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FDC help: Engine Group
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<h2>
Subsystem <i>Engine Group (Beaver)</i>
</h2>
<p>The subsystem <i>Engine Group (Beaver)</i> of the <i><a href="beaver.htm">Beaver</a></i> model is used to compute the forces and moments which
arise due to the operation of the engine. These include slipstream effects,
induced by the propeller. In the case of the 'Beaver', this is done
by first computing the engine power and the closely related increase of
pressure across the propeller, then using this result for determining the
magnitude of non-dimensional force and moment coefficients, and finally
computing the forces and moments in [<i>N</i>] and [<i>Nm</i>], respectively. A
similar sequence will usually be followed for other piston-engined
aircraft.</p>
<p><i>Engine Group (Beaver)</i> consists of three blocks: <i><a
href="power.htm">Power (Beaver)</a></i>, <i><a href="engmod.htm">Engmod
(Beaver)</a></i>, and <i><a href="fmdims.htm">FMdims</a></i>. <i>Power</i>
computes the engine power and pressure increase across the propeller,
<i>Engmod</i> contains the actual engine model according to <a href=
"#References">ref.[1]</a> which determines the dimensionless force and
moment coefficients, and <i>FMdims</i> computes the forces and moments in
<i>N</i> and <i>Nm</i>.</p>
<p>The block <i>Power</i> uses the state vector
<i>x</i>, the vector with external inputs to the engine <i>uprop</i>, and
the outputvector <i>yatm</i> from the block <i><a href=
"atmosph.htm">Atmosph</a></i> in the subsystem <i><a href=
"adgrp.htm">Airdata Group</a></i> as inputs. <i>Engmod</i> uses <i>x</i>
and the outputvector <i>ypow</i> from the block <i>Power</i>, hence,
<i>Engmod</i> has been placed on the lower right side of <i>Power</i>.
Finally, <i>FMdims</i> uses the outputvector of the block <i>Engmod</i>,
<i>Cprop</i>, and the outputvector <i>yad1</i>of the block <i><a href=
"airdata1.htm">Airdata1</a></i> in the subsystem <i>Airdata Group</i>.
Hence, <i>FMdims</i> is located on the right side of the block
<i>Engmod</i>. <i>Power</i>, <i>Engmod</i>, and <i>FMdims</i> have also
been shifted vertically with respect to each other, in order to make it
possible to connect their outputs to the <i>Outport</i> blocks on the right
side of the subsystem <i>Engine Group (Beaver)</i>. </p>
<h3>
Inputs: <i>x</i>, <i>uprop</i>, <i>yatm</i>, <i>yad1</i>
</h3>
<pre>
x = [V alpha beta p q r psi theta phi xe ye H]' (states)
uprop= [n pz]' (external engine inputs (propulsive))
yatm = [rho ps T mu g]' (atmosphere variables, computed in
the masked subsystem <a href=
"atmosph.htm">Atmosph</a>)
yad1 = [a M qdyn]' (airdata variables, computed in the
masked subsystem <a href=
"airdata1.htm">Airdata1</a>)
V : true 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, relative to Earth-axes [m] }
{ye : Y-coordinate, relative to Earth-axes [m] }
{H : altitude above sea level [m] }
n : engine speed [RPM]
pz : manifold pressure ["Hg]
rho : air density [kg/m^3]
{ps : static pressure [N/m^2] }
{T : air temperature [K] }
{mu : dynamic viscosity [kg/(m*s)] }
{g : acceleration of gravity [m/s^2] }
{a : speed of sound [m/s] }
{M : Mach number [-] }
qdyn : dynamic pressure [N/m^2]
</pre>
<p>The variables which are not actually used by any of the blocks from the
subsystem <i>Engine Group (Beaver)</i> have been put between curly braces. </p>
<h3>
Outputs (prop = 'propulsive'): <i>ypow</i>, <i>Cprop</i>,
<i>FMprop</i>
</h3>
<pre>
ypow = [dpt P]'
Cprop = [CXp CYp CZp Clp Cmp Cnp]'
FMprop= [Xp Yp Zp Lp Mp Np]'
dpt : dimensionless pressure increase across the propeller [-]
P : engine power [Nm/s]
CXp, CYp, CZp: propulsive force coefficients along body-axes [-]
Clp, Cmp, Cnp: propulsive moment coefficients along body-axes [-]
Xp, Yp, Zp: propulsive force components along body-axes [N]
Lp, Mp, Np: propulsive moment components along body-axes [Nm]
</pre>
<h3>
Parameters to be defined in the Matlab workspace
</h3>
<ul>
<li>
<i>GM1</i>: vector with some important geometrical properties of the
'Beaver' aircraft, and the mass of the aircraft (which is
assumed to be constant during the motions of interest). Here, it is
needed by <i><a href="fmdims.htm">FMdims</a></i> in order to extract geometrical data for the
determination of dimensional forces and moments from the
non-dimensional force and moment coefficients.
</li>
<li>
<i>EM</i>: matrix with stability and control derivatives of the
'Beaver' (valid only for the nonlinear engine forces and
moments model of the DHC-2 'Beaver', see <a href=
"#References">ref.[1]</a>). This matrix is needed by <i><a href="engmod.htm">Engmod
(Beaver)</a></i>.
</li>
</ul>
<p><i>EM</i> and <i>GM1</i> can be loaded into the workspace from datafile by
running the utility <i><a href="datload.htm">DATLOAD</a></i>. Run <i><a
href="modbuild.htm">MODBUILD</a></i> first if the datafile does not yet
exist.</p>
<h3>
<a name="References">References</a>
</h3>
<ol>
<li>
R.T.H. Tjee and J.A. Mulder. <i>Stability and Control Derivatives of
the De Havilland DHC-2 "Beaver" aircraft</i>. Report LR-556,
Delft University of Technology, 1988.
</li>
</ol>
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