How to Go Fast Faster: The Math Behind Turbocharging. Part 5b: Compressor Efficiency


Part 1 is here.

Part 2 is here.

Part 3 is here.

Part 3b is here.

Part 4 is here.

Part 4b is here.

Part 5 is here.

     Efficiency is how well a part is performing vs its theoretical performance (under perfect conditions).  We know our parts will never perform at 100%, so we have to factor into our equations how “well” each part performs.  Volumetric Efficiency (%) was one example, as we measured how much air actually is used by the engine as opposed to how much air the engine can actually hold (displacement).  This time we’ll be looking at compressor efficiency and see how this affects our calculations.

     Remember how our engine didn’t use up as much air as the engine specifications/perfect conditions allow?  This is the same with our turbo.  Our turbo should compress a certain amount of air and shove it into the engine, but conditions are never perfect.  As with all energy being used, heat is constantly being released.  We can see how temperature affected our Volumetric Efficiency as it made our air less dense, resulting in a smaller amount of volume of air flowing through the engine.  For the turbo, the same applies.  As the turbo is doing its job, it releases heat, which in turn raises the temperature of our compressed air.  Once again, this is not good, as it’s undoing the job of the turbo; bloating  up the air while the compressor tries to compress it.  Heat is the result of wasted energy, and the less energy we waste (ie: the higher the efficiency is), the more power we can make.

     Before looking at the equation for the Compressor Efficiency (%), we’ll need a few variables; your Pressure Ratio, The Absolute Temperature (°) of the Compressor Inlet Temperature, and the Temperature Rise (°F) due to the compressor itself.  The Absolute temperature scale’s lowest point is 0°, where there is no heat at all.  This is equivalent to 460°F below if converted to Fahrenheit readings.  Thus, the Absolute temperature scale has no negatives.  But luckily it is very easy to convert from Fahrenheit to Absolute using this equation:

Absolute Temperature (°) = Absolute Temperature

Simple.  Add 460 to your Fahrenheit temperature.

      The Temperature Rise, on the other hand, is easier to solve for.  All we need here is the Ambient Air Temperature (°) and the Compressor Outlet Temperature (°):

Temperature Rise (°F) =

Temperature Rise

Simple again, just find the difference of the two.  What we’re looking for here is the change in between the before and after temperatures to tell us how much heat the compressor is giving off.

     Now we can solve for our Compressor Efficiency.  Plug in the Compressor Inlet Absolute Temperature (°) and Temperature Rise (°F), as well as your Pressure Ratio into this equation, and you’re done:

Compressor Efficiency (%) =

Compressor Efficiency

This one’s a bit more complicated.  The 0.28 exponent is determined by the gas constant.  We’re multiplying the Pressure Ratio to the 0.28th power by the Absolute Temperature of the Compressor Inlet, and then subtracting by the same thing.  Divide all that by the Temperature Rise, and then multiply by 100% to convert to percentage form.

     Here’s some visual representations of how Compressor Efficiency (%) is affected:


 ”Fig. 3-4.” Chart. Maximum Boost, Designing, Testing and Installing Turbocharger
     Systems. By Corky Bell. Cambridge, MA: Bentley Publishers, 1997. 26.

     Taking a simple look at this graph shows that with lower Compressor Efficiency percentages, we also get a reduction in Density Ratio.  With a lower density, we’re packing less air into a volume of space, thus we’re making the turbo less effective.  You must’ve also noticed the shaded area of the graph which increases our Compressor Efficiency.  Intercooling is a great way to add to our Compressor Efficiency by lowering the temperature of our compressed air, which in turn increases our density (The Pressure-Temperature Law).  I’ll go into intercooling in another post.  Another graph here:


 ”Fig. 3-6.” Chart. Maximum Boost, Designing, Testing and Installing Turbocharger
     Systems. By Corky Bell. Cambridge, MA: Bentley Publishers, 1997. 29.

     This one clearly shows that with a decrease in Pressure Ratio, we get an increase in Compressor Dischange Temperatures.  Once again, heat is our enemy.  

     Finally, take a look at these next two graphs:


 ”Fig. 3-2 & Fig. 3-3.” Chart. Maximum Boost, Designing, Testing and Installing Turbocharger
     Systems. By Corky Bell. Cambridge, MA: Bentley Publishers, 1997. 25.

     You can clearly see that at the lowest point in the temperature curve on the Temperature vs Boost Pressure (psi) graph is equivalent to the highest torque point on the Torque vs Rpm x1000 graph.  With an even lower temperature, we can achieve even higher torque curves.  And the vice versa is true; the higher the temps, the lower the power.  So you can see the worth in having the highest Compressor Efficiency as possible.

     Next post I’ll work with the “hot” side of the turbo; the turbine.  Stay tuned.


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

August 2009
« Jul   Sep »


Contact Info:

If you'd like to contact me, please feel free to email me at Any and all opinions/ideas are welcome.


© 2009 Rusi Li

%d bloggers like this: