3S-GTE Turbo Sizing Primer
To really determine what a given turbo could potentially do on your 3S-GTE
engine, you need to cut throw away the marketing and advertising claims and go
straight to the heart of the matter: the compressor map. Above is a compressor
map for a TO4E 40-trim compressor wheel. Looks somewhat intimidating, doesn't
it? What are all the numbers and the formulas? Let's not worry too much about
that and take it one thing at a time.
The first thing that we need to look at are the numbers across the axis on
the left side of the graph that start with 1 and go up. These indicate the
pressure ratio at which the turbine is operating. The pressure ratio is just the
absolute pressure at the outlet of the compressor divided by the absolute
pressure at the intake of the compressor. Most often, we make these calculations
at sea level atmospheric pressures, but if you live at altitude, you should use
the atmospheric pressure representative of your location. The following table
gives you the average atmospheric pressure for nearly all inhabited areas.
[TABLE="width: 200, align: center"]
[TR]
[TD="width: 50%, align: center"]
Altitude (ft)
[/TD]
[TD="width: 50%, align: center"]
Pressure (psi)
[/TD]
[/TR]
[TR]
[TD="width: 50%, align: center"]Sea Level
[/TD]
[TD="width: 50%, align: center"]14.7
[/TD]
[/TR]
[TR]
[TD="width: 50%, align: center"]1000
[/TD]
[TD="width: 50%, align: center"]14.2
[/TD]
[/TR]
[TR]
[TD="width: 50%, align: center"]2000
[/TD]
[TD="width: 50%, align: center"]13.7
[/TD]
[/TR]
[TR]
[TD="width: 50%, align: center"]3000
[/TD]
[TD="width: 50%, align: center"]13.2
[/TD]
[/TR]
[TR]
[TD="width: 50%, align: center"]4000
[/TD]
[TD="width: 50%, align: center"]12.7
[/TD]
[/TR]
[TR]
[TD="width: 50%, align: center"]5000
[/TD]
[TD="width: 50%, align: center"]12.2
[/TD]
[/TR]
[TR]
[TD="width: 50%, align: center"]6000
[/TD]
[TD="width: 50%, align: center"]11.8
[/TD]
[/TR]
[TR]
[TD="width: 50%, align: center"]7000
[/TD]
[TD="width: 50%, align: center"]11.3
[/TD]
[/TR]
[TR]
[TD="width: 50%, align: center"]8000
[/TD]
[TD="width: 50%, align: center"]10.9
[/TD]
[/TR]
[/TABLE]
Now, to determine the absolute pressure at the outlet of the turbo, add the
turbo boost pressure to the intake pressure which should be atmospheric pressure
unless your air filter is very dirty or your air intake is too restrictive for
your setup. Suppose we want to determine the pressure ratio for 15psi of boost
at sea level. That will be:
Pressure Ratio = (15 + 14.7) / 14.7 = 29.7 / 14.7 = 2.02
So if you take a ruler and lay it down horizontally across the compressor map
just a tiny bit above the "2" on the left axis scale you can see that it cuts a
pretty nice line across the middle of the map. Trust me for now that that's a
good thing if we plan to operate this turbo at 15psi.
Across the bottom axis on the graph we see air flow given in pounds per
minute. Some compressor maps give it in Cubic Feet per Minute (CFM) which is
actually better. To convert pounds per minute into CFM, you need to take the
temperature of the air into consideration (the ideal gas law tells us that as
gas heats up, it expands, which means that the hotter the gas, the less it
weighs per cubic feet, which is why a hot air balloon rises). Fortunately, most
compressor maps are taken at 85F (you can usually tell by looking at the formula
written on the map which has a temperature number like 545 and subtracting 460
from that number to convert it to Fahrenheit). One cubic foot of air at 85F
weighs 0.07282 pounds. So, at 85F, convert pounds per minute to CFM by
multiplying by 13.73.
So, if we take our ruler again and set it horizontal just above the "2"
pressure ratio mark and then look at the range from the surge line to the end of
the balloon, we have a permissible range from 15 pounds per minute to 35 pounds
per minute. This translates to 205 CFM and 480 CFM, respectively. This is a big
range. Will the 3S-GTE with this compressor be able to flow this much air? No,
we need to consider the fact that an engine is an air pump and at a given intake
pressure it will only be able to ingest so much air.
To determine how much air will flow through the you have to start with
engine displacement and an RPM point, then plug it into:
CFM for 4 stroke = Displacement in CI / 3456 * RMP * VE
The stock 3S-GTE has a stock displacement of 1998cc which is 121.9 cubic
inches (up to 2010cc if overbored), so at 6000 RMP it will flow:
CFM = 121.9 / 3456 * 6000 * VE = 211.6 CFM * VE
VE is volumetric efficiency, which is a value indicating how much of the
potential air flow volume actually makes it through the engine at a given RPM.
If you throw in a guestimate of about a 90% VE for the 3S-GTE @ 6000 RPM, you
get:
CFM = 211.6 * 0.9 = 190.5 CFM
This appears to be outside the compressor map into the surge area. It is not
quite the case, however, because this is only telling you what the engine can
flow in a naturally aspirated mode. To determine what it will do under boost,
you have to determine what density ratio the compressor and intercooling system
you have will give you. To do that we need to take our boost point and determine
how hot the compressor is going to make the air at a that boost:
Tout (in F) = (((Tin (in F) + 460) * (Pressure
Ratio[SUP]0.283[/SUP])) - 460)
So, let say you set the boost controller for 15psi of boost at sea level at
an ambient temp of 85F (85F in this case so that our computed CFM ends up
matching that of the compressor map).
Tout = (85 + 460) * 2.02[SUP]0.283[/SUP] - 460 = 205F
This assumes an ideal, 100% efficient compressor. The round
circles in the compressor map tell us how efficient the compressor is going to
at a given pressure ratio and flow level. Since most of the map is at least 70%
efficient or better, we'll use that figure and double check later to make sure
we were either close or underestimating a little. Our real outlet temperature is
going to be:
delta T actual = delta T ideal / efficiency
For our example, the delta T ideal is 205F - 85F or 120F:
delta T actual = 120F / 0.70 = 171F
171F is how much the compressor is going to heat the air above the
inlet temp, so the real outlet temp is 171 + 85, or 256F. What happens when this
air mass hits the IC? Two things: first, a pressure drop and second, a
temperature drop. The pressure drop is going to be about 0.5psi for a good
sidemount IC such as the GReddy, HKS or Spearco units and we will assume a 65%
efficiency number which is reasonable for a good side mount IC:
T IC drop = (T IC in - T ambient) * IC efficiency
So we get:
T IC drop = (256 - 85) * 0.65 = 111F
Therefore the IC will drop the turbo outlet temp by 111F, turning
the 256F air into 145F air and dropping the pressure 0.5psi to 14.5psig. What
does this do to our normally aspirated engine? Well, the density of the air is
increased by a ratio:
density ratio = ((Tin + 460) / (Tout + 460)) * (Pout / Pin)
For out example, we get:
density ratio = ((85+460)/(145+460))*(14.5+14.7)/14.7 = 1.79
This density ratio means that you will get 1.79 times as much air
flowing through the engine with this compressor and intercooler combination at
this pressure point and this ambient temperature than you would in normally
aspirated mode.
Going back to our 190.5 CFM value, we multiply that by the density
ratio to get 341 CFM (which converts to 24.8 pounds per minute). This is still
inside the compressor's map so we have a reasonable value (if it weren't, you
wouldn't be getting 15psi out of the compressor, your actual pressure would have
dropped). Additionally, this is right in the compressor's maximum efficiency
range, so our manifold temperature will probably be a little lower than we
calculated with our 70% efficiency value and our density ratio just a tad
higher. This means we are close enough to the money to make it work for our
purposes. No real need to go back and try to get the value to be more accurate,
since we are already guessing on a number of other things (such as VE) which is
having a bigger impact on our actual flow.
Given what we have calculated,
we can approximate how much horsepower we will produce. The basic crank HP
formula is:
Crank HP = MAP (in absolute psi) * Compression ratio * CFM /
228.6
The compression ratio for a genII 3S-GTE is 8.8 (8.5 for a 3S-GTE). So, we
plug in the real numbers into our HP formula and get:
Crank HP = 29.2 * 8.8 * 341 / 228.6 = 383 HP
Throw in 20% drivetrain loss and you have 306rwhp @ 6000RPM.
So, what
makes it a little tough to predict what you really are going to get is getting
an idea of what the final VE of the system will be (which is not constant, but
changes across the RPM/Manifold pressure range) since the turbine housing and
wheel themselves are going to have an effect on the VE map. For example, the
stock CT-26 turbine and turbine housing is so restrictive that it drops the
engine VE well below 90% at 6000 RPMs (also known as "choking" the engine).
One other item we should check since we have the numbers calculated is
whether the compressor will not be forced into the surge line. Surge is caused
when the engine cannot ingest enough air to keep the compressor inside its map.
We saw that at a 2.02 pressure ratio, the surge line is around 15 pounds per
minute or 205 CFM. Now, let's assume that the turbine and turbine housing we
will choose can power the compressor to reach 15psi by 3500RPMs. We keep the
density ratio the same, but we have to re-compute the flow for the engine at
3500RPMs. The VE at this point should be better than at 6000, so we'll use a
value of 95%. At 3500RPMs, the engine will be ingesting:
CFM = 121.9 / 3456 * 3500 * 0.95 = 117.3 CFM
That's in normally aspirated mode. Multiplying the density ratio,
we get:
117 CFM * 1.79 = 210 CFM
This is near the surge limit for this compressor. Granted the VE
might be even better, but we could be off. We could fix this problem on most
turbos by putting in a turbine housing with a larger AR which would slow down
the spool time to bring the compressor up to this pressure ratio when the engine
is revving a little faster and thus ingesting more air. The larger AR also
allows more exhaust to flow and thus improve VE to also increase air flow and
move the system even farther into the compressor map away from the surge line.