How to Go Fast Faster: The Math Behind Turbocharging. Part 3b: Brake Specific Fuel Consumption (BSFC)

turboheader

Part 1 is here.

Part 2 is here.

Part 3 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. 

     In the last post I explained bits about the Electronic Fuel Injection (EFI) system and how to modify it to cope with the upcoming turbo power.  Near the end, I introduced the idea of the Brake Specific Fuel Consumption (BSFC) to estimate the amount of fuel the engine will need per hour.  Here I’ll expain a bit more on the BSFC and how it affects our cars.

     So I’ve already defined the BSFC as the amount of fuel the engine requires to produce one horsepower per hour, but I didn’t specify a unit.  We can figure that out by looking at how to calculate the BSFC.  You’ll only need two variables: the Fuel Rate (Lb/Hr) and the Power (Hp).  Here is the equation:

BSFC (Lb/Hp*Hr) = BSFC

Just divide the Fuel Rate by the Power.  And if you use only the units, you’ll see that the unit for BSFC is Lb/Hp*Hr.

     When you take a look at the equation, it’s very simple.  We’re just multiplying two numbers.  But if you start comparing the two variables, Fuel Rate and Power, you realize that you can never have an exact BSFC for an engine or car.  Why?  Because the BSFC is the rate of fuel consumption over one hour of operation.  What if for the first hour you drove mildly on the highway, and then the second  hour you were sitting in bumper to bumper traffic?  The two Fuel Rates would be completely different.  As would the Power as well.  When we’re sitting in traffic, we’re not using and power at all.  And when we’re cruising on the highway, I doubt you’re using all your engine’s power for a full hour.

     So the problem becomes the use of BSFC if we can’t calculate an exact number for an engine.  Well, we can get a range of BSFCs for engines.  For example, in our last post I used 0.65 as a safe number for a turbocharged engine.  Most turbo’d engines run between 0.6 and 0.65 BSFC while supercharged cars have a BSFC between 0.55 and 0.6, and naturally aspirated engines use only 0.45 to 0.5 Lbs/Hp*Hr.  These are only approximations, but you can clearly see the difference between naturally aspirated engines and turbocharged engines.  Turbocharged engines usually require more fuel to keep detonation at bay due to the increased temperature and pressure of the intake air.  This is why a turbocharged engine uses more fuel per horsepower per hour.  Now that we’ve established that the BSFC of an engine is in constant flux, let’s take a look at how and why it changes.

     First let’s take a look at how the BSFC changes in relation to the Engine’s Speed (RPM).  One would guess that at the car’s maximum RPM would be when the BSFC is the highest, and vice versa.  But take a look at this:

GraphBSFCvsEngineSpeed

Edgar, Julian. “Brake Specific Fuel Consumption.” AutoSpeed. Web Publications
     Pty Limited, 10 Apr. 2008. Web. 27 Sept. 2009. <http://autospeed.com/cms/
     title_Brake-Specific-Fuel-Consumption/A_110216/article.html>
 

     The red curve shows the Power (in kW for this graph) while the green curve represents the Torque (shown as the Brake Mean Effective Pressure here) so then the pink curve is obviously the engine’s BSFC (in g/kWh this time).  What’s interesting is that the pink curve isn’t linear or exponential and that the lowest point isn’t at the lowest RPM, but the curve begins around the 1,000 RPM point, and then drops to its lowest point at around the 2,500 RPM area.  It can’t be linked to either the highest Torque point or the highest Power point, so it seems that power can’t be directly linked to the BSFC. 

     There are a few reasons that I can think of for the BSFC being at neither the lowest nor the highest engine speeds:

  1.      At lower RPMs, time between the engine cycles lets the intake air cool down too much during the compression cycle.  We want the coolest air to fill up the cylinder to pack more air in there (The Pressure-Temperature Law), but once the valves close and the compression cycle starts, we want the pressure and temperature to increase to give us more torque.  Remember that heat is a form of energy, and the more there is in the compressed air, the more energy is converted when ignition occurs.
  2.      At high RPMs, there is an exponential increase in frictional loss within the engine, from cylinders to camshafts to belts.  Faster engine speeds = more friction.
  3.      Also at high RPMs, the speed the piston is descending on its intake stroke is faster than the air filling up the cylinder.  This is what creates a vacuum at higher RPMs, since the engine doesn’t get the air fast enough.  This vacuum creates extra work for the engine, thus reducing efficiency.
  4.      Most engines are tuned for mid-range torque, meaning all the geometry of the engine, the timing of the cams,camshafts etc are all optimized for the best efficiency in the middle of the RPM range, not the lowest or the highest point.

     But there’s another problem.  This is more or less a dyno graph, meaning the data logged is when the car is going full-throttle from 1,000 all the way to 7,000 RPMs.  Our engines rarely run full throttle while puttering around town.  So lets take a look at how Throttle Position (%) (or engine load) affects our BSFC.

GraphBSFCvsThrottle

 Edgar, Julian. “Brake Specific Fuel Consumption.” AutoSpeed. Web Publications
     Pty Limited, 10 Apr. 2008. Web. 27 Sept. 2009. <http://autospeed.com/cms/
     title_Brake-Specific-Fuel-Consumption/A_110216/article.html>

     Going by this graph, by using 100% throttle, we’re actually getting the most efficienct BFSC, and we’re getting the worst by using “only” 25% throttle.  You can once again see that the lowest point on each curve is in the middle of the RPM range; between 2500 and 3500 RPM in this case. 

     The BSFC for full throttle (100%) is at most 0.50 Lb/Hp*Hr, with a 0.43 Lb/Hp*Hr best.  But when we look at the 50% throttle curve, it has a horrible 0.80 Lb/Hp*Hr best, but a decent 0.48 Lb/Hp*Hr best.  But when we take a look at the 25% throttle curve, it gets alot worse.  Its worst BSFC is a 1.50 Lb/Hp*Hr, with only a 0.70 Lb/Hp*Hr best.  That’s about three times the fuel consumption at its worst, and just under twice at its best.  So if we had to two engines running at the same RPM (lets use 3,000 RPM), one at 100% throttle, the other at 25% and producing the same amount of power, the engine using only 25% throttle would use up almost twice the amount of fuel.  It seems that while we linearly decrease our throttle, our BSFC increases exponentially.  Now please remember that BSFC does NOT equate to the fuel efficiency at a certain throttle or engine speed, but the fuel efficiency of a certain throttle or engine speed in comparison to the Power produced.  When we were comparing the 100% throttle and 25% throttle, we were saying that an engine using 100% throttle is using 0.43 Pounds of fuel per Horsepower per Hour

     In mathematical terms, the more power we’re using, the smaller our BSFC (if the Fuel Rate doesn’t change), since BSFC is equal to Fuel Rate divided by Power.  But to get more Power, we usually have to increase our Engine Speed, which in turns raises our Fuel Rate, and eventually our BSFC (you see the dilemma?).  This is why the BSFC of an engine isn’t as simple as just the lowest or highest RPM.  What if we ran our car at a constant 3,200 RPM with 100% throttle?  We’d obviously be getting the best BSFC possible.  But on the other hand, using 100% throttle means increasing the Engine Speed faster, and in turn increasing our Power faster.  And the larger our Power, we lower the BSFC (once again if the Fuel Rate doesn’t change).  Also, there’s no way we can keep the throttle open all the way yet keep it at 3,200 RPM.  Its like a dog chasing its own tail.

     On the last note, we’ll take a look at a graph of an engine’s actual BSFC in comparison to its Engine Speed (RPM) and Engine Load/Torque (BMEP):

GraphSpecificBSFC

Edgar, Julian. “Brake Specific Fuel Consumption.” AutoSpeed. Web Publications
     Pty Limited, 10 Apr. 2008. Web. 27 Sept. 2009. <http://autospeed.com/cms/
     title_Brake-Specific-Fuel-Consumption/A_110216/article.html>

     As you can see, the best BSFC is a 0.42 Lb/Hp*Hr (the red island), at round 2,000 RPM while using 100 BMEP (Torque).  The black dots represent a car’s BSFC taken at 1 second intervals.  See how they rarely enter the 0.42 Lb/Hp*Hr island, and are mostly spread out between 0.50 and 1.70 Lb/Hp*Hr.  And at the worst BSFC is when the car is idling, where the engine consumes fuel, but doesn’t create any Power, and ultimately doesn’t get anywhere.

     This post is actually quite a diversion from the turbocharging process, but it interested me, so I decided to add it in here.  Mathematically I haven’t solved anything (I haven’t found how to achieve the “best” BSFC in a real world setting), but this was a fun research topic.  Stay tuned for the next post where I’ll get back on topic.

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