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Does fuel injection amount change even if RPMs don't change?

In a hypothetical scenario, if you are cruising at 50, lets say you press the gas to accelerate. Does the amount of fuel injected into the cylinders increase right when you do that or only when the actual RPMs increase?

Yes.
The amount of fuel injected at any moment is dependent on many factors but the 2 main ones are RPM and engine load. Engine load is defined as a percentage of the maximum amount of air the engine can breathe at a fixed RPM (wide open throttle). When you hit the gas at 3000RPM the injector pulse width will increase instantaneously before there is an appreciable change in RPM.

Engine load can be detected several different ways. The most common on modern EFI engines is a MAF (mass air flow)sensor which is solid state can tell how much air is passing through a fixed diameter hole. An older version of this was a trap door AFM (air fuel meter) which used a spring loaded door in the intake to sense how much air is flowing through the intake. Both of these sensors are before the throttle plate A third method is to measure the vacuum level inside the intake manifold after the throttle plate.

MAF
http://www.aa1car.com/library/maf_sensor_ford.gif

Trap door AFM
http://www.mirafiori.com/~thad/fi/afm.gif

MAP sensor. This one is usually very small and some times its mounted remotely away from the engine via a small vacuum hose. This sensor can measure both vacuum and boost. Some engines (especially turbo or supercharged) use a combination of MAP and MAF to calculate load.
http://www.enginebasics.com/EFI%20Tu...P%20sensor.jpg

A rare few cars (mostly off highway race engines) rely only on a TPS (throttle position sensor) to calculate load. This method sacrifices smooth idle, part load drivability and fuel economy in favor of incredibly quick throttle response and peak power. Most street cars also have a TPS but its used for acceleration enrichment rather than outright load. AE is only needed for a split second between the moment you hit the gas and the moment your MAF or AFM detects a change in load. Its also useful for idle control, cruise control and warm up phase of the drive cycle.

The typical TPS based race engine lacks a manifold or a common intake to determine load.
http://forum.mazda6club.com/attachme..._s2000_itb.jpg

when you open the throttle
there is a large increase in injector pulse width of relatively short duration , followed by a milder increase of what the average injector pulse was at cruise

the amount of the increase depends on the load determined by the ECM .
there are many variables taken into account .

the ECM focuses on rate of change of the TPS. the actual value at any given time is less important than how quickly the value is decreasing or increasing
the ECM uses this input to mimic the function of an accelerator pump in a carburetor

after that the load sensor , MAP or MAF is the primary input to determine injector pulse width and the whole mess is corrected by inputs from the AFR or 02 sensor or sensors if the system trims on both front and rear

there are many other inputs also looked at to determine IPW
that is a simple version to answer the immediate question

good write up tjts.

here is another way to think about it. for every other revolution of the engine, the injectors fire for a certain duration.

The duration is PRIMARILY a function of how much air is in the intake manifold.

When we open the throttle, we get more air. When we close the throttle, we get less air.

The ecu takes this primary starting point and starts adjusting.

if the engine is cold, more fuel. if the air temperature is cold, more fuel. if the 02 sensors tell it otherwise, it adjusts the fuel amounts.

Also seeing that the OP has a 5th gen civic as his avatar it is important to note that he likely is running the speed-density which uses a combination of the MAP sensor and intake air temperature to estimate the airflow into the engine in his setup. This type of fuel injection system was standard on Hondas until the 7th gen Civics as far as I know.

I built a FI system from the ground up for a single cylinder engine. It ran off of a TPS for load calculations because the MAP readings were transient and you couldn't get consistent data because of the sharp intake pulses. The TPS worked great best for my application and that thing screamed. But there was also a throttle acceleration which looked at the rate of change of the throttle and above 20% per second rate of change it would increase the fuel by some amount so the engine wouldnt bog. I threw a lot at it so we had snappy throttle response but we were racing so consumption wasn't an issue. But I had a ritch spot in my O2 data where you could tell when the driver got on the throttle. Modern cars are better but I always roll on the throttle slowly. You can actually see puffs of black smoke in modern gasoline cars when people romp on the throttle. Look for someone who is impatient in traffic and you will see it.

next time, if you put a T in the vacuum line to the MAP sensor you can get rid of a lot of the pulses. even on single cylinders.