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Re: McMath - DL, DW et. al.

In a message dated 97-06-21 18:33:52 EDT, DW writes:

<< Good job bringing this to the light of day!  I haven't had a chance to
> go through it all in the detail it deserves, but would like to build on
> one part that jumps right out:  compressor efficiency is usually taken
> as (ideal work / actual work) rather than (ideal temperature gain /
> actual temperature gain).  The MacInnes book does treat efficiency as a
> ratio of temperature gain, perhaps because that's a safe approximation;
> the rigorous method yields a lower discharge temp...
Dave, Dave et. al.:
DW, altho your math did work well in getting close to DL's numbers, your
McMath method is recognized as more of an approximation than DL's when
applied to turbo/superchargers.  Garrett uses DL's method (a more detailed
version), best described by Freeman and Walsham in "A guide to some
analytical turbocharger matching techniques"  (SAE paper, don't have the
number handy).  Altho your "work loss" technique came to a close number, it
is recognized by most turbo manufacturers that Ti and Ta are the more
accurate calculations for turbo outlet or manifold inlet temps (no IC vs IC,
respectively).   Remember, all these numbers are to help you point at a
turbocharger application that best suits the motor, so ideal is what you
estimate, actual is when the turbo is bolted to the motor.   Also, specific
to your "numbas", since you accepted DL's P1 = 12.2,  P2 is a fixed value
(assuming audis computer; as altitude compensating or absolute). So, P2 =
boost absolute pressure+ ambient pressure = (in your example) 13.05
(=.9*14.504) + 12.2 = 25.25, so, your r = 13.05 + 12.25/12.25 = 2.07 

DL, a rerun of your numbers might be in order, 95% VE (volumetric efficiency)
is very high, the accepted standard is 80% for a given motor, and would argue
that as max on an MC, given non crossflow head design and 2vpc, and marginal
thermal efficiency.  I doubt you would get close to 90 with a 20vt motor.
Also, since you have not changed the stock MC motor, you should use the stock
peak power output as your target max, so use 5500 instead of 6000 for a more
accurate equation.  Then, actually, you offset your VE correction with an
increased turbo efficiency (72%).  The reason you get a power surge at 3000
is that, again, you have a stock MC motor which has a tuned IM for that rpm
as the peak torque, which has good Mach effect on the turbo, which increases
it's efficiency in terms of PR on the MAP right AT 3000rpm, albeit still at a
65% efficiency.  

Both of you have done some excellent math, and DL especially a great job in
explaining the concepts.  There are some charts available that can
"standardize" things like PR vs DR vs Turbo Efficiency, as well as baseline
cfm flow vs displacement @ 80% VE.  These tend to place some historical
"value" to coolant and heat loss in the charts.  

Bottom line, this is the stuff I like to see here.  Hope these numbers can be
correlated to the "real world" by someone soon.  I smile some at my
voluminous files and this "McMath", unfortunately, as one delves into the
lit, math is a great estimator, but a lot of magic still lies in the drop and
measure technique.  I've found these numbers easy to identify a series of a
turbo (ala k2x or TOx), but the variations there are pretty high, min 18 for
the k26 alone.  So, some "art" goes with all the "science".  

Great posts gentleman.

Scott Justusson
'87 5ktq/w
'84 Urq