alpha-N equations?

[Tony Bryant]

Date sent:      	Thu, 03 Dec 1998 13:27:00 +1300
To:             	diy_efi at efi332.eng.ohio-state.edu
From:           	Mike Morrin <mikem at southern.co.nz>
Subject:        	alpha-N equations?
Send reply to:  	diy_efi at efi332.eng.ohio-state.edu

> Just wondering about alpha-N injection systems (ones that meter fuel just
> from throttle position and RPM, without measuring either MAP or MAF).
> 
> In general, air_volume = f(TPS, RPM).
> 
> Is it necessary to keep a 3D map, or can it be reduced to a 2D lookup and a
> calculation to correct for the other parameter?
> 
> I think that the relationship between TPS and air flow is likely to be
> highly non-linear, so the question reduces to whether at a constant
> throttle position, there is an easy relationship between RPM and air volume?
> 
> How about if it is assumed that one knows the function VE(RPM) for the
> engine at WOT?
> 
> Just playing with ideas.
> 

THEORY:

You are playing with two formulas here:

(1)  airflow = VE(RPM,MAP)*RPM  (this is how MAP ECU work)

(2)  airflow = compressflowfunction(Throttle open area,MAP,IAT)  -
i.e known pressure drop across an orifice of known area at a given 
temperature yeilds a known airflow  

-  see back of heywood or any gas dynamics text etc  for details 
this one. 

first consider (1):

For mild cams, or at reasonable RPMs. VE is proportional to MAP:
(1a)  airflow=VEw(RPM)*RPM*MAP    (VEw=VE at WOT)

But of course the whole point of alpha-N is not having MAP, so if 
you simultaneously solve (1a) and (2), you are able to get airflow & 
MAP, for a RPM & ThrPos pair.

Hint: you can use successive approximation to solve the equation 
for each pair.

PROBLEMS:

(2) is incredibly sensitive at small throttle opening at low MAP (i.e. 
at idle). I.e. don't expect any sort of reasonable idle without alot of 
fine tuning.

(1a) doesn't apply for any sort of performance cam. Doesn't even 
apply at any reasonable idle with a stock cam. Self EGR will totally 
screw up this scheme.

Oversensitive is the word I would use to describe this scheme.

When I was trying it out, I couldn't get enough accuracy in the TPS 
at small openings to get it to idle even half decently.

Running EGO feedback could probably tame it down enough for 
street use, but running open loop with this is race only IMHO.   

MAP seems like a much more robust idea to me.

Good luck.