Maximum advance

[Bernd Felsche]

Eric Fahlgren tapped away at the keyboard with:

> > programmatically combine the pressure transducer data together
> > with the crank angle data, to create a pressure-volume (PV)
> > diagram for a given cylinder.  Then you would have a good visual
> > representation of the entire cylinder experience, including peak
> > combustion pressures and phasing of same.  The number of things
> > you can deduce from a PV diagram are endless.

> Are there other useful diagrams of this sort?  I'm thinking of a
> (just made this up) PQ diagram where
> 
>    Q = cos(a) * sin(b)
>    a = angle between rod and bore centerline, as the rod aligns
>        with the bore, this goes to 1.0
>    b = angle between rod and crank throw, as the rod/crank angle
>        goes to 90d this goes to 1.0
> 
> which describes the vector component of the pressure that is
> actually doing useful work (or so it seems to me).  The Q term
> is interesting in and of itself, so I think I'll write a little
> plotter that produces a bunch of curves for various rod/stroke
> ratios (and maybe with bore offsets, too).

The integral of the product of P(t).Q(t) during the power stroke is
the gross torque produced. The crank angle (along with crank and rod
length) defines a and c and the crank angle itself is a function of
time (at a particular engine speed).

Unfortunately, P(t) is less-straightforward to define.  One could
start by assuming a constant flame speed without swirl or tumble
after initial ignition delay and assume a hemispherical front until
"walls" are encountered. Leave swirl, etc for 'ron. :-)

Beyond that, I'm almost entirely ignorant of how one would normally
predict pressure based on the combustion process. I suppose one
could assume an energy conversion based on the proportion of the
mixture burnt behind the flame front and derive the gas pressure by
perhaps also assuming adiabatic expansion. Total combustion chamber
volume is "constrained" by the piston(*) so the gas pressure and
temperature) would vary.  Does that seem reasonable?

Assuming that the temperature doesn't vary by much behind the flame
front, and that the pressure is uniform throughour the cylinder, a
rough numerical model would then be feasible.

The model would at least demonstrate how changing the ignition
timing influences pressure distribution and hence engine torque with
varying engine speeds.  Changing parameters such as bore, stroke and
rod lengths in the model would also show their effects on timing.

(*) In practice, the pressure tries to make room for itself, but the
"static" model can be used as a basis for determining piston-speed
fluctuations due to pressure as well. The relaxation method could be
applied to "balance" the actual piston position based on cylinder
pressure (piston force) and crank reaction. The crank reaction is as
a result of the gross load on the crankshaft at that particular
point in time. The actual piston position would then not be a fixed
parameter, but a variable with time.  

Although this is not immediately interesting in this perspective,
one shouldn't "close" the simulation to prevent this being
implemented. A simple way to allow for it is to incorporate the
crank angle into the model as a function of time. For this
particular case, we can simply make that a constant rate dependent
on the nominal engine speed and time relative to TDC (for example).

-- 
Bernd Felsche - Innovative Reckoning, Perth, Western Australia
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