Brief Tech Article: Area under the curve
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n00b Logic:
"My E36 M3 has more HP than your Civic Si and is therefore superior and faster.... dont even get me started on how cool RWD is either."
The automotive world functions on metrics of peak performance. Sure, these are good metrics, but they do not tell the whole story.
But most of us are better than n00bs and know that its not about peak power, but about area under the HP curve of a dyno plot.
So I have taken 3 Dynojet dyno charts for 3 cars and posted them on 1 chart for comparison. I have also calculated the area under the curve for each one.
Disclaimer: YES, I KNOW these 3 dynos were done at different times on different days by different people at different elevations etc etc etc..... at least I had the sense to make sure they were all Dynojet results.... sheesh.....
The area under the HP curve is just like the area of a rectangle
EXCEPT:
-Dyno charts are a tid-bit more squiggly than rectangles
-The units generated from the area under the curve are HP*RPM which can be simplified all the way down to something along the lines of ((length*force)/time)*(length/time)
we shall simply call them "units" for ease of discussion.
So what do we have here?
A K20 powered Civic Si from 2007 generating a peak 180 WHP. The K20 being one of Hondas better 4cyl engines in regards to low-end power thanks to 2 liters of displacement and iVTEC
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An S52 powered E36 M3 generating a peak 208 WHP. (Most stock S52 cars seem to dyno between 200 and 220 whp on a dynojet)
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AND AN M20 refreshed in Spec E30 trim generating 157 (shut up) WHP. (Most healthy stock M20 engines seem to dyno between 135 and 155 whp on a dynojet and 150 to 160whp in SpecE30 trim)
So since we are all better than n00bs, which of these 3 is going to have the most area under the curve. S52 by a landslide, right? It has so much more low end power than a Honda and makes more power everywhere than an M20.
NOPE, not quite. Even though the S52 (green line) has much more low RPM AND high RPM power than the K20, the Hondas ability to breathe well at high RPM allows it to be crowned the king of this years official WIBIMMERS 1st ANNUAL AREA UNDER THE CURVE CHAMPIONSHIP. (not an actual championship)
Area under the curve totals:
M20: 514,250 units
S52: 721,000 units
K20: 728,000 units
Since HP=Torque *(RPM/5252) a car with a very small displacement, and very short stroke like an F1 car will make very little torque and must rev to the moon in order to make power.
260 lb-ft @ 16,000 rpm from those stubby little connecting rods gets you 792 hp.
Not everyone likes a car that needs to run at high RPM to get moving and therefore the area under the curve doesn't necessarily determine which car or engine is best for YOU, but when considering different engine swaps or deciding how to build an NA engine, looking at area under the curve can offer a different way to look at things.
I bring an M20 into the picture because as a 2 valve per cylinder engine, low end power is going to be sacrificed quite a bit in order to run a large cam and make good high rpm power so I was fiddling around with some calculations to justify building an engine that enhances the already nice mid-range powerband of the M20.
Thats really all. Im sure theres nothing earth-shattering in here but I have been going nuts trying to decide what to do with my engine and dipped into these sort of calculations along the way.
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talk about a cliffhanger.
post it!
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get ready for the trapezoidal rule.
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Yes, trapezoidal rule, Runga-Kutta, all that jazz.
I couldnt decide between a high RPM M20 build with higher peak power (240 hp range) vs a lower power lower rpm (7000 as opposed to 7800) making 190-195hp which sacrifices less low end power and driveability.
Im still working out some cylinder head flow calculations, I am certainly understanding more and more as to why modding the M20 NA is not everyones knee-jerk reaction
It is a very good motor though, just very well optimized in stock form, making it tough to extract more.
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high rpm gets my vote.
very cool write up Mr. Snap
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