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<H2>The turbulence block <I><FONT FACE="Arial","Helvetica","Sans Serif">Turb2</FONT></I></H2>

<I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Turb2</FONT></I> is a S<SMALL>IMULINK</SMALL> subsystem which is contained in the Atmospheric Turbulence sublibrary of the library <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="windlib.htm">WINDLIB</A></FONT></I>. It contains the Dryden filters <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="udryd2.htm">UDRYD2</A></FONT></I>, <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="vdryd2.htm">VDRYD2</A></FONT></I>, and <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="wdryd2.htm">WDRYD2</A></FONT></I> for longitudinal, lateral and vertical turbulence, respectively. The filters have been implemented in masked subsystem blocks, in which the user must specify the scale lengths <I>L<SUB>u<SUB>g</SUB></SUB></I>, <I>L<SUB>v<SUB>g</SUB></SUB></I>, and <I>L<SUB>w<SUB>g</SUB></SUB></I>, and the standard deviations <I>sigma_u<SUB>g</SUB></I>, <I>sigma_v<SUB>g</SUB></I>, and <I>sigma_w<SUB>g</SUB></I>.<BR><BR>

In <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Turb2</FONT></I>, the coefficients of the Dryden filters vary with the true airspeed <I>V</I>, which enters this subsystem through an <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Inport</FONT></I> block. The value of the true airspeed must be obtained from the non-linear model of the aircraft under consideration, e.g., <I>V</I> may be extracted from the outputvector of the non-linear aircraft model <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="beaver.htm">Beaver</A></FONT></I>, which itself uses the outputs of <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Turb2</FONT></I> as input signals.<BR><BR>

In many cases, the variations of <I>V</I> due to atmospheric turbulence are not very large, so the resulting changes in filter coefficients may be neglected. In such cases, it is recommended to use <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="turb1.htm">Turb1</A></FONT></I> in stead of <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Turb2</FONT></I>, thus eliminating the feedback-loop of <I>V</I> from the aircraft model to <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Turb2</FONT></I> within the resulting S<SMALL>IMULINK</SMALL> system. <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Turb1</FONT></I> uses the simpler Dryden implementations <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="udryd1.htm">UDRYD1</A></FONT></I>, <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="vdryd1.htm">VDRYD1</A></FONT></I>, and <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="wdryd1.htm">WDRYD1</A></FONT></I>.

<H3>Inputsignal</H3>
<PRE>  V = true airspeed [m/s]
</PRE>

<H3>Outputvector</H3>
<PRE>  uwind = [uw vw ww uwdot vwdot wwdot]'
</PRE>
(Actually, this vector should have been called <CODE>ugust = [ug vg wg ugdot vgdot wgdot]'</CODE>, since the wind velocities and their time-derivatives from the subsystem <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Turb1</FONT></I> represent gust velocities only; contributions due to <I>wind</I> (-shear) still have to be added to this vector! See <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="cwind.htm">Cwind</A></FONT></I> and <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="blwind.htm">BLwind</A></FONT></I> for more information on the implementation of constant wind and a wind-profile in the Earth's boundary layer, respectively.).
<PRE> uw   : wind (gust-) velocity along XB-axis of aircraft [m/s]
 vw   : wind (gust-) velocity along YB-axis of aircraft [m/s]
 ww   : wind (gust-) velocity along ZB-axis of aircraft [m/s]

 uwdot: time-derivative of uw [m/s^2]
 vwdot: time-derivative of vw [m/s^2]
 wwdot: time-derivative of ww [m/s^2]
</PRE>

<H3>Parameters to be set in dialog boxes of <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Turb1</FONT></I></H3>

Before starting a simulation of a system in which the subsystem <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Turb1</FONT></I> is involved, the parameters of the masked subsystem blocks <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="udryd2.htm">UDRYD2</A></FONT></I>, <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="vdryd2.htm">VDRYD2</A></FONT></I>, and <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="wdryd2.htm">WDRYD2</A></FONT></I> have to be defined by double-clicking these blocks and entering the correct values in their dialog-boxes. These parameters are:<BR><BR>

<I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">UDRYD2</FONT></I>:
<PRE>        Lug     = scale length for longitudinal turbulence [m]
        sigma_ug= standard deviation for longitudinal
                                                  turbulence [m/s]
        V       = value of airspeed, used to determine filter
                    coefficients for longitudinal turbulence [m/s]
</PRE>
<I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">VDRYD2</FONT></I>:
<PRE>        Lvg     = scale length for lateral turbulence [m]
        sigma_vg= standard deviation for lateral turbulence [m/s]
        V       = value of airspeed, used to determine filter
                         coefficients for lateral turbulence [m/s]
</PRE>
<I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">WDRYD2</FONT></I>:
<PRE>        Lwg     = scale length for vertical turbulence [m]
        sigma_wg= standard deviation for vertical turbulence [m/s]
        V       = value of airspeed, used to determine filter
                        coefficients for vertical turbulence [m/s]
</PRE>

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