On Thursday 24 February 2011 11:41:43 Geoff McLane wrote:
> Hi,
>
> Re: http://www.geoffair.net/tmp/tilted-001.png (updated)
>
> Thanks Ron, and Stuart, for the tailwind c172.xml
> change. As stated, all tests so far on this are great...
> with due care can now taxi, takeoff and land with a
> modest tail wind ;=))
>
> Is there any 'documentation' I can read on why
> putting <sin> ... </sin> around the
>  <property>aero/alpha-rad</property>
> did the trick?


I have a few spare moments, maybe I can shine a bit of light...  Traditional 
aerodynamics texts concern themselves with the normal flight envelope. To 
simplify things they tend to use linear equations that work within the few 
degrees alpha +/- that make up that flight envelope. Our c172p was written 
with those simplifications in mind.  For example, the pitching moment was 
expressed as a negative linear function of alpha.  That means the higher the 
alpha angle became the more pitch down force was applied.  For alpha angles 
below stall this is a pretty close approximation, however, for larger values 
of alpha the approximation rapidly breaks down. Causing, as noted, huge 
values of pitching moments for alphas near 180 degrees.

The sine(alpha) function is fairly linear and equal to the radian alpha angle 
measurement in the normal flight envelope the textbook functions are written 
for, but it increases less rapidly above 15 degrees alpha, peaks at 90 
degrees and falls back to zero as alpha approaches 180 degrees giving us 
reasonable behavior for all alpha angles.  I'm not claiming aerodynamic 
truth, just reasonable behavior.

> Just so maybe I, or others, could try to be more
> helpful next time, if there is one ;=))

Hope that was helpful.

Thanks,
Ron

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