📄 udryd2.htm
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<H2><I><FONT FACE="Arial","Helvetica","Sans Serif">UDRYD2</FONT></I>: Longitudinal Dryden filter with varying coefficients</H2>
The masked subsystem block <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">UDRYD2</FONT></I>, which is contained in the library <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="windlib.htm">WINDLIB</A></FONT></I> from the FDC subdirectory <SMALL>WIND</SMALL>, implements a longitudinal Dryden filter with coefficients that vary with the true airspeed <I>V</I>. The user must specify the scale lenght <I>L<SUB>u<SUB>g</SUB></SUB></I> and the standard deviation <I>sigma_u<SUB>g</SUB></I>. The airspeed <I>V</I> is used as inputsignal to the block <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">UDRYD2</FONT></I>. Often, the changes in <I>V</I> due to atmospheric turbulence are not very large, which means that it may be more straightforward to use a Dryden filter with constant coefficients, computed under the assumption that <I>V</I> is constant and equal to a user-specified value. The block <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="udryd1.htm">UDRYD1</A></FONT></I> contains such a filter for longitudinal turbulence.<BR><BR>
The longitudinal gust velocity is obtained by passing white noise through a Dryden filter, which is defined by the following transfer function:
<PRE> K
Hug = ----------- K = sigma_ug * sqrt(2*Lug/V)
1 + tau*s tau = Lug/V
</PRE>
where:
<PRE> V : true airspeed [m/s]
sigma_ug: standard deviation of longitudinal gust velocity [m/s]
Lug : scale length for longitudinal gust [m]
</PRE>
Here, <I>V</I> is the <I>input</I> signal to the masked subsystem block. <I>V</I> itself has to be obtained from the aircraft model considered, e.g., <I>V</I> may be an outputsignal from the non-linear aircraft model (such as the system <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="beaver.htm">Beaver</A></FONT></I>), which uses the turbulence velocity <I>u<SUB>g</SUB></I> and its time-derivative as inputsignals!
<H3>Input signal</H3>
<PRE> V : true airspeed [m/s]
</PRE>
<H3>Output signals</H3>
<PRE> ug : longitudinal gust velocity [m/s]
d(ug)/dt: time derivative of ug [m/s^2]
</PRE>
<H3>More information</H3>
While <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">UDRYD1</FONT></I> and <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">UDRYD2</FONT></I> contain longitudinal Dryden filters, the blocks <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="vdryd1.htm">VDRYD1</A></FONT></I>, <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="vdryd2.htm">VDRYD2</A></FONT></I>, <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="wdryd1.htm">WDRYD1</A></FONT></I>, and <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="wdryd2.htm">WDRYD2</A></FONT></I> can be used to determine lateral and vertical turbulence (the suffix 1 denotes filters with constant coefficients and 2 denotes filters with velocity-dependent coefficients). Practical combinations of the longitudinal, lateral, and vertical Dryden filters can be found in the subsystems <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="turb1.htm">Turb1</A></FONT></I> and <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="turb2.htm">Turb2</A></FONT></I>. Those subsystems combine the turbulence velocity-components and their time-derivatives in a vector <I>uwind</I>, which can be connected to the non-linear aircraft model <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="beaver.htm">Beaver</A></FONT></I>.<BR>
<BR>
<B>Note:</B> the vector <I>uwind</I> that leaves <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Turb1</FONT></I> and <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Turb2</FONT></I> does not contain deterministic wind velocity components. Add this vector to the outputs from <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="blwind.htm">BLwind</A></FONT></I> or <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="cwind.htm">Cwind</A></FONT></I> if you want to take into account those components as well.<BR>
<BR>
All wind and turbulence systems have been gathered in the blocklibrary <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="windlib.htm">WINDLIB</A></FONT></I>.
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