3SGTE Turbo Sizing Primer
To really determine what a given turbo could potentially do on your
3SGTE 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 40trim 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.
Altitude (ft) 
Pressure (psi) 
Sea Level 
14.7 
1000 
14.2 
2000 
13.7 
3000 
13.2 
4000 
12.7 
5000 
12.2 
6000 
11.8 
7000 
11.3 
8000 
10.9 
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 3SGTE 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 3SGTE 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
3SGTE @ 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^{0.283}))  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^{0.283}  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 3SGTE is 8.8 (8.5 for a 3SGTE). 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 CT26 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 recompute 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.
