Air Flow and Fuel Flow Calculators

by Jeff Lucius

This web page is designed to help predict air and fuel flow or the Mitsubishi 3000GT VR4 and Dodge Stealth TT turbocharged cars when these cars are operated at wide-open throttle (WOT). Dataloggers for our cars, at least for 1991-1993 OBDI models, cannot report volume air flow because of a "too few bits reported" response from the ECU after a query. So another method must be used to determine air flow, and from that to determine fuel requirements for our engine.

For background information on some of the theory and formulas used on this page, please see my Pressurization Primer. My Pressurization Primer has a dyno chart that can be used to estimate "natural capacity" volumetric efficiency for our engines (explained below). Unit conversion calculators can be found at Unit Convertors.

As you use a calculator, note that some input and result values will be assigned in the empty input fields in the calculators that follow it. You will have to reset these "lower" calculators before changing values in the "upper" calculators if you want the values to carry through. Text boxes with a white background can be changed at any time. Text boxes with a yellow background (maybe still white in Netscape, Opera, and other browsers) are read-only. Please remember that by using your browser to "View Source" and saving the HTML file to your local disk drive, you can have this page available offline.

NOTE: These calculators were originally developed many years ago in Internet Explorer.

For those of you with IE 7 (or beyond), you may get a warning about my web site using ActiveX controls. It does not. I do use JavaScript for my calculators. If you want the functionality of the calculators, allow "ActiveX" controls (see instructions by clicking on the IE bar above my web page, if it is there).



Air Density

Air density can be calculated using the following equation or the JavaScript calculator below.

D = D0 x (T0/T) x (P/P0),

where T0 = 545.69R (86F) or 303.15K (30C),
P0 = 14.7 psi (= 1 atm = 760 mm Hg = 29.92 in. Hg = 1.033 kg/cm2 = 1.013 bar = 33.9 ft H2O), and
D0 = 1.1649 g/L = 32.986 g/CF = 0.072751 lb/CF.
T, P, T0, and P0 must be in absolute temperature and pressure. Values for T0, P0, and D0 were taken from tables in the CRC Handbook of Chemistry and Physics. For F add 459.69 to get Rankine and for C add 273.15 to get Kelvin. Just use Fahrenheit or Celsius below.

For the Air Density calculator, use the underhood air temperature and the absolute atmospheric pressure. The underhood air temperature for our cars when driving is usually 5F to 20F above ambient temperatures. Atmospheric pressure decreases at the rate of about 1 in. Hg or 0.49 psi for every 1000 feet (304.8 m) increase in elevation. Where I live at (5500' elevation), "standard" air pressure is about 12 psi (24.42 in. Hg), not the 14.7 psi (29.92 in. Hg) found at sea level.


Air Density
Temperature Pressure Density  
F C psi in. Hg g/L g/CF lb/CF


Volume Air Flow

Approximately the same volume of air is drawn in as the piston moves down regardless of engine speed (RPM), load (throttle opening), or intake manifold pressure. This volume is the cylinder displacement, with the consideration that exhaust gas reversion and other factors may reduce this volume somewhat. However, the density of the air that is drawn in varies quite a bit. When the air density is less than atmospheric pressure we measure a vacuum in the intake manifold, like during idle. In a normally-aspirated engine at WOT the air density approaches that of atmospheric pressure. When the density is greater than atmospheric, there is positive pressure (or boost) in the manifold. Rather than measure the air density in the cylinders or manifold, we measure the equivalent volume of outside air. The Volume Air Flow (VAF) is the amount of outside air that goes through an engine during a specified time period. The ratio of this volume of outside air to the engine displacement is what is usually referred to as Volumetric Efficiency (VE). VE rarely exceeds 100% for normally-aspirated engine. VE exceeds 100% for forced-induction engines.

The JavaScript calculator below calculates the VAF (volume of outside air flow) in cubic feet per minute (CFM) and liters per minute (LPM) based on engine displacement (CI or L), speed (RPM), and volumetric efficiency (VE). For this exercise, I define the volumetric efficiency as the product of the natural flow capacity (NC) of the engine, at a particular RPM and load, and the overall density ratio (DR), due to boost pressure. When the actual volume of air (compressed or at partial vacuum) entering the cylinders equals the engine displacement then the NC is 100%.

The next two formulas calculate VAF in CFM. The following one is for displacement in CI.

VAF = (CI/1728) x (RPM/2) x VE,

where, VE equals the natural capacity (NC) times the overall density ratio (DR). If the displacement is in liters then use the following formula.

VAF = (L/28.317) x (RPM/2) x VE.

Negative input values are not allowed. In addition, NC must range from 0 to 100 (percent), and the DR cannot be greater than 5. For a stock, turbocharged, Mitsubishi 6G72 2.972-L engine, NC ranges from 75% to 95% at WOT. Overall density ratios are usually less than 2.5 (that is boost pressure is less than 24 psi). The overall density ratio is less than the ratio of absolute boost pressure to atmospheric pressure (the pressure ratio) because of frictional and heating losses. For normally-aspirated engines use a DR equal to 1. Engine redline is around 7300 RPM. However, peak NC usually occurs between 5000 and 6000 RPM in the 6G72 engine.


Volume Air Flow
Displacement RPM Volumetric Efficiency Volume Air Flow  
cubic
inches
liters   Natural
capacity, %
Density
ratio
CFM LPM


Mass Air Flow

Mass air flow (MAF) is calculated using the volume air flow as determined and explained above, and a value for density calculated from the temperature and pressure near the air filter. Once the mass air flow is known, the engine electronic control unit (ECU) can calculate the amount of fuel to add to achieve a pre-determined air/fuel mixing ratio. The same data entry restrictions used above apply to the MAF calculator with the additional restriction that air density is in grams per cubic foot (g/CF) and must be greater than 0. For air density, use the value from the air density calculator for uncompressed, outside air. For normally-aspirated engines use a DR equal to 1.


Mass Air Flow
Displacement RPM Volumetric Efficiency Density Mass Air Flow  
cubic
inches
liters   Natural
capacity, %
Density
ratio
g/CF g/min lb/hr


Fuel Flow

Air/Fuel Ratio Limits
   6.0:1
   9.0:1
 11.5:1
 12.5:1
 13.2:1
 14.7:1
 15.5:1
 16.2:1
 18-22:1
 Rich run limit 
 Low power, black smoke 
 Rich best torque at WOT 
 Safe best power at WOT 
 Lean best torque at WOT 
 Chemically ideal 
 Lean light load, part throttle 
 Best economy, part throttle 
 Lean run limit 
 

Of course, once we know MAF we can calculate fuel flow using a specific air/fuel mixing ratio (A/F). MAF must not be negative, and A/F can range from 6 to 22. Using an average density of gasoline of 6 pounds per gallon, then lb/hr (mass) fuel flow times 10.5 is equivalent to (volume) fuel flow in cc/min.

Optional input: You can predict engine power (HP) output by assuming a certain brake specific fuel consumption (BSFC). BSFC must be a value between 0 and 1. High-performance race engines can have BSFC values (they vary a little across the RPM range) below 0.4. The average street engine has BSFC values near 0.5. Turbocharged vehicles' BSFCs are often near 0.6. I think values from 0.55 to 0.60 are representative for our stock to mildly modifed Mitsubishi 6G72 turbocharged engines. Our highly modified engines may have a BSFC as low as 0.45.


Fuel Flow
Mass Air Flow A/F Fuel Flow BSFC Power  
g/min lb/hr   lb/hr cc/min   HP


Fuel Injector Sizing

The JavaScript calculator below will calculate total fuel flow based on the injector size (static fuel flow rating), fuel line pressure, number of cylinders, and the injector duty cycle (IDC). The industry recommends a continuous, maximum IDC of no more than 80% (that is, injectors opened 80% of the time avaliable to them). 90% is probably OK for brief intervals. Injectors may actually flow less fuel above 95% IDC than predicted as they may just cycle between partly opened and partly closed. You should leave the injector rated pressure (@ psi) at 43 unless you know that the injector was tested at another pressure.

When the base fuel line pressure is different than the rated injector pressure, then the injectors will flow differently than rated according the following formula.

FN = F0 x SQRT(PN/P0),

where FN equals the new flow rate when the differential fuel line pressure is PN and the injector has a rated flow rate of F0 at a rated pressure of P0. The differential fuel line pressure (psi) is the difference between the actual line pressure and the boost pressure in the manifold. Our cars are designed to maintain a 43 psi differential pressure.

Optional input: If you assign a value for BSFC then engine power (HP) will be estimated. If an A/F value from 6 to 22 is entered then mass air flow (lb/hr) is calculated. In addition, if you also assign values for the underhood air temperature and the ambient air pressure, then volume air flow (CFM) is calculated.


Fuel Injector Sizing
Injector Rated Flow Fuel line Cylinders IDC Total Fuel Flow BSFC Power  
cc/min lb/hr @ psi psi   % cc/min lb/hr   HP
  Temperature Pressure A/F Total Air Flow  
F C psi in. Hg   CFM lb/hr


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Page last updated July 8, 2004.