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Equation 65 presents the quasistatic differential equation for
manifold pressure
.

(65) 
For high speed engines, this equation could be numerically unstable
with the simulator's time step size; in such cases, it is appropriate
to ignore the transients by setting
to zero and solving
Equation 65 directly for p_{m}. (Reference 18
reports that the time constant of the Equation 65 is 2 to 4
times the length of an intake stroke. At 2400 RPM, twice the intake
stroke is 0.025 seconds. A typical time step size for a flight
simulator is 0.01 seconds.)
In Equation 65, the volumetric efficiency
is only
weakly dependent on the manifold pressure; this paper assumes it to be
independent of p_{m}. The manifold temperature T_{m} is assumed
known; an adequate estimate is to use outside air temperature.
V_{d} and
V_{m} are constants for the engine, and N is
the engine speed. Only
is left to be determined.
If
p_{m} > 0.528p, then the flow is not choked at the throttle. The
mass flow rate past the throttle is given by
Equation 66
:

(66) 
The coefficient of discharge C_{D} in Equation 66 is
an empirical, enginedependent parameter, which accounts for the
pressure loss due to all of the obstacles in the intake (air filter,
throttle, venturi, etc.). It is a function of the engine speed and
throttle plate open area. One can obtain a firstorder estimate of
C_{D} by setting it so that Equation 65 yields the observed
manifold pressure drop at steady state with a wideopen throttle at a
high engine speed. p_{th} is the pressure at the throttle. It is
not clear from Reference 18 how to determine this;
however, it seems that, although technically invalid, the manifold
pressure is used for p_{th}.
If
p_{m} < 0.528p, then the flow is choked at the throttle. In this
case, mass flow rate is given by
Equation 67
:

(67) 
Next: Propeller Modeling
Up: Piston Engine Modeling
Previous: Piston Engine Modeling
Carl Banks
20000811