358 , it seemed like a golden opportunity to validate Matthew Snare's Acceleration model for our X3s against documented data. GoogleEarth shows Island Dragway to be oriented East-Southeast at an elevation of 515 feet (+/- 1 foot) along its entire length, so the grade is essentially 0%.

It is unclear whether the dragstrip has the ability to weigh vehicles, but if the exact weight with occupant is known for each race, that could be inserted into the construct for a more refined calculation. As can be seen, the model actually does a remarkably good job at modeling Crash's runs. It is apparent the takeoff appears a bit slow for the sim compared with Crash's actual starts, but if that were to pan out with more runs documented then the equations for the 35i could be refined to capture that.

For those interested, there are 2 different equations for the force curves for every vehicle. Because the initial stage of acceleration is highly dependent on the ability of the tires to grip the road without spinning, the initial force equation remains constant and unique for each individual vehicle and its settings until the power being generated by the engine decreases to a force lower than the 'loss of friction' limit. It is simply the weight of the vehicle, the coefficient of friction of the tires, and a constant. Then the second force equation kicks in which takes into account the available horsepower and the effects of speed. As such, acceleration changes minimally while the first equation is being used, decreasing only because of the increasing aerodynamic and roll resistance. After the second equation of Force begins, then acceleration begins to fall off at a much faster rate.

It seems likely, then, that Crashnbrn's X3 is able to utilize more of its power early (without the tires losing friction and spinning) than the model is giving it credit for, and I think if I just adjust the coefficient to allow for this it might be more exact. But is Crashnbrn's faster take-off a result of his tire choice, or has BMW allowed its anti-skid technology to allow a more efficient transfer of the energy, or a combination of both?

Apologies for the lengthy entry, but it seemed a few out there might be interested in how the simulation makes these calculations, and why.

If any others have their drag slips and wish to have a similar graph made for their vehicle, I'm pleased to enter your data when I have the time. I will need to know your vehicle type (28i or ...), what your HP is (if it has been tuned to a higher than stock), and if you do know your pre-race weight that would be even better.
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Last edited by Max Well; 07-29-2015 at 10:01 AM.. Reason: Corrected italicized words. The Acceleration equation remains the same and is always a=[F-R]/m. It is the Force component which requires 2 equations. Apologies.
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      07-29-2015, 01:29 PM   #20
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Quote:
Originally Posted by Max Well View Post
X3 35i Sim vs Crashnbrn5 at Island Dragway:

As Crashnbrn provided two of his drag slips in his previous thread 'X3 35i Vs. E55 AMG at Island Dragway, NJ' http://x3.xbimmers.com/forums/showthread.php?t=1144358 , it seemed like a golden opportunity to validate Matthew Snare's Acceleration model for our X3s against documented data. GoogleEarth shows Island Dragway to be oriented East-Southeast at an elevation of 515 feet (+/- 1 foot) along its entire length, so the grade is essentially 0%.

It is unclear whether the dragstrip has the ability to weigh vehicles, but if the exact weight with occupant is known for each race, that could be inserted into the construct for a more refined calculation. As can be seen, the model actually does a remarkably good job at modeling Crash's runs. It is apparent the takeoff appears a bit slow for the sim compared with Crash's actual starts, but if that were to pan out with more runs documented then the equations for the 35i could be refined to capture that.

For those interested, there are 2 different equations for the force curves for every vehicle. Because the initial stage of acceleration is highly dependent on the ability of the tires to grip the road without spinning, the initial force equation remains constant and unique for each individual vehicle and its settings until the power being generated by the engine decreases to a force lower than the 'loss of friction' limit. It is simply the weight of the vehicle, the coefficient of friction of the tires, and a constant. Then the second force equation kicks in which takes into account the available horsepower and the effects of speed. As such, acceleration changes minimally while the first equation is being used, decreasing only because of the increasing aerodynamic and roll resistance. After the second equation of Force begins, then acceleration begins to fall off at a much faster rate.

It seems likely, then, that Crashnbrn's X3 is able to utilize more of its power early (without the tires losing friction and spinning) than the model is giving it credit for, and I think if I just adjust the coefficient to allow for this it might be more exact. But is Crashnbrn's faster take-off a result of his tire choice, or has BMW allowed its anti-skid technology to allow a more efficient transfer of the energy, or a combination of both?

Apologies for the lengthy entry, but it seemed a few out there might be interested in how the simulation makes these calculations, and why.

If any others have their drag slips and wish to have a similar graph made for their vehicle, I'm pleased to enter your data when I have the time. I will need to know your vehicle type (28i or ...), what your HP is (if it has been tuned to a higher than stock), and if you do know your pre-race weight that would be even better.
Great stuff Brah!!
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      07-30-2015, 04:34 AM   #21
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Thanks, Crash, and if others post their actual slips I'll be happy to produce graphs for each of their tuned HP X3s as well.

To take this a step further, I was wondering how a completely different model from BMW's stable would perform in a 'virtual drag race' with our X3 35i stock model at Island Dragway. In order to make it a fair competition it seemed a similarly-powered vehicle with better aerodynamics was out of the question. I also need to stay in the AWD realm, because then I don't have to adjust the equations to account for the percentage of mass on the single traction axle (in xDr cars that number is simply 1 since all mass of the vehicle provides traction to both axles). So I chose the 328i xDr, with 241 HP, Cd of only 0.3, wt of 1631 kg, and frontal surface area of 2.20. This compares to the X3 35i with its 300 HP, Cd of 0.35, wt of 1890 kg, and frontal surface area of 2.63. Dramatically different vehicles across the board. So who would win, and how do these different factors interact to produce the aerodynamic result?

I am attaching some graphs to cover: 1). A 15 second run at 'Virtual' Island Dragway 2). An 88 second virtual Salt Flats run at maximal acceleration covering over 3 miles which illustrates how their vastly different parameters still mesh to produce a nearly identical result. It was especially interesting to see the different velocity phases in which one has the advantage over the other.

I would like to run our X3s against some of the other Mnfrs models as well, but I'm having trouble finding real data for the frontal surface areas of most of them. I'll post a chart to see if anyone knows the numbers, but if not, I can always use the 85% estimate based on height and width.

And if anyone in the NJ and NY area has a friend with a 328i xDr who wishes to join you at your gathering, that would be an interesting race to watch (or at least the models suggest it should be)!
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      08-01-2015, 01:56 PM   #22
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Having completed the X3 performance analysis another question arose - how does the X3 35i match up with current competition?. I made a table to clarify some of the dimensions for headroom, legroom and cargo capacity with rear seat up in hopes of comparing a similar category so as not to base it on acceleration alone. Once I run the acceleration curves a simple ranking system for each category and then averaged per vehicle might prove interesting. This seems relevant as comparisons are sometimes made between models without similar attributes (cargo capacity for instance with the X3 and Macan).

And interestingly, I was unable to find the internal dimensions of the Macan anywhere online (despite some effort). On one of the Porsche forums someone mentioned they thought a Swedish publication printed something for those, but I couldn't find it if they did. If anybody knows those it will allow a more accurate comparison with the Macan included. And for those wondering, the MB ML 63 AMG probably does not belong here but none of the other current MB products seemed to fit, and I do not have the new GLC as I was unable to find all the data. I parked next to a MB ML 63 AMG at a mall last weekend - it looked interesting so I'm placing it in the ring as well.

And if anyone sees any errors in this chart please share corrections.
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