Fuel Injection Simulation
by Bowling
Algorithm
Imagine one cylinder of a car as exactly that - a cylinder. When the piston is at the bottom of the bore, the volume of the cylinder is greatest, and is equal to the cubic inch displacement divided by the number of cylinders. If the engine was a perfect air pump, there would be exactly this much volume of air pressed in the cylinder under atmospheric pressure, just like an empty coffee can. However, due to several mechanical and time-related factors, there is usually less air in the cylinder, and this is given by the engines Volumetric Efficiency, expressed as a percent. So a cylinder with a volumetric efficiency of 80% means that the volume of air inside is only 80 percent of the same volume of air at atmosphere. Note that for turbocharged, supercharged, and race vehicles, the volumetric efficiency can be greater than 100%, meaning that air is shoved in under a greater pressure than atmosphere. Also, the amount of air introduced into the cylinder is a function of the Manifold Absolute Pressure (MAP), which can be measured with a vacuum gauge attached to the intake. When there is high measured vacuum (or low MAP) less air gets into the cylinder (think of the throttle plates as a restriction to air flow, thus creating the "vacuum" in the intake).
Now that we have a known volume of air within a cylinder (lets use cubic feet for this example - any unit of volume will work), we can multiply this by the current air density (in pounds per cubic feet) to get pounds of air living in the cylinder. Our ultimate goal is to "squirt" the proper amount gasoline in this cylinder. Most people use a air to fuel ratio of 14.7, meaning 14.7 pounds of air to 1 pound of gasoline.
Electronic fuel injectors are rated at a flow of so many pounds of gasoline per hour time, example - 25 Lbs/hr at some fuel rail pressure. This rating is with the injector held open for an hour. But the ECU controller can open the injector for a much smaller time, usually somewhere in the millisecond range. With the above information (i.e the pounds of fuel in the cylinder, the desired gas-to-air ratio, and the injector flow per unit time, we can determine how long to hold the injector open, which is the computed pulse width above.
Injectors are not perfect - they need a little time to move the pintle in order get fuel to start flowing out. This factor is the injector turn on time, and is somewhere around a millisecond, but depends on the injector. This time is added to the pulse width computed above to yield the total pulse width.
Adjust the parameters above to see the effect on the pulse width. For instance, change the elevation number to that of Denver, (something like 5280 feet), and see that the pulse width is less than compared to sea level (0 feet elevation). This makes sense, because there is less atmospheric pressure to ram air into the cylinder, which means that we need less fuel injected, or a shorter pulse width.
Many Thanks to Mr. Bruce Bowling
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