How to Go Fast Faster: The Math Behind Turbocharging. Part 3: Increasing Fuel Delivery


Part 1 is here.

Part 2 is here.

*EDIT: Sorry this is out of order.  I pushed every post up since I had to squeeze this post in between Part 2 and Part 4.  I expanded the fuel system section quite a bit and decided it needed its own post.

     Our next step will involve our fuel system.  We have to make sure our fuel system is up to the job for our soon-to-be turbo’d engine.  So if we’re increasing the performance of our engine by stuffing more air in the engine, then we have to also increase the fuel in the cylinder to balance it out.  We can’t just add more air without fuel since that won’t achieve anything.  So if we’re deciding to stuff more air, and thus more fuel, we have to make sure our fuel system can pump the necessary amount of fuel with the increased amount of air.  There are a number of ways in which we can supply the engine with more fuel, but each one has its own advantages and disadvantages. 

     The first option would be to increase the Pulse Duration (msec) of the injectors.  The Pulse Duration is how long each injector’s nozzle is open to mix the fuel with the air.  The problem is that the length of the duration is limited to the time for the engine to complete one whole cycle.  So the faster an engine speeds up, (increase in revolutions, or RPMs), the less time the injectors have to spray its fuel.  Obviously even at the highest RPMs of a stock engine, the stock injectors have enough time to do its job despite the fact that its limited to just milliseconds.  Here’s a simple graph to illustrate my point:


 “Fig. 7-3.” Chart. Maximum Boost, Designing, Testing and Installing Turbocharger
     Systems. By Corky Bell. Cambridge, MA: Bentley Publishers, 1997. 88.

     To increase  our Pulse Duration, we must first figure out how long it takes for one revolution of the engine.  We just need our engine’s maximum Revolutions (RPM) here.  Here’s the equation for the Time of one Revolution:

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

Here we’re just dividng 60,000 by our maximum RPM.  The 60,000 is to convert from minutes to milliseconds (msec).

     You then need to find out how long the stock pulse duration is for our fuel injector, since this is different for every engine/car.  This I can’t help you calculate.  You have to research that number on your own.  Once we find that, we can calculate how much we can push the stock fuel system before it maxes out.  We then need the Time for one Revolution (msec) and the Stock Pulse Duration (msec) to find out if our Available Increase:

Available Increase (%) = Available Increase 

Just divide your previous answer (Time of one Revolution) by the Stock Pulse Duration, subtracting by one, and then multiplying by 100% to convert to percentages.

     This will calculate how much room we have to increase our fuel supply for the cylinders.  Some engines might have alot of headroom, while others have none.  Typically, a low-boost (under 7 psi) turbo’d engine will have enough headroom for the stock injectors to satisfy the power demand, but do make sure before you install your turbo.  Then we need to compare this Available Increase percentage with our Performance Gain (%) from the last post.  If our Available Increase is more than our Performance Gain, then we don’t have to physically modify our fuel system for our turbocharging project.  We do, however, need to make changes to the Pulse Duration at the software end, meaning we still need to make changes to the ECU (once again, not covered here).  This is just one option to increase our fuel supply into the cylinders, but should only be used if your Boost Pressure (psi) is under 10 psi.  If this option doesn’t work (ie. the Available Increase isn’t enough), then keep on reading.

     The next option would be to increase the system’s Fuel Pressure by either installing a Fuel Pressure Regulator, or once again modifying the ECU to make the changes via the software.  A Fuel Pressure Regulator increases the Fuel Pressure linearly to the amount of Boost Pressure (psi) in the intake manifold as long as your stock fuel system can handle it.  To calculate how much extra Fuel Pressure you’re going to need, you’ll need your Performance Gain (%) and your car’s Stock Fuel Pressure (psi).  (If you don’t remember what that is, just divide your Desired Bhp by your Stock Bhp, subtract by one, and then multiply by 100%):

Fuel Pressure Required (psi) =

Required Fuel Pressure

What we’re doing here is approximating the required Fuel Pressure with a certain amount of Performance Gain.  The approximation is squaring the sum of the Performance Gain and one, and then multiplying that by your car’s stock Fuel Pressure.  Most engine’s use a stock Fuel Pressure of 43.5 psi, but don’t take my word for it, do some research.

     When you’ve found that out, check to make sure that your stock fuel system can handle that pressure/flow.   The problem with this solution is that although you might be able to squeeze out a few more psis of pressure, the stock pump will reach its limit quite quickly since it’s rated for the engine’s original power.  Once again, this option should only be considered if you’re running a low-boost turbo (10 psi or less).  You can also install a new Fuel Pump to cope with the stock pump’s limitations, but without upgrading the rest of the fuel system, this isn’t a recommended solution.

     If your Boost Pressure is over 10 psi, or your Available Increase isn’t enough, then your best option is to take a look at your whole fuel system and start looking to replace a few parts.  A typical fuel system includes a Fuel Pump, a Fuel Pressure Regulator, the Fuel Lines, and the Fuel Injectors.  This isn’t the most cost effective way, but it is the safest for your engine (if done right).  Let’s start by looking at the Fuel Injectors.  This is the tail end of the fuel system, and is what can actually restrict the amount of fuel you want from mixing with the air.  A Fuel Injector is rated by its Fuel Flow, which can be represented in either pounds per hour (lb/hr) or cubic centimeters per minute (cc/min).  If you’re looking to convert between them, here’s the simple equation:

Fuel Flow Unit Conversion (cc/min) = Fuel Flow

Just multiply your lb/hour Fuel Flow by 10.5 to change your units to cc/min.  Or divide  your cc/min Fuel Flow by 10.5 to get lb/hour.

     To figure out your desired Injector Fuel Flow is quite simple too.  You just need your Desired Bhp (Hp) and the Number of Injectors you have (usually 1 per cylinder, but double check in case):

Injector Fuel Flow (lb/hr) = Injector Flow Rate

We’re just multiplying our Desired Bhp by 0.65 and then dividing by the number of injectors for equal fuel distribution among each injector.

     The 0.65  is the Brake Specific Fuel Consumption (BSFC), a number estimated to be the amount of fuel needed to produce 1 hp for 1 hour for turbocharged engines.  I will go into the BSFC in another post (Part 3b) in more detail.  This tells us how much fuel our injectors need to push out, but you should always choose the next larger size to be on the safe side.  You don’t want your engine running lean do you or have to replace your injectors if you want just a small increase in power?

     Now that you’ve figured out the size of your injectors, we can take a look at the Fuel Pump.  The pump must be able to supply the amount of fuel demanded by the engine so make sure you don’t starve the engine of fuel on this end either.  A Fuel Pump is rated by three variables:  the Voltage it requires, the Fuel Flow, and its Fuel Pressure capabilities.  The Voltage is simple, as most pumps are rated at either 12 or 13.5 volts.  Double check the voltage your engine supplies, and the amount your pump requires and make sure they match.  The Fuel Flow is simple too since it was basically just calculated.  Here it is again:

Fuel Flow (gal/hr) = Flow Rate

We’re just multiplying our Desired Bhp by the BSFC (Brake Specific Fuel Consumption) and then dividing by 6.34 to convert the lb/hr to gal/hr since 6.34 is the weight of fuel per pound in a gallon.

     Fuel Pressure isn’t that hard to solve for either.  Your Base Fuel Pressure (psi) should be around 43.5 psi, and you just have to add your Boost Pressure (psi) to it.  I’ll also be adding in another 10 psi for pumping losses due to hydrodynamic losses (friction, bends etc.) since there is always a pumping loss (usually around 5 psi, but I’ll be using 10 psi just in case).

Fuel Pressure (Psi) = Fuel Pressure

Just add the 43.5 to your desired Boost Pressure, and then add another 10 to that.

     This should give us a safe estimate for the amount of Fuel Pressure our pump needs to be able to handle.  We just then need to search for a suitable Fuel Pump using those numbers.  You should always buy “up”, meaning buy a part with a little bit of headroom in case the engine is more thirsty than we’ve calculated for.

     After taking a look at our Fuel Pump and Fuel Injector, make sure your Fuel Lines and Fuel Pressure Regulator is also up to par, and you’re basically done with this part.

     The next post will be about the Brake Specific Fuel Consumption (BSFC).  Stay tuned.


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September 2009
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© 2009 Rusi Li

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