bad math humor (was re: Re: HIP9010)

[Dale Ulan]

> I don't know. I'd imagine a quadratic or cubic interpolation
> would be nice.  Everyone wants their engine to run continuously,
> but I want mine to run *smooth*!
> 
> Mark

Internally, linear interpolation is fine, but engines are horribly
non-linear devices. They often have 5+ order differential equations
that describe their behaviour. Check out any of Elbert Hendricks'
SAE papers... :-) The implication of this is that you need a fuel
table that's at least 16x16 to catch the peaks. With some clever
software, you can time the peaks to match up with boundaries, but
this is not often done. Memory is cheap, programmer's time is not.

So although the fuel map can be interpolated in the ECM linearly,
when you have an engine 'map' that only has a few points on it, you
may want to run it through a PC or workstation based math package to
come up with a full table.

In most engine control platforms, there just isn't time to do anything
other than linear interpolation. A typical engine computer has over
fifty tables that it has to do interpolations on... and it typically
goes through most of them in about 5 ms or so... along with the
other calculations the ECM has to do. It really isn't necessary either,
depending on the resolution of the map.

The normal way of doing ECM work is to do the math 'grunt-work' in 
a workstation in someone's office, then leave the ECM firmware as
simple as possible when it comes to math. Memory in a computer is
cheap, processing speed is not. Neither is a programmer's time to
come up with an optimum quadratic or cubic curve-fitting interpolation
and have it execute in the required (insane) amount of time.

-Dale