How to Go Fast Faster: The Math Behind Turbocharging. Part 8b: The Result


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.

Part 5b is here.

Part 6 is here.

Part 7 is here.

Part 7b is here.

Part 8 is here.

     After doing all that math to piece together the most efficient turbo system for the C30A engine for the Acura NSX, Mr. Bell goes on to verify and test his math with actual data.  Keep in mind that a twin-turbo setup was used, with one intercooler for each turbo.  The aim was around 375 bhp, an increase of about 36% power over stock (275 bhp).  The engine’s already been tuned and broken in, so no worries about that.  Let’s take a look at the end result.

     First we’ll take a look at the compressor and the Compressor Efficiency to see how well it’s performaing.  If you remember from our previous post, to calculate our Compressor Efficiency we need the Ambient Temperature, Pressure Ratio, Compressor Inlet Temperature, and Compressor Outlet Temperature.  For our Pressure Ratio, we’ll use the equation involving the Boost Pressure since that’s what we’re given:

Pressure Ratio = Pressure Ratio

Pressure Ratio 1.41

Here’s the rest of the information in a table:


     We see three sets of runs at around 100 °F ambient using engine speeds of 4,000 and 6,000 RPMs at 6 psi of boost.  Using these numbers, we can calculate for the Compressor Efficiency and then compare that to the theoretical compressor efficiency of the compressor map.  Since there are three sets of runs, I’ll calculate the compressor efficiency for each set, and then find the average:

Compressor Efficiency (%) = Compressor Efficiency

Compressor Efficiency Run 1 (%) ≈ 77.4%

Compressor Efficiency Run 2 (%) ≈ 74.0%

Compressor Efficiency Run 3 (%) ≈ 74.3%

Average Compressor Efficiency (%) ≈ 75.2%

      As a reminder, the compressor map for the Model 128 ,which we installed, peaked at an efficiency of  76% when running at 60% load.  And I just calculated for an Average Compressor Efficiency of 75.2% over three seperate runs at both 4,000 and 6,000 RPMs.  This is very encouraging, as our end result was less than 1% off from the theoretical compressor efficiency.

     Looking at the table, we can see a small downward trend in efficiency from the first run to the last one due to the increase in heat.  Obviously, with the first run, the engine hasn’t been pushed yet, so is quite cool.  But by the 8th run, we can see that the efficiency has dropped from 78.4% and evened out around 74.4%.  With just this engine, from a change of 6°F, we get a decrease of about 5% or so in efficiency.  I thought there would be a noticible difference between the 4,000 and 6,000 RPM runs, but there’s not enough data to support this.  The first two sets of runs showed a decrease in efficiency when raising the engine load from 4,000 to 6,000 RPM of either 2.1% or 1.1%, but the third run actually showed an increase in efficiency of .3%.  By now, you can see I’m over-analyzing the results, but this is interesting nontheless.  Let’s move

      As for the turbine side, Mr. Bell attached a pressure gauge to a fitting on the turbine inlet and recorded a boost pressure of 15 psi, with a maximum of 15.5 psi.  An efficient turbine which produces minimal backpressure has a turbine inlet pressure anywhere between 2 to 3 times the boost pressure.  In our case that would be anywhere between 12 to 18 psi, so our 15 psi is good enough for good low-speed response at the cost of a tiny increase in exhaust backpressure.  He states that increasing the turbine size wouldn’t be worth the increase in turbo response, and is thus happy with his turbine selection.

     Now let’s take a look at the intercooler and how efficient its running.  We’re aiming for the maximum temperature drop while having a pressure loss of less than 1 psi.  Unfortunately, the pressure loss was recorded at a “tick over 1 psi at 7700 to 7800 RPM.”  Mr. Bell was a bit disappointed, but nevertheless stuck with his selection.  As for the temperatures, here’s a table of the data collected:


     Once again, these runs were done under 100 degree weather.  He made 4 runs here at 4,000 RPM.  Now let’s plug in the numbers to find our Intercooler Efficiency:

Intercooler Efficiency (%) =

Intercooler Efficiency Run 1 (%) ≈ 83.1%

Intercooler Efficiency Run 2 (%) ≈ 80.6%

Intercooler Efficiency Run 3 (%) ≈ 81.7%

Intercooler Efficiency Run 4 (%) ≈ 81.6%

Average Intercooler Efficiency (%) ≈ 81.8%


     This gives us an intercooler which operates at an efficiency of around 82%, around 3% less than the 85% Mr. Bell used earlier.  He seemed a bit dissapointed at the 1 psi loss of pressure through the intercooler, but he expected this from a street-application intercooler.

     And finally, the result of all our math.  First the logged stock performance data:

  • 0-60: 5.7 seconds
  • 1/4-mile time: 14.0 seconds
  • 1/4-mile speed: 101.0 mph
  • Power: 268 bhp

     And the end result:

  • 0-60: 4.7 seconds
  • 1/4-mile time: 13.0 seconds
  • 1/4-mile speed: 111.5 mph
  • Power: 390 bhp

     Shaved off one second from the average 0-60 time.  Not bad for a fully CARB legal turbo system for the streets.

     This concludes our section on the math behind turbocharging.  The next section will be about engine management tuning.  Stay tuned.


1 Response to “How to Go Fast Faster: The Math Behind Turbocharging. Part 8b: The Result”

  1. 1 Michal February 10, 2010 at 2:39 pm


    what’s about sequential twin turbo? You wrote it is difficult to make it. I know it takes long time to write it, but I am REALLY interested in it. It is a great set up. How should I make one? What is the math formulae like? Where can I find it.

    I am interested in it, because I would like to have daily car, that can be used for hard race. I mean 800hp and 8000RPM (Nissan Skyline GT-R 34 with an engine RB30DETT (head RB26DETT stage 3) – standard is RB26DETT).

    Thank you

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November 2009
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