2011/6/19 Jon S. Berndt <jonsber...@comcast.net>:
> Hal,
>
> Oops! Sorry I attributed code to you that came from somewhere else. :-) I
> now seem to recall experimenting with your model at that time - actually
> replacing the older one in JSBSim cvs with yours, then adding the estimated
> propwash effects.
>
>                Hal wrote:
>
>                These were never in any of the code I worked with and were
> removed before I started working on the FDM. My current Cmde function looks
> like this:
>
>                <function name="aero/coefficient/Cmde">
>                  <description> Pitch_moment_due_to_elevator </description>
>                  <product>
>                    <property> aero/qbar-psf </property>
>                    <property> metrics/Sw-sqft </property>
>                    <property> metrics/cbarw-ft </property>
>                    <property> fcs/elevator-pos-rad </property>
>                    <table>
>                      <independentVar> velocities/mach </independentVar>
>                      <tableData>
>                        0.0000  -0.9
>                        0.66    -0.6
>                        0.74    -0.4
>                        1.0000  -0.05
>                      </tableData>
>                    </table>
>                  </product>
>                </function>
>
>                This is using the qbar-psf which is not influenced by prop
> wash. The Cmde function Jon has above has a lookup table that goes from MACH
> 0 to MACH 2 in a linear fashion. This looks like something intended for a
> supersonic aircraft and is not what I would expect from a subsonic aircraft.
> The table I am using goes from MACH 0 to MACH 1 and has a strong inflection
> at MACH 0.74 which is unlike the one in Jon's function since it is
> non-linear.
>
> Yes, the above mach effects table looks better. I can't remember where that
> came from.
>
>                ...
>
>                Jon thanks for the above code. I will look into integrating
> this into the current P-51D. Also shouldn't the same sort of thing happen
> with the rudder?
>
> Yes - in fact, in the version I have in JSBSim cvs, the modified qbar is
> used for: CLde, Cldr, Cmde, and Cndr. I haven't tested any of these for
> validity, though.
>
>                And Jon do you have any ideas on how to go about writing a
> function to implement downwash pitch moment affects?
>
> Yes, that's another thing that could be done. I've thought about that
> sometimes, too. When the wing is generating lift, the airflow is being
> deflected downward behind the wing, and so the alpha that the tail sees is
> affected, since the normal airflow has been given an additional component in
> the body Z direction (downward from the pilot perspective). Also, if there
> is an appreciable pitch rate, the alpha at the tail is affected. Finally, if
> the propeller is producing thrust, then there is that affect, too. So, how
> do we calculate the alpha at the horizontal tail?
>
> I'm making this up right here as we go, but here are my thoughts. First,
> calculate the wind velocity that the H. tail sees:
>
> U_adjusted = U + U_prop
>
> Next, the Z axis velocity that the H. tail sees:
>
> W_adjusted = W + q*ht_arm - i_wing
>
> Where W is the aircraft Z axis wind velocity at the CG, q is the pitch rate,
> ht_arm is the distance from the CG to the horizontal tail, and i_wing is the
> induced velocity produced by the wing. At zero lift i_wing would be zero,
> and at lift=weight (such as at cruise) the i_wing value would be some value
> - and it might not be trivial to calculate what that would be, though you
> might be able to estimate it to produce a plausible qualitative effect.
> There is a NASA paper that might be helpful in calculating this: "The
> Calculation of the Induced Velocity Field of a Wing". It is the translation
> of a technical paper by Klaus Gersten. It is NASA Technical Translation TT
> F-12, 436, and you can download it at this URL:
> http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690023298_1969023298.
> pdf.
>
> Anyhow, then, of course, the calculation is just this:
>
> alpha_tail = atan2(W_adjusted, U_adjusted)
>
> Maybe I've gone wrong somewhere here, but something similar might work.
> Also, in situations like a flat spin or tail slide this probably falls
> apart!
>

To improve our bibliography I suggest to add this paper "Prediction of
the effects of propeller operation on the static longitudinal
stability of single-engine tractor monoplanes with flaps retracted" -
J. Weil, W. C. Sleeman - NACA Report 941 available at this URL:
http://hdl.handle.net/2060/19930092006

Figures 12 and 13 are of particular interest : you can see the
influence of propwash on CL and Cm. On figure 12, the slopes of CL and
Cm for a tail incidence of 0 deg are roughly increased by 30% and 60%
respectively.

Bertrand.

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