Plenum Volume & Intake Runner Calculations

[James Bruce]

Hi guys,

I am designing the intake system for this years vehicle. The problem I'm having is there seems to be a large variety of different, conflicting calculations for calculating runner length and plenum volumes. This is for a single cylinder KMT500 engine. Any help on which equations are trust worthy?

[Jon Burford]

James, hello and welcome.
How do they conflict?
what equations are you trying to use?

[James Bruce]

Thanks Jon,

L = ((EVCD × 0.25 × V × 2) ÷ (rpm × RV)) - ½D
Where: EVCD = Effective Valve Closed Duration
RV = Reflective Value
V = Pressure Wave Speed
D = Runner Diameter.

This is the formula I found on an older thread for runner length. This presumes however, that the runner remains the same diameter. How would I calculate this with a taper?
Also do you know what the numbers 0.25 & 2 denote?

[jlangholzj]

your "resonant frequency" for the plenum and intake runners can occur at different RPM points depending on plenum size and runner diameter/length.

The Helmholtz eqn put our intake runner resonance spot on this last year (calculated vs actual). Its a tad more work but I'd recommend looking at it:

http://www.dinamoto.it/dinamot...ore/risuonatore.html (http://www.dinamoto.it/dinamoto/8_on-line_papers/risuonatore/risuonatore.html)

[thescreensavers]

Just as an FYI Its been mentioned in a few engine books that Helmholtz eqn isn't really great to use after 4k RPM.

Check out this paper it speaks about various Runner Geometries.

http://etd.ohiolink.edu/view.c...cc_num=osu1184187415 (http://etd.ohiolink.edu/view.cgi?acc_num=osu1184187415)

Also you can look into a program called Pipemax which is another tool you can use.

Runner Calculations will never be 100% accurate you need to test it, they can be way off or you may get lucky and hit it.

If you do not have money to test it, which is the same issue I face. Get tons of Papers and sources as to why you designed it that way and have explanations as to why you did it that way. Following an Empirical Method to figure these things out is just fine in my opinion and I believe should be good for the judges.

[Jay Lawrence]

Also remember that your port length is part of the runner, and is unlikely to be a nice consistent cross section (perhaps this helps to explain some of the difference in theory vs. practice?)

[Jon Burford]

Sorry for my late response,
The Helmholtz Resonator is tried and tested and it's something we have used in the past.

Have you tried Dacvid Vizard's rule?

My belief is that whereas these calculations can be correct or incorrect there are many additional factors that need to correct, the plenum characteristics need to well matched to the engine as does whatever you have at the top of the runner in the plenum.

Back to the topic, if you do some more research you will find all kinds of techniques for calculating the runner length, some people will just base it on a simple length and then calculate the first second and third harmonics etc.
It won't take you very long to try a couple of different methods.

Lastly, the most practical way of doing it, is to do it in practise.
Could you design your intake system in a way that you could alter the runner length? for example our plenum is made by SLS and has aluminium runners leading down to the engine. Whilst tuning we were able to shorten the runners simply by cutting material off the top, the calculation method I used, I don't remember what I went for in the end, ended up about 300-400 rpm off, so we reduced the length slightly and got it spot on.

Not the most academic way to do it, but still effective.

[Mbirt]

Engelman's Helmholtz theory (cylinder as volume, intake tract as throat) happens to predict the torque peak for our engine too, but it wasn't used in the design process for good reason. It is convenient, however, that it seems to predict peak intake ramming RPM pretty reliably for intake runner lengths and diameters commonly seen in FSAE for 600/4's and 450/1's.

What I found is that the Helmholtz predictions for those two setups match the more comprehensive results from other methods, namely the duct resonance James shows above and Blair's ramming constants. Both show the 2nd returned wave to come at approximately the same speed predicted by Engleman for the 600. They show the 4th returned wave to come at around the same speed predicted by Engleman for the 450. The "common" baseline duct dimensions I used for the analysis were 16" length and 1.25" ID for 600's and 10" length, 1.62" ID for 450's.

And then you think about it some more and discover the other factors in play. The charge inertia given to the 600/4 by the long runners could be equally as important as the resonance tuning. With the single, which does not need so much help at low speed, you can employ at least two intake ramming peaks to widen the racing operating speed range. I have seen this in simulation and in practice and that is why I do not spend much time on Helmholtz-based design.

These equations serve alright as a starting point, but a quality simulation program such as Boost, GT-Power, or WAVE is what you need if you are aiming to narrow the scope of your testing.

[James Bruce]

Ok guys - after reviewing the calculations and understanding the complete process in my head, it seems that the equations for calculating runner length and plenum volume are co-dependant on having a value for either runner or plenum and visaversa. Is there an "easy" way to generate an optimum runner length or plenum volume before working out the other counterpart component - or is it just a case of trial and error?

Most papers I have read have just plucked a runner length and/or plenum volume out of thin air and based the other components around that value.

[Owen Thomas]

If you have been or will be using a simulation software for your engine, I would try putting a range of values through it and seeing which gives the best results. If you know your target RPM for the "resonant peak" of your intake, you can calculate the corresponding runner length at different plenum volumes. What volumes you check are up to you, but for our 4 cyl I would start at 2L and go up by steps of 0.1 to 5L, or whatever the largest packageable size is. Oh and if you haven't already, putting these equations into MatLab or something similar will save you a ridiculous amount of time. Plus charts are pretty.

As an added bonus, you can avoid the "trial and error" and tell people you "iterated" instead, it totally sounds better http://fsae.com/groupee_common/emoticons/icon_wink.gif

[James Bruce]

Considering a variable system - any ideas for actuation?

[JWard]

Ones I remember:
- Running snail (LC4 single cyl)
- Rutgers (4 cyl)
- Raceyard Kiel (4cyl - rotary rapid prototyped all in one)

[Rex Chan]

Take a look at what other FSAE teams are running, and then use some simulation software to "iterate".

If you're new at this, I'd leave the moving parts for the bits of the car that actually have to move to work. Though, I've seen electric linear motors used, I think.

[James Bruce]

Hi guys,

Considering a variable intake system design - all runner lengths have been calculated. Initial thoughts were to use an electric linear actuator with control box to read the rpm signal from the ECU to set the required length.

Has anyone tried this setup or have any other recommendations?

[Mbirt]

This thread contains some good information about the implementation of variable intakes: http://fsae.com/eve/forums/a/t...607348/m/71720652941 (http://fsae.com/eve/forums/a/tpc/f/125607348/m/71720652941)

My favorite quote is the following:


Originally posted by ST:
All I can say is good luck, the idea of variable intake manifolds is awesome but it's the sealing that kills them.

UWA did two, in 04 and 05. One had awful sealing and good flow paths, the other had horrible flow paths and good sealing.

The net result was an awesomely flat torque, unfortunately it was a collection of all the local minimums.

The guy who did the motor in 06 ripped off all that junk and chucked on an ally welded box for a dyno run just to check things out. The dyno printout was just hilarious when laid over the top of of variable intake curve.

[Nbruno]

I've got what may be a dumb question on this subject, bear with me because I've been reading papers and forum discussions all night so my brain is sort of fried. I understand the idea behind Helmholtz and I've seen calculations in SAE 2002-01-0457 "Formula SAE Dual Plenum Induction System Design". The final result of these calcs is two Helmholtz tuning peaks which is great, but what am I supposed to do with these peaks? Can I go back specify where I want my tuning peaks and rework my eqns to get required runner lengths? Is this even a good idea?

[Dash]

Originally posted by Nbruno:
I've got what may be a dumb question on this subject, bear with me because I've been reading papers and forum discussions all night so my brain is sort of fried. I understand the idea behind Helmholtz and I've seen calculations in SAE 2002-01-0457 "Formula SAE Dual Plenum Induction System Design". The final result of these calcs is two Helmholtz tuning peaks which is great, but what am I supposed to do with these peaks? Can I go back specify where I want my tuning peaks and rework my eqns to get required runner lengths? Is this even a good idea?

That depends on if you care where your power peaks at. What would be the point of doing the math if you just make the runner whatever length you feel like?

[Nbruno]

Originally posted by Dash:
That depends on if you care where your power peaks at. What would be the point of doing the math if you just make the runner whatever length you feel like?
That's what I'm saying. What's the advantage of knowing where your Helmholtz tuning peaks are? I don't understand how people design their manifolds using Helmholtz information. If you must specify runner length, pleunum size etc to know where your Helmholtz tuning peaks are, what design is there to be done? Am I just iterating so that I get my Helmholtz tuning peaks where I want them?

[jlangholzj]

where do you want your power to be made? what advantages/disadvantages are there to placing your power curves at those points? Why would it be important to make sure the plenum and runners are peaking at the same points, or different for that matter?

So for a team like ours, running an N/a R6, why would it be a bad idea to have the power peak at say 4k?

Use your equations to tailor the lengths/volumes to a targeted point to optimize where you want to make power.

[James Bruce]

The Helmholtz calculations allow you to calculate your runner lengths for a given plenum volume based on pressure wave resonance. Iterating between different volumes will alter the length of runner and therefore determine your power peak. You cannot "design" a tuned intake system without any figure to tune it to? I suggest you establish with your team where you want your power peak and for specifically which event (unless you're going for a variable system).

[Owen Thomas]

To echo what the two above said, the idea is to use the resonant "peak(s)" to add some torque/power to a certain area of your torque/power curve (ie at a certain rpm). Where should it go? Well that's up to you and your team to decide. Your decision should be in line with your overall design strategy (easy to drive vs. gut wrenching max power at WOT).

In my opinion, the best place to start would be to ask anyone and everyone who has driven the car with that engine in it. If you have a semi-experienced driver (1 season +) who has driven it with a well tuned engine, he/she is going to be an excellent resource to find current peaks or dead zones. Your next step is to try and get a hold of an old power curve from your engine (if you can get one from the most recent year, you're in luck). You can use this to clear out some of the smoke that driver just blew in your face, and get some real numbers (you can also verify that your equations are correct for that intake/exhaust setup). Hopefully the driver opinion and the power curve somewhat agree, and you can get an idea from those things.

OK, so maybe you don't have either of those things, but you found a power curve lying around from (probably) 2008 and you're pretty sure the design hasn't changed since then. That's ok too, but you're also pretty sure the guy who designed it was a wank, since your peak torque is at 4500 rpm on a 13000 rpm engine. Er... [/rant]

Failing any type of resource, I would say the simplest thing to do would be to look at the torque figures of the stock engine. The peak numbers will typically be lower, and at a lower rpm with the restrictor, but it will most definitely get you in the ball park. From there, decide if you want to add to peak, flatten it out, extend power to a higher/lower rpm, etc.

[Nbruno]

Thank you guys! Finally makes sense. I have it all on a spreadsheet so it should be cake at this point. One more question: Which reflected wave are these tuning peaks at? I'm assuming first. We are looking at a variable (2 step, not continuous, similar to Yamaha's YCC-I design on the R6) but our short runners are something like 22in long from our preliminary calcs. If we go to the second wave or even third could we shorten our runner lengths to a reasonable number? I'd imagine you'd run into timing issues given the speed at everything is happening at.

I'm just thinking out loud, I know I'll have to work this out myself, haha

[jlangholzj]

Originally posted by Nbruno:
Thank you guys! Finally makes sense. I have it all on a spreadsheet so it should be cake at this point. One more question: Which reflected wave are these tuning peaks at? I'm assuming first. We are looking at a variable (2 step, not continuous, similar to Yamaha's YCC-I design on the R6) but our short runners are something like 22in long from our preliminary calcs. If we go to the second wave or even third could we shorten our runner lengths to a reasonable number? I'd imagine you'd run into timing issues given the speed at everything is happening at.

I'm just thinking out loud, I know I'll have to work this out myself, haha

22in seems to be a bit much, IMO. We shot for ~8500 rpm peak on the runners and ~9500 on the plenum and our intake runners were 12" +/- 1 inch. I think the preliminary calcs showed that 9" runners would bump it up to somewhere around 9500 IIRC

[James Bruce]

Because I'm British I use mm (GO TEAM GB) but 22in does seem fairly long however it depends what your target rpm is. You should find that for a constant sized plenum the higher the engine speed the shorter the runner length required.

[thescreensavers]

22in seems to be a bit much, IMO. We shot for ~8500 rpm peak on the runners and ~9500 on the plenum and our intake runners were 12" +/- 1 inch. I think the preliminary calcs showed that 9" runners would bump it up to somewhere around 9500 IIRC

I have read about tuning the plenum geometries to the rpm range like you speak of but I never found any books on the issue. Could you recommend any?

[James Bruce]

The best one I managed to find is called Advanced Engine Technology by Heinz Heisler which has been useful for alot more than just intake geometries and theories.

[Nbruno]

The 22in come from the fact that we're trying to do a variable length plenum. We figured we would have one length for before we entered our powerband, at about 4500 RPM and that length turned out to be about 22in. We estimated that our powerband would go from about 8000-10000 RPM based on other teams GSXR dyno graphs,and we got about 12in, like you guys have said.

[jlangholzj]

Originally posted by Nbruno:
The 22in come from the fact that we're trying to do a variable length plenum. We figured we would have one length for before we entered our powerband, at about 4500 RPM and that length turned out to be about 22in. We estimated that our powerband would go from about 8000-10000 RPM based on other teams GSXR dyno graphs,and we got about 12in, like you guys have said.

Valid, but have you thought about packaging that mess?! either it a)has to fit in the plenum (which would be a rather large plenum) or b) some sort of slinky runners....which would be pretty sweet! lol.

our SS guy relates it to "an 8-headed, 8-tailed snake eating itself" you make one change and that affects something on the other end of the spectrum.

Shooting for a peak power band at 4500 rpm then jumping to 8000 is quite a leap, I'd imagine the dyno graph would be pretty "peaky" and you'd have a nice sketch of the rocky mountains.... I have no experience with the variable length...but isn't 4k a bit of a jump??

also (Thinking out loud) if you went with ~2k jump, thats probably another 3 inches or so...so why is your 4k an additional 4-8 inches?? (considering that a 4k jump would then be ~6 inches).

[Nbruno]

Originally posted by jlangholzj:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Nbruno:
The 22in come from the fact that we're trying to do a variable length plenum. We figured we would have one length for before we entered our powerband, at about 4500 RPM and that length turned out to be about 22in. We estimated that our powerband would go from about 8000-10000 RPM based on other teams GSXR dyno graphs,and we got about 12in, like you guys have said.

Valid, but have you thought about packaging that mess?! either it a)has to fit in the plenum (which would be a rather large plenum) or b) some sort of slinky runners....which would be pretty sweet! lol.

our SS guy relates it to "an 8-headed, 8-tailed snake eating itself" you make one change and that affects something on the other end of the spectrum.

Shooting for a peak power band at 4500 rpm then jumping to 8000 is quite a leap, I'd imagine the dyno graph would be pretty "peaky" and you'd have a nice sketch of the rocky mountains.... I have no experience with the variable length...but isn't 4k a bit of a jump??

also (Thinking out loud) if you went with ~2k jump, thats probably another 3 inches or so...so why is your 4k an additional 4-8 inches?? (considering that a 4k jump would then be ~6 inches). </div></BLOCKQUOTE>
Yes, packaging is the issue. That's why I'm going to explore the possibility of using a second or third reflected wave instead of the first (assuming Helmholtz uses the first). The idea is to still have our peak torque around 8-9k, but to also increase the low end torque with the longer runner.

I really couldn't tell you why the length changes that much. I've been having a hard enough time wraping my head around the different methods and formulas to go in depth about why they do what they. However, I can tell you that the low RPM runners are consistently that much longer with all of the methods and formulas I have found.

[Owen Thomas]

If you're having a hard time wrapping your head around it, it is probably because you are using empirical formulae with scaling factors and no apparent physical connections. I have seen so many different intake/exhaust runner length formulae posted here on the interweb, they all have different units and coefficients but all seem to be within a few centimeters in the end. Suggestion: try deriving the basic theory yourself. It is remarkably simple, and can be done in a matter of minutes if you understand the principles.

Just to get you started; "pressure wave tuning" is the idea that a pressure wave (generated by a valve event) is capable of reflecting somewhere in your runner (at a change in diameter) and subsequently returning to the valve to provide a charging or scavenging effect on the cylinder. Whether it is a positive pressure wave (charging) or negative (scavenging) at the port depends on the geometry of the reflection point (converging/diverging), but this isn't a physics lesson and I'm a tad fuzzy on the details myself (ie. go read up on pressure waves). Since pressure waves travel at the local speed of sound, you can then determine how long it takes for said pressure wave to travel up and back down a runner. Why is this useful? Because you also have the timing of the valve events (in crank angle), which you can use in conjunction with RPM to get a time.

Different theories will tell you when the "best" time (in the valve event) is to have a ramming charge fill your cylinder, hence the many equations giving similar values. It all comes down to cylinder pressure, and the often quoted article"Back to Basics" by Professor Blair (http://www.profblairandassociates.com/pdfs/Back_to_basics.pdf) gives a magnificent run down on this. Now all you have to do is some thinking about when you want your cylinder charged, at what RPM, then a sprinkle of math, a dash of MatLab and you have a solid range of decisions just begging to be validated by dyno data! I have not personally validated this method aside from some limited engine simulation in WAVE, but it gives similar results to the empirical formulae (provided gas assumptions are the same).

One other thing to mention, since you are asking about it, is that every time the wave gets reflected, some of it "continues" and some is bounced back. The amount is based on geometry change, but you can generally say that a reflected wave is smaller in magnitude than the primary. Thus, more reflections = less effective ram charging (this may not be a bad thing). The method discussed above allows you to dictate how many times the pressure wave travels the length of the runner (2 = first reflection, 4 = second, etc).

It has just occurred to me that there must be a way of communicating on this forum without writing a massive wall of text, and I promise to look into that. Either way, hope this was useful.