Tools to calculate AUC?

[M3takesNYC]

You often read about area under the curve of the horsepower tracing to really see the true impact of a cars powerband, especially if tuned and there is perhaps a small peak increase but area under the curve is large.

You would need to calculate the area within the powerband obviously so with the m3 its roughly from 6k-8400.

I would love to see some comparisons for AUC from the m3 to whatever else. RS4 with same peak power, 335, tuned 335, 1m etc.

Someone savvy at math or who has a program this would be awesome.

Also what units would this be measured in I guess?

[dvpouldar26]

To calculate AUC, use excel to plot the points of the dyno graph then use an integral function to calculate the AUC. The units are hp*rpm or hp*1000rpm depending on how you plot your data points. It's a pretty simple calculation if you have the time.

[M3takesNYC]

Thanks but I have no idea to get a dyno plot onto an excel sheet! I am a total computer illiterate! Manually enter the plot data?

[IMG]

I have a buddy that will make a HowTo video tonight. He'll show you how to export dyno charts to excel and how to calculate area under the curve. Just hang in there another 12 hours.

[klammer]

Originally Posted by img

I have a buddy that will make a HowTo video tonight. He'll show you how to export dyno charts to excel and how to calculate area under the curve. Just hang in there another 12 hours.

That would be great. Thanks for that

[IMG]

Originally Posted by klammer

That would be great. Thanks for that

[urBan_dK]

The tool is called calculus.

[BMRLVR]

I will leave it to Izzy to deliver the tools to do this, however, here is an interesting article for you to read on the subject: http://www.hotrod.com/techarticles/h...e/viewall.html

[klammer]

Originally Posted by urBan_dK

The tool is called calculus.

excel=calculus?? Think we're all looking at the "tool" to apply the calculus in, and I think we've found him

[M3takesNYC]

Awesome!! I don't think I have ever seen someone actually compare AUC between cars. Its always power or torque at their peaks. Should be a nice display of why this car hangs with many cars and why its significantly faster than many.

And yes sorry most of us do not know integrals/calculus and related math to even approach being able to do this.

Really awesome there is someone who will post a tool or DIY. Thanks!

[dvpouldar26]

Originally Posted by BMRLVR

I will leave it to Izzy to deliver the tools to do this, however, here is an interesting article for you to read on the subject: http://www.hotrod.com/techarticles/h...e/viewall.html

I've read that article before as well, great article!

Originally Posted by klammer

excel=calculus?? Think we're all looking at the "tool" to apply the calculus in, and I think we've found him

Excel is used to find the best-fit regression line for all the data points in excel. You integrate that best fit line to get the AUC. There's several other methods of calculating AUC that are a little less accurate, such as splitting the area under the curve into areas of specific width, and finding area of each of those sections by finding the area of a trapezoid. Or you could count the squares under the curve.

[M3takesNYC]

This was what was referred to as the guy who was going to give us the answer? No offense but counting the squares...I think we all have already realized that is an option but when you realize how inaccurate that is for a piece of the curve especially I was hoping for some more math but thanks! Ill read about excel some more!

[dvpouldar26]

Originally Posted by M3takesNYC

This was what was referred to as the guy who was going to give us the answer? No offense but counting the squares...I think we all have already realized that is an option but when you realize how inaccurate that is for a piece of the curve especially I was hoping for some more math but thanks! Ill read about excel some more!

No, I am not the guy IMG was referring to....we're still waiting for him to chime in. I didn't know you're looking for a more mathematical approach but here's there more mathematical explanation. If you get a best fit regression line's equation, and integrate it from x=0 (0 rpm) to redline (for example x= 8.3 as in 8.3Krpm), you should obtain the area under the curve. A simple integral will be needed for this and this will give the most accurate sum of the AUC. Another approximation is using the trapezoidal rule. Again, split the x-axis into even intervals (say every 1Krpm), and find the area of each segment by calculating the are of the trapezoid. The area of a trapezoid is found by [(y2-y1)/2] x (x2-x1). Hope this helps.

Refer to this link if you're looking for more help in excel to find the integrated area and area from by trapezoidal rule:
http://people.stfx.ca/bliengme/Excel...UnderCurve.htm

[IMG]

Originally Posted by BMRLVR

I will leave it to Izzy to deliver the tools to do this, however, here is an interesting article for you to read on the subject: http://www.hotrod.com/techarticles/h...e/viewall.html

Great article,Thank you Sir

[IMG]

Sorry it took so long. Here's the first part. This video tutorial shows how to export data from Dynojet software and import into Excel.

Tomorrow, my buddy will do the HowTo video for calculating area under the curve. He already wrote the software part of it, he just needs time to make the video tutorial (tomorrow).

[M3takesNYC]

Cool thanks so much!

[CanAutM3]

Originally Posted by dvpouldar26

Another approximation is using the trapezoidal rule. Again, split the x-axis into even intervals (say every 1Krpm), and find the area of each segment by calculating the are of the trapezoid. The area of a trapezoid is found by [(y2-y1)/2] x (x2-x1). Hope this helps.

In my opinion, for this exercise, the approximation method proposed by dvpouldar26 would be accurate enough. Naturally the more data points are used, the more precise the result becomes. I think the equation should read [(y2+y1)/2] x (x2-x1) though.

I guess the AUC number could be useful to compare the gains achieved on a given car for a given power band before and after mods. Or comparing two same cars for a given RPM range.

I am however questioning how meaningful that number is in general, regardless of how precisely it was established. Comparing absolute area under the curve numbers for power vs RPM of different engines does not tell you much. Especially if you want to compare different types of cars (M3 vs C63 vs RS4 vs 335i). Transmission gearing determines the power band used in each gear and what power is produced for a given road speed. A different area under the curve needs to be calculated for every gear for each car.

The area under the curve of power vs road speed would be more appropriate to compare different cars. And again, the number itself would not tell you much, as the power required to accelerate an object at a given rate increases linearly with speed ( P=m*a*v ).

The best way to visually assess the acceleration capabilities of a drivetrain is to plot torque at the wheel in each gear vs road speed. Superimposing the graphs of two different cars will tell you which cars will pulls stronger at a given speed (assuming similar drag characteristics).

Here is an example of a 6MT M3 vs a DCT M3.

[klammer]

Good stuff guys! This is why I still come here all the time, learn something new everyday

[dvpouldar26]

Originally Posted by CanAutM3

In my opinion, for this exercise, the approximation method proposed by dvpouldar26 would be accurate enough. Naturally the more data points are used, the more precise the result becomes. I think the equation should read [(y2+y1)/2] x (x2-x1) though.

I guess the AUC number could be useful to compare the gains achieved on a given car for a given power band before and after mods. Or comparing two exact same cars for a given RPM range.

I am however questioning how meaningful that number is in general, regardless of how precisely it was established. Comparing absolute area under the curve numbers for power vs RPM of different engines does not tell you much. Especially if you want to compare different types of cars (M3 vs C63 vs RS4 vs 335i). Transmission gearing determines the power band used in each gear and what power is produced for a given road speed. A different area under the curve needs to be calculated for every gear for each car.

The area under the curve of power vs road speed would be more appropriate to compare different cars. And again, the number itself would not tell you much, as the power required to accelerate an object at a given rate increases linearly with speed ( P=m*a*v ).

The best way to visually assess the acceleration capabilities of a drivetrain is to plot torque at the wheel in each gear vs road speed. Superimposing the graphs of two different cars will tell you which cars will pulls stronger at a given speed (assuming similar drag characteristics).

Here is an example of a 6MT M3 vs a DCT M3.

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.

[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.

[M3takesNYC]

Calculating the AUC for the powerband is not really useful under 5500-6k. A measure of WOT power really for the M3 would be 6k-8400k as that is the power curve for virtually 1st, 2nd,3rd, 4th give or take 500 rpms.

It actually argues that it is a great tool to measure or compare other cars. You don't need to do it every gear although you could to be more specific but you could take the power band for a 335 for example at WOT is essentially 4.5-5k-7k You look at the AUC for that band of power which under WOT it never dips below that and you can take the power AUC.

Interesting to compare to other 320 peak power cars or even higher peak hp cars with less AUC or any other combo. Even to compare a 1m to a m3 woul be interesting. Taking the hp band between 5k-7k and comparing the 6k-8400k area and seeing which one produces more and by how much. I know the M3 does but to see how much would be more telling than a peak number

[CanAutM3]

Originally Posted by M3takesNYC

It actually argues that it is a great tool to measure or compare other cars.

No it is not.

Originally Posted by M3takesNYC

I know the M3 does but to see how much would be more telling than a peak number.

Again, No. If you are looking for a single number to assess the acceleration capabilities of an engine, peak HP is it. Period .

If you want to compare the power produced in the power band (the upper RPM range for every gear), I would calculate the average power produced in that RPM band instead of the AUC.

How do you pick the RPM range for which you will calculate the AUC? Your picks seem very arbitrary. You picked 5k-7k for the N54. Do you realize that changing that band by only 200RPM can affect the calculated AUC by as much as 10% ?

Have you ever wondered why no one publishes HP vs RPM AUC numbers? The answer is very simple, it is because it does not mean anything.

If you have time to spare, go ahead and calculate away. You might learn something in the process. However, after 6 years of science and engineering studies and 20 years in the aircraft engine industry, I believe it is a futile exercise.

I fully understand that only looking at peak power does not provide a complete appreciation of a drivetrain characteristics. As I mentioned in my previous post, a good way to compare cars and drivetrains is to plot wheel torque vs road speed in every gear for each car and then compare the graphs.