Tools to calculate AUC?

[M3takesNYC]

No offense but AUC is not something I or some small sect of society has made up. Its completely accepted as a great measure of a cars actual performance.

Take the 1M for example. If you go off of the peak HP number which occurs right about 5200 RPM's but fail to take into account the power band in which it spends its time in during a WOT pull its quite easy to see the relevence.

The N54 peaks around 5400 rpms for peak hp. Its easy to simply watch a few wot runs on youtube to see that Powerband is
1-2 Shift 4500-7k
2-3 5k-7k
3-4 5500-7k
4-5 6k-7K

Take the M3 peak power at 8300 and powerband range as follows
1-2 5600-8400
2-3 6k-8400
3-4 6500-8400
4-5 7-8400

You can cross check absolutely exact shift points and powerbands to the 100th RPM but for illustration this is almost exact. Given 1st gear is so short for illustration look at each car starting in 2nd. The N54 engine has hit its peak hp at 5400-5000 and then continues on down to 7k where power quickly is dropping off. Gets worse with each shift in terms of how far out of its peak powerband it spends more and more time. By 3rd it does not even get to hit its peak power at a WOT pull and by 4th it spends no time at peak hp.

M3 on the other hand takes full advantage of its peak power in every single gear and as it increases in the gears, the more and more it is within the peak power area. Now you would have to calculate the AUC for each range for both cars but if you did I am positive the M3 would make far more AUC than the 1M and its ratio of AUC M3/AUC 1m would be much higher than Peak HP m3/ Peak hp 1M (or any tuned N54 with peak power relatively close or even the same with a tune).

So to say peak power is the whole picture does not make a lot of sense if you look at where the car spends its time at WOT and in the N54 engined car it spends so little time relatively speaking on the actual peak area of power and so much time on the end of the curve where power is falling off that its a huge difference in how that effects performance.

SUre you can shift earlier on the 335 but than you cut your time spent in each gear down and lose gear mutliplication factor which tends to negate or even further worsen power applied to the ground which then is pointless if trying to measure maximum performance.

If you want to compare non-WOT than you can see how a 335/N54 is nice car part throttle because you can be in the 3500-5500 at part throttle and be right in the meat of the curve whereas part throttle with the m3 never even gets you to its peak power band.

I guess if this is all inaccurate you are the engineer but to me and a million articles on AUC it seems relevent!

edit-Its also nice to illustrate the benefit of the high RPM and wide power band in each gear as the M3 spends about 500 more RPM in every gear and thus has 500 more RPM where it can take advantage of gear multplication as well as 500 more rpm when its within its peak power band. These kind things don't show up on peak power comparisons

[knolow]

Originally Posted by img

Sorry this is taking longer than expected. Here's the notes I got back from my buddy on this.

You can download the Excel spreadsheet and it has all of the formulas to calculate area. He's just lagging behind on the tutorial video and says it's taking longer than expected. Maybe by the end of the weekend he can finish and I'll start a new thread about it. But for now, here's what you can do.

1. Download the files:
http://www.rcollins.org/public/Artic...Under%20Curve/

2. Load the "HowTo - Area Under Curve.xlsm" spreadsheet.
3. If you see a warning message saying the document is protected, click to enable editing.
4. If you see a warning message that you need to enable macros, then click to enable macros.
5. Make sure macros are enabled.
A) Click "File -> Options -> Trust Center -> Trust Center Settings -> Macro settings."
B) Check box "Trust access to the VBA project object model."
C) Check box "Enable all macros (not recommended...)" D) Click "OK -> OK"

This spreadsheet is already populated with four different dyno charts from different M3 supercharger solutions.
1) ESS VT2-625, 586whp, 379wtq
2) Gintani Stage-2+, 585whp, 384wtq
3) VF-620, 587whp, 381wtq
4) Active Autowerke, Stage-2, Level-3, 589whp, 379wtq

To calculate area under the curve.
1) Select one of the four tabs containing the dyno data.
2) Find an open cell under the graph to place the "=TrapRule" function. T45 and T46 are already populated with the function.
3) "=TrapRule" uses five parameters to calculate area.
=TrapRule(rpmColumn, hptqCol, startRPM, endRPM, dummyCell)
Where:
rpmColumn = Spreadsheet column containing RPM data (Column-A in this example)
hptqColumn = Spreadsheet column containing HP or TQ data
(Column-J, Column-I in this example)
startRPM = Start RPM (e.g. 3000)
endRPM = Ending RPM (e.g. 8350)
dummyCecll = (OPTIONAL) If you want to automatically recalulate the results after changing dyno correction factors, then fill in this cell with any reference to data in your HP or TQ column. For example: putting "I2" in this parameter would force an automatic recalculation.

Examples:
=TrapRule("A", "J", 3000, 8400) - Calculate HP from 3000-8400 RPMs. No automatic recalculation.=TrapRule("A", "I", 2500, 8600, I2) - Calculate TQ from 2500-8600 RPMs. Automatically recalculates if HP correction formula is changed.

See the spreadsheet. Each dyno chart already has the area calculated under the graph.

Any questions, send me a PM.

Izzy great work. I will def look to use this once I Dyno the M this summer.

[CanAutM3]

I am not sure where you got your numbers, but they do not seem accurate.

First, I believe that the 1M reaches its peak power at 5900RPM, not 5200 or 5400.

Then using the gear ratios you can find the theoretical RPM range in each gear, if you pull every gear to redline in the 1M. Here too, I am not getting the same numbers as you .

1: 0-7000
2: 3950-7000
3: 4665-7000
4: 5350-7000
5: 5940-7000? (not sure it will pull to 7000...)
6: 5920-... (Will not pull to 7000 due to aero drag)

So most shifts will bring the RPM down to below the power peak except for the 4 to 5 shift. To me, this is an indication that it would be best to short shift 4th gear to maximize acceleration. No point in talking about the 5-6 shift as the 1M reaches top speed in 5th gear. I would also be curious to find out if it is worth pulling 3rd all the way to red line in the 1M.

Further, as you posted yourself, the RPM range is very different in each gear, which means that the power-RPM AUC number for every gear is significantly different (the point I made previously).

To maximize acceleration, you need to maximize the area under the curve (there, I said it ). However, you don't need to calculate the area under the curve to do so. Simply plot wheel torque vs road speed for each gear. When the torque line for the lower gear crosses the torque line of the next gear, this is the optimal shift point for that gear. Note that for the M3, the torque lines never cross, so it is best to pull every gear to red line.

I am not disputing the "concept" behind the "area under the curve". The fatter the power or torque curve indicate more useable power or torque. I use the concept as a visual reference when looking at dyno charts. I do however question the usefulness of the number obtained by calculating the AUC.

Could one use AUC numbers to assess performance? Most likely. But the calculations are cumbersome and the selected RPM ranges need to be extremely accurate to produce meaningful results (it does not take much variance to throw the numbers off, 100RPM is not negligible). Further the numbers one would obtain are difficult to present and understand.

My point is that there are much simpler and easier means to compare engines or engine/drivetrain combinations than using the power vs RPM AUC .

[M3takesNYC]

I actually watched about 3 or 4 videos on you tube for each car (a couple tuned N54's and one 1M so perhaps slight variation.) Also looked at the many available dyno graphs of each car for peak power. They are all WOt runs and you can see where the tach runs through each gear and all were identical is where I got the numbers. If peak power was 5400-5900 variance that is possible because I looked at 335si's and a 1M. The tach still stayed in the same powerband but the dyno may have varied with the 1M as I know its not the same engine exactly as the is.

So sure 500 RPMS would matter but not much in that the powerband of the N54 car still shoots past its peak power and spends a good chunk of time in the dropping or flat part of the power curve and in 4th nowhere in the peak power area vs as I said the M3 simply uses more and more of its absolute peak power in each gear.

Peak power is a good tool but when you have cars that are pretty close in power I think it can be misleading. Weight and peak power do a great job and giving you the performance but many cars with similar weight and power can perform differently and AUC is a great measure of how much

[M3takesNYC]

Sorry but you have a very common but very important flaw in your statements here. Peak engine torque is NOT the best place to shift or even after peak engine torque for each gear. Peak power or a bit beyond peak power is the place to shift. That is such a misconception. If you applied this theory to an M3 that means you would shift at around 6k every gear and you cannot tell me that yields more acceleration than shifting at its peak power of 8300-8400? If you do say that than its simply not accurate.

Peak power is where you shift a car or within a range where the loss of power is made up for by staying in the lower gear with its mulptlicaiton benefit. This is usually within a 500 rpm range after peak power or so.

Peak wheel torque which equates to peak HP is where you shift. Engine torque kind of meaningless on where to shift

Goes back to where a car accelerates its fastest and again the misconception its at its peak engine torque when in reality its at its peak power but lets not even go there

Originally Posted by CanAutM3

I am not sure where you got your numbers, but they do not seem accurate.

First, I believe that the 1M reaches its peak power at 5900RPM, not 5200 or 5400.

Then using the gear ratios you can find the theoretical RPM range in each gear, if you pull every gear to redline in the 1M. Here too, I am not getting the same numbers as you .

1: 0-7000
2: 3950-7000
3: 4665-7000
4: 5350-7000
5: 5940-7000? (not sure it will pull to 7000...)
6: 5920-... (Will not pull to 7000 due to aero drag)

So most shifts will bring the RPM down to below the power peak except for the 4 to 5 shift. To me, this is an indication that it would be best to short shift 4th gear to maximize acceleration. No point in talking about the 5-6 shift as the 1M reaches top speed in 5th gear. I would also be curious to find out if it is worth pulling 3rd all the way to red line in the 1M.

Further, as you posted yourself, the RPM range is very different in each gear, which means that the power-RPM AUC number for every gear is significantly different (the point I made previously).

To maximize acceleration, you need to maximize the area under the curve (there, I said it ). However, you don't need to calculate the area under the curve to do so. Simply plot wheel torque vs road speed for each gear. When the torque line for the lower gear crosses the torque line of the next gear, this is the optimal shift point for that gear. Note that for the M3, the torque lines never cross, so it is best to pull every gear to red line.

I am not disputing the "concept" behind the "area under the curve". The fatter the power or torque curve indicate more useable power or torque. I use the concept as a visual reference when looking at dyno charts. I do however question the usefulness of the number obtained by calculating the AUC.

Could one use AUC numbers to assess performance? Most likely. But the calculations are cumbersome and the selected RPM ranges need to be extremely accurate to produce meaningful results (it does not take much variance to throw the numbers off, 100RPM is not negligible). Further the numbers one would obtain are difficult to present and understand.

My point is that there are much simpler and easier means to compare engines or engine/drivetrain combinations than using the power vs RPM AUC .

[CanAutM3]

Originally Posted by M3takesNYC

I actually watched about 3 or 4 videos on you tube for each car

WOW, that is very scientific

[CanAutM3]

Originally Posted by M3takesNYC

Sorry but you have a very common but very important flaw in your statements here. Peak engine torque is NOT the best place to shift or even after peak engine torque for each gear. Peak power or a bit beyond peak power is the place to shift. That is such a misconception. If you applied this theory to an M3 that means you would shift at around 6k every gear and you cannot tell me that yields more acceleration than shifting at its peak power of 8300-8400? If you do say that than its simply not accurate.

Peak power is where you shift a car or within a range where the loss of power is made up for by staying in the lower gear with its mulptlicaiton benefit. This is usually within a 500 rpm range after peak power or so.

Peak wheel torque which equates to peak HP is where you shift. Engine torque kind of meaningless on where to shift

Goes back to where a car accelerates its fastest and again the misconception its at its peak engine torque when in reality its at its peak power but lets not even go there

Where did I ever mention peak torque???

Did you even read my post?

All your points are seriously lacking sound foundations. You are just too thick, I am giving up on you

[IMG]

OK, this finally got finished. It was a lot more work that my buddy expected. I'll keep this short.

HowTO: Export Dynojet dyno data and import to Excel:

HowTo: Advanced Dyno Graphing in Excel

HowTo: Calculate area under HP and TQ curves in Excel

Files for download:
Dyno Database: http://www.s65dynos.com
Spreadsheet with AUC forumula: http://www.rcollins.org/public/Artic...Under%20Curve/

Instructions for using advanced techniques and AUC formula:
1. Download the files:
http://www.rcollins.org/public/Artic...Under%20Curve/

2. Load the "HowTo - Area Under Curve.xlsm" spreadsheet.
3. If you see a warning message saying the document is protected, click to enable editing.
4. If you see a warning message that you need to enable macros, then click to enable macros.
5. Make sure macros are enabled.
A) Click "File -> Options -> Trust Center -> Trust Center Settings -> Macro settings."
B) Check box "Trust access to the VBA project object model."
C) Check box "Enable all macros (not recommended...)" D) Click "OK -> OK"

This spreadsheet is already populated with four different dyno charts from different M3 supercharger solutions.
1) ESS VT2-625, 586whp, 379wtq
2) Gintani Stage-2+, 585whp, 384wtq
3) VF-620, 587whp, 381wtq
4) Active Autowerke, Stage-2, Level-3, 589whp, 379wtq

To calculate area under the curve.
1) Select one of the four tabs containing the dyno data.
2) Find an open cell under the graph to place the "=TrapRule" function. T45 and T46 are already populated with the function.
3) "=TrapRule" uses five parameters to calculate area.
=TrapRule(rpmColumn, hptqCol, startRPM, endRPM, dummyCell)
Where:
rpmColumn = Spreadsheet column containing RPM data (Column-A in this example)
hptqColumn = Spreadsheet column containing HP or TQ data
(Column-J, Column-I in this example)
startRPM = Start RPM (e.g. 3000)
endRPM = Ending RPM (e.g. 8350)
dummyCell = (OPTIONAL) If you want to automatically recalulate the results after changing dyno correction factors, then fill in this cell with any reference to data in your HP or TQ column. For example: putting "I2" in this parameter would force an automatic recalculation.

Examples:
=TrapRule("A", "J", 3000, 8400) - Calculate HP from 3000-8400 RPMs. No automatic recalculation.=TrapRule("A", "I", 2500, 8600, I2) - Calculate TQ from 2500-8600 RPMs. Automatically recalculates if HP correction formula is changed.

See the spreadsheet. Each dyno chart already has the area calculated under the graph.

Any questions, send me a PM.

[M3takesNYC]

Thanks so much for doing this!

[M3takesNYC]

Originally Posted by CanAutM3

WOW, that is very scientific

What is not accurate. You can see under WOT the exact rpm the Tach drops to with each gear and you can watch the tach hit 7k each time. You get accuracy down to the 100th RPM. That is about as accurate as your going to get and you are not correct that 100 RPMS or even 500 RPMS either way are going to significantly change the outcome.

I was referring to your post where you said where torque plots crosses the power plot as being the ideal shift point. That has no bearing on where to shift as its always at peak power or beyond that is the ideal shift

[CanAutM3]

Originally Posted by M3takesNYC

What is not accurate. You can see under WOT the exact rpm the Tach drops to with each gear and you can watch the tach hit 7k each time. You get accuracy down to the 100th RPM. That is about as accurate as your going to get and you are not correct that 100 RPMS or even 500 RPMS either way are going to significantly change the outcome.

I was referring to your post where you said where torque plots crosses the power plot as being the ideal shift point. That has no bearing on where to shift as its always at peak power or beyond that is the ideal shift

[M3takesNYC]

Ok lets agree to disagree

But did you not say the best shift point is where torque and hp cross on a cars dyno? The m3 torque crosses the power and that point is clearly not the ideal shift point. So perhaps I misunderstood your comment but its actually really simple. Best shift point is a couple hundred rpms or so past peak power. Not sure how you can argue something that is all math but hey I agree to disagree man! no probs!

Great info you added as well which is appreciated

[CanAutM3]

Originally Posted by dvpouldar26

You are correct, my equation had a typo. the y-values should be added. I think the trapezoidal rule should suffice as well. An integral is basically the same calculation as the trapezoidal rule, but a little more accurate since you are splitting the area under the curve into an infinite number of sections.

The AUC is valuable because unlike comparing peak horsepower and torque numbers, it compares essentially an average of useable power a car makes. It sums up the power over the entire power-band showing how much useable power the engine is making, regardless or rpm. An example of this is comparing a 800rwhp supra with a very small powerband vs a 500rwhp supra with a fatter, more useable powerband. Both cars will have similar AUC. Mods that are most effective are not mods that make great peak power, but those which make more power consistently through the powerband; those mods have the greatest impact on AUC.

I think calculating AUC for some of these cars is a great idea, something that hasn't been done yet, and has the potential to show what mods are most worthwhile in making useful power.

Sure, power vs RPM AUC numbers can be used as analysis tools. However, I still question how easy it is to interpret the numbers. If it has not been done before, there is a reason why… Let me use a simplistic example to illustrate the point.

Let’s do a comparison for a 3rd gear pull on a 6MT M3, which equates to a 5600 to 8400 RPM range (if 2nd gear was redlined). Lets assume an engine mod that provides no gains at 5600RPM but linearly increases to 10lb-ft at 8400RPM. This equates to 0hp at 5600 and 16hp at 8400, thus increasing the area under the curve by 22400hp-RPM (16*(8400-5600)/2). Now consider another engine modification that does the opposite, adding 10lb-ft at 5600 linearly decreasing to 0lb-ft at 8400RPM. This equates to 10.7hp at 5600 and 0hp at 8400, increasing the area under the curve by 14980hp-RPM. Now if you calculate the area under the torque curve, both mods would yield the same increase: 14000 lb-ft-RPM (10*(8400-5600)/2).

Now the big question, which is the better modification? According to the power AUC calculation, it would be the first mod by a factor of 1.5. According the torque AUC calculation, both mods are equal. However, in real life, the car with the second mod would pull away from the first since it is pulling harder early on; with the second car matching the speed at the end of the pull but staying a distance behind. The power AUC number is clearly misleading here.

So if it is difficult to interpret the numbers in this simple example, just try to imagine interpreting AUC numbers for different cars with different gear ratios and power bands. IMO, almost impossible .

[M3takesNYC]

With all due respect the AUC under the torque curve is as irrelevent as the torque at the engine anyway. All about HP and AUC under power curve. Any mod that maximizes the power under the curve for HP will yield faster acceleration.

By the way for kicks I logged with my BT tool acceleration which it can do and as expected acceleration was greatest at 8300 rpms. Progressively from lower rpms to redline and the peak engine torque at a much lower rpm had a much lower acceleration than at 8300 which is peak power. It is an aside but to the age old debate where highest acceleration occurs hp vs torque engine. I saw actual numbers illustrating of course its at peak hp that acceleration is the highest. This was in 2nd and 3rd