📄 uvw.htm
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<TITLE>FDC help: uvw</TITLE>
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<H2>The subsystem <I><FONT FACE="Arial","Helvetica","Sans Serif">uvw</FONT></I></H2>
The block <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">uvw</FONT></I> is a masked S<SMALL>IMULINK</SMALL> subsystem, which is used to compute the body-axes velocities <I>u</I>, <I>v</I>, and <I>w</I>. Since the aircraft model uses the true airspeed <I>V</I>, angle of attack <I>alpha</I>, and sideslip angle <I>beta</I> as state variables, the equations for <I>u</I>, <I>v</I>, and <I>w</I> are simple output equations. The body-axes velocity components are needed to solve the equations for the coordinates <I>x<SUB>e</SUB></I>, <I>y<SUB>e</SUB></I>, and the altitude <I>H</I>, so the block <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">uvw</FONT></I> may <I>not</I> be deleted from the system! The outputs from <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">uvw</FONT></I> are used by the block <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="xyhdot.htm">xyHdot</A></FONT></I> in the
subsystem <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="12odes.htm">12 ODEs</A></FONT></I>. <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">uvw</FONT></I> is included in the subsystem <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="eqmotion.htm">Aircraft Equations of Motion</A></FONT></I> of the S-function <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="beaver.htm">Beaver</A></FONT></I>.
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Since <I>u</I>, <I>v</I>, and <I>w</I> are not state variables, their time-derivatives are not necessary to solve the equations of motion. However, for some purposes, knowledge of these time-derivatives still may be useful; therefore, a separate block <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="uvwdot.htm">uvwdot</A></FONT></I> has been included in the subsystem <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="moreouts.htm">Additional Outputs</A></FONT></I> within the S-function <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Beaver</FONT></I>.
<H3>Inputvectors: <I>x</I> and <I>yhlp</I></H3>
<PRE> x = [V alpha beta p q r psi theta phi xe ye H]' (states)
yhlp = [cos(alpha) sin(alpha) cos(beta) sin(beta) ...
... tan(beta) sin(psi) cos(psi) sin(theta) ...
... cos(theta) sin(phi) cos(phi)]'
(frequently used sines and cosines, coming from <A HREF="hlpfcn.htm">Hlpfcn</A>)
V : airspeed [m/s]
{alpha: angle of attack [rad] }
{beta : sideslip angle [rad] }
{p : roll rate [rad/s] }
{q : pitch rate [rad/s] }
{r : yaw rate [rad/s] }
{psi : yaw angle [rad] }
{theta: pitch angle [rad] }
{phi : roll angle [rad] }
{xe : x-coordinate in Earth-fixed reference frame [m] }
{ye : y-coordinate '' '' '' '' [m] }
{H : altitude above sea-level [m] }
</PRE>
The inputvariables which are not actually used by the block <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">uvw</FONT></I> have been displayed between accolades. From <I>yhlp</I> the signals <I>cos(alpha)</I>, <I>cos(beta)</I>, <I>sin(alpha)</I> and <I>sin(beta)</I> are used.
<H3>Outputvector: <I>ybvel</I> (bvel = 'body-axes velocities')</H3>
<PRE> ybvel = [u v w]',
u : component of the true airspeed V along XB-axis [m/s]
v : component of the true airspeed V along YB-axis [m/s]
w : component of the true airspeed V along ZB-axis [m/s]
</PRE>
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