Sizing the turbo

Sizing a turbo can seem like a daunting task if you have no clue where to start. I didn't when I started looking, but a little research can go a long ways. This first thing you need to do is familiarize yourself with how to read a turbo compressor map. The Garrett website has some really good documents about turbo charging and what all that junk on a compressor map means.
I recommend starting there as I will be using most of the information on this page:
Garrett Turbo Tech Information

"Okay, I skimmed through this and didn't really pay close attention to it all cause words are hard." Boy random person I couldn't agree more! But I highly recommend you take your time and read it to fully understand everything. I am not necessarily going to hold your hand through this as I think it is extremely beneficial to have to put forth effort to understand something. If you do, you will remember it for much longer.

"Alright, for reals, now what?" Now we have to do math. "OH MY GOD READING AND MATH, WHAT IS THIS? SOMEWHERE WITH A GOOD EDUCATIONAL SYSTEM?" Lucky for you guys I have a spread sheet that I am willing to share that will do pretty much all of the math. I encourage you to double check my math as I am not perfect.

https://turbobygarrett.com/turbobygarrett/compressor_maps (all rights reserved by Garrett for this image, it is not mine)

So on that compressor map we have the x-axis and y-axis which are mass flow and pressure ratio respectively. We are going to generate some points based on the engine to help figure out where on the compressor map our turbo will run for various RPM and boost values.

Really the only thing we need to calculate is air flow through the engine at given boost values and RPM as it is dependent on both. This is actually very easily done using the engine parameters that can be looked up in the owners manual and PV=nRT. This is the ideal gas law if you are unfamiliar, but the one we use is actually just a little different. What we are going to use is PV=mRT where m is the static mass of air in a cylinder and that is what we are solving for. The variables are as follows:

P: Boost pressure in absolute, units of kPa
V: Volume of a cylinder (this should include clearance volume), units of m^3
R: Gas constant = 0.287 kJ/kg*K
T: Gas temperature post intercooler (or post turbine if no intercooler used), units of Kelvin

Determine an appropriate value for the temperature and boost pressure(again absolute). This gives you a mass of air in a cylinder. Breaking down RPM into RPSec we can determine the lb/min of air through the engine. Now using that same boost pressure, calculate the pressure ratio. This is PR = Boost/Ambient. I hate typing out equations on these things, so I will reference you to the excel document for all of them.

Now by changing the RPM value and recalculating the mass air flow for a fixed pressure we can plot something that looks like this:

Then we re-do it all for another fixed pressure:

What does this all mean? We want our operating points to be to the right of the surge line and to the left of the choke lines. The closer we are too the pool in the middle, the better the efficiency we get. So as you probably noticed, at redline and 12psi of boost I am to the right of the choke line. This is bad and I do not plan on operating the engine in that area. Even the 10psi and 8psi graphs are right on the edge. Luckily these are ideal calculations and I actually have losses working in my favor to keep me from running over the choke line. This turbo will work for this engine but it does not have much over head. So if I planned on going any higher than 12psi of boost, I would be seriously considering a larger turbo.

Here is another example I did for my dad's land speed racing bikes. They are 125cc honda engines that are turbo charged. Only problem is that no one makes a turbo small enough for them to make any real boost. He just got a new Garrett turbo (the smallest one they make) which says it is rated down to 100cc engines. I find this to be false. You can see on the chart below that we aren't anywhere near close to being to the right of the surge lines, even at 12psi of boost. This is a good example of a turbo that is sized poorly.

You now know the gist of how to size a turbo properly for a given engine size and desired boost pressure. It should be noted that Garrett says that a rough estimate can be made of 10HP for every lb/min of air flowing through the engine. This will give you an idea of what the engine will make at the crank.

Here is a link to download my excel sheet to help calculate all this. There are comments on most of it explaining how to use it. It also has a sheet in there to calculate injector size and fuel pump size once you figure out what your max air mass flow rate is.

Turbo Sizing Calculations