With my crayons and scrap paper.....
Quite simply,... The fuel rail is dead ended (isn't it?) instead of looped. And also of a smaller diameter than it SHOULD be so that...... The injector pulsing creates pressure waves in the rail and changes fuel pressures in an unbalanced manner in der tube affecting the injectors ability to deliver on a smooth curve along the rev range. Hence and Why the #1 cylinder is always the "leanest factory"=least wave affected. And why the #4 is always the "richest"=most affected..
:wacko:
No... Eh.... Oh well.
-Don
What you are supposing is true. Called the "water hammer" effect....like when you close the facet suddenly and you hear the pressure spike in the water pipe "hammer." Always an issue with a non-return type fuel rail. So much of an issue it is one reason why return-less port fuel injection systems are just starting to show up on production engines. So much of an issue you can bet your bottom dollar that Yamaha knows about it, too, and has compensated for it in the fuel injection calibration.
The problem with the theory you propose is that it oversimplifies the problem in proposing a reaction. And would it never simply manifest itself as one of the positions or injectors always being richer..or leaner...than the other. As each injector closes it creates a pressure spike (or water hammer) in the fuel rail that bounces back and forth thru the rail. An extremely fast pressure transducer in the rail would show a sinusoidal pressure change at any given point along the rail. Since there are four injectors there are four different pressure spikes bouncing back and forth across the rail from each injector closing. If another injector happens to open or be open just as a high pressure spike were to occur from an injector closing it would cause that injector to deliver rich, or vice versa if a lean spike happened along. Since any injector closing can affect any other injector up and down the rail it gets complicated. The second problem with the theory is that the nodes of the pressure spikes are always changing in frequency with RPM. At one RPM a node of a negative pressure spike might coincide with a particular injector. At a different RPM a node of a positive pressure spike might ovelay that injector opening. The water hammer effect can/could cause any given injector to go rich at one RPM and lean at another RPM.
All this is measured by the fuel injection system development team and software in the ECM compensates for it. Each injector would typically have a lookup table for water hammer effect compensation that is calibrated for each load and speed/RPM point to "tweak" the injector pulse width calculated to compensate for the water hammer effect.
This is also why there is generally a pressure accumulator on the fuel rail to dampen the pressure spikes caused by the water hammer effect in a return-less fuel injection rail. I don't know specifically if the 07 FJR has that or not but I would bet it does. It would look like a small can mounted on the fuel rail, looking much like the pressure regulator in the return style systems.
Sooo....it is true that returnless fuel injection rails do have a water hammer effect going on that does affect the fuel delivery from any given injection depending on the engine speed and load (injector pulse width.) However, suppossing that this phenomenon causes one end of the engine to always run lean and the other end to run rich all the time is highly highly unlikely. I would bet on this partly because I suspect Yamaha is compensating for the phenomenon in the ECM operation and partly the effect is way to random and rare and RPM specific accidently stackup so as to make one end lean all the time and the other end rich all the time. One of those "could happen" sorts of things but highly unlikely in the real world.
You realize that the 03/04/05 FJRs are return style systems and the 06/07 changed to the returnless system...??
There have been cases in the field where a company put a returnless fuel injection system on an engine and suffered some serious failures due to their lack of understanding of the water hammer effect and lack of appropriate compensation. In one specific case I recall in a marine engine the water hammer effect would cause lean related failures in one cylinder if the engine were operated at one load/speed point continously (like you do when towing a skier) and rich related problems in another cylinder at another operating condition (like towing a wake boarder). The guys that did the marine conversion switched to a returnless system due to coast Guard requirements regarding fuel return systems and did not appreciate the potential effect of the water hammer phenomenon.
Return-less fuel injection systems have several "positives" associated with them. Less heating of the fuel in the tank since the system is not circulating the fuel thru the (hot) fuel rail and then returning it to the tank. Less fuel vapor formed as a result and less strain on the evaporative emissions system. Less costly due to eliminating the return line and some fittings. Less leak potentials as the low pressure side is eliminated with all the plumbing assciated with it.
As far as the proposal that the fuel rail is is of a smaller diameter than it should be....???.....what makes you think that or leads one to that conclusion. The orfice in the injectors are tiny and only one injector is open at a time so the fuel rail is highly unlikely to become a fuel flow restriction even if all the injectors were stuck open 100% of the time. Nothing I can see about the fuel rail would support the idea that it is "of a smaller diameter than it should be."