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Rocky Mountain Boost - the long and the nerdy

Many posts recently on the effects of altitude on audi Turbo car
performance....  Hope to not get too nerdy (or too helpful, depending on
who's reading), but here's what happens with boost and altitude...   Coupla
points to start:

*  Audi computers are the absolute pressure type and ARE ALTITUDE
CORRECTING....  P (atmospheric) + P (boost pressure) = Absolute Pressure
(guage pressure)....   So at sea level, a 5ktq shows .9 (or 1.0 depending on
the guage) when engine off which is atmosphere...  The computer allows ~.425
bar pressure (max), so a stock turbo motor (lets take an 87 MC motor with a
stock computer) should see 1.425 bar on the guage at sea level

*  At 5000 feet the Density of air is 87% of sea level Density.....
 Simplisically translating this, on a 100hp N/A motor @ sea level (no other
changes), will make 87hp (= 87% HP efficient) at 5000 ft....  On a turbo
motor this is mathed differently.  First, the NON ALTITUDE compensating
method.   Assuming your guage to read 1.0 bar at sea level, it will now read
.845 at 5000 ft.  Add in the boost pressure .425bar you get (.845 + .425 =
1.270guage)....  Taking this further, lets assume that the turbo motor is
putting out 100hp @ 1.425bar @ sea level.....  Go to 5000 ft and you get
1.270 bar absolute of boost, so on a turbo motor (non altitude compensating),
you will be making 89.12hp (89.12% HP efficient) at the same altitude as the
N/A making 87hp.....  

*  The audi computer has altitude correction built in, so at 5000 ft, the
boost is increased from .425 to .575 (yo, that's audi-eeez, so +/- .250 is
allowed, took mean for all calculations)...  So, with the guage reading .845,
add the .575 = 1.42 absolute...  Translating this, the MC motor will be
99.64% HP efficient (and given the altitude pressure table variance of +/-
.250 of mean, 100% is within spec) of sea level HP @ 5000ft....  All other
things be equal (caveat), there should be NO DIFFERENCE IN POWER LEVELS

*  The rule of thumb for turbine speed:  +1% for every 5000ft above sea
*  The audi K26 in stock trim spins @ ~100,000 rpm @ 5krpm @ sea level @
*  Above 2.0 bar, the efficiency of the turbo DECREASES, as does the cooling
efficiency of the IC
*  At 6200rpm the the turbo is spinning ~105,000rpm yet the efficiency of
it's output is reduced by  ~3%....  The definition I suppose, of spinning
your wheel without going anywhere....

Slowing this down some, lets look back to altitude and the k26....  What the
k26 was designed to do is to run at a very wide range of rpm to turbo
efficiency (more than 65% from 4000 to ~redline) 65% being the low target
efficiency acceptance for most turbos.  What is significant also, is that at
the 1.425bar of the example above, puts the turbo @ about 70,000 rpm and at a
less than 60% efficiency for a more significant amount of time, esp where one
needs it most, at the low-mid and the very hi rpm ranges....  Add to this,
the CIS system is lean most in both these ranges, hp and volumetric
effiiciencies not looking good....

Solution:  Get the boost to where the k26 is designed, specifically the K26
in stock trim is very well suited to a 1.9 bar mod (hello Ned et. al.) at SEA
LEVEL.....  Beyond that you are losing more than gaining with the stock 26
and the stock IC....  Let's take a look when you apply the altitude to a
1.9bar mod:

Sea Level = 1.0 bar + .9bar boost = 1.9bar absolute (100% HP efficient)

5000ft (non altitude compensating) = .845 + .9 bar boost = 1.745bar absolute
(91.8% HP efficient)
5000ft (altitude compensating) = .845bar +  1.155bar boost = 1.9bar absolute
(100% HP efficient) 

Yow sikes batman!!!!  The problem with this boost level @ 5000ft altitude is
that  1.155 bar boost pressure gives a 2.2 pressure ratio.  PR - Pressure
Ratio = Pressure @ compressor outlet(absolute boost pressure or ambient
pressure + boost pressure) P2/ Pressure @ compressor inlet (absolute ambient
pressure @ altitude)P1= P2/P1 = 1.9/.845 = 2.2   ----   corrected to my k26
MAP; you are less than 65% of turbo efficiency at up to 3800rpm, and never
are you in the max efficiency of the stock k26, and in fact you MAX at
65%....  Add in the fact that you are spinning that turbine at excess of
110,000 rpm from 3800rpm up, disaster awaits you  (k26 was designed not to
exceed 105,000 on the I5), as does the dark side of heat soak....  So, if I
were selling mods, I might be very wary of your altitude (ok maybe attitude
towards the pedal too), cuz in actualiy a 1.8 bar mod at 5000ft is better
suited than the 2.0bar mod with a stock k26

Running 1.1 bar in CO with a stock 5ktq, I would suspect that you have a worn
WG spring, or worn bearing shaft ( the latter should be addressed
pronto)......  A 1.3-1.4 is most acceptable, and depending on your guage
(that dash thing really sucks) you might be pretty close, but at .8 bar
resting, you should see .8xx + .575 = 1.32 (min) @ 5000ft,  .7 resting you
should see .7xx + .575 = 1.275 (min) @ 5000ft, and .8xx + .600 = 1.4xx (max)
@ 5000ft, .7xx + .600 = 1.3xx (max) @ 5000ft or a range of:

1.275 to 1.445 Absolute (guage) boost @ 5000ft

Lots of assumptions here, but the concept is pretty straight forward....
Leaves lots open for discussion and contemplation.....  Pressure is good to a
specific point on turbos, then other factors need to be addressed....
 Interesting that the Sport q's make all that hp with 1 bar boost
pressure....  Hmmmm, more ideas....