Choosing a Compressor: Cut through the hype

[Moai]

Ah, the BFT. No, not the kind you grab at the drive thru from the local grease pit. BFT in this case stands for a Big F-in' Turbo and there are a TON of them out there on the aftermarket. Before you start peeking through the Garrett catalog or play Add to Cart with a multi-thousand dollar turbokit, you should know what you're buying and how it's going to work. Moreover, you should know whether or not it'll mesh with what your plans are.

First things first, lose the Bigger is Better mentality. Turbo size is NOT going to tell you everything you need to know about having a fun to drive, powerful and flexible ride. Turbo size should be looked at like shoe size. Too small might crimp and hurt when you try to stretch your car's legs. Too big and you're waddling in it, feeling sloppy and slow because there is no way you'll ever use all that room it's giving you.


So HOW exactly DO you go about answering the question: "Which turbo is right for me?" Some of you may not like the answer, but that answer is "you're going to use some math."

You NEED to know a little math to get the gist of what you're doing. It's all high school algebra we're going to use, so most everybody can figure it out just by looking at it.

Alright. Let's get things started by having a look at a compressor map:


Welcome to the T04E-40 trim compressor map.
In case you want to follow along with a different compressor, here are a bunch more maps to play with on this website:
http://not2fast.com/turbo/maps/
I can already see some of you squirming behind your monitors. Relax. This is easy.

First off, we're looking at the left axis of the graph. It starts with 1 and goes up. These numbers represent your pressure ratio. Pressure ratio is simply the ratio of what boost you're planning on running, with respect to the current atmospheric pressure. At sea level, that pressure is 14.7psi. At higher altitudes, it goes down. Since engines create vacuum when they run, the 15psi you see on your boost gauge really is NOT 15psi.
In reality, most engines will pull in the ballpark of 20 inches of vacuum [or we could call it nearly 15psi of VACUUM, if that measurement existed] at idle. When you see 15psi dancing across your boost gauge, your turbocharger has first compressed the vacuum to zero, then kept on compressing until the positive 15psi registered across your gauge. Mathematically speaking, the compressor has put nearly 30psi-worth of work into that airflow. Since the atmospheric pressure determines how hard the turbocharger has to work, we must take altitude into account via Pressure Ratio.

Determining the pressure ratio for 15psi of boost at sea level [0 ft] looks like this:

Pressure Ratio = (Target Psi + Atmospheric Psi) / (atmospheric psi)

Therefore:

Pressure Ratio = (15 + 14.7) / 14.7 = 29.7 / 14.7 = 2.02

Now, draw a line across the map, starting just a tiny bit above the "2" on the compressor map. [where 2.02 would be]. You can see it cuts pretty nicely right through the middle of the map. That's good.

Across the bottom axis, we see air flow in pounds per minute. Some compressor maps use Cubic Feet per Minute [CFM's], which actually works better, since you'll have to convert to that measurement eventually.
To convert Pounds per Minute into CFM, you need to take the air temp into consideration, since the ideal gas law tells us that the hotter a gas gets, the more it expands and the less it weighs per cubic foot. [Those who have argued with girlfriends understand this law well].
Most compressor maps assume an 85 degree air temperature. [You can always check the given temperature formula on the map for proper temperature and subtract 460 from the number you get, to get temp in degrees F.]

One Cubic Foot of air at 85 degrees weighs 0.07282 lbs. So at 85F, convert lbs per minute to CFM by multiplying by 13.73.

So, look at that line you drew on the map. Now look at the range from the left side of the graph, usually a solid or dotted line [called the surge line], to the far right edge of the graph. That shows us we have a range from 15lbs per minute to 35 lbs per minute. That translates to 205CFM and 480 CFM. What that's telling you is, if you want to make 15psi with this compressor at sea level, you will need airflow between 205 and 480cfm to do it. As you rev a motor, you increase the CFM of exhaust it spits out. So, in essence what you're learning now is "where does the turbo spool up and where does it start losing boost at higher RPM's?"

Well, since an engine is an air pump, we first need to figure out a few things. First, what's the displacement of the motor? Second, what RPM point are you looking at? You have to choose a particular RPM to get a CFM value, unless you want to use more complicated math.
Didn't think so.

Pick an RPM and plug that into this equation:

CFM for 4 stroke = (Displacement in Cubic Inches) / 3456 x RPM x VE

So for my 3S-GTE, my stock displacement is 1998cc's, or 121.9 cubic inches. So at 6000 rpm, it will flow:

CFM = 121.9 / 3456 x 6000 x VE = 211.6 CFM x VE

Now, VE is volumetric efficiency. VE is a percentage measurement of how much air ACTUALLY makes it into the cylinders on each stroke, compared to how much can THEORETICALLY make it. On a stock unmodified engine, it's nearly always less than 100% For your average near-stock block at 6000rpm, a 90% VE is a decent ballpark guess, which means:

CFM = 211.6 x 0.9 = 190.5 CFM

Hey, didn't we need at least 205 CFM for that turbo to make the boost we wanted? Well, we forgot one thing: this equation gives you CFM's in naturally aspirated mode. [i.e. if the motor were simply just a nonturbo motor]. Now you need to figure out how much it'll do under boost.
That requires something called Density Ratio.

To calculate Density Ratio, we use our Pressure Ratio and figure out how hot the compressor's going to heat the air up using the temp going in and the temp coming out of it:

Temp Out (in F) = (((Temp In (in F) + 460) x (Pressure Ratio ^ 0.283)) - 460)

So, let's say you set the boost controller for 15psi of boost at sea level, on an 85 degree day.

Temp Out = (85 + 460) x (2.02)^0.283 - 460 = 205F

This assumes a 100% efficient compressor... which is ideal but not realistic. Since most of the compressor map is around 70%, let's use that figure as a ballpark guess.

That makes our compressor's outlet temperature:

Actual Temp Change= (Ideal Temp Change) / Efficiency

For our example, the Ideal Temp Change is 205F - 85F or 120F:

Actual Temp Change = 120F / 0.70 = 171F

So the compressor is going to heat the air 171 degrees above what it already is. Add 171 to 85 degrees and we get 256 degrees of baking heat coming out of that turbo, going into your engine. Glad you spent all that money for a decent intercooler, aren't you? Speaking of which, what happens when that air hits the IC? Well, first you get a little drop in pressure and second, the temperature drops a bunch. Your average pressure drop for a smaller high quality side mount IC is around 0.5psi. For a larger front mount it could be over 1psi. For the IC, we will assume a 65% efficiency, which is reasonable for a decent sidemount. For a larger front mount getting a lot of airflow, you could assume perhaps 70 to 75%. If you're using water spray or that nitrous fogger on the IC's surface, you could increase efficiency another 5-10% or more! All you need to determine efficiency is a thermometer measuring the temperature at the compressor's outlet and at the throttlebody inlet. If the compressor heats up the air 150 degrees above ambient, but the throttlebody is registering 85 degree air [i.e. the intercooler cooled the air 150 degrees], then you have a 100% efficient intercooler.

Okay, now for some math:

T IC drop = (T IC in - T ambient) x IC efficiency
T IC drop = (256 - 85) x 0.65 = 111F

So that means the IC is dropping the turbo's outlet temp by 111 degrees. That transforms our 256 degree temp into 145 degrees and drops the pressure from 15psi to 14.5. [Remember the ideal gas law?]

So what does this do for our normally aspirated engine? Well, density of the air is increased by a certain ratio:

Density Ratio = ((Temp In + 460) / (Temp Out + 460)) x (Pressure Out / Pressure In)

For out example, we get:

Density Ratio = ((85+460)/(145+460))*(14.5+14.7)/14.7 = 1.79

That means you're going to get 1.79 times as much air flowing through the engine with this compressor and IC combo as you would if the engine were operating as a naturally aspirated motor.

Now let's go back to that original 190.5 CFM value we got. Multiply that by our density ratio of 1.79 and now we have 341 CFM (or 24.8 lbs per minute). That's right in the middle of the airflow we need to make the boost we want. Excellent!
If it were NOT within the range we need, you simply wouldn't be getting 15psi out of the compressor at that rpm. At lower RPM's, you would be surging the turbocharger, which would sound like pops and backfires coming out the intake. On the higher RPM scale, you would simply see the boost fall away as you kept revving the motor. This is exactly what happens when smaller turbos tend to lose boost at higher rpm's. By the looks of things, the 341 CFM value falls within the highest efficiency range on the map, so that means our actual temperature at the throttlebody will be a little lower than we'd calculated and our density ratio a tad higher. Hey, it's close enough to give us a good idea of what we're working with. If you REALLY wanted accuracy, you could go back and redo the calculations with the new efficiency you've deduce, to get a more accurate CFM value.

Now, given what we've calculated, we finally have reached the part that everybody likes - approximating hosepower output.

The basic crank HP formula is:

Crank HP = Manifold Air Pressure (in absolute psi) x Compression ratio x (CFM / 228.6)

The compression ratio for a Gen II 3S-GTE such as mine is 8.8, so we plug in the real numbers into our HP formula and get:

Crank HP = 29.2 x 8.8 x (341/228.6) = 383 HP

Toss in a rough 20% drivetrain loss and you'll have 306whp at 6000RPM.

Ok you think you've got it all now? Not so fast. What makes things real tough to predict is figuring what the final VE of the system will be, since the value changes continuously across the RPM and Manifold Pressure range. The turbine and wheel will have a large effect on the volumetric efficiency's behavior and therefore its overall HP output. For example, the stock CT-26 turbine and its housing are so restrictive that it easily drops the engine's VE well below 90% at the 6000RPM we looked at. [also known as "choking" the engine]. Air cannot flow in if air cannot flow out fast enough to get out of its own way.
On a stock MR2 turbine housing mated to the 40 trim wheel we're working with, the most you'll see out of the Mr2's output is in the ballpark of 260-270whp. That's around 30 horses shy of what we'd calculated. Turbine sizing and A/R really DO make that much of a difference. On a T3/T4 turbo using the same compressor wheel but a larger turbine outlet, you will see numbers closer to the 306whp at 15psi we have calculated. Remember, the 306whp is an ideal figure based upon the "ideal" turbine housing, ideal octane and ideal combustion which of course, don't exist. Reality dictates parasitic losses everywhere energy is transferred, so don't get disappointed when your 40 trim compressor needs you to pull out all the stops and run racegas to get you near where you calculated it could. This isn't supposed to be a perfect way to calculate power output. It's simply a guideline of what you can expect, and what you can disprove.

Alright. One other thing we should check now that we have the numbers, is whether the compressor will be forced into the surge line. Surge is caused when the engine cannot ingest enough air to keep the compressor inside its map and the symptoms we listed above, will happen. Surge KILLS your turbocharger's bearings, so it's something we want to prevent.
We saw that at a 2.02 pressure ratio, the surge line is around 15 lbs per minute, or 205 CFM. Now, let's just assume the turbine and housing we choose will power the compressor to reach 15psi by 3500RPM. Let's keep the density ratio the same, but recompute flow for the engine at 3500RPM, using a higher VE of 95% due to the lower RPM:

CFM = 121.9 / 3456 x 3500 x 0.95 = 117.3 CFM

That's in normally aspirated mode. Multiplying by the density ratio, we get:

117 CFM * 1.79 = 210 CFM

And... that is really close to the surge limit for this compressor. Now, the VE might be even better than we'd assumed, but we're not going to play around like that and surge a turbo when it's that close. 15psi at 3500RPM is about the best spool we're going to get out of this thing. We could dial the spool back a bit with most turbos by using a larger turbine housing with a larger A/R. That would delay the spool until the engine reached an RPM more suitable for the pressure ratio we want to use. The larger A/R also allows more exhaust to flow and thus improve VE, increase airflow and move the system farther into the compressor map away from the surge line.

Now you should ask yourself "Are these numbers what i want? Do I want more power? Do I want to have more power at a different rpm? Do I like where the surge line is? Is this amount of boost pressure okay or can I run more? Will my car always be at sea level or am I moving to Denver in a month?" Basically this is where you start tailoring your turbo to fit your needs. If you want something different, pull out a different compressor's map and go to town.
Be careful to strike a balance here. Too large and you'll have a laggy turbo that spools too late and surges too low. Too small and you choke the engine and still possibly end up surging it.
Remember to pick the shoe that fits!






and for those of you who are incredibly lazy, shame on you . here is a general idea of where turbochargers fall in the scheme of things. Remember - it's just a point on a scale. The math i've drawn out above allows you to determine how they behave on the other 99% of their capability. So the next time someone advertises a GT3037 kit that "spools just like stock and makes 800hp", you can call their BS and save yourself from getting burned.



ps is the symbol for pferdestärke, which is German for horsepower. They're close to interchangeable, but if you want to be a complete nerd:
1 pferdestarke = 0.9863201 horsepower

And if you're REALLY a complete nerd, you will use your exact altitude above sea level and derive the pressure value from this list:


Sea Level -- 14.7 psi
1000 feet -- 14.2 psi
2000 feet -- 13.7 psi
3000 feet -- 13.2 psi
4000 feet -- 12.7 psi
5000 feet -- 12.2 psi
6000 feet -- 11.8 psi
7000 feet -- 11.3 psi
8000 feet -- 10.9 psi


Again, a list of compressor maps:
http://not2fast.com/turbo/maps/

[mikecentola]

wow thats awfully long....weren't you supposed to be working on elliot's car instead :P

good from what i had read though

[mikecentola]

oh and hopefully it'll help out some of the noobs here :bigwink:

[MNIMNIAC]

wow is all i got.
long, informative, but long.

[AFTRMRKT]

Where's the chart for the IHI's?

:disturbed:

Great post

[RUReadyForThis32]

That's a fun post! The GT-RS turbo's are probably my favorite...if nothing else but for the "disco potato" name that has swept the boosted nation.

[mikecentola]

i think my FP green falls around the TD06-25G area...

[RUReadyForThis32]

Mine falls around...wait...nevermind

[gimmemore4door]

"Maximum Boost" by Corky Bell > ALL

hehe j/k, man.
Good informative post :salute:

[AussieDan]

Indeed, Maximum Boost and Supercharged! are both excellent books for anyone interested in FI.

That said, props to eric for an excellent primer! Pretty much Maximum Boost distilled down to its very core.