Powerband Modeling

I've been looking at various dyno graphs lately, and I realized they all got pretty much the same shape. In the meantime I've been reading about how LS6 and FAST intakes are the restrictions, and how they really shape the powerband. My curiosity was peaked how could one part have so much influence on what we get out of a system with so many other parts.
Another important reason behind this inquiery was trying to figure out if making huge peaky cams really makes any sense, can we take advantage of the extra power we get, since all the power seems to show up at the very upper end of the rpm spectrum.

Let's start with few assumptions:
LS6 intake--peak HP (from now on refered to as PH) occurs at 6200rpm, peak TQ (PT) at 4600rpm.
FAST intake--PH is at 6500rpm, PT is at 5200rpm

Let's run through the logic using the LS6 intake's properties.

From most dyno's I've seen, peak torque was about 430lb/ft @ 4600rpm, so let's start with that:
HP=TQ*RPM/5252 and TQ=5252*HP/RPM

HP(TQ=430, RPM=4600)=430*4600/5252=376.6 hp

So if 430@4600rpm is the peak torque value, let's say we design a cam that can hold it all the way to PH, we'd have a flat line, dictating the HP numbers through the RPM dependancy.
with that in mind, we know HP must peak at 6200rpm, so we have:
PH=HP(TQ=430, RPM=6200)=430*6200/5252=507.6 hp

That's the max hp we'll get with this setup. again, let's assume this setup (cam, heads, whatever else is necessary) can carry on that airflow all the way to 6800rpm (a realistic shiftpoint for most LS1's)

With HP curve now being flat to 6800rpm, your torque at redline (RT) will be:
RT=TQ(HP=507.6, RPM=6800)=5252*507.6/6800=392 lb/ft


So we have points for RPM={4600, 5252(freebie), 6200, 6800} which is quite perfect, as the spacing of the T56 usually keeps RPMs above 4600. If you go below that, you're really not utilizing your powerband, but that's a whole different story for another time, thus I will ignore such cases for the sake of this writeup.

Now let's take a look at the same thing, but with FAST intake. Of course, the logic would be the same, just with different peak points, so I did a quick spreadsheet and this is what it looks like side by side for comparison. I know that FAST usually puts out bit more power than LS6, but this is just for comparison's sake.



Notice that both cases make the same power until 6200rpm. It's past 6200, where FAST starts to shine. Just because it extended the full torque a bit longer (only 300rpm), it quickly translates into significant.

But these are just few points. what does it look like once put into a dyno-like graph?
I used my old powerband optimization spreadsheet to demonstrate the two cases.
I used the points from the tables above, and whatever values in between got filled out by Excel's very nice Edit->Fill->Series->Trend->Linear trick (just highlight the range with end values and empties in between first).

Here's what I got (I mangled the pictures a bit to make them smaller for ease of comparison):


On the left, we got the LS6 numbers highlighted, on the right, the FAST.
I also decided to go to 7000rpm instead of 6800rpm in previous part, just to see a bigger change from the power 'up top' power. And the results are...disappointing. FAST, even though by looking at the absolute numbers did pick up quite a bit of power, it did so on such a small portion of the powerband, that the average comes out nowhere near as impressive: 461 vs 467 hp average. that's 6 hp difference on a 460+ hp car. You'll probably get better gains by ignoring free donuts in the office for a week before the race ;)

So how do we make FAST worth the money? Shorter gears would help quite a bit, as we'd have less intervals total if we started at 5000 not 4600rpm, so we'd spend relatively speaking more time on the improved portion of the powerband.

Now, the real gains will be different of course, because FAST doesn't just extend the peak power, but also adds a decent amount throughout the whole powerband, and that's when the big gains would show up in black in white. However, this is a study of shape-shifting powerbands, not adding airflow/compression.

The real value of this little exercise is in quantifying gains that apply only to a portion of a powerband. The real problem lays with the numbers from 4600 to 6200rpm, the range between peak torque and peak horsepower. They're the ones that lower our average HP in the race powerband, and they're the ones to have much greater improvements than optimizing the seldom-visited 6200+rpm territory.

The short version: don't spend your money on mods that shift your power until later, until you already fixed everything else that adds power before peak HP.