The Lost Art of Compressor Mapping

Copyright 2005

Illustrations courtesy of Garrett

In the world of import tuning, the greatest power adder today is the turbocharger. However, designing a proper turbocharging system is not as simple as ordering up the latest Garrett and bolting it on. The turbocharger must be sized properly for the engine. The import scene abounds with tales of people running Garrett T04E turbos on 1.8 liter engines and getting lacklustre results. "I can't get it to spool before 5000 rpm" and "the lag is awful" are becoming common phrases. The problem is that the builder clearly paid no attention to the flow characteristics of the compressor. So, how do you prevent this from happening to you? You learn to read a compressor map.

Before we start, it may help you to know the basic anatomy of a turbocharger by reading the turbo tutorial.
For this tutorial, I've tried to eliminate as much of the theoretical stuff as I can so that the first-timer can get a grasp for it quickly. This means that for some things, you will just have to take my word for it.
Reading a compressor map will require you to do some basic math. If you can handle high school algebra, you'll be fine. You'll also have to make calculations for several rpm ranges, so it will also be repetetive. Don't give up - this stuff is what separates the men from the boys, the real tuners from the wanna-bes. So read on and learn to kick ass.

The first thing you will need is some basic info about your engine. You will need to know its displacement and the amount of boost that you plan to run. You will also need to find compressor maps for the turbos that you are considering. Turbo maps for some turbochargers are available online from their manufacturers (for Garrett turbos, check

You will need to start off by calculating your engine's displacement in cubic inches (ci). Why? Because 90% of compressor maps are in English units (pounds and feet) so starting off in the right system will make things a lot easier later. For those who are not unit-savvy one liter is 1,000 cubic centimeters (cc). To convert from cc to ci, multiply by 0.061. So a 1.8L engine is 1,800 cc or 109 ci.
Note to guys with Mazda rotaries: double your quoted engine displacement; the 13B IS NOT a 1.3L, it is a 2.6L engine.

Next convert your boost pressure into a pressure ratio. The pressure ratio, as the name implies, is the ratio of the pressure before the compressor and after it. This is how a turbocharger works. It does not matter what pressure enters the turbocharger, it will be multiplied by the pressure ratio of the turbo and that will the pressure at the exit to the turbocharger. Assuming you are at sea level, the inlet pressure for the compressor will be 14.7 psi. If the turbocharger is functioning at a pressure ratio of 2:1, then the outlet pressure will be 14.7 x 2 = 29.4 psi. If the same turbocharger is given an inlet pressure of 20 psi, the outlet pressure will be 40 psi.
To convert your boost pressure into a pressure ratio, add the amount of boost to the inlet pressure and divide by the inlet pressure. Typical intercoolers lose about 1.5 psi of boost, so if you are running one (and you better) then you should add 1.5 psi. So an intercooled car at sea level running 20 psi boost is running at a pressure ratio of

Now, we need to calculate the charge air density. To do this, we will use the Ideal Gas Law. I'll skip the details and just give you the formula:

þ is the Greek letter rho (pronounced like ROWing a boat) and is the symbol for density.
P is the pressure of the gas, atmospheric plus boost.
R is the ideal gas constant, which relates the properties of a gas. It's only exact at absolute zero, but it gives us a good approximation of what to expect.
T is the temperature of the gas, but it must be in absolute degrees for the formula to work.
First let's convert the temperature. Why we need to do this is another tutorial altogether, so you'll just have to take my word for it. Absolute degrees are not in Fahrenheit, but in Rankine. To convert from Fahrenheit to Rankine add 460.
We'll assume that the temperature of air just before the throttle body is 130°F, or 130 + 460 = 590°R. 590°R is a good guess for a typical inlet temperature on an intercooled car.
The ideal gas constant when using inches and pounds is 639.6 - just trust me.
Plugging in gives us

Next, we'll calculate the mass air flow rate of the engine. The symbol for mass flow rate is m', and the formula is:

The VE is the volumetric efficiency of the engine. Due to losses in the airflow of the engine, the cylinders rarely get completely filled with clean air on the intake stroke. The volumetric efficiency relates how much air is actually in the cylinders to the displacement of the cylinder. For most import engines the VE will be between 0.85 and 0.95, we'll assume a VE of 0.90.
This gives us a mass air flow rate of

In case you are wondering why to divide the RPM by 2, it is because a four stroke engine inhales only once in two revolutions.

Like I said earlier, the Ideal Gas Law is only exact at absolute zero, so we need to correct the equation to get a better estimate. To do that use this formula:

Inlet temperature is the temperature of air at the inlet to the compressor, usually the same as the underhood temperature. We'll use 85°F or 545°R to keep the math easy.
The 545°R (85°F; see how it makes the math easy?) in the equation is the standard temperature that Garrett uses in its compressor maps, you may need to change this if you are using one from a different manufacturer.
Atmospheric pressure is usually 14.7 psi.
The inlet pressure takes into account the pressure drop across an air filter. A good approximation is 13.9 psi. I If you are not using an air filter, use 14.7 for this as well.
This gives us

This is the maximum amount of air that your engine will be able to swallow at this pressure ratio. To increase the amount of air that the engine can consume, you MUST increase the volumetric efficiency.
To estimate the power output of your engine, multiply the mass flow rate by 10. Engines vary widely, so your engine may make more or less than the approximation suggests, but this should get you in the ballpark. When considering turbos, you can use this flow rate to help get an idea of which one is right for you - simply select a turbo that is still at a high efficiency at the flow rate and pressure ratio you want to run.

You should repeat this for several different RPM values to get an idea of how the engine will behave over its entire powerband. OK, you're done with the math for now, so set the pencil aside and let it cool off.
What you will eventually do is compare your calculations to the characteristics of a turbocharger. But, first, I'm going to explain the basic anatomy of a compressor map so that you know what you are looking at.
Now, on to the maps!

Pictured below is a typical compressor map (thanks, Garrett). The first thing you probably notice is that it displays both pressure and flow. And, hey, they are in the same units as your calculations! What you probably don't know is that the map also displays compressor wheel speed and compressor efficiency.

Illustration courtesy of Garrett

The compressor wheel speed is displayed in horizontal lines across the map. As the lines rise, so does compressor speed. This is not something most tuners will need to consider, but it's nice to know what they are anyway. Notice that the lines and map stop when the wheel speed gets too high or low, this is because it is outside of the useable range of the compressor.

The compressor efficiency is shown in the not-very-circular blobs in the middle of the map. As you move closer to the center of the map, the efficiency gets higher, peaking in the center of the map. Some maps display the actual efficiency in small numbers next to a blob. This is something that you should consider when selecting a turbo. The higher the efficiency of the turbo at a given pressure and flow, the lower the charge temperature will be. Lower charge temps allow for more power and reduce the risk of detonation.

The left side of the compressor map is known as the surge line. If the turbo tries to operate to the left of this line, the airflow will begin to move back into the outlet of the turbo. This backward moving air opposes the normal rotation of the compressor wheel. In the best case scenario, this leads to severe turbo lag and poor throttle response. In extreme cases the high loads that surge places on the turbo can break the center shaft, turning your turbo into an expensive paper weight.

Now, you will need to get your calculations back out. Compare them to the flow characteristics of the turbocharger by plotting them on the compressor map. It helps to have the compressor map printed out so that you can actually draw your engine's characteristics onto it. Make sure that your engine is not forcing the turbocharger to work in an inefficient area and that you are right of the surge line.
As an example let's look at our previous calculations: a 1.8L at 7500 rpm and a 2.46 pressure ratio will flow 31.97 lb/min.
The compressor map on the left shows a turbo that is too large; even at redline, the engine cannot swallow the amount of air that this turbo will flow. The turbo will go into surge and could be damaged.
The compressor map in the middle shows a turbo that is too small; it will be forced to operate in an area that is inefficient and will yield high charge temperatures.
The compressor map on the right shows a turbo that is properly sized to the engine, at redline the compressor is still operating at a relatively high efficiency, and the map is wide enough to allow the turbo to function properly at lower rpm as well.

Maps courtesy of Garrett

You should remember when looking at these turbochargers that all turbos take time to spool. Therefore, you do not need to try to find a turbo that you will not surge at idle. Generally, a well selected turbo will be spooled between 2000 and 3000 rpm, so as long as your engine can keep up with the turbo by around 3000, you should be OK.

If your power goals make it hard to find a properly sized turbocharger, you could select a turbo that is too large for the engine by varying the boost level with rpm. By running a lower pressure ratio at lower rpm, you could keep the turbo out of surge until the engine is ready to keep up. Fortunately, there are electronic boost controllers that can do this.

As an example, lets consider another engine. This time we'll use a 1.6L at 20 psi boost running the turbo shown below. By performing the same calculations as before, you can see that the engine can intake 32.6 lb/min at 8500 rpm, which puts the engine right in the sweet spot of the turbo. However, at 5000 rpm, the engine will only take in 19.2 lb/min, which is right on the surge line. Obviously trying to run 20 psi before 5000 rpm could damage the turbo. By lowering the boost setting at 4000 rpm to 15 psi, the engine can swallow 13.2 lb/min, which puts it just inside the safe zone. Further lowering the boost at 3000 rpm to 10 psi again keeps the turbo alive. The nice thing about this arrangement is that the turbo, which is technically too large, can still be used on the engine without causing the turbo to enter the surge region. By looking at the mass flow rate, you can see that this turbo on this engine has the capability to make well over 300hp!

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