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.

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 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 Ratio0.283)) - 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) * 2.020.283 - 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 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.

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