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Re: [T3] too much mind time

I've been really busy lately and haven't had time to look at things 
like this in detail. Thus this has taken a back seat until I could 
work thru it and see where the disagreements really were.

On 15 Aug 2001, at 0:55, sml214@casbah.it.northwestern wrote:

Jim originally wrote:

> > If we take into account the length of pipe contained in the intake
> > air distributor and in the head, the total runner length comes out
> > to ~20". For that, we can calculate the resonance: V=freq x
> > wavelength and the lowest resonant wavelength will be 80" (4 x 20",
> > as this pipe will be a quarter wave pipe.) V is the speed of sound
> > or 1100 ft/sec = 13,200 in/sec. 
> > 
> > So freq = 13,200/80 = 165, but a given pipe gets an intake pulse
> > every other revolution so the engine rpm that corresponds to this
> > pulse rate is 330 rpm. 

This is where I made my really silly mistake.The 330 is Hertz, not 
RPM, so I have to multiply by 60 to get RPM, which converts to 
19,800 rpm. Some of you may recall that I expressed surprise at 
how low my first number came out. It CERTAINLY was, a factor of 
60 makes a BIG difference!

Then Shad added in his next post:

> Yes, but one detail: the pulse doesn't get 720 degrees - it gets
> 720 minus the time that the intake valve is open.  I don't have the
> specs for the stock cam offhand, but I'm guessing that it's about
> 210 degrees at 0.050" lift. 

> The total timescale goes from x=0 to x=A.  A=[(720-ECD)/360]*[60/W]
> where ECD is the effective cam duration in degrees, W is the engine
> speed in RPM, and x is in seconds. 

> A quarter-wave is one travel through the runner.  So, T=4*L/V where T
> is the period in seconds, L is the effective runner length (i.e.
> runner length plus port length plus 1/2 the diameter of the runner) in
> inches, and V is the speed of sound in hot air in inches per second. 

The intake air should be cooler than ambient after expanding 
adiabatically in the throttle body, but I don't think that's important 
here. I understand how you're approaching this and it makes sense 
to me now. Note that we are actually calculating the SAME thing 
except that I was using the full period, and you are using only the 
time from the valve closing to its next opening. I agree that your 
method is the correct one.

> The goal, obviously, is to make that timescale an integral multiple of
> the period of the wave.  So, A=N*T where N is our reflection value. 
> Result: 
> V*(720-ECD)=24*W*N*L 
> Let's plug this in: 
> L=20.625 in 
> V=15000 in/sec 
> ECD=210 degrees 
> For N=1, W=15455rpm.  For N=2, W=7727rpm.  For N=3, W=5151rpm. 

It took me awhile to figure out how you got there, but I finally 
managed to duplicate it:

V*t = V*t

but t = [(720-ECD)/360]*[60/w] (in seconds), so
V*[(720-ECD)/360]*[60/w] = V*t

but V*t is the length that the pulse has to travel, which is 4*L, or 
we can allow the pulse to travel this distance more than once so 
V*t=4*L*N, where N is an integer.

thus: V*[(720-ECD)/360]*[60/w] = 4*L*N, or

V*(720-ECD)/(6*w) = 4*N*L

V*(720-ECD) = 6*4*w*N*L = 24*w*N*L

This allows us to use the "subharmonics" of the natural frequency  
of the pipe to get down into a reasonable operating range for the 
engine, just as you explained.

Just as a curiosity, I wonder if there is ever any application of the 
true harmonics which would come out to:

V*[(720*N)-ECD] = 24*w*L

I think only the odd harmonics would work here, because the even 
ones would hit an open valve on an intermediate bounce. Note that 
for large values of N, this approaches the numbers I started out 
with, or meant to, if I had only made the proper conversion from Hz 
to RPM.. I think these resonances would be much stronger, but 
they only occur at impractically high RPMs.

Then Shad added:

> We can also consider when the resonance effect decreases performance. 
> This corresponds to the valleys of the cosine wave, when N=1.5, 2.5,
> and 3.5.  Those correspond to 10303rpm, 6182rpm, and 4416rpm.  That
> last one is interesting: the -3db range of that valley is from about
> 4263rpm-4579rpm. Here there is a DECREASE in performance thanks to the
> runners, which is where the stock 1600 T3 engine has its peak. 
> Between this and the unequal-length runners, I don't think that the VW
> engineers were too concerned with resonance when they designed this
> system :-) 

That's not at all clear to me. It seems to me that this is exactly 
what you would want for a street car, which is what they were 
designing, after all. By placing an intake resonant depression right 
on top of the other peaks they were thereby placing the resonant 
peaks just to either side of the other peaks. The result would have 
been to broaden the power band at the expense of the peak power, 
but this is a desirable thing in a street car. 

You should also just forget about the unequal-length runner 
business; they differ by only 1.5%.

Finally I asked: 

> > Define VE (Volumetric Efficiency?) please. 
> You're correct.  Q=A*V=VOL*VE*T, where flow is Q, area is A, velocity
> is V, cylinder volume is VOL, volumetric efficiency is VE, and time
> (i.e. the amount of time the intake valve is open) is
> T=[ECD/360]*[60/RPM]. 

There's a problem here, in that I can't get the dimensions of the 3 
parts of your definition to agree. If we use English units, 

Q is in in**3/sec
A*V is in**3/sec, but
Vol*VE*T is in**3*sec

The more I think about this, the more I think it was just a simple 
typo, and it should read Q=A*V=Vol*VE/T. Is that what you 

I checked, and VE is just defined as VE= Q1/Q2=Q1/(d*Vol), 
where Q1 is the mass of the air that actually gets in the cylinder, d 
is the air density, and Vol is the displacement of the cylinder. 
There are different ways of calculating Q2 depending on whether 
you use atmospheric pressure or the pressure outside the intake 
valve to calculate the air density. Different definitions are used 
depending on what you're interested in.

Sorry for the delay, and the length....

Jim Adney
Madison, WI 53711-3054

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