Tuned intake length 3

Calculate the resultant units and see if it 'balances'.

What is "10.Cs"? Does that mean "10 times Cs"? And what are the units of engine speed? What is "Amt"? What is meant by the "harmonic number"? Is Ac the minimum cross sectional area, or the average?

I was going to comment on the "about 0.25" until I noticed that the formula doesn't actually use it.

It's interesting that there is no involvement of the cam timing.

I have an engine with its intake system apart in my shop right now, and I can measure all this and check it for plausibility in that one particular case. I also know roughly at what RPM that engine produces peak torque and peak power.

Rough guesstimation the "u/Cs" factor will be about 0.05, "S/Ac" will be around 4, the multiplication of those by the 1.62 will be around 0.32, not knowing what "Amt" is I'm going to guess that the factor that it's included in cancels out to be around 1. Simplifying where we can ...

10.Cs/n[1/(K/(1-(1.62 u/Cs S/Ac)^2))+((1-K)/(1-(1.62 u/Cs S/Ac 2/(Amt/Ac+1))^2))]
10.Cs/n[1/(K/(1-0.32^2))+((1-K)/(1-0.32^2))]
10.Cs/n[1/(K/(1-0.1024))+((1-K)/(1-0.1024))]
10.Cs/n[1/(K/0.8976)+((1-K)/0.8976)] Now we need to know what the mysterious "K" is. Guess 2
10.Cs/n[1/(2/0.8976)+((1-2)/0.8976)]
10.Cs/n[1/2.228+((-1)/0.8976)]
10.Cs/n[0.4488-1.114] Obviously that's going to produce a negative number, which is a wrong answer. Guess "K" to be 0.5 to avoid that one term flipping negative
10.Cs/n[1/(0.5/0.8976)+(0.5/0.8976)]
10.Cs/n[1/0.557+0.557]
10.Cs/n[1.7952+0.557]
10.Cs/n[2.35224]
Taking Cs = 340 m/s and n = 200 revs per second then the Cs/n*2.35224 piece of this works out to be about 4. I don't know what to do with the "10." term in front of it but if this is meant to be "10 times" then the answer is about 40. 40 what, we don't know.

If I've screwed up the order of operations or messed up when simplifying all the bracketed terms or guessed way wrong on one of the terms that I didn't understand, please correct me.

It's conceptually correct that whatever the outcome is, will be in proportion to the speed of sound (not that you can influence this much anyhow) and in inverse proportion to the engine speed.

Perhaps the 10.Cs/n[big mess] really means (10 x Cs) / (n * big mess) in which case it's 3400 / 470.448 in my example, which is a number around 7.2 which still makes no sense. Getting rid of the "10." in front of the whole mess gives 0.72 (metres, presumably) which is in the right order of magnitude but still way long for an engine that's spinning 12,000 rpm. But, "k" was a guess. Tell me what it really means.

By the way, the units work. All the terms inside that big mess where one variable is divided by another, have the same units top and bottom (if one assumes consistent use of SI units) and become a non-dimensional factor. So, the big mess is a big non-dimensional factor multiplied by a linear speed (m/s) and divided by a rotation speed (1/s) so it does indeed come out with the units of metres. I'm just not convinced of the physical relevance of that big mess.

Thanks for your involvenment in answering this Brian,

Unfortunately i dont know the AMT value, this was from an argument on a forym where the guy claims to be some kind of engine guru but dont provide relevent answers on pertinent quedtions.


It dont take in account cam timing so i guess it is all wrong. At first i tought it was some kind of "Helmholtz" Formula.

Here's my go at intake length equation:

TF: 720 -(IO+180+IC) closed time intake (Crank deg)
Cs : sound speed m/s
N : rpm

Time available "TA" : [1/((N/60)x360)]xTF
(TA x Cs)/4 = 1st harmonic length in Meters.

Is that about correct ?

That depends upon what your objective is.

By focusing upon the duration that the intake valve is closed, it's evident that your objective in this case is to have a positive reflection happening at the intake valve during the subsequent valve-overlap period.

That's well and good if your engine has a narrow operating RPM range. (Or, perhaps, if your engine has fully variable runner lengths and thus can adjust itself to conditions.) Otherwise, it will be found that you can plug in a lower or higher engine RPM that corresponds to the next higher or lower harmonic (respectively) so as to obtain the same tuned length. Now, what happens at an RPM that is in between those points? Simple; you no longer have a positive reflection happening during valve overlap, you have a negative one. This phenomenon helps at some RPM points but hinders at others - peaks and valleys through the RPM operating range that average out to nil unless you are always at an almost-constant RPM corresponding to a peak and never deviate far enough to reach the adjacent valley.

In my roadracing application (DOHC 4-valve engine with a single individual throttle per cylinder), I of course want top end power (target 12,000 rpm in my case) but I also want torque from around 8000 rpm coming out of a corner, and for following the 1st-to-2nd shift so as to hopefully not get beaten to turn one, and for it to not bog down too badly if traffic conditions (or a missed downshift!) happen to get it a little lower than that. This is a wide enough operating range that no matter what harmonics you choose, it will always be sometimes in favour and sometimes against. If it's going to be like that then it's not worth pursuing, as long as the effect isn't too extreme.

Through engine simulations and thus far backed up by practical reality, I have found it better to focus upon the intake ramming effect at the end of the intake stroke, and not concern myself with the minor positive and negative effects during overlap from the valve-closed reflections. Roughly speaking it seems that one wants the wave to travel out from the intake valve to the airbox and back to the valve in about 90 degrees at the peak-power RPM. The next trip out to the airbox is an expansion wave that accelerates the airflow further, and takes longer because it's against the already-established direction of flow. Then that gets reflected back at the airbox into the runner as another positive reflection further increasing flow velocity, and this takes less time because it's travelling with the already-established direction of flow. At around this time the piston is nearing the bottom of its stroke but you now have a column of air moving towards the cylinder at a good part of the speed of sound which hasn't gotten the message yet that the piston has stopped.

Of course the valve overlap period has the job of getting this process started. The job of pulling the cylinder down to a healthy partial vacuum that dominates over anything the reflections in the intake runner will do, is that of the exhaust system.

My previous car (2008 MB E350, recently handed down) has an intake manifold with adjustable runners. Long runners up to just under 4000 RPM, and then redirected to short runners above that RPM.

Very noticeable effect.

Most everything you read on the web regarding engine design is nonsense. In this instance you're missing most of the important info regarding runner geometry, valve number/size/location, etc. If it gets you in the ballpark for a specific engine then count yourself lucky.

I believe any fixed induction runner will be peaky and that peak can be tailored to work with a fixed cam set to either yield a larger peak or to smooth the peak to some extent. Back in the day, I used a mated cam/manifold set from Edelbrock in my 400 HO GTO, so I didn't have to do the calculations. Today, I would likely rely on CFD analysis. I gave up my GTO long ago and now do all my aggressive driving in my Wankel powered '93 RX-7. Folks who race Wankels sometimes use very cool variable length intake horns, but I'm committed to keeping my engine close to stock (it has K&N intakes, a chipped computer, and a boost controller but I still have all the stock parts on hand so I can easily return to stock).

Well. In this time of being trapped at home, I remembered this thread ... and that the engine in question, in which I focused on intake velocity and intake ramming as opposed to harmonics, is now back together, back in the bike, and running, AND I have a dyno chart!

Looks like it has gained about 15% in power compared to the untouched stock engine, and it has over 90% of peak torque from 7000 to 12000 rpm with a nice smooth curve. BMEP at peak torque is 11.7 bar, which still isn't anything special, but it's a lot closer to a decent range than where it was, and with a broad flat curve. I can work with that. Cam timing was changed in addition to intake runner length and port shape. This is a DOHC 4-valve engine.

Can you share the dyno chart? Extra credit if you have a before and after, with list of mods.

"Schiefgehen wird, was schiefgehen kann" - das Murphygesetz

By the late, great, usually technically pretty solid Roger Huntington -
Inertia // or // resonant ram effects.
A simplified runner length equation, and a graph for those in a hurry or a nice cross check for those going the mathematical route.


1950s - 1960s tech. 10% more torque at 2800 rpm.

The Mopar superstocks and maybe Chrysler letter cars had the shared inner wall cast several inches shorter to create the "short ram version" to work better at high rpm..

The exact numbers and details remain confidential ... never know who's reading this.

Not even without x and y scales?

"Schiefgehen wird, was schiefgehen kann" - das Murphygesetz

Tmoose, Your link is broken. Were you trying to link to "That Crazy Manifold" by Roger Huntington?

That's a cool article. Their really simple formula L = 90,000 / RPM (where RPM is that at which you want it to tune) in my case suggests that the tuning RPM is around 11,000 ... which is about right for my installation (my actual torque peak is around 10,000 rpm but there's a pretty wide range on either side of that). Also implies that the stock intake runners were tuned for around 8000 - 8500 rpm, which also makes sense. Doesn't talk about the cross-sectional area, though ...

Hi Rod Rico, Yes, "That crazy manifold" was the first link. Roger actually talks about 2 flavors of crazy manifolds MOPAR came up with.

The second link was to show the difference between the long and short ram versions of the early 60s sonoramic intakes.

Maybe these will work better -

First on-track test run was yesterday. It's healthy Pulls all the way to redline. It's a little soggy below 7000 rpm, but on track, the only time it's below that is if I make a mistake. It stayed together, the oil stayed clean, the water stayed where it belonged.

The fuel injection needed some re-calibration at part throttle; this was expected. You can't feel momentary hesitations and surges on the dyno, but the track reveals that pronto. There's still something funny happening when rolling on the throttle in the 8000 rpm range. I tried giving it 2 degrees more ignition advance throughout part throttle; that seemed to mostly cover it up, I may try giving it another degree in the affected area. Dyno said it needed 2 degrees more advance at full load everywhere except in that RPM range, so there is something funny going on right around that RPM. I suspect that this RPM range is where the intake and/or exhaust systems are hurting it. It's not a major concern for how I'm going to be riding this bike. It would suck if it were a street bike. That's probably why the stock setup has two different-length velocity stacks, both longer than what I have now.

I intentionally don't have any on-track comparisons with other bikes in my class. On the practice day, I'm eligible to go out in two different sessions although I can only choose one ... "lightweight" bikes, or "expert" riders. I'm both, all the other small bikes at the practice day picked the "lightweight" session, so I picked the "expert" session The situation will reveal itself in two weeks. I know mine isn't the only built engine ... but I spent less money.

Brian's on top of it again.

There are also a lot of both engineering and practical publications on porting and intake blueprinting that are fantastic in information presentation you might want to look in to. An "at hand" reference never hurts.