Picking out the right turbo for yout car

Ok, so Ive seen tons of people asking what turbo to put in their car, and for the most part people give good answers, if they have the same engine and a turbo on it. However some people just simply put get turbo X because it is a turbo. If your going to get all the juice out of your engine you need the right compressor. For those of you who want to go turbo id reccomend doing this to find out which turbo will give you the most hp the easiest. For those of you who arent great with math this might seem like a little much, but just break out the calculator its not that bad. Im also not great with computers so forgive me if some of these equations are slightly confusing, maybe someone out there can fix them after they see this post. For now heres a legend:
SQR = Square root
^ = to x power example B^5 is B to the fifth power

Your going to need to find the compressor map for turbos before you can make any of these numbers work for you. I found a website http://not2fast.wryday.com/turbo/maps/
this has a few turbos for you to compare.

Now for the fun part!

Im using a VW 1.8T for this

Pick a proposed boost level: For this im going to use 20 psi
Pressure drop across the intercooler: assume 1.5psi in most cases
Atmospheric Pressure: 14.7psi is sea level

From these assumptions you can calculate absolute pressure out of the compressor(pco)

pco=boost+atmospheric pressure+intercooler pressure drop

which in my case is
pco=20psi + 14.7psi +1.5psi = 36.2psi

Now to find the pressure ratio
pco
Pr= ______________________
atmospheric pressure


which in my case is
36.2psi
Pr= __________ = 2.46
14.7psi


Next, to calculate the approximate air density of the air after the intercooler, Which is called Di
To do this, you have to guess what the post intercooler temp might be. 130 Degrees is a good starting point and is normally what you see on turbo cars with a good aftermarket intercooler.

R= 53.3 (from ideal gas law PV=nRT)
12 is there to preserve the inch units in the equation
460 is there to convert degrees farenheit to rankin

Boost pressure + Atmospheric pressure
Di= ____________________________________
R x 12 x (460 + post intercooler temp)

So in my case

20psi + 14.7psi
Di= _____________________ = 9.19x10^-5 pounds per cubic inch
53.3 x 12 x (460+130)

From this we can calculate the mass flow rate of the engine at the rp where we want to do the match.

If you dont know your displacement in cubic inches divide displaement cc x 16.387

For volumetric efficency we can assume 90% which is typical for a modern 5 valve DOHC engine, this will vary from engine to engine and from one rpm point to another but thats what makes this a simple model

Also remember this is just for one rpm point, youll have to do this over and over plugging in different rpm's to get a useful picture of the turbos performance across the power band

Di x Displacement in cubic inches x rpm
Mf= _________________________________
2x Volumetric Efficency


In my case

9.19 x 10^-5lb/in^3 x 108.7in^3 x 7000rpm
Mf= __________________________________________ =38.9lbs/minute
2 x .90

Now compressor maps use corrected mass flow, not the mass flow weve calculated, this means its to the standard test conditions used to make the compressor map

The 545 is rankin temp for 85 degrees farenheit, the standard temp garrett uses on its compressor maps, I also used 545 as the intake temp since 85 degrees is a good average for me. The atmospheric pressure is again 14.7 and garrett uses 13.95psi as the compressor inlet pressure considering the pressure drop across the air filter.

Mf x SQR{(compressor inlet temp in R) / (545 degrees R)}
CMf= __________________________________________________ __
Atmospheric pressure
__________________________
Compressor inlet pressure

In my case

38.9lb/in x SQR {(545 degrees R)/(545 degrees R)}
CMF= ____________________________________________ = 36.9lb/min
14.7psi
_________
13.95psi


After all this hard work find the compressor map for the turbo you wish to look at, match up the numbers, and then find out if that turbo is right for you!

Hope this helps a few of yall out, just remember making a car that runs well takes time and patience, this will just take a little bit of time and will help you find out what will work best for your car, besides whats the point in spending thousands on a turbo if it doesnt make the most power possible?

I apologize the equations dont look right, for some reason it wont let me use multiple spaces