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### Manifold Pressure Calculation

Equation 65 presents the quasi-static 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 pm. (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 pm. The manifold temperature Tm is assumed known; an adequate estimate is to use outside air temperature. Vd and Vm are constants for the engine, and N is the engine speed. Only is left to be determined.

If pm > 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 CD in Equation 66 is an empirical, engine-dependent 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 first-order estimate of CD by setting it so that Equation 65 yields the observed manifold pressure drop at steady state with a wide-open throttle at a high engine speed. pth 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 pth.

If pm < 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
2000-08-11