Introduction
Combustion requires two things: air and fuel. Well, technically, oxygen, fuel and a little heat, but the real chemistry behind combustion is not in the scope of this tutorial. For gasoline engines, the stoichiometric ratio of air to fuel is 14.7:1. For maximum power, a ratio closer to 12:1 is ideal. But no matter how much fuel you feed an engine, if there isn't sufficient air, you cannot increase the power. Of course, the converse is also true - if you have more air, you also need more fuel.
All engines have a fixed volume which can be occupied by air and fuel - this is what we measure when we speak of the size of an engine in CID (cubic inch displacement) or Liters. Now, the effective displacement of a given engine can change based on several factors, including cam duration, engine speed, exhaust flow, etc. This is why changing these things can create more power - by allowing more air (and thus, more fuel) into the engine per revolution. The percentage of the engine which is able to be filled with combustibles is referred to as volumetric efficiency (VE). Most modern, stock engines have a volumetric efficiency between 75-90%. The goal of most engine modifications is to increase this number.
Turbocharging an engine, on the other hand, affords us an opportunity to increase the amount of air in an engine without these expensive modifications. Turbochargers (and superchargers) force air into an engine, and they do this by compressing the air. That means, per unit volume, there is more air. How can this be? Because PV = nRT. If you hold V and T constant (R is already constant), as you increase P, so must n (or the number of air molecules) increase. But, I promised this wouldn't be a chemistry lesson.
Allow me to digress a little more and make a note about the cost effectiveness of turbocharging. All the other performance modifications I mentioned earlier are very costly - especially when you consider how little good they do. Consider this - if your engine has a volumetric efficiency of 80%, realistically, you're not going to get your volumetric efficiency above 100% (it's possible, but that would take a physics lesson to explain). So, we're talking about a 25% gain in power - and at an incredible expense. Turbocharge the same engine, and depending on its compression ratio, you can often get a 60% gain in power on pump gas. Add an intercooler and we're talking about doubling your power with very little sacrifice in reliability or driveability. A turbocharger is an incredible machine!
The Problem
So, let's get some piping and a turbo and slap it on. Check out TurboCalculator's list of free compressor maps (or get the real version and see the rest), and you'll see that the T100 flows the most air. Well, more air means more power, so lets put that monster on our engine. But our engine wouldn't be able produce enough air to turn the turbine. And even if it could, the relatively small amount of air our engine would need would cause the turbo to surge, which could damage it. So, you're telling me that I can't use just any turbocharger?
Yes, there is a science to turbocharging, and each turbocharger has an amount of air that it's able to supply efficiently and consistently. The problem is to select the correct turbo.

Turbo Selection
So, I've got to select the right turbo. The T3 I saw in Don's Turbo Emporium with the polished housing looked pretty nice, and it's not too big. Let's slow it down just a little and think this one through ok?
Every turbocharger compressor has what's called a compressor map. You probably already knew that or you wouldn't be here. The compressor map tells the efficiency at which a turbo operates given a pressure ratio and air flow requirements of the engine to which it is attached. This is where the islands come from. Each of these marks an equal compression efficiency. Anything inside a given island represents points of higher efficiency.
What on earth does it mean to compress air inefficiently? The less efficient the compression, the hotter the air. Compression Efficiency essentially tells what portion of the energy used is going to compression rather than heating up the air that's being compressed. The general rule of thumb is to keep efficiency above or near 65%, but this will obviously depend on the application.
So, why do we want cooler air? For two main reasons. First, hot air is more prone to pre-ignition (also known as pre-detonation) or auto-detonation, which can damage your engine. Second, colder air is denser. Let's look again at PV = nRT. If all is constant but n and T, as T decreases, n must increase. In other words, given a pressure (boost level) and volume (the size of your engine), as temperature increases, the number of air molecules decreases. Bottom line: hot air supports less power.
The process of turbo selection is plotting the air requirements of your engine on each compressor map to determine which turbo is best for your application. Beside the pain in the butt of plotting several points on every map for every engine configuration, proper turbo selection requires you to calculate the air requirements of your engine at each of the points of interest. Air requirements? How do we come up with those? With a lot of math.
The Math
For a detailed discussion of the math involved, have a look at this link.
More Problems
There are a few problems that anyone wishing to select a turbocharger for their engine is going to run into. First, turbo shop employees and owners either lack the time, knowledge, or experience to suggest the bet turbo for your application - especially if it's not a common project. Second, turbo charger compressor maps are very difficult to come by. For some reason, most manufacturers are very protective of most of the compressor maps. Fortunately, at TurboCalculator, we have been able to locate 84 public domain maps, many of which are very hard to come by. Feel free to have a look at the Garrett Maps which are available on our website. Last, it truly is a pain in the butt to do all of these calculations and plot the data by hand.
The Solution
TurboCalculator was born out of a desire to make the whole process much easier. TurboCalculator is an expert at selecting turbos. It's had plenty of practice and it knows the correct formulas. With TurboCalculator, you have 84 compressor maps at your disposal. And there's no reason to be timid about breaking free from the mold and working on a truly interesting project. TurboCalculator is useful for selecting turbos for nearly any application. We've had customers wanting to turbocharger rotary engines for aviation, bike engines, big block gas engines, smaller engines, diesels - you name it! So let TurboCalculator help you with your project.