Airflow was written by Craig Watson. It shows the physical relationships of various parameters of a turbocharged motor. I had been modeling the performance using a spreadsheet for a couple of years and it seemed like good practice to make it into a web page.
The basic idea is to calculate how much air is going into the motor. Knowing the required airflow and compressor ratio (CR) one can shop for a turbo with the flow and efficiency characteristics desired. See Turbonetics web site for example turbo compressor maps.
Once the air flow is determined, the air to fuel ratio is used to determine the fuel consumption. This allows sizing of injectors and fuel pumps. Incidentally, knowing the fuel flow and using the BSFC, the horsepower can be estimated. Patrick Hale (al la Quarter Jr.) came up with the relationships of ET and MPH from the horsepower. It is amazing how well they work.
There are three parameters which are "fudge factors". The rest is basic physics. The primary utility I see this being used for is to assist in sizing turbos, fuel injectors, and fuel pumps. The three fudge factors are:
The "defaults" are my approximation of a stock Buick Grand National.
Email:Craig Watson
Manifold Pressure is boost or vacuum pressure relative to ambient pressure. Use a negative number for vacuum readings.
RPM is engine speed in revolutions per minute. See the discussion concerning ET and MPH estimates. See the gear table for speed at a given rpm
Injectors are typically rated in pounds per hour of fuel flowed at a pressure of 3 Bar (44.19 PSI).
This is the fuel pressure measured with the vacuum line disconnected
from the fuel pressure regulator. Stock pressure on a Buick Turbo Regal
is 37 psi with most racers setting their fuel pressure to 45 psi. Most
injectors are rated at a pressure of 3 BAR which is around 44.19 PSI. A
change in the static fuel pressure changes the injector flow rating based
upon the folowing relationship.
actual flow = rated flow * square root( actual pressure / rated pressure )
This is the air to fuel mixture ratio based upon mass, not volume. The stoichiometric ratio is 14.7:1 for gasoline. That's the ideal chemical ratio for complete combustion. The ratio for best power is usually considered to be a little richer, around 12.9:1. A lot of people have reported their cars perform better around 11.5:1. This is one of the parameters that can easily make the performance predictions a joke. I have found setting it to 12.9 is good for performance predictions but for injector sizing and fuel requirements you need to set it to your actual A/F ratio. Some of the people who tell me their cars run better at an A/F ratio of 11:1 also talk about running as lean as possible with exhaust gas temperatures over 1700 degrees. These guy go fast and their BSFC numbers must be better than the 0.47 I use. They also melt heads and burn holes in pistons. I don't know how to reconcile the rich 11:1 mixture with the lean talk and high EGT's. I do know the calculations here don't do it and you can get bogus performance numbers by plugging in a real rich mixture. A really rich mixture will cool the exhaust and lower the exhaust gas pressure which shows up as turbo lag. No matter what these numbers say, you will be real disappointed if you try to run with a 8:1 A/F ratio. Of course I once had a boost sensor failure and suddenly was running at a 17:1 A/F ratio with 21 pounds of boost. I blew the head gaskets in four cylinders and beat up the rod bearings. Too lean is no fun either. :-(
This is the drop in pressure through the air filter. Pressures through filters are often measured in inches of water (K&N specs that way) so the default here reflects that.
This is the drop in pressure across the intercooler.
When air is compressed, the temperature rises. In an ideal situation this would be done without adding any energy (adiabatic) but turbochargers and superchargers aren't perfect and do add energy (heat). The relative heat added is determined by the efficiency rating of the compressor. This is found in the compressor map specifications for a given turbo. Typical numbers for turbos are in the range of 60% to 80%. Supercharger efficiencies max out at 50%. The numbers on the compressor map are based upon the air flow (cfm at intake) and compressor ratio (CR). The efficiency affects the output temperature and horsepower required to compress the air. Of course, a lot of heat into the motor is bad and that is why intercoolers are used. See Turbonetics web site for example turbo compressor maps.
The Volumetric Efficiency describes how well the intake manifold, exhaust manifold, and heads flow air. The values used here are a WAG based upon racing these cars in various configurations for several years. I use 80% for a totally stock car, 85% for Champion Iron Heads, 90% for Champion and M&A aluminum racing heads, and 95% for Bill's "fully ported aluminum heads."
Intercooler Efficiency is a WAG that is pretty easy to hone in on. The approach I used was to adjust it to calculate the actual measured temperatures of my manifold. I have found 50% works pretty well for a stock IC going up to 85% for some of Tony DeQuick's better front mounts. The best intercoolers are the liquid and freon types. They have efficiencies greater than 100% (when you ice the fluid in the liquid ones).
This is supposedly a measure of how efficient the fuel is burned. It is affected by the compression ratio, combustion chamber design, the air to fuel ratio, atomization of the fuel, etc. Some dynamometer tests give BSFC figures. BSFC is really a big fudge factor lumping the engine friction, accessory drag, exhaust and intake "pumping work", and actual power (indicated power) of the cylinder together. The form has an input for adjusting the expected BSFC. Note this is a fraction of the total BSFC without the turbo load. The default "adjusted BSFC" value provided here is a real WAG. I came upon the 0.47 value based upon experimentation and several magazine articles. Corky Bell says the total (Net) can go up to 0.55 as a worst case value in turbo-charged cars. I've seen some other documents showing 0.6 for total BSFC in turbo applications. Some cars get numbers as good as 0.40. A little change has a big impact. The total BSFC lumps the turbo load into the calculation. I have broken out the turbo load separately to allow examination of various boost levels and efficiencies. When you do this, the BSFC number drops into the more conventional 0.47 range seen by normally aspirated motors. This is to be expected. After all, the cylinder efficiency isn't really being drastically altered as boost is increased and the friction and accessory drags are similiar. These cars do burn efficiently or they would never pass emissions tests. I calculate the net BSFC based upon the corrected horsepower and actual fuel used. This is the number a dyno would measure. Good luck playing with the BSFC numbers.
This is the temperature of the air exiting the turbo. The value
calculated here takes into account the specified efficiency of the
compressor. The equation used to determine the adiabatic temperature
rise is:
T2 = T1 * ( P2/P1)0.283
After figuring this, you have to adjust it for the efficiency of the turbo. Note the temperatures here are degrees Rankin and the pressures are referenced to an absolute vacuum (psia).
This is the temperature after the intercooler has cooled the hot air from the compressor (turbocharger or supercharger).
The Turbo Compression Ratio is the ratio of the input pressure to the output pressure of the turbo. It is used with the input flow to determine a particular turbo's efficiency from the published compressor map.
This is the minimum injector size required to flow the fuel to maintain the air to fuel ratio at the boost levels specified.
This is the time required for an injector to remain open to flow the amount of fuel needed. Note this assumes an ideal injector (they aren't) that opens and closes instantaneously.
This is the maximum time allotted for an injector during an engine cycle. Basically the injector is open continuously if it "goes static."
This is the ratio of injector pulse width to static pulse width. A value greater than 100% indicates too small an injector. Then you "lean out", have detonation and blow a head gasket. I've done this and it isn't fun.
Torque is the rotational force exerted by the wheels to drive
the car forward. The relationship of torque to horsepower and RPM is simple.
T = HP * 5252 / RPM
The ET and MPH are the quarter mile drag strip performance measures.
The ET, MPH, and 60' estimates are just that, estimates. Don't be
surprised when your mileage varies. That being said, I have been
surprised at how well the ET and MPH estimates work. The governing
parameter seems to be getting an accurate number for the RPM. The
tendency is to say "I'm going to figure out how fast it will go if
I run it at 6000 rpm." That isn't realistic. A stock GN finishes
the quarter mile around 4600 rpm and a 12 second car with a loose
torque convertor runs around 5200 rpm. The trailer queen 8, 9 and
10 second cars do reach the 6000+ rpm ranges. A look at the MPH
estimate and the speed at
a given rpm based upon gear ratios and tire diameters will give
some feedback here. Mostly, it will suggest you lower your
expectations down to numbers that become realistic.
No matter what these numbers say, the real test is at the track.
That means tuning. Getting the pressures and air/fuel ratio right,
getting the timing curve right, learning to launch the car, setting
up the suspension, etc. All the tuning will get you to run the
numbers. You may think, okay, I have these numbers predicting my cars
current performance pretty well. Now all I have to do is put in a
higher boost number and I'll find out how fast my car can go. Maybe,
within reason, in an ideal world. You won't really know if you have
a problem until you go to the track.
The 60 foot time is the time a car takes to travel the first sixty feet from a standing start. The 60' estimates here are based upon some statistical studies I did for another project (my Masters actually). They are only applicable to stock G-body Buick Regals and only for the turbo-charged V6 motors in full-bodied cars running in the 10-15 second range. I think Stage 2 motors change the weight, balance, and power of the car too much to be included here. Again, these are estimates and this is the most nebulous calculation on the page. I can prove however, that "a tenth in the sixty foot is two tenth's in the quarter mile" is not realistic. My calculation seems to do better than that. For a long time I had a slower car and always resented people saying "Well, if you just get your sixty foot down to the 1.40s my 10 second car does, your 12 second car will be in the 11s. Yeah, right. It takes horsepower along with traction and a good launch.
MEP and PLAN basically look at the pressure in the cylinder and take into account the area of the piston and the leverage of the rods and the crankshaft to derive a torque and horsepower estimate. Here it is worked backwards to find the MEP from the horsepower.
Several good books that delve into MEP, PLAN and other aspects of
turbocharging are:
The Auto Math Handbook
by J. Lawlor (1991) HP Books Los Angeles, CA
Maximum Boost
by Corky Bell (1997) Bentley
Publishers Cambridge, MA
Turbochargers
by Hugh MacInnes (1984) HP Books Los Angeles, CA
If you want to hurt your brain, try these books:
The Internal Combustion Engine in Theory and Practice
Volume I: Thermodynamics, Fluid Flow, Performance
Second edition, Revised
by Charles Fayette Taylor (1985) The M.I.T. Press Cambridge, MA
The Internal Combustion Engine in Theory and Practice
Volume II: Combustion, Materials, Design
Revised Edition
by Charles Fayette Taylor (1985) The M.I.T. Press Cambridge, MA
This is the power required to compress the air. Some people think this is free power. This power is actually derived from the back pressure the turbo puts in the exhaust stream. The increased backpressure pushes against the piston during the exhaust stroke. This has the effect of robbing horsepower from the motor. See the section on MEP. A consequence of this is that turbocharged motors need larger fuel injectors than a simple horsepower analysis would indicate.
This is a precise engineering acronym standing for: Wild Ass-ed Guess