triple
An engine requires about 2.2 CFM per horsepower, and exhaust gas flows about 115 CFM per square inch.
Assuming 1,400 hp / 2 (since there are two exhaust pipes) means we have 700 hp per exhaust pipe. Multiply that by 2.2 cfm / horsepower and we see we need 1,440 cfm. Divide that by 115 cfm / square inch, and we need 12.5 square inches of pipe area. The area of a 4-inch round pipe is equal to (pi r (squared) = 3.14 x 2 (squared) = 12.6 square inches. So a 4-inch exhaust is just barely big enough to support 1,400 hp.
As an aside, 1,400 hp means each primary tube in the header needs to support 1400 / 8 hp = 175 hp. Doing the same calculation 175 x 2.2 / 115 = 3.3 square inches. The area of a 2-inch tube is 3.1 square inches
So I’ve been sitting here today thinking through the whole header size dilemma and I’ve run some math, that, actually matches right up with real world dyno results. First some measurements:
CES Primary Pipes = 44mm (1.732”)
CES after collector = 57mm (2,244”)
That is Outer Diameter, assuming 0.625” wall you get
1.607” ID = Primary or 2.01 Square inches
2.119” ID = Rear Section or 3.526 Square inches
Using the formula
Area x 115 = CFM for exhaust / 2.2 = HP supported for each pipe you get
105hp for each Primary - All good
184hp for the rear section - not enough...
Now if it were
2” OD Primary
2.5” OD rear section
You’d get
144hp per Primary worth of flow
231hp for rear section
The rear part math doesn’t work like this because the gases have cooled some, but it clearly shows the biggest restriction isn’t the primaries, they’re already a good bit oversized. I posit that a stock motor bike, won’t find anything from diameter increased any bigger than 44mm and 57mm but a built motor certainly might find gains from a larger pipe after the collector.
Further, I’d suggest the Carpenter pipes work as well as they do more because, on his design the 2.25” section acts like a venturi to increase gas velocity and then immediately opens into the flaring megaphone which supports the flow volume and smooths the gas flow. The choke point immediately after the collector is also known to assist in timing sound wave reflections against the exhaust valve to arrive at the right time and prevent reversion, like in a 4-2-1 instead of a 4-1.
There’s a saying “you won’t gain any power after the collector but you can certainly lose it” and I think that’s exactly what’s happening when my CES setup is 20hp behind the Brute same dyno same day same bike.
To go a small step further those flow estimates are based on straight pipe with no restriction. Considering our headers tend to look like spaghetti, they’re certainly causing some restriction, so the 1.75” primaries may actually be a bit of a restriction on a built motor, further validating 2” primaries.
Thoughts?