How to Go Fast Faster: The Math Behind Turbocharging. Part 8: An Example

turboheader

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.

     By now we’ve covered most of the basics of designing your own turbocharger kit, as well as some other random stuff I decided was relevant using a whole lot of math and graphs.  This will probably be the last post of this section where I’ll provide a full example using most, if not all, of the steps using Corky Bell’s Maximum Boost: Designing, Testing and Installing Turbocharger Systems.  It’s in Chapter 17 and starts on page 196 if you want to double check/follow along.  On with the show.

The *< and >* denotes parts which were not included in the chapter.   I have taken the liberty to add them in myself and do the math to show an example for each of the equations I’ve covered.

     We’ll be using the Honda/Acura NSX as our base car, which uses the 3.0 liter C30A engine designed specifically for this supercar.  I’ll provide a full in-depth look for the NSX later in the Spotlight section, but for now all you need to know is the engine specs.  It produces around 275 horsepower and 210 pounds of torque to the crank in a compact V-6 form.  It was also the first car in the U.S. to use their revolutionary VTEC system, creating a very linear and flat torque curve for both low-RPM and high-RPM driving.  It maxes out at a stratospheric 8,000 RPM due to its lightweight internals, but the maximum power output was a bit disappointing for a supercar.  Here’s a rundown of the stock performance measured by Mr. Bell:

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

     And this is where a turbo comes into play.  Using a turbo, we will give it more juice yet keep it street-legal and CARB legal, meaning the original catalytic converters stay put and emissions must stay within CARB limits.  Let’s go.

     Mr. Bell decided that in order to keep the C30A’s flat torque, one huge turbo wouldn’t work out since it wouldn’t provide enough power down low.  So it came down to either a sequential or parallel twin turbo setup.  Sequential turbo systems are very complicated, so that was elimanted.  That leaves us with a twin-turbo setup, splitting the work between two smaller turbos and thus giving us the low down torque we want. Our end goal is around 375 ponies, so let the math start.

     First the we want to find the Performance Gain (%).  Our Desired Bhp is obviously 375, while our Stock Bhp is 275.  Let’s plug it in:

Performance Gain (%) = Performance Gain

Performance Gain (%) = 36%

*<

     Using our Performance Gain, we can now solve for the Boost Required:

Boost Required (psi) = Boost Required

Boost Required (psi) ≈ 5.3 psi

>*

     So we’re aiming for a 36% increase in horsepower.  First let’s make sure our Fuel System is up to the job of our increased power.  Our Maximum RPM for the C30a is 8,000 RPM.  Plug it in:

Time of One Revolution (msec) = Time of One Revolution

Time of One Revolution (msec) = 7.5 msec

     Time to see if we have enough headroom to increase our Injector Pulse Duration.  The Stock Pulse Duration was measured at 5.0 msec, so plug that in along with the 7.5 msec from our previous equation:

Available Increase (%) = Available Increase

Available Increase (%) = 50%

     Our injectors have the extra time to cope with the extra airflow, but let’s check to see if our fuel pump can handle the extra Fuel Pressure:

Fuel Pressure Required (psi) = Required Fuel Pressure

Fuel Pressure Required (psi) = 83 psi

     According to Mr. Bell, the stock fuel system can handle the increased Fuel Pressure.  So now that our fuel systems are sorted out, let’s move on to our actual turbo selection.

     First up is the Pressure Ratio, which is simple:

Pressure Ratio = Pressure Ratio2

Pressure Ratio = 1.36

*<

     Now that we have that, let’s move onto our Airflow Rate.  We’re first going to need to convert our Displacement from Liters to Cubic Inches using this equation:

Displacement (in3) = Displacement Converter

Displacement (in3) = 183 in3

     With our converted Displacement, we can solve for our stock Airflow Rate while using a Volumetric Efficiency of 90%:

Airflow Rate (cfm) =

Theoretical Flow Rate

Airflow Rate (cfm)381 cfm

>*

     Then plug in our 8,000 RPM, Pressure Ratio of 1.36, Volumetric Efficiency of 0.90, and our 183 in3 of Displacement into our Turbo Airflow Rate equation:

Turbo Airflow Rate (cfm) =

Turbo Airflow Rate2

Turbo Airflow Rate (cfm) ≈ 519 cfm

     Since we’re going with a twin-turbo setup, only 260 cfm will flow through each turbo at Maximum RPM (8,000 RPM).

     With our Pressure Ratio and Turbo Airflow Rate figured out, we can start looking at compressors and compressor maps.  Corky Bell used two examples here, the Aerocharger model 101 and model 128:

Model 101:

page201top

”Fig. 17-10.” Chart. Maximum Boost, Designing, Testing and Installing Turbocharger
Systems. By Corky Bell. Cambridge, MA: Bentley Publishers, 1997. 201.
Print.

Model 128:

page201bottom

”Fig. 17-11.” Chart. Maximum Boost, Designing, Testing and Installing Turbocharger
Systems. By Corky Bell. Cambridge, MA: Bentley Publishers, 1997. 201.
Print.

     Fortunately for us, Mr. Bell has already drawn the Pressure Ratio line.  All we have to do is read the map and decide between the two.  Model 101’s maximum efficiency is a nice 78%, but as our engine speeds increase, it drops off pretty quickly into the low 50s.  Model 128, on the other hand, although its maximum efficiency is less (at 76%), its maximum efficiency is closer to the middle of the torque band, and doesn’t drop off as badly in terms of efficiency.  Mr. Bell decided here to choose the Aerocharger compressor Model 128 over the 101 due to its greater efficiency at maximum load instead of the one with just the highest maximum efficiency.

*<

     As for the turbine side, let’s solve for the Exducer Bore (in) diameter:

page31bottom

”Fig. 3-10.” Chart. Maximum Boost, Designing, Testing and Installing Turbocharger
Systems. By Corky Bell. Cambridge, MA: Bentley Publishers, 1997. 31.
Print.

     Using our Turbo Airflow Rate of around 260 cfm for each turbocharger, we should use an Exducer Bore between 1.5 and 2.0 inches.  While Mr. Bell doesn’t go into details about the Turbine Selection, he does settle for an Exducer Bore diameter of 2.0 inches.

>*

     Now we’re going to calculate the Temperature Rise at Maximum Compressor Efficiency using the Compressor Efficiency equation moved around a bit.  We’ll be plugging in an Ambient Temperature of 80°F and a Compressor Efficiency of 76%:

Temperature Rise at Max Compressor Efficiency (°F) =

Temperature Rise at Maximum Compressor Efficiency

Temperature Rise at Max Compressor Efficiency (°F) = 63°F

     We have the Temperature Rise when the compressor is at its maximum efficiency, but we need to also calculate for the Temperature Rise at Maximum Load, which is 8,000 RPM in our case.  Calculating for the Maximum Load will always give you the highest Temperature Rise, since that’s when the engine is working its hardest.  We need the Temperature Rise from before, and the highest efficiency and lowest efficiency percentages which the Pressure Ratio line passes through (on the Compressor Map).  Here’s the equation:

Temperature Rise at Maximum Load (°F) = Temperature Rise at Maximum Load

Temperature Rise at Maximum Load (°F) = 79°F

     Now onto intercooling.  Using the last answer, we can actually solve for the Temperature Post-Intercooler (°F) due to the heat removal (use °F as your unit here, not absolute):

Intercooled Temperature (°F) =

Intercooled Temperature (°F) = 13°F

     We can then use that to find the Intercooler Gain (%) by using an Intercooler Efficiency of 85% (an assumption), the previous Ambient Temperature of 80°F, and the Intercooled Temperature of 13°F:

Intercooler Gain (%) =

Intercooler Gain

Intercooler Gain (%) = 11.9%

     Now to figure out the dimensions for our intercooler.  This starts with finding a suitable Internal Flow Area (in²) for our output.  We’ll use the equation instead of the graph here:

Internal Flow Area (in3) = Internal Flow Area

Internal Flow Area (in3) ≈ 23 in2

     With that, we can find the Area of the Charge Air Face, or the “top” of the intercooler:

Area of the Charge Air Face (in2) = Area of the Charge Face

Area of the Charge Air Face (in2 51 in2

     So if we use an intercooler with a 3 inch depth, our width would be around 17 inches.  With a 2 inch deep intercooler, it would be around 26 inches.  We then have the problem of finding a good place to put the intercooler so it gets fresh air.  Mr. Bell found a suitable area just behind the rear wheel well, with enough spacec for an intercooler core measuring 3.5 by 9 inches.  It was enough to split the intercooler into two cores, one behind each wheel well using a 3 inch deep intercooler while satisfying our specifications of a 3 by 17 inch intercooler.

*<

     Moving onto the Intercooler Piping, let’s plug in our Turbo Airflow Rate of 260 cfm (since each turbo will have its own intercooler) and use a Velocity of 440 ft/sec, or Mach 0.4:

Pipe Diameter (in) = Pipe Diameter

Pipe Diameter (in)  0.90 in

>*

     And there we go.  We’ve solved for the “best” or most efficient in our case, turbo setup for a C30A engine from the Honda/Acura NSX.  Now since this book was published a while ago (1997), I’m sure there are a slew of new and (maybe) better parts to turbocharge this engine.  This is just an example of what you can do.

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